id	sid	tid	token	lemma	pos
ejpam-5470	1	1	european	european	PROPN
ejpam-5470	1	2	journal	journal	PROPN
ejpam-5470	1	3	of	of	ADP
ejpam-5470	1	4	pure	pure	ADJ
ejpam-5470	1	5	and	and	CCONJ
ejpam-5470	1	6	applied	applied	ADJ
ejpam-5470	1	7	mathematics	mathematic	NOUN
ejpam-5470	1	8	2025	2025	NUM
ejpam-5470	1	9	,	,	PUNCT
ejpam-5470	1	10	vol	vol	NOUN
ejpam-5470	1	11	.	.	PROPN
ejpam-5470	1	12	18	18	NUM
ejpam-5470	1	13	,	,	PUNCT
ejpam-5470	1	14	issue	issue	NOUN
ejpam-5470	1	15	1	1	NUM
ejpam-5470	1	16	,	,	PUNCT
ejpam-5470	1	17	article	article	NOUN
ejpam-5470	1	18	number	number	NOUN
ejpam-5470	1	19	5470	5470	NUM
ejpam-5470	1	20	issn	issn	PROPN
ejpam-5470	1	21	1307	1307	NUM
ejpam-5470	1	22	-	-	SYM
ejpam-5470	1	23	5543	5543	NUM
ejpam-5470	1	24	–	–	PUNCT
ejpam-5470	1	25	ejpam.com	ejpam.com	X
ejpam-5470	1	26	published	publish	VERB
ejpam-5470	1	27	by	by	ADP
ejpam-5470	1	28	new	new	PROPN
ejpam-5470	1	29	york	york	PROPN
ejpam-5470	1	30	business	business	PROPN
ejpam-5470	1	31	global	global	ADJ
ejpam-5470	1	32	cordial	cordial	ADJ
ejpam-5470	1	33	labeling	labeling	NOUN
ejpam-5470	1	34	of	of	ADP
ejpam-5470	1	35	corona	corona	NOUN
ejpam-5470	1	36	product	product	NOUN
ejpam-5470	1	37	of	of	ADP
ejpam-5470	1	38	paths	path	NOUN
ejpam-5470	1	39	and	and	CCONJ
ejpam-5470	1	40	fourth	fourth	ADJ
ejpam-5470	1	41	order	order	NOUN
ejpam-5470	1	42	of	of	ADP
ejpam-5470	1	43	lemniscate	lemniscate	PROPN
ejpam-5470	1	44	graphs	graphs	PROPN
ejpam-5470	1	45	atef	atef	PROPN
ejpam-5470	1	46	abd	abd	PROPN
ejpam-5470	1	47	el	el	PROPN
ejpam-5470	1	48	-	-	PUNCT
ejpam-5470	1	49	hay1	hay1	PROPN
ejpam-5470	1	50	,	,	PUNCT
ejpam-5470	2	1	khalid	khalid	PROPN
ejpam-5470	2	2	a.	a.	PROPN
ejpam-5470	2	3	alsatami2,ashraf	alsatami2,ashraf	PUNCT
ejpam-5470	3	1	elrokh1,∗,aya	elrokh1,∗,aya	NOUN
ejpam-5470	3	2	rabie3	rabie3	NOUN
ejpam-5470	3	3	1	1	NUM
ejpam-5470	3	4	mathematics	mathematic	NOUN
ejpam-5470	3	5	and	and	CCONJ
ejpam-5470	3	6	computer	computer	NOUN
ejpam-5470	3	7	science	science	PROPN
ejpam-5470	3	8	department	department	PROPN
ejpam-5470	3	9	,	,	PUNCT
ejpam-5470	3	10	faculty	faculty	NOUN
ejpam-5470	3	11	of	of	ADP
ejpam-5470	3	12	science	science	PROPN
ejpam-5470	3	13	menoufia	menoufia	PROPN
ejpam-5470	3	14	university	university	PROPN
ejpam-5470	3	15	,	,	PUNCT
ejpam-5470	3	16	menoufia	menoufia	PROPN
ejpam-5470	3	17	,	,	PUNCT
ejpam-5470	3	18	egypt	egypt	PROPN
ejpam-5470	3	19	.	.	PROPN
ejpam-5470	4	1	2	2	NUM
ejpam-5470	4	2	department	department	NOUN
ejpam-5470	4	3	of	of	ADP
ejpam-5470	4	4	mathematics	mathematic	NOUN
ejpam-5470	4	5	,	,	PUNCT
ejpam-5470	4	6	college	college	NOUN
ejpam-5470	4	7	of	of	ADP
ejpam-5470	4	8	science	science	NOUN
ejpam-5470	4	9	,	,	PUNCT
ejpam-5470	4	10	qassim	qassim	PROPN
ejpam-5470	4	11	university	university	PROPN
ejpam-5470	4	12	,	,	PUNCT
ejpam-5470	4	13	buraydah	buraydah	PROPN
ejpam-5470	4	14	,	,	PUNCT
ejpam-5470	4	15	ksa	ksa	PROPN
ejpam-5470	4	16	.	.	PROPN
ejpam-5470	4	17	3	3	NUM
ejpam-5470	4	18	department	department	NOUN
ejpam-5470	4	19	of	of	ADP
ejpam-5470	4	20	planning	planning	NOUN
ejpam-5470	4	21	technique	technique	NOUN
ejpam-5470	4	22	center	center	NOUN
ejpam-5470	4	23	,	,	PUNCT
ejpam-5470	4	24	institute	institute	NOUN
ejpam-5470	4	25	of	of	ADP
ejpam-5470	4	26	national	national	PROPN
ejpam-5470	4	27	planning	planning	NOUN
ejpam-5470	4	28	,	,	PUNCT
ejpam-5470	4	29	cairo	cairo	PROPN
ejpam-5470	4	30	,	,	PUNCT
ejpam-5470	4	31	egypt	egypt	PROPN
ejpam-5470	4	32	.	.	PUNCT
ejpam-5470	5	1	abstract	abstract	PROPN
ejpam-5470	5	2	.	.	PUNCT
ejpam-5470	6	1	a	a	DET
ejpam-5470	6	2	graph	graph	NOUN
ejpam-5470	6	3	g	g	NOUN
ejpam-5470	6	4	=	=	SYM
ejpam-5470	6	5	(	(	PUNCT
ejpam-5470	6	6	v	v	NOUN
ejpam-5470	6	7	,	,	PUNCT
ejpam-5470	6	8	e	e	NOUN
ejpam-5470	6	9	)	)	PUNCT
ejpam-5470	6	10	is	be	AUX
ejpam-5470	6	11	called	call	VERB
ejpam-5470	6	12	cordial	cordial	ADJ
ejpam-5470	6	13	if	if	SCONJ
ejpam-5470	6	14	it	it	PRON
ejpam-5470	6	15	is	be	AUX
ejpam-5470	6	16	possible	possible	ADJ
ejpam-5470	6	17	to	to	PART
ejpam-5470	6	18	label	label	VERB
ejpam-5470	6	19	the	the	DET
ejpam-5470	6	20	vertex	vertex	NOUN
ejpam-5470	6	21	by	by	ADP
ejpam-5470	6	22	the	the	DET
ejpam-5470	6	23	function	function	NOUN
ejpam-5470	6	24	f	f	NOUN
ejpam-5470	6	25	:	:	PUNCT
ejpam-5470	6	26	v	v	PROPN
ejpam-5470	6	27	→	→	SYM
ejpam-5470	6	28	0	0	NUM
ejpam-5470	6	29	,	,	PUNCT
ejpam-5470	6	30	1	1	NUM
ejpam-5470	6	31	and	and	CCONJ
ejpam-5470	6	32	label	label	VERB
ejpam-5470	6	33	the	the	DET
ejpam-5470	6	34	edges	edge	NOUN
ejpam-5470	6	35	by	by	ADP
ejpam-5470	6	36	f∗	f∗	NOUN
ejpam-5470	6	37	:	:	PUNCT
ejpam-5470	6	38	e	e	X
ejpam-5470	6	39	→	→	SYM
ejpam-5470	6	40	0	0	NUM
ejpam-5470	6	41	,	,	PUNCT
ejpam-5470	6	42	1	1	NUM
ejpam-5470	6	43	,	,	PUNCT
ejpam-5470	6	44	where	where	SCONJ
ejpam-5470	6	45	f∗(uv	f∗(uv	NOUN
ejpam-5470	6	46	)	)	PUNCT
ejpam-5470	6	47	=	=	PUNCT
ejpam-5470	6	48	(	(	PUNCT
ejpam-5470	6	49	f(u	f(u	PROPN
ejpam-5470	6	50	)	)	PUNCT
ejpam-5470	7	1	+	+	NUM
ejpam-5470	7	2	f(v))mod2	f(v))mod2	PROPN
ejpam-5470	7	3	,	,	PUNCT
ejpam-5470	7	4	u	u	NOUN
ejpam-5470	7	5	,	,	PUNCT
ejpam-5470	7	6	v	v	PROPN
ejpam-5470	7	7	∈	∈	NOUN
ejpam-5470	7	8	v	v	NOUN
ejpam-5470	7	9	so	so	SCONJ
ejpam-5470	7	10	that	that	SCONJ
ejpam-5470	7	11	|v0−v1|	|v0−v1|	AUX
ejpam-5470	7	12	≤	≤	NUM
ejpam-5470	7	13	1	1	NUM
ejpam-5470	7	14	and	and	CCONJ
ejpam-5470	7	15	|e0−e1|	|e0−e1|	NOUN
ejpam-5470	7	16	≤	≤	NUM
ejpam-5470	7	17	1.a	1.a	NUM
ejpam-5470	7	18	lemniscate	lemniscate	NOUN
ejpam-5470	7	19	graph	graph	NOUN
ejpam-5470	7	20	is	be	AUX
ejpam-5470	7	21	a	a	DET
ejpam-5470	7	22	plane	plane	NOUN
ejpam-5470	7	23	curve	curve	NOUN
ejpam-5470	7	24	with	with	ADP
ejpam-5470	7	25	a	a	DET
ejpam-5470	7	26	characteristic	characteristic	ADJ
ejpam-5470	7	27	shape	shape	NOUN
ejpam-5470	7	28	,	,	PUNCT
ejpam-5470	7	29	consisting	consist	VERB
ejpam-5470	7	30	of	of	ADP
ejpam-5470	7	31	two	two	NUM
ejpam-5470	7	32	loops	loop	NOUN
ejpam-5470	7	33	that	that	PRON
ejpam-5470	7	34	meet	meet	VERB
ejpam-5470	7	35	at	at	ADP
ejpam-5470	7	36	a	a	DET
ejpam-5470	7	37	central	central	ADJ
ejpam-5470	7	38	point	point	NOUN
ejpam-5470	7	39	as	as	SCONJ
ejpam-5470	7	40	shown	show	VERB
ejpam-5470	7	41	below	below	ADV
ejpam-5470	7	42	.	.	PUNCT
ejpam-5470	8	1	the	the	DET
ejpam-5470	8	2	curve	curve	NOUN
ejpam-5470	8	3	is	be	AUX
ejpam-5470	8	4	also	also	ADV
ejpam-5470	8	5	known	know	VERB
ejpam-5470	8	6	as	as	ADP
ejpam-5470	8	7	the	the	DET
ejpam-5470	8	8	lemniscate	lemniscate	NOUN
ejpam-5470	8	9	of	of	ADP
ejpam-5470	8	10	bernoulli	bernoulli	PROPN
ejpam-5470	8	11	.	.	PUNCT
ejpam-5470	9	1	a	a	DET
ejpam-5470	9	2	fourth	fourth	ADJ
ejpam-5470	9	3	order	order	NOUN
ejpam-5470	9	4	of	of	ADP
ejpam-5470	9	5	lemniscate	lemniscate	PROPN
ejpam-5470	9	6	graph	graph	NOUN
ejpam-5470	9	7	is	be	AUX
ejpam-5470	9	8	a	a	DET
ejpam-5470	9	9	graph	graph	NOUN
ejpam-5470	9	10	of	of	ADP
ejpam-5470	9	11	two	two	NUM
ejpam-5470	9	12	fourth	fourth	ADJ
ejpam-5470	9	13	order	order	NOUN
ejpam-5470	9	14	of	of	ADP
ejpam-5470	9	15	circles	circle	NOUN
ejpam-5470	9	16	that	that	PRON
ejpam-5470	9	17	have	have	VERB
ejpam-5470	9	18	two	two	NUM
ejpam-5470	9	19	vertex	vertex	NOUN
ejpam-5470	9	20	in	in	ADP
ejpam-5470	9	21	common	common	ADJ
ejpam-5470	9	22	.	.	PUNCT
ejpam-5470	10	1	in	in	ADP
ejpam-5470	10	2	this	this	DET
ejpam-5470	10	3	paper	paper	NOUN
ejpam-5470	10	4	,	,	PUNCT
ejpam-5470	10	5	we	we	PRON
ejpam-5470	10	6	give	give	VERB
ejpam-5470	10	7	the	the	DET
ejpam-5470	10	8	conditions	condition	NOUN
ejpam-5470	10	9	that	that	PRON
ejpam-5470	10	10	the	the	DET
ejpam-5470	10	11	corona	corona	NOUN
ejpam-5470	10	12	product	product	NOUN
ejpam-5470	10	13	of	of	ADP
ejpam-5470	10	14	paths	path	NOUN
ejpam-5470	10	15	and	and	CCONJ
ejpam-5470	10	16	fourth	fourth	ADJ
ejpam-5470	10	17	order	order	NOUN
ejpam-5470	10	18	of	of	ADP
ejpam-5470	10	19	lemniscate	lemniscate	PROPN
ejpam-5470	10	20	graphs	graph	NOUN
ejpam-5470	10	21	be	be	AUX
ejpam-5470	10	22	cordial	cordial	ADJ
ejpam-5470	10	23	.	.	PUNCT
ejpam-5470	11	1	2020	2020	NUM
ejpam-5470	11	2	mathematics	mathematic	NOUN
ejpam-5470	11	3	subject	subject	NOUN
ejpam-5470	11	4	classifications	classification	NOUN
ejpam-5470	11	5	:	:	PUNCT
ejpam-5470	11	6	05c78,05c15	05c78,05c15	NUM
ejpam-5470	11	7	key	key	ADJ
ejpam-5470	11	8	words	word	NOUN
ejpam-5470	11	9	and	and	CCONJ
ejpam-5470	11	10	phrases	phrase	NOUN
ejpam-5470	11	11	:	:	PUNCT
ejpam-5470	11	12	cordial	cordial	ADJ
ejpam-5470	11	13	labeling	labeling	NOUN
ejpam-5470	11	14	,	,	PUNCT
ejpam-5470	11	15	corona	corona	PROPN
ejpam-5470	11	16	,	,	PUNCT
ejpam-5470	11	17	lemniscate	lemniscate	PROPN
ejpam-5470	11	18	,	,	PUNCT
ejpam-5470	11	19	social	social	ADJ
ejpam-5470	11	20	networking	networking	NOUN
ejpam-5470	11	21	,	,	PUNCT
ejpam-5470	11	22	network	network	NOUN
ejpam-5470	11	23	security	security	NOUN
ejpam-5470	11	24	,	,	PUNCT
ejpam-5470	11	25	edge	edge	NOUN
ejpam-5470	11	26	computing	compute	VERB
ejpam-5470	11	27	1	1	NUM
ejpam-5470	11	28	.	.	PUNCT
ejpam-5470	12	1	introduction	introduction	NOUN
ejpam-5470	12	2	let	let	VERB
ejpam-5470	12	3	g	g	NOUN
ejpam-5470	12	4	be	be	AUX
ejpam-5470	12	5	a	a	DET
ejpam-5470	12	6	graph	graph	NOUN
ejpam-5470	12	7	with	with	ADP
ejpam-5470	12	8	p	p	NOUN
ejpam-5470	12	9	vertices	vertex	NOUN
ejpam-5470	12	10	and	and	CCONJ
ejpam-5470	12	11	q	q	NOUN
ejpam-5470	12	12	edges	edge	NOUN
ejpam-5470	12	13	.	.	PUNCT
ejpam-5470	13	1	all	all	DET
ejpam-5470	13	2	graphs	graph	NOUN
ejpam-5470	13	3	considered	consider	VERB
ejpam-5470	13	4	here	here	ADV
ejpam-5470	13	5	are	be	AUX
ejpam-5470	13	6	simple	simple	ADJ
ejpam-5470	13	7	,	,	PUNCT
ejpam-5470	13	8	finite	finite	NOUN
ejpam-5470	13	9	,	,	PUNCT
ejpam-5470	13	10	connected	connected	ADJ
ejpam-5470	13	11	and	and	CCONJ
ejpam-5470	13	12	undirected	undirected	ADJ
ejpam-5470	13	13	.	.	PUNCT
ejpam-5470	14	1	the	the	DET
ejpam-5470	14	2	concept	concept	NOUN
ejpam-5470	14	3	of	of	ADP
ejpam-5470	14	4	graph	graph	NOUN
ejpam-5470	14	5	labeling	labeling	NOUN
ejpam-5470	14	6	was	be	AUX
ejpam-5470	14	7	introduced	introduce	VERB
ejpam-5470	14	8	during	during	ADP
ejpam-5470	14	9	the	the	DET
ejpam-5470	14	10	sixties	sixty	NOUN
ejpam-5470	14	11	’	'	PUNCT
ejpam-5470	14	12	of	of	ADP
ejpam-5470	14	13	the	the	DET
ejpam-5470	14	14	last	last	ADJ
ejpam-5470	14	15	century	century	NOUN
ejpam-5470	14	16	by	by	ADP
ejpam-5470	14	17	rosa	rosa	PROPN
ejpam-5470	14	18	[	[	X
ejpam-5470	14	19	16	16	NUM
ejpam-5470	14	20	]	]	PUNCT
ejpam-5470	14	21	.	.	PUNCT
ejpam-5470	15	1	hundreds	hundred	NOUN
ejpam-5470	15	2	of	of	ADP
ejpam-5470	15	3	researches	research	NOUN
ejpam-5470	15	4	have	have	AUX
ejpam-5470	15	5	been	be	AUX
ejpam-5470	15	6	working	work	VERB
ejpam-5470	15	7	with	with	ADP
ejpam-5470	15	8	different	different	ADJ
ejpam-5470	15	9	types	type	NOUN
ejpam-5470	15	10	of	of	ADP
ejpam-5470	15	11	labeling	labeling	NOUN
ejpam-5470	15	12	graphs	graph	NOUN
ejpam-5470	15	13	[	[	X
ejpam-5470	15	14	5	5	NUM
ejpam-5470	15	15	,	,	PUNCT
ejpam-5470	15	16	13	13	NUM
ejpam-5470	15	17	,	,	PUNCT
ejpam-5470	15	18	14	14	NUM
ejpam-5470	15	19	,	,	PUNCT
ejpam-5470	15	20	17	17	NUM
ejpam-5470	15	21	]	]	PUNCT
ejpam-5470	15	22	.	.	PUNCT
ejpam-5470	16	1	a	a	DET
ejpam-5470	16	2	labeling	labeling	NOUN
ejpam-5470	16	3	of	of	ADP
ejpam-5470	16	4	a	a	DET
ejpam-5470	16	5	graph	graph	NOUN
ejpam-5470	16	6	g	g	NOUN
ejpam-5470	16	7	is	be	AUX
ejpam-5470	16	8	a	a	DET
ejpam-5470	16	9	process	process	NOUN
ejpam-5470	16	10	of	of	ADP
ejpam-5470	16	11	allocating	allocate	VERB
ejpam-5470	16	12	numbers	number	NOUN
ejpam-5470	16	13	or	or	CCONJ
ejpam-5470	16	14	labels	label	NOUN
ejpam-5470	16	15	to	to	ADP
ejpam-5470	16	16	the	the	DET
ejpam-5470	16	17	nodes	node	NOUN
ejpam-5470	16	18	of	of	ADP
ejpam-5470	16	19	g	g	NOUN
ejpam-5470	16	20	or	or	CCONJ
ejpam-5470	16	21	lines	line	NOUN
ejpam-5470	16	22	of	of	ADP
ejpam-5470	16	23	g	g	NOUN
ejpam-5470	16	24	or	or	CCONJ
ejpam-5470	16	25	both	both	PRON
ejpam-5470	16	26	through	through	ADP
ejpam-5470	16	27	mathematical	mathematical	ADJ
ejpam-5470	16	28	functions	function	NOUN
ejpam-5470	16	29	[	[	X
ejpam-5470	16	30	1	1	NUM
ejpam-5470	16	31	]	]	PUNCT
ejpam-5470	16	32	.	.	PUNCT
ejpam-5470	17	1	labeling	labeling	NOUN
ejpam-5470	17	2	graphs	graph	NOUN
ejpam-5470	17	3	are	be	AUX
ejpam-5470	17	4	used	use	VERB
ejpam-5470	17	5	for	for	ADP
ejpam-5470	17	6	a	a	DET
ejpam-5470	17	7	wide	wide	ADJ
ejpam-5470	17	8	range	range	NOUN
ejpam-5470	17	9	of	of	ADP
ejpam-5470	17	10	applications	application	NOUN
ejpam-5470	17	11	in	in	ADP
ejpam-5470	17	12	different	different	ADJ
ejpam-5470	17	13	subjects	subject	NOUN
ejpam-5470	17	14	including	include	VERB
ejpam-5470	17	15	astronomy	astronomy	NOUN
ejpam-5470	17	16	,	,	PUNCT
ejpam-5470	17	17	coding	code	VERB
ejpam-5470	17	18	theory	theory	NOUN
ejpam-5470	17	19	and	and	CCONJ
ejpam-5470	17	20	communication	communication	NOUN
ejpam-5470	17	21	networks	network	NOUN
ejpam-5470	17	22	.	.	PUNCT
ejpam-5470	18	1	cordial	cordial	ADJ
ejpam-5470	18	2	labeling	labeling	NOUN
ejpam-5470	18	3	is	be	AUX
ejpam-5470	18	4	a	a	DET
ejpam-5470	18	5	weaker	weak	ADJ
ejpam-5470	18	6	version	version	NOUN
ejpam-5470	18	7	of	of	ADP
ejpam-5470	18	8	graceful	graceful	ADJ
ejpam-5470	18	9	labeling	labeling	NOUN
ejpam-5470	18	10	and	and	CCONJ
ejpam-5470	18	11	harmonious	harmonious	ADJ
ejpam-5470	18	12	labeling	labeling	NOUN
ejpam-5470	18	13	introduced	introduce	VERB
ejpam-5470	18	14	by	by	ADP
ejpam-5470	18	15	cahit	cahit	NOUN
ejpam-5470	18	16	in	in	ADP
ejpam-5470	18	17	[	[	X
ejpam-5470	18	18	3	3	NUM
ejpam-5470	18	19	]	]	PUNCT
ejpam-5470	18	20	.	.	PUNCT
ejpam-5470	19	1	in	in	ADP
ejpam-5470	19	2	1990	1990	NUM
ejpam-5470	19	3	,	,	PUNCT
ejpam-5470	19	4	cahit	cahit	ADJ
ejpam-5470	19	5	[	[	X
ejpam-5470	19	6	4	4	NUM
ejpam-5470	19	7	]	]	PUNCT
ejpam-5470	19	8	,	,	PUNCT
ejpam-5470	19	9	proved	prove	VERB
ejpam-5470	19	10	the	the	DET
ejpam-5470	19	11	following	following	NOUN
ejpam-5470	19	12	:	:	PUNCT
ejpam-5470	19	13	each	each	DET
ejpam-5470	19	14	tree	tree	NOUN
ejpam-5470	19	15	is	be	AUX
ejpam-5470	19	16	cordial	cordial	ADJ
ejpam-5470	19	17	;	;	PUNCT
ejpam-5470	19	18	an	an	DET
ejpam-5470	19	19	euerlian	euerlian	ADJ
ejpam-5470	19	20	graph	graph	NOUN
ejpam-5470	19	21	is	be	AUX
ejpam-5470	19	22	not	not	PART
ejpam-5470	19	23	cordial	cordial	ADJ
ejpam-5470	19	24	if	if	SCONJ
ejpam-5470	19	25	its	its	PRON
ejpam-5470	19	26	size	size	NOUN
ejpam-5470	19	27	is	be	AUX
ejpam-5470	19	28	congruent	congruent	ADJ
ejpam-5470	19	29	to	to	ADP
ejpam-5470	19	30	2(mod	2(mod	NUM
ejpam-5470	19	31	4	4	NUM
ejpam-5470	19	32	)	)	PUNCT
ejpam-5470	19	33	;	;	PUNCT
ejpam-5470	19	34	a	a	DET
ejpam-5470	19	35	complete	complete	ADJ
ejpam-5470	19	36	graph	graph	NOUN
ejpam-5470	19	37	kn	kn	PROPN
ejpam-5470	19	38	is	be	AUX
ejpam-5470	19	39	cordial	cordial	ADJ
ejpam-5470	19	40	if	if	SCONJ
ejpam-5470	19	41	and	and	CCONJ
ejpam-5470	19	42	only	only	ADV
ejpam-5470	19	43	if	if	SCONJ
ejpam-5470	19	44	n	n	PRON
ejpam-5470	19	45	≤	≤	ADV
ejpam-5470	19	46	3	3	NUM
ejpam-5470	19	47	and	and	CCONJ
ejpam-5470	19	48	a	a	DET
ejpam-5470	19	49	complete	complete	ADJ
ejpam-5470	19	50	bipartite	bipartite	PROPN
ejpam-5470	19	51	graph	graph	NOUN
ejpam-5470	19	52	kn	kn	PROPN
ejpam-5470	19	53	,	,	PUNCT
ejpam-5470	19	54	m	m	VERB
ejpam-5470	19	55	is	be	AUX
ejpam-5470	19	56	cordial	cordial	ADJ
ejpam-5470	19	57	for	for	SCONJ
ejpam-5470	19	58	all	all	DET
ejpam-5470	19	59	positive	positive	ADJ
ejpam-5470	19	60	integers	integer	NOUN
ejpam-5470	19	61	n	n	NOUN
ejpam-5470	19	62	and	and	CCONJ
ejpam-5470	19	63	m.	m.	NOUN
ejpam-5470	19	64	let	let	VERB
ejpam-5470	19	65	∗corresponding	∗corresponde	VERB
ejpam-5470	19	66	author	author	NOUN
ejpam-5470	19	67	.	.	PUNCT
ejpam-5470	20	1	doi	doi	NOUN
ejpam-5470	20	2	:	:	PUNCT
ejpam-5470	20	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5470	https://doi.org/10.29020/nybg.ejpam.v18i1.5470	ADJ
ejpam-5470	20	4	email	email	NOUN
ejpam-5470	20	5	address	address	NOUN
ejpam-5470	20	6	:	:	PUNCT
ejpam-5470	20	7	ashraf.hefnawy68@yahoo.com	ashraf.hefnawy68@yahoo.com	X
ejpam-5470	20	8	(	(	PUNCT
ejpam-5470	20	9	a.	a.	NOUN
ejpam-5470	20	10	elrokh	elrokh	PROPN
ejpam-5470	20	11	)	)	PUNCT
ejpam-5470	21	1	atef	atef	PROPN
ejpam-5470	21	2	1992@yahoo.com	1992@yahoo.com	X
ejpam-5470	21	3	(	(	PUNCT
ejpam-5470	21	4	a.	a.	PROPN
ejpam-5470	21	5	abd	abd	PROPN
ejpam-5470	21	6	el	el	PROPN
ejpam-5470	21	7	-	-	PROPN
ejpam-5470	21	8	hay	hay	PROPN
ejpam-5470	21	9	)	)	PUNCT
ejpam-5470	21	10	,	,	PUNCT
ejpam-5470	21	11	satamy@qu.edu.sa	satamy@qu.edu.sa	PROPN
ejpam-5470	21	12	(	(	PUNCT
ejpam-5470	21	13	k.	k.	PROPN
ejpam-5470	21	14	a.	a.	PROPN
ejpam-5470	21	15	alsatami	alsatami	PROPN
ejpam-5470	21	16	)	)	PUNCT
ejpam-5470	21	17	,	,	PUNCT
ejpam-5470	21	18	aya.ebrahim@inp.edu.eg	aya.ebrahim@inp.edu.eg	NOUN
ejpam-5470	21	19	(	(	PUNCT
ejpam-5470	21	20	a.	a.	NOUN
ejpam-5470	21	21	rabie	rabie	PROPN
ejpam-5470	21	22	)	)	PUNCT
ejpam-5470	21	23	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5470	21	24	1	1	NUM
ejpam-5470	21	25	copyright	copyright	NOUN
ejpam-5470	21	26	:	:	PUNCT
ejpam-5470	21	27	©	©	PROPN
ejpam-5470	21	28	2025	2025	NUM
ejpam-5470	21	29	the	the	DET
ejpam-5470	21	30	author(s	author(s	NOUN
ejpam-5470	21	31	)	)	PUNCT
ejpam-5470	21	32	.	.	PUNCT
ejpam-5470	22	1	(	(	PUNCT
ejpam-5470	22	2	cc	cc	NOUN
ejpam-5470	22	3	by	by	ADP
ejpam-5470	22	4	-	-	PUNCT
ejpam-5470	22	5	nc	nc	PROPN
ejpam-5470	22	6	4.0	4.0	NUM
ejpam-5470	22	7	)	)	PUNCT
ejpam-5470	22	8	a.	a.	NOUN
ejpam-5470	22	9	abd	abd	PROPN
ejpam-5470	22	10	el	el	PROPN
ejpam-5470	22	11	-	-	PROPN
ejpam-5470	22	12	hay	hay	PROPN
ejpam-5470	22	13	et	et	PROPN
ejpam-5470	22	14	al	al	PROPN
ejpam-5470	22	15	.	.	PUNCT
ejpam-5470	22	16	/	/	SYM
ejpam-5470	22	17	eur	eur	PROPN
ejpam-5470	22	18	.	.	PUNCT
ejpam-5470	23	1	j.	j.	PROPN
ejpam-5470	23	2	pure	pure	PROPN
ejpam-5470	23	3	appl	appl	PROPN
ejpam-5470	23	4	.	.	PROPN
ejpam-5470	23	5	math	math	PROPN
ejpam-5470	23	6	,	,	PUNCT
ejpam-5470	23	7	18	18	NUM
ejpam-5470	23	8	(	(	PUNCT
ejpam-5470	23	9	1	1	NUM
ejpam-5470	23	10	)	)	PUNCT
ejpam-5470	23	11	(	(	PUNCT
ejpam-5470	23	12	2025	2025	NUM
ejpam-5470	23	13	)	)	PUNCT
ejpam-5470	23	14	,	,	PUNCT
ejpam-5470	23	15	5470	5470	NUM
ejpam-5470	23	16	2	2	NUM
ejpam-5470	23	17	of	of	ADP
ejpam-5470	23	18	14	14	NUM
ejpam-5470	23	19	g1	g1	NOUN
ejpam-5470	23	20	,	,	PUNCT
ejpam-5470	23	21	g2	g2	PROPN
ejpam-5470	23	22	respectively	respectively	ADV
ejpam-5470	23	23	be	be	VERB
ejpam-5470	23	24	(	(	PUNCT
ejpam-5470	23	25	p1	p1	NOUN
ejpam-5470	23	26	,	,	PUNCT
ejpam-5470	23	27	q1	q1	PROPN
ejpam-5470	23	28	)	)	PUNCT
ejpam-5470	23	29	,	,	PUNCT
ejpam-5470	23	30	(	(	PUNCT
ejpam-5470	23	31	p2	p2	X
ejpam-5470	23	32	,	,	PUNCT
ejpam-5470	23	33	q2	q2	NOUN
ejpam-5470	23	34	)	)	PUNCT
ejpam-5470	23	35	graphs	graph	NOUN
ejpam-5470	23	36	.	.	PUNCT
ejpam-5470	24	1	the	the	DET
ejpam-5470	24	2	fourth	fourth	ADJ
ejpam-5470	24	3	power	power	NOUN
ejpam-5470	24	4	of	of	ADP
ejpam-5470	24	5	a	a	DET
ejpam-5470	24	6	lemniscate	lemniscate	PROPN
ejpam-5470	24	7	graph	graph	NOUN
ejpam-5470	24	8	is	be	AUX
ejpam-5470	24	9	defined	define	VERB
ejpam-5470	24	10	as	as	ADP
ejpam-5470	24	11	the	the	DET
ejpam-5470	24	12	union	union	NOUN
ejpam-5470	24	13	of	of	ADP
ejpam-5470	24	14	fourth	fourth	ADJ
ejpam-5470	24	15	power	power	NOUN
ejpam-5470	24	16	of	of	ADP
ejpam-5470	24	17	cycles	cycle	NOUN
ejpam-5470	24	18	where	where	SCONJ
ejpam-5470	24	19	both	both	PRON
ejpam-5470	24	20	have	have	VERB
ejpam-5470	24	21	a	a	DET
ejpam-5470	24	22	common	common	ADJ
ejpam-5470	24	23	vertex	vertex	NOUN
ejpam-5470	24	24	;	;	PUNCT
ejpam-5470	24	25	it	it	PRON
ejpam-5470	24	26	is	be	AUX
ejpam-5470	24	27	denoted	denote	VERB
ejpam-5470	24	28	by	by	ADP
ejpam-5470	24	29	l4	l4	PROPN
ejpam-5470	24	30	n	n	CCONJ
ejpam-5470	24	31	,	,	PUNCT
ejpam-5470	24	32	m	m	PROPN
ejpam-5470	24	33	≡	≡	PROPN
ejpam-5470	24	34	c4	c4	NOUN
ejpam-5470	24	35	n♯c	n♯c	PROPN
ejpam-5470	24	36	4	4	NUM
ejpam-5470	24	37	m	m	NOUN
ejpam-5470	24	38	as	as	SCONJ
ejpam-5470	24	39	shown	show	VERB
ejpam-5470	24	40	in	in	ADP
ejpam-5470	24	41	fig.1	fig.1	PROPN
ejpam-5470	24	42	.	.	PUNCT
ejpam-5470	25	1	obviously	obviously	ADV
ejpam-5470	25	2	,	,	PUNCT
ejpam-5470	25	3	l4	l4	PROPN
ejpam-5470	25	4	n	n	CCONJ
ejpam-5470	25	5	,	,	PUNCT
ejpam-5470	25	6	m	m	PROPN
ejpam-5470	25	7	has	have	AUX
ejpam-5470	25	8	n+m−	n+m−	PROPN
ejpam-5470	25	9	1	1	NUM
ejpam-5470	25	10	vertices	vertex	NOUN
ejpam-5470	25	11	and	and	CCONJ
ejpam-5470	25	12	4n+4m−	4n+4m−	NUM
ejpam-5470	25	13	18	18	NUM
ejpam-5470	25	14	edges	edge	NOUN
ejpam-5470	25	15	.	.	PUNCT
ejpam-5470	26	1	for	for	ADP
ejpam-5470	26	2	more	more	ADJ
ejpam-5470	26	3	details	detail	NOUN
ejpam-5470	26	4	about	about	ADP
ejpam-5470	26	5	the	the	DET
ejpam-5470	26	6	cordial	cordial	ADJ
ejpam-5470	26	7	labeling	labeling	NOUN
ejpam-5470	26	8	and	and	CCONJ
ejpam-5470	26	9	types	type	NOUN
ejpam-5470	26	10	of	of	ADP
ejpam-5470	26	11	labeling	labeling	NOUN
ejpam-5470	26	12	,	,	PUNCT
ejpam-5470	26	13	the	the	DET
ejpam-5470	26	14	reader	reader	NOUN
ejpam-5470	26	15	can	can	AUX
ejpam-5470	26	16	refer	refer	VERB
ejpam-5470	26	17	to	to	ADP
ejpam-5470	26	18	[	[	X
ejpam-5470	26	19	2	2	NUM
ejpam-5470	26	20	,	,	PUNCT
ejpam-5470	26	21	6–12	6–12	NOUN
ejpam-5470	26	22	,	,	PUNCT
ejpam-5470	26	23	15	15	NUM
ejpam-5470	26	24	]	]	PUNCT
ejpam-5470	26	25	.	.	PUNCT
ejpam-5470	27	1	the	the	DET
ejpam-5470	27	2	corona	corona	PROPN
ejpam-5470	27	3	g1⊙g2	g1⊙g2	PROPN
ejpam-5470	27	4	of	of	ADP
ejpam-5470	27	5	two	two	NUM
ejpam-5470	27	6	graphs	graph	NOUN
ejpam-5470	27	7	g1	g1	PROPN
ejpam-5470	27	8	(	(	PUNCT
ejpam-5470	27	9	with	with	ADP
ejpam-5470	27	10	n1	n1	ADJ
ejpam-5470	27	11	vertices	vertex	NOUN
ejpam-5470	27	12	,	,	PUNCT
ejpam-5470	27	13	figure	figure	NOUN
ejpam-5470	27	14	1	1	NUM
ejpam-5470	27	15	:	:	PUNCT
ejpam-5470	27	16	the	the	DET
ejpam-5470	27	17	fourth	fourth	ADJ
ejpam-5470	27	18	power	power	NOUN
ejpam-5470	27	19	of	of	ADP
ejpam-5470	27	20	a	a	DET
ejpam-5470	27	21	lemniscate	lemniscate	PROPN
ejpam-5470	27	22	graph	graph	NOUN
ejpam-5470	27	23	l4	l4	PROPN
ejpam-5470	27	24	7,7	7,7	NUM
ejpam-5470	27	25	.	.	PUNCT
ejpam-5470	28	1	m1	m1	NOUN
ejpam-5470	28	2	edges	edge	NOUN
ejpam-5470	28	3	)	)	PUNCT
ejpam-5470	28	4	and	and	CCONJ
ejpam-5470	28	5	g2	g2	PROPN
ejpam-5470	28	6	(	(	PUNCT
ejpam-5470	28	7	with	with	ADP
ejpam-5470	28	8	n2	n2	ADJ
ejpam-5470	28	9	vertices	vertex	NOUN
ejpam-5470	28	10	,	,	PUNCT
ejpam-5470	28	11	m2	m2	PROPN
ejpam-5470	28	12	edges	edge	NOUN
ejpam-5470	28	13	)	)	PUNCT
ejpam-5470	28	14	is	be	AUX
ejpam-5470	28	15	defined	define	VERB
ejpam-5470	28	16	as	as	ADP
ejpam-5470	28	17	the	the	DET
ejpam-5470	28	18	graph	graph	NOUN
ejpam-5470	28	19	obtained	obtain	VERB
ejpam-5470	28	20	by	by	ADP
ejpam-5470	28	21	taking	take	VERB
ejpam-5470	28	22	one	one	NUM
ejpam-5470	28	23	copy	copy	NOUN
ejpam-5470	28	24	of	of	ADP
ejpam-5470	28	25	g1	g1	NOUN
ejpam-5470	28	26	and	and	CCONJ
ejpam-5470	28	27	copies	copy	NOUN
ejpam-5470	28	28	of	of	ADP
ejpam-5470	28	29	g2	g2	PROPN
ejpam-5470	28	30	,	,	PUNCT
ejpam-5470	28	31	and	and	CCONJ
ejpam-5470	28	32	then	then	ADV
ejpam-5470	28	33	joining	join	VERB
ejpam-5470	28	34	the	the	DET
ejpam-5470	28	35	ith	ith	PROPN
ejpam-5470	28	36	vertex	vertex	NOUN
ejpam-5470	28	37	of	of	ADP
ejpam-5470	28	38	g1	g1	PROPN
ejpam-5470	28	39	with	with	ADP
ejpam-5470	28	40	an	an	DET
ejpam-5470	28	41	edge	edge	NOUN
ejpam-5470	28	42	to	to	ADP
ejpam-5470	28	43	every	every	DET
ejpam-5470	28	44	vertex	vertex	NOUN
ejpam-5470	28	45	in	in	ADP
ejpam-5470	28	46	the	the	DET
ejpam-5470	28	47	ith	ith	PROPN
ejpam-5470	28	48	copy	copy	NOUN
ejpam-5470	28	49	of	of	ADP
ejpam-5470	28	50	g2	g2	PROPN
ejpam-5470	28	51	.	.	PUNCT
ejpam-5470	29	1	it	it	PRON
ejpam-5470	29	2	is	be	AUX
ejpam-5470	29	3	easy	easy	ADJ
ejpam-5470	29	4	to	to	PART
ejpam-5470	29	5	see	see	VERB
ejpam-5470	29	6	that	that	SCONJ
ejpam-5470	29	7	the	the	DET
ejpam-5470	29	8	corona	corona	PROPN
ejpam-5470	29	9	g1⊙g2	g1⊙g2	PROPN
ejpam-5470	29	10	that	that	PRON
ejpam-5470	29	11	has	have	VERB
ejpam-5470	29	12	n1	n1	NOUN
ejpam-5470	29	13	+	+	CCONJ
ejpam-5470	29	14	n1n2	n1n2	NUM
ejpam-5470	29	15	vertices	vertex	NOUN
ejpam-5470	29	16	and	and	CCONJ
ejpam-5470	29	17	m1	m1	PROPN
ejpam-5470	29	18	+	+	CCONJ
ejpam-5470	29	19	n1m2	n1m2	X
ejpam-5470	29	20	+	+	CCONJ
ejpam-5470	29	21	n1n2	n1n2	NOUN
ejpam-5470	29	22	edges	edge	NOUN
ejpam-5470	29	23	.	.	PUNCT
ejpam-5470	30	1	2	2	X
ejpam-5470	30	2	.	.	X
ejpam-5470	30	3	terminology	terminology	NOUN
ejpam-5470	30	4	and	and	CCONJ
ejpam-5470	30	5	notation	notation	NOUN
ejpam-5470	30	6	given	give	VERB
ejpam-5470	30	7	a	a	DET
ejpam-5470	30	8	path	path	NOUN
ejpam-5470	30	9	or	or	CCONJ
ejpam-5470	30	10	a	a	DET
ejpam-5470	30	11	cycle	cycle	NOUN
ejpam-5470	30	12	with	with	ADP
ejpam-5470	30	13	4r	4r	ADJ
ejpam-5470	30	14	vertices	vertex	NOUN
ejpam-5470	30	15	,	,	PUNCT
ejpam-5470	30	16	we	we	PRON
ejpam-5470	30	17	let	let	VERB
ejpam-5470	30	18	l4r	l4r	PRON
ejpam-5470	30	19	denote	denote	VERB
ejpam-5470	30	20	the	the	DET
ejpam-5470	30	21	labeling	labeling	NOUN
ejpam-5470	30	22	0011	0011	NUM
ejpam-5470	30	23	...	...	PUNCT
ejpam-5470	30	24	0011	0011	NUM
ejpam-5470	30	25	(	(	PUNCT
ejpam-5470	30	26	repeated	repeat	VERB
ejpam-5470	30	27	r	r	NOUN
ejpam-5470	30	28	-	-	PUNCT
ejpam-5470	30	29	times	time	NOUN
ejpam-5470	30	30	)	)	PUNCT
ejpam-5470	30	31	,	,	PUNCT
ejpam-5470	30	32	let	let	VERB
ejpam-5470	30	33	l′	l′	PROPN
ejpam-5470	30	34	4r	4r	NUM
ejpam-5470	30	35	denote	denote	VERB
ejpam-5470	30	36	the	the	DET
ejpam-5470	30	37	labeling	labeling	NOUN
ejpam-5470	30	38	1100	1100	NUM
ejpam-5470	30	39	...	...	SYM
ejpam-5470	30	40	1100	1100	NUM
ejpam-5470	30	41	(	(	PUNCT
ejpam-5470	30	42	repeated	repeat	VERB
ejpam-5470	30	43	r	r	NOUN
ejpam-5470	30	44	times	time	NOUN
ejpam-5470	30	45	)	)	PUNCT
ejpam-5470	30	46	.	.	PUNCT
ejpam-5470	31	1	the	the	DET
ejpam-5470	31	2	labeling	labeling	NOUN
ejpam-5470	31	3	1001	1001	NUM
ejpam-5470	31	4	1001	1001	NUM
ejpam-5470	31	5	...	...	SYM
ejpam-5470	31	6	1001	1001	NUM
ejpam-5470	31	7	(	(	PUNCT
ejpam-5470	31	8	repeated	repeat	VERB
ejpam-5470	31	9	r	r	NOUN
ejpam-5470	31	10	times	time	NOUN
ejpam-5470	31	11	)	)	PUNCT
ejpam-5470	31	12	and	and	CCONJ
ejpam-5470	31	13	0110	0110	NUM
ejpam-5470	31	14	...	...	PUNCT
ejpam-5470	31	15	0110	0110	NUM
ejpam-5470	31	16	(	(	PUNCT
ejpam-5470	31	17	repeated	repeat	VERB
ejpam-5470	31	18	r	r	NOUN
ejpam-5470	31	19	times	time	NOUN
ejpam-5470	31	20	)	)	PUNCT
ejpam-5470	31	21	are	be	AUX
ejpam-5470	31	22	denoted	denote	VERB
ejpam-5470	31	23	by	by	ADP
ejpam-5470	31	24	s4r	s4r	PROPN
ejpam-5470	31	25	and	and	CCONJ
ejpam-5470	31	26	s′	s′	ADJ
ejpam-5470	31	27	4r	4r	NOUN
ejpam-5470	31	28	.	.	PUNCT
ejpam-5470	32	1	let	let	VERB
ejpam-5470	32	2	m2r	m2r	NOUN
ejpam-5470	32	3	denote	denote	VERB
ejpam-5470	32	4	the	the	DET
ejpam-5470	32	5	labeling	labeling	NOUN
ejpam-5470	32	6	0101	0101	NUM
ejpam-5470	32	7	...	...	PUNCT
ejpam-5470	32	8	01	01	NUM
ejpam-5470	32	9	,	,	PUNCT
ejpam-5470	32	10	zero	zero	NUM
ejpam-5470	32	11	-	-	PUNCT
ejpam-5470	32	12	one	one	NUM
ejpam-5470	32	13	repeated	repeat	VERB
ejpam-5470	32	14	r−times	r−time	NOUN
ejpam-5470	32	15	if	if	SCONJ
ejpam-5470	32	16	r	r	NOUN
ejpam-5470	32	17	is	be	AUX
ejpam-5470	32	18	even	even	ADV
ejpam-5470	32	19	and	and	CCONJ
ejpam-5470	32	20	0101	0101	NUM
ejpam-5470	32	21	...	...	PUNCT
ejpam-5470	33	1	010	010	NUM
ejpam-5470	33	2	if	if	SCONJ
ejpam-5470	33	3	r	r	NOUN
ejpam-5470	33	4	is	be	AUX
ejpam-5470	33	5	odd	odd	ADJ
ejpam-5470	33	6	.	.	PUNCT
ejpam-5470	34	1	sometimes	sometimes	ADV
ejpam-5470	34	2	,	,	PUNCT
ejpam-5470	34	3	we	we	PRON
ejpam-5470	34	4	modify	modify	VERB
ejpam-5470	34	5	labeling	labeling	NOUN
ejpam-5470	34	6	by	by	ADP
ejpam-5470	34	7	adding	add	VERB
ejpam-5470	34	8	symbols	symbol	NOUN
ejpam-5470	34	9	at	at	ADP
ejpam-5470	34	10	one	one	NUM
ejpam-5470	34	11	end	end	NOUN
ejpam-5470	34	12	or	or	CCONJ
ejpam-5470	34	13	the	the	DET
ejpam-5470	34	14	other	other	ADJ
ejpam-5470	34	15	(	(	PUNCT
ejpam-5470	34	16	or	or	CCONJ
ejpam-5470	34	17	both	both	PRON
ejpam-5470	34	18	)	)	PUNCT
ejpam-5470	34	19	.	.	PUNCT
ejpam-5470	35	1	if	if	SCONJ
ejpam-5470	35	2	g	g	PROPN
ejpam-5470	35	3	and	and	CCONJ
ejpam-5470	35	4	h	h	NOUN
ejpam-5470	35	5	are	be	AUX
ejpam-5470	35	6	two	two	NUM
ejpam-5470	35	7	graphs	graph	NOUN
ejpam-5470	35	8	,	,	PUNCT
ejpam-5470	35	9	where	where	SCONJ
ejpam-5470	35	10	g	g	PROPN
ejpam-5470	35	11	has	have	VERB
ejpam-5470	35	12	n	n	NUM
ejpam-5470	35	13	vertices	vertex	NOUN
ejpam-5470	35	14	,	,	PUNCT
ejpam-5470	35	15	the	the	DET
ejpam-5470	35	16	labeling	labeling	NOUN
ejpam-5470	35	17	of	of	ADP
ejpam-5470	35	18	the	the	DET
ejpam-5470	35	19	corona	corona	NOUN
ejpam-5470	35	20	g⊙h	g⊙h	NOUN
ejpam-5470	35	21	is	be	AUX
ejpam-5470	35	22	often	often	ADV
ejpam-5470	35	23	denoted	denote	VERB
ejpam-5470	35	24	by	by	ADP
ejpam-5470	35	25	[	[	X
ejpam-5470	35	26	a	a	DET
ejpam-5470	35	27	:	:	PUNCT
ejpam-5470	35	28	b1	b1	NOUN
ejpam-5470	35	29	,	,	PUNCT
ejpam-5470	35	30	b2	b2	NOUN
ejpam-5470	35	31	,	,	PUNCT
ejpam-5470	35	32	b3	b3	PROPN
ejpam-5470	35	33	,	,	PUNCT
ejpam-5470	35	34	...	...	PUNCT
ejpam-5470	35	35	,	,	PUNCT
ejpam-5470	35	36	bn	bn	X
ejpam-5470	35	37	]	]	PUNCT
ejpam-5470	35	38	,	,	PUNCT
ejpam-5470	35	39	where	where	SCONJ
ejpam-5470	35	40	a	a	PRON
ejpam-5470	35	41	is	be	AUX
ejpam-5470	35	42	the	the	DET
ejpam-5470	35	43	labeling	labeling	NOUN
ejpam-5470	35	44	of	of	ADP
ejpam-5470	35	45	the	the	DET
ejpam-5470	35	46	n	n	DET
ejpam-5470	35	47	vertices	vertex	NOUN
ejpam-5470	35	48	of	of	ADP
ejpam-5470	35	49	g	g	NOUN
ejpam-5470	35	50	,	,	PUNCT
ejpam-5470	35	51	and	and	CCONJ
ejpam-5470	35	52	bi	bi	NOUN
ejpam-5470	35	53	,	,	PUNCT
ejpam-5470	35	54	1	1	NUM
ejpam-5470	35	55	≤	≤	NUM
ejpam-5470	36	1	i	i	X
ejpam-5470	36	2	≤	≤	NOUN
ejpam-5470	36	3	n	n	PRON
ejpam-5470	36	4	is	be	AUX
ejpam-5470	36	5	the	the	DET
ejpam-5470	36	6	labeling	labeling	NOUN
ejpam-5470	36	7	of	of	ADP
ejpam-5470	36	8	the	the	DET
ejpam-5470	36	9	vertices	vertex	NOUN
ejpam-5470	36	10	of	of	ADP
ejpam-5470	36	11	the	the	DET
ejpam-5470	36	12	copy	copy	NOUN
ejpam-5470	36	13	of	of	ADP
ejpam-5470	36	14	h	h	NOUN
ejpam-5470	36	15	that	that	PRON
ejpam-5470	36	16	is	be	AUX
ejpam-5470	36	17	connected	connect	VERB
ejpam-5470	36	18	to	to	ADP
ejpam-5470	36	19	the	the	DET
ejpam-5470	36	20	i−th	i−th	PROPN
ejpam-5470	36	21	vertex	vertex	NOUN
ejpam-5470	36	22	of	of	ADP
ejpam-5470	36	23	g.	g.	PROPN
ejpam-5470	36	24	for	for	ADP
ejpam-5470	36	25	a	a	DET
ejpam-5470	36	26	given	give	VERB
ejpam-5470	36	27	labeling	labeling	NOUN
ejpam-5470	36	28	of	of	ADP
ejpam-5470	36	29	the	the	DET
ejpam-5470	36	30	corona	corona	NOUN
ejpam-5470	36	31	g⊙h	g⊙h	NOUN
ejpam-5470	36	32	,	,	PUNCT
ejpam-5470	36	33	we	we	PRON
ejpam-5470	36	34	denote	denote	VERB
ejpam-5470	36	35	vi	vi	PROPN
ejpam-5470	36	36	and	and	CCONJ
ejpam-5470	36	37	ei	ei	X
ejpam-5470	36	38	(	(	PUNCT
ejpam-5470	36	39	i=	i=	PROPN
ejpam-5470	36	40	0	0	NUM
ejpam-5470	36	41	,	,	PUNCT
ejpam-5470	36	42	1	1	NUM
ejpam-5470	36	43	)	)	PUNCT
ejpam-5470	36	44	to	to	PART
ejpam-5470	36	45	represent	represent	VERB
ejpam-5470	36	46	the	the	DET
ejpam-5470	36	47	numbers	number	NOUN
ejpam-5470	36	48	of	of	ADP
ejpam-5470	36	49	vertices	vertex	NOUN
ejpam-5470	36	50	and	and	CCONJ
ejpam-5470	36	51	edges	edge	NOUN
ejpam-5470	36	52	,	,	PUNCT
ejpam-5470	36	53	respectively	respectively	ADV
ejpam-5470	36	54	,	,	PUNCT
ejpam-5470	36	55	labeled	label	VERB
ejpam-5470	36	56	by	by	ADP
ejpam-5470	36	57	i.	i.	PROPN
ejpam-5470	36	58	let	let	VERB
ejpam-5470	36	59	us	we	PRON
ejpam-5470	36	60	denote	denote	VERB
ejpam-5470	36	61	xi	xi	X
ejpam-5470	36	62	and	and	CCONJ
ejpam-5470	36	63	ai	ai	VERB
ejpam-5470	36	64	to	to	PART
ejpam-5470	36	65	be	be	AUX
ejpam-5470	36	66	the	the	DET
ejpam-5470	36	67	numbers	number	NOUN
ejpam-5470	36	68	of	of	ADP
ejpam-5470	36	69	vertices	vertex	NOUN
ejpam-5470	36	70	and	and	CCONJ
ejpam-5470	36	71	edges	edge	NOUN
ejpam-5470	36	72	labeled	label	VERB
ejpam-5470	36	73	by	by	ADP
ejpam-5470	36	74	i	i	PRON
ejpam-5470	36	75	for	for	ADP
ejpam-5470	36	76	the	the	DET
ejpam-5470	36	77	graph	graph	NOUN
ejpam-5470	36	78	g.	g.	PROPN
ejpam-5470	36	79	also	also	ADV
ejpam-5470	36	80	,	,	PUNCT
ejpam-5470	36	81	we	we	PRON
ejpam-5470	36	82	let	let	VERB
ejpam-5470	36	83	yi	yi	NOUN
ejpam-5470	36	84	and	and	CCONJ
ejpam-5470	36	85	bi	bi	NOUN
ejpam-5470	36	86	be	be	AUX
ejpam-5470	36	87	those	those	PRON
ejpam-5470	36	88	for	for	ADP
ejpam-5470	36	89	h	h	NOUN
ejpam-5470	36	90	,	,	PUNCT
ejpam-5470	36	91	which	which	PRON
ejpam-5470	36	92	are	be	AUX
ejpam-5470	36	93	connected	connect	VERB
ejpam-5470	36	94	to	to	ADP
ejpam-5470	36	95	the	the	DET
ejpam-5470	36	96	vertices	vertex	NOUN
ejpam-5470	36	97	labeled	label	VERB
ejpam-5470	36	98	0	0	NUM
ejpam-5470	36	99	of	of	ADP
ejpam-5470	36	100	g.	g.	PROPN
ejpam-5470	36	101	likewise	likewise	ADV
ejpam-5470	36	102	,	,	PUNCT
ejpam-5470	36	103	let	let	VERB
ejpam-5470	36	104	y′i	y′i	NOUN
ejpam-5470	36	105	and	and	CCONJ
ejpam-5470	36	106	b′i	b′i	PROPN
ejpam-5470	36	107	be	be	VERB
ejpam-5470	36	108	those	those	PRON
ejpam-5470	36	109	for	for	ADP
ejpam-5470	36	110	h	h	NOUN
ejpam-5470	36	111	,	,	PUNCT
ejpam-5470	36	112	which	which	PRON
ejpam-5470	36	113	are	be	AUX
ejpam-5470	36	114	connected	connect	VERB
ejpam-5470	36	115	to	to	ADP
ejpam-5470	36	116	the	the	DET
ejpam-5470	36	117	vertices	vertex	NOUN
ejpam-5470	36	118	labeled	label	VERB
ejpam-5470	36	119	1	1	NUM
ejpam-5470	36	120	of	of	ADP
ejpam-5470	36	121	g.	g.	PROPN
ejpam-5470	37	1	it	it	PRON
ejpam-5470	37	2	is	be	AUX
ejpam-5470	37	3	easily	easily	ADV
ejpam-5470	37	4	to	to	PART
ejpam-5470	37	5	verify	verify	VERB
ejpam-5470	37	6	that	that	DET
ejpam-5470	37	7	v0	v0	NOUN
ejpam-5470	37	8	=	=	NOUN
ejpam-5470	37	9	x0	x0	PROPN
ejpam-5470	38	1	+	+	CCONJ
ejpam-5470	38	2	x0y0	x0y0	X
ejpam-5470	39	1	+	+	CCONJ
ejpam-5470	39	2	x1y	x1y	PROPN
ejpam-5470	39	3	′	′	NUM
ejpam-5470	39	4	0	0	NUM
ejpam-5470	39	5	,	,	PUNCT
ejpam-5470	39	6	v1	v1	NOUN
ejpam-5470	39	7	=	=	SYM
ejpam-5470	39	8	x1	x1	PROPN
ejpam-5470	39	9	+	+	X
ejpam-5470	39	10	x0y1	x0y1	X
ejpam-5470	40	1	+	+	CCONJ
ejpam-5470	40	2	x1y	x1y	PROPN
ejpam-5470	41	1	′	′	NUM
ejpam-5470	41	2	1	1	NUM
ejpam-5470	41	3	,	,	PUNCT
ejpam-5470	41	4	e0	e0	PROPN
ejpam-5470	41	5	=	=	SYM
ejpam-5470	41	6	a0	a0	PROPN
ejpam-5470	41	7	+	+	CCONJ
ejpam-5470	41	8	x0b0	x0b0	PROPN
ejpam-5470	42	1	+	+	CCONJ
ejpam-5470	42	2	x1b	x1b	PROPN
ejpam-5470	42	3	′	′	VERB
ejpam-5470	43	1	0+x0y1+x1y	0+x0y1+x1y	NUM
ejpam-5470	44	1	′	′	NUM
ejpam-5470	44	2	0	0	NUM
ejpam-5470	45	1	and	and	CCONJ
ejpam-5470	45	2	e1	e1	PROPN
ejpam-5470	45	3	=	=	PROPN
ejpam-5470	45	4	a1+x0b1+x1b	a1+x0b1+x1b	NOUN
ejpam-5470	45	5	′	′	NOUN
ejpam-5470	45	6	1+x0y0+x1y	1+x0y0+x1y	NUM
ejpam-5470	46	1	′	′	NUM
ejpam-5470	46	2	1	1	NUM
ejpam-5470	46	3	.	.	PUNCT
ejpam-5470	47	1	thus	thus	ADV
ejpam-5470	47	2	v0−v1=	v0−v1=	PUNCT
ejpam-5470	47	3	(	(	PUNCT
ejpam-5470	47	4	x0−x1)+x0(y0−	x0−x1)+x0(y0−	PROPN
ejpam-5470	47	5	y1)+x1(y	y1)+x1(y	PROPN
ejpam-5470	47	6	′	′	PROPN
ejpam-5470	48	1	0−y′1	0−y′1	NUM
ejpam-5470	48	2	)	)	PUNCT
ejpam-5470	48	3	and	and	CCONJ
ejpam-5470	48	4	e0−e1=	e0−e1=	NUM
ejpam-5470	48	5	(	(	PUNCT
ejpam-5470	48	6	a0−a1)+x0(b0−b1)+x1(b	a0−a1)+x0(b0−b1)+x1(b	PROPN
ejpam-5470	49	1	′	′	NUM
ejpam-5470	49	2	0−b′1)+x0(y0−y1)−x1(y	0−b′1)+x0(y0−y1)−x1(y	NUM
ejpam-5470	50	1	′	′	NUM
ejpam-5470	51	1	0−y′1	0−y′1	X
ejpam-5470	51	2	)	)	PUNCT
ejpam-5470	51	3	in	in	ADP
ejpam-5470	51	4	particular	particular	ADJ
ejpam-5470	51	5	,	,	PUNCT
ejpam-5470	51	6	if	if	SCONJ
ejpam-5470	51	7	we	we	PRON
ejpam-5470	51	8	have	have	VERB
ejpam-5470	51	9	only	only	ADV
ejpam-5470	51	10	one	one	NUM
ejpam-5470	51	11	labeling	labeling	NOUN
ejpam-5470	51	12	for	for	ADP
ejpam-5470	51	13	all	all	DET
ejpam-5470	51	14	copies	copy	NOUN
ejpam-5470	51	15	of	of	ADP
ejpam-5470	51	16	h	h	NOUN
ejpam-5470	51	17	,	,	PUNCT
ejpam-5470	51	18	i.e.	i.e.	X
ejpam-5470	51	19	,	,	PUNCT
ejpam-5470	51	20	yi	yi	PROPN
ejpam-5470	51	21	=	=	NOUN
ejpam-5470	51	22	y′i	y′i	NOUN
ejpam-5470	51	23	and	and	CCONJ
ejpam-5470	51	24	bi	bi	NOUN
ejpam-5470	51	25	=	=	NOUN
ejpam-5470	51	26	b′i	b′i	NOUN
ejpam-5470	51	27	,	,	PUNCT
ejpam-5470	51	28	then	then	ADV
ejpam-5470	51	29	v0	v0	PROPN
ejpam-5470	51	30	=	=	SYM
ejpam-5470	51	31	x0+ny0	x0+ny0	PROPN
ejpam-5470	51	32	,	,	PUNCT
ejpam-5470	51	33	v1	v1	NOUN
ejpam-5470	51	34	=	=	SYM
ejpam-5470	51	35	x1+ny1	x1+ny1	PROPN
ejpam-5470	51	36	,	,	PUNCT
ejpam-5470	51	37	e0	e0	PROPN
ejpam-5470	51	38	=	=	SYM
ejpam-5470	51	39	a0+nb0+x0y1+x1y0	a0+nb0+x0y1+x1y0	NUM
ejpam-5470	51	40	and	and	CCONJ
ejpam-5470	51	41	e1	e1	NOUN
ejpam-5470	51	42	=	=	NOUN
ejpam-5470	51	43	a1+nb1+x0y0+x1y1	a1+nb1+x0y0+x1y1	NOUN
ejpam-5470	51	44	.	.	PUNCT
ejpam-5470	52	1	thus	thus	ADV
ejpam-5470	52	2	v0	v0	VERB
ejpam-5470	52	3	−	−	PROPN
ejpam-5470	52	4	v1=	v1=	ADP
ejpam-5470	52	5	(	(	PUNCT
ejpam-5470	52	6	x0	x0	PROPN
ejpam-5470	52	7	−	−	PROPN
ejpam-5470	52	8	x1	x1	PROPN
ejpam-5470	52	9	)	)	PUNCT
ejpam-5470	53	1	+	+	CCONJ
ejpam-5470	53	2	n(y0	n(y0	NOUN
ejpam-5470	53	3	−	−	PROPN
ejpam-5470	53	4	y1	y1	PROPN
ejpam-5470	53	5	)	)	PUNCT
ejpam-5470	53	6	and	and	CCONJ
ejpam-5470	53	7	e0	e0	PROPN
ejpam-5470	53	8	−	−	PROPN
ejpam-5470	53	9	e1=	e1=	PROPN
ejpam-5470	53	10	(	(	PUNCT
ejpam-5470	53	11	a0	a0	PROPN
ejpam-5470	53	12	−	−	PROPN
ejpam-5470	53	13	a1	a1	PROPN
ejpam-5470	53	14	)	)	PUNCT
ejpam-5470	53	15	+	+	NUM
ejpam-5470	53	16	n(b0	n(b0	ADJ
ejpam-5470	53	17	−	−	NOUN
ejpam-5470	53	18	b1	b1	NOUN
ejpam-5470	53	19	)	)	PUNCT
ejpam-5470	53	20	+	+	CCONJ
ejpam-5470	54	1	(	(	PUNCT
ejpam-5470	54	2	x1	x1	ADJ
ejpam-5470	54	3	−	−	PROPN
ejpam-5470	54	4	x0)(y0	x0)(y0	PROPN
ejpam-5470	54	5	−	−	PROPN
ejpam-5470	54	6	y1	y1	PROPN
ejpam-5470	54	7	)	)	PUNCT
ejpam-5470	54	8	,	,	PUNCT
ejpam-5470	54	9	where	where	SCONJ
ejpam-5470	54	10	n	n	X
ejpam-5470	54	11	is	be	AUX
ejpam-5470	54	12	the	the	DET
ejpam-5470	54	13	order	order	NOUN
ejpam-5470	54	14	of	of	ADP
ejpam-5470	54	15	g.	g.	PROPN
ejpam-5470	54	16	section	section	PROPN
ejpam-5470	54	17	one	one	NOUN
ejpam-5470	54	18	contains	contain	VERB
ejpam-5470	54	19	a	a	DET
ejpam-5470	54	20	brief	brief	ADJ
ejpam-5470	54	21	literary	literary	ADJ
ejpam-5470	54	22	analysis	analysis	NOUN
ejpam-5470	54	23	of	of	ADP
ejpam-5470	54	24	the	the	DET
ejpam-5470	54	25	topic	topic	NOUN
ejpam-5470	54	26	of	of	ADP
ejpam-5470	54	27	this	this	DET
ejpam-5470	54	28	work	work	NOUN
ejpam-5470	54	29	,	,	PUNCT
ejpam-5470	54	30	and	and	CCONJ
ejpam-5470	54	31	section	section	NOUN
ejpam-5470	54	32	two	two	NUM
ejpam-5470	54	33	deals	deal	NOUN
ejpam-5470	54	34	with	with	ADP
ejpam-5470	54	35	the	the	DET
ejpam-5470	54	36	terminology	terminology	NOUN
ejpam-5470	54	37	employed	employ	VERB
ejpam-5470	54	38	throughout	throughout	ADP
ejpam-5470	54	39	.	.	PUNCT
ejpam-5470	55	1	section	section	NOUN
ejpam-5470	55	2	three	three	NUM
ejpam-5470	55	3	examines	examine	NOUN
ejpam-5470	55	4	and	and	CCONJ
ejpam-5470	55	5	study	study	VERB
ejpam-5470	55	6	the	the	DET
ejpam-5470	55	7	cordiality	cordiality	NOUN
ejpam-5470	55	8	of	of	ADP
ejpam-5470	55	9	the	the	DET
ejpam-5470	55	10	corona	corona	NOUN
ejpam-5470	55	11	product	product	NOUN
ejpam-5470	55	12	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	55	13	n	n	CCONJ
ejpam-5470	55	14	,	,	PUNCT
ejpam-5470	55	15	m	m	NOUN
ejpam-5470	55	16	of	of	ADP
ejpam-5470	55	17	paths	path	NOUN
ejpam-5470	55	18	and	and	CCONJ
ejpam-5470	55	19	fourth	fourth	ADJ
ejpam-5470	55	20	power	power	NOUN
ejpam-5470	55	21	of	of	ADP
ejpam-5470	55	22	lemniscate	lemniscate	PROPN
ejpam-5470	55	23	graphs	graph	NOUN
ejpam-5470	55	24	,	,	PUNCT
ejpam-5470	55	25	and	and	CCONJ
ejpam-5470	55	26	show	show	VERB
ejpam-5470	55	27	that	that	SCONJ
ejpam-5470	55	28	this	this	PRON
ejpam-5470	55	29	is	be	AUX
ejpam-5470	55	30	cordial	cordial	ADJ
ejpam-5470	55	31	for	for	ADP
ejpam-5470	55	32	all	all	DET
ejpam-5470	55	33	positive	positive	ADJ
ejpam-5470	55	34	integers	integer	NOUN
ejpam-5470	55	35	a.	a.	PROPN
ejpam-5470	55	36	abd	abd	PROPN
ejpam-5470	55	37	el	el	PROPN
ejpam-5470	55	38	-	-	PROPN
ejpam-5470	55	39	hay	hay	PROPN
ejpam-5470	55	40	et	et	PROPN
ejpam-5470	55	41	al	al	PROPN
ejpam-5470	55	42	.	.	PUNCT
ejpam-5470	55	43	/	/	SYM
ejpam-5470	55	44	eur	eur	PROPN
ejpam-5470	55	45	.	.	PUNCT
ejpam-5470	56	1	j.	j.	PROPN
ejpam-5470	56	2	pure	pure	PROPN
ejpam-5470	56	3	appl	appl	PROPN
ejpam-5470	56	4	.	.	PROPN
ejpam-5470	56	5	math	math	PROPN
ejpam-5470	56	6	,	,	PUNCT
ejpam-5470	56	7	18	18	NUM
ejpam-5470	56	8	(	(	PUNCT
ejpam-5470	56	9	1	1	NUM
ejpam-5470	56	10	)	)	PUNCT
ejpam-5470	56	11	(	(	PUNCT
ejpam-5470	56	12	2025	2025	NUM
ejpam-5470	56	13	)	)	PUNCT
ejpam-5470	56	14	,	,	PUNCT
ejpam-5470	56	15	5470	5470	NUM
ejpam-5470	56	16	3	3	NUM
ejpam-5470	56	17	of	of	ADP
ejpam-5470	56	18	14	14	NUM
ejpam-5470	56	19	k	k	PROPN
ejpam-5470	56	20	≥	≥	NUM
ejpam-5470	56	21	1	1	NUM
ejpam-5470	56	22	,	,	PUNCT
ejpam-5470	56	23	n	n	CCONJ
ejpam-5470	56	24	,	,	PUNCT
ejpam-5470	56	25	m	m	VERB
ejpam-5470	56	26	≥	≥	NOUN
ejpam-5470	56	27	3	3	NUM
ejpam-5470	56	28	.	.	PUNCT
ejpam-5470	57	1	the	the	DET
ejpam-5470	57	2	last	last	ADJ
ejpam-5470	57	3	section	section	NOUN
ejpam-5470	57	4	,	,	PUNCT
ejpam-5470	57	5	is	be	AUX
ejpam-5470	57	6	the	the	DET
ejpam-5470	57	7	conclusion	conclusion	NOUN
ejpam-5470	57	8	which	which	PRON
ejpam-5470	57	9	summarize	summarize	VERB
ejpam-5470	57	10	the	the	DET
ejpam-5470	57	11	important	important	ADJ
ejpam-5470	57	12	points	point	NOUN
ejpam-5470	57	13	of	of	ADP
ejpam-5470	57	14	our	our	PRON
ejpam-5470	57	15	finding	finding	NOUN
ejpam-5470	57	16	in	in	ADP
ejpam-5470	57	17	this	this	DET
ejpam-5470	57	18	paper	paper	NOUN
ejpam-5470	57	19	3	3	NUM
ejpam-5470	57	20	.	.	PUNCT
ejpam-5470	57	21	main	main	ADJ
ejpam-5470	57	22	results	result	NOUN
ejpam-5470	57	23	.	.	PUNCT
ejpam-5470	58	1	in	in	ADP
ejpam-5470	58	2	this	this	DET
ejpam-5470	58	3	section	section	NOUN
ejpam-5470	58	4	,	,	PUNCT
ejpam-5470	58	5	we	we	PRON
ejpam-5470	58	6	show	show	VERB
ejpam-5470	58	7	that	that	SCONJ
ejpam-5470	58	8	the	the	DET
ejpam-5470	58	9	corona	corona	NOUN
ejpam-5470	58	10	product	product	NOUN
ejpam-5470	58	11	of	of	ADP
ejpam-5470	58	12	paths	path	NOUN
ejpam-5470	58	13	and	and	CCONJ
ejpam-5470	58	14	fourth	fourth	ADJ
ejpam-5470	58	15	power	power	NOUN
ejpam-5470	58	16	of	of	ADP
ejpam-5470	58	17	lemniscate	lemniscate	PROPN
ejpam-5470	58	18	graphs	graph	NOUN
ejpam-5470	58	19	,	,	PUNCT
ejpam-5470	58	20	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	58	21	n	n	CCONJ
ejpam-5470	58	22	,	,	PUNCT
ejpam-5470	58	23	m	m	VERB
ejpam-5470	58	24	,	,	PUNCT
ejpam-5470	58	25	is	be	AUX
ejpam-5470	58	26	cordial	cordial	ADJ
ejpam-5470	58	27	for	for	SCONJ
ejpam-5470	58	28	all	all	DET
ejpam-5470	58	29	k	k	PROPN
ejpam-5470	58	30	≥	≥	NUM
ejpam-5470	58	31	1	1	NUM
ejpam-5470	58	32	,	,	PUNCT
ejpam-5470	58	33	n	n	CCONJ
ejpam-5470	58	34	,	,	PUNCT
ejpam-5470	58	35	m	m	VERB
ejpam-5470	58	36	≥	≥	NOUN
ejpam-5470	58	37	3.throughout	3.throughout	NUM
ejpam-5470	58	38	our	our	PRON
ejpam-5470	58	39	proofs	proof	NOUN
ejpam-5470	58	40	,	,	PUNCT
ejpam-5470	58	41	the	the	DET
ejpam-5470	58	42	way	way	NOUN
ejpam-5470	58	43	of	of	ADP
ejpam-5470	58	44	labelling	label	VERB
ejpam-5470	58	45	l4	l4	PROPN
ejpam-5470	58	46	n	n	CCONJ
ejpam-5470	58	47	,	,	PUNCT
ejpam-5470	58	48	m	m	PROPN
ejpam-5470	58	49	starts	start	VERB
ejpam-5470	58	50	always	always	ADV
ejpam-5470	58	51	from	from	ADP
ejpam-5470	58	52	a	a	DET
ejpam-5470	58	53	vertex	vertex	NOUN
ejpam-5470	58	54	that	that	PRON
ejpam-5470	58	55	next	next	ADP
ejpam-5470	58	56	the	the	DET
ejpam-5470	58	57	common	common	ADJ
ejpam-5470	58	58	vertex	vertex	NOUN
ejpam-5470	58	59	and	and	CCONJ
ejpam-5470	58	60	go	go	VERB
ejpam-5470	58	61	further	far	ADV
ejpam-5470	58	62	opposite	opposite	ADV
ejpam-5470	58	63	to	to	ADP
ejpam-5470	58	64	this	this	DET
ejpam-5470	58	65	common	common	ADJ
ejpam-5470	58	66	vertex	vertex	NOUN
ejpam-5470	58	67	.	.	PUNCT
ejpam-5470	59	1	before	before	ADP
ejpam-5470	59	2	considering	consider	VERB
ejpam-5470	59	3	the	the	DET
ejpam-5470	59	4	general	general	ADJ
ejpam-5470	59	5	form	form	NOUN
ejpam-5470	59	6	of	of	ADP
ejpam-5470	59	7	the	the	DET
ejpam-5470	59	8	final	final	ADJ
ejpam-5470	59	9	result	result	NOUN
ejpam-5470	59	10	,	,	PUNCT
ejpam-5470	59	11	let	let	VERB
ejpam-5470	59	12	us	we	PRON
ejpam-5470	59	13	first	first	ADV
ejpam-5470	59	14	prove	prove	VERB
ejpam-5470	59	15	it	it	PRON
ejpam-5470	59	16	in	in	ADP
ejpam-5470	59	17	the	the	DET
ejpam-5470	59	18	following	follow	VERB
ejpam-5470	59	19	specific	specific	ADJ
ejpam-5470	59	20	case	case	NOUN
ejpam-5470	59	21	.	.	PUNCT
ejpam-5470	60	1	theorem	theorem	VERB
ejpam-5470	60	2	3.1	3.1	NUM
ejpam-5470	60	3	.	.	PUNCT
ejpam-5470	61	1	the	the	DET
ejpam-5470	61	2	corona	corona	PROPN
ejpam-5470	61	3	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	61	4	n	n	CCONJ
ejpam-5470	61	5	,	,	PUNCT
ejpam-5470	61	6	m	m	VERB
ejpam-5470	61	7	between	between	ADP
ejpam-5470	61	8	paths	path	NOUN
ejpam-5470	61	9	pk	pk	NOUN
ejpam-5470	61	10	and	and	CCONJ
ejpam-5470	61	11	fourth	fourth	ADJ
ejpam-5470	61	12	power	power	NOUN
ejpam-5470	61	13	of	of	ADP
ejpam-5470	61	14	lemniscate	lemniscate	PROPN
ejpam-5470	61	15	graphs	graphs	PROPN
ejpam-5470	61	16	l4	l4	PROPN
ejpam-5470	61	17	n	n	CCONJ
ejpam-5470	61	18	,	,	PUNCT
ejpam-5470	61	19	m	m	VERB
ejpam-5470	61	20	is	be	AUX
ejpam-5470	61	21	cordial	cordial	ADJ
ejpam-5470	61	22	for	for	ADP
ejpam-5470	61	23	al	al	PROPN
ejpam-5470	61	24	k	k	PROPN
ejpam-5470	61	25	≥	≥	PROPN
ejpam-5470	61	26	1	1	NUM
ejpam-5470	61	27	,	,	PUNCT
ejpam-5470	61	28	n	n	CCONJ
ejpam-5470	61	29	,	,	PUNCT
ejpam-5470	61	30	m	m	VERB
ejpam-5470	61	31	≥	≥	NOUN
ejpam-5470	61	32	3	3	NUM
ejpam-5470	61	33	.	.	PUNCT
ejpam-5470	62	1	in	in	ADP
ejpam-5470	62	2	order	order	NOUN
ejpam-5470	62	3	to	to	PART
ejpam-5470	62	4	prove	prove	VERB
ejpam-5470	62	5	this	this	DET
ejpam-5470	62	6	theorem	theorem	NOUN
ejpam-5470	62	7	,	,	PUNCT
ejpam-5470	62	8	we	we	PRON
ejpam-5470	62	9	will	will	AUX
ejpam-5470	62	10	introduce	introduce	VERB
ejpam-5470	62	11	a	a	DET
ejpam-5470	62	12	number	number	NOUN
ejpam-5470	62	13	of	of	ADP
ejpam-5470	62	14	lemmas	lemma	NOUN
ejpam-5470	62	15	as	as	SCONJ
ejpam-5470	62	16	follows	follow	VERB
ejpam-5470	62	17	.	.	PUNCT
ejpam-5470	63	1	lemma	lemma	PROPN
ejpam-5470	63	2	1	1	NUM
ejpam-5470	63	3	.	.	PUNCT
ejpam-5470	63	4	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	63	5	3,m	3,m	PROPN
ejpam-5470	63	6	is	be	AUX
ejpam-5470	63	7	cordial	cordial	ADJ
ejpam-5470	63	8	for	for	ADP
ejpam-5470	63	9	all	all	DET
ejpam-5470	63	10	k	k	PROPN
ejpam-5470	63	11	≥	≥	NUM
ejpam-5470	63	12	1	1	NUM
ejpam-5470	63	13	and	and	CCONJ
ejpam-5470	63	14	m	m	PROPN
ejpam-5470	63	15	≥	≥	NOUN
ejpam-5470	63	16	3	3	NUM
ejpam-5470	63	17	.	.	PUNCT
ejpam-5470	64	1	proof	proof	NOUN
ejpam-5470	64	2	.	.	PUNCT
ejpam-5470	65	1	we	we	PRON
ejpam-5470	65	2	need	need	VERB
ejpam-5470	65	3	to	to	PART
ejpam-5470	65	4	examine	examine	VERB
ejpam-5470	65	5	the	the	DET
ejpam-5470	65	6	following	follow	VERB
ejpam-5470	65	7	cases	case	NOUN
ejpam-5470	65	8	:	:	PUNCT
ejpam-5470	65	9	case	case	NOUN
ejpam-5470	65	10	1	1	NUM
ejpam-5470	65	11	.	.	PUNCT
ejpam-5470	66	1	at	at	ADP
ejpam-5470	66	2	m=3	m=3	PROPN
ejpam-5470	66	3	,	,	PUNCT
ejpam-5470	66	4	we	we	PRON
ejpam-5470	66	5	consider	consider	VERB
ejpam-5470	66	6	the	the	DET
ejpam-5470	66	7	following	follow	VERB
ejpam-5470	66	8	subcases	subcase	NOUN
ejpam-5470	66	9	.	.	PUNCT
ejpam-5470	67	1	subcase	subcase	PROPN
ejpam-5470	67	2	1.1	1.1	NUM
ejpam-5470	67	3	.	.	PUNCT
ejpam-5470	68	1	k	k	PROPN
ejpam-5470	68	2	is	be	AUX
ejpam-5470	68	3	even	even	ADV
ejpam-5470	68	4	.	.	PUNCT
ejpam-5470	69	1	let	let	VERB
ejpam-5470	69	2	k=	k=	PRON
ejpam-5470	69	3	2r	2r	NUM
ejpam-5470	69	4	,	,	PUNCT
ejpam-5470	70	1	r	r	NOUN
ejpam-5470	70	2	≥	≥	NOUN
ejpam-5470	70	3	1	1	NUM
ejpam-5470	70	4	.	.	PUNCT
ejpam-5470	71	1	then	then	ADV
ejpam-5470	71	2	,	,	PUNCT
ejpam-5470	71	3	one	one	PRON
ejpam-5470	71	4	can	can	AUX
ejpam-5470	71	5	choose	choose	VERB
ejpam-5470	71	6	the	the	DET
ejpam-5470	71	7	labelling[m2r;00100	labelling[m2r;00100	PROPN
ejpam-5470	71	8	,	,	PUNCT
ejpam-5470	71	9	11011	11011	NUM
ejpam-5470	71	10	,	,	PUNCT
ejpam-5470	71	11	...	...	PUNCT
ejpam-5470	71	12	,	,	PUNCT
ejpam-5470	71	13	(	(	PUNCT
ejpam-5470	71	14	r−times	r−time	NOUN
ejpam-5470	71	15	)	)	PUNCT
ejpam-5470	71	16	]	]	PUNCT
ejpam-5470	71	17	for	for	ADP
ejpam-5470	71	18	p2r⊙l4	p2r⊙l4	NOUN
ejpam-5470	71	19	3,3	3,3	NUM
ejpam-5470	71	20	.	.	PUNCT
ejpam-5470	72	1	therefore	therefore	ADV
ejpam-5470	72	2	x0	x0	PROPN
ejpam-5470	72	3	=	=	PROPN
ejpam-5470	72	4	x1	x1	PROPN
ejpam-5470	72	5	=	=	SYM
ejpam-5470	72	6	r	r	NOUN
ejpam-5470	72	7	,	,	PUNCT
ejpam-5470	72	8	a0=	a0=	PROPN
ejpam-5470	72	9	0,a1=	0,a1=	NOUN
ejpam-5470	72	10	2r	2r	NUM
ejpam-5470	72	11	−	−	NUM
ejpam-5470	72	12	1,y0=	1,y0=	PROPN
ejpam-5470	72	13	4	4	NUM
ejpam-5470	72	14	,	,	PUNCT
ejpam-5470	72	15	y1=	y1=	PROPN
ejpam-5470	72	16	1,b0=	1,b0=	NUM
ejpam-5470	72	17	2,b1=	2,b1=	NUM
ejpam-5470	72	18	4,y′0=	4,y′0=	NUM
ejpam-5470	72	19	1,y′1=	1,y′1=	NUM
ejpam-5470	72	20	4,b′0=	4,b′0=	NUM
ejpam-5470	72	21	2	2	NUM
ejpam-5470	72	22	and	and	CCONJ
ejpam-5470	72	23	b′1=	b′1=	ADP
ejpam-5470	72	24	4	4	NUM
ejpam-5470	72	25	.	.	PUNCT
ejpam-5470	73	1	hence	hence	ADV
ejpam-5470	73	2	,	,	PUNCT
ejpam-5470	73	3	it	it	PRON
ejpam-5470	73	4	is	be	AUX
ejpam-5470	73	5	easy	easy	ADJ
ejpam-5470	73	6	to	to	PART
ejpam-5470	73	7	show	show	VERB
ejpam-5470	73	8	that	that	SCONJ
ejpam-5470	73	9	|v0	|v0	NOUN
ejpam-5470	73	10	−	−	NOUN
ejpam-5470	73	11	v1|	v1|	NOUN
ejpam-5470	73	12	=	=	SYM
ejpam-5470	73	13	0	0	NUM
ejpam-5470	73	14	and	and	CCONJ
ejpam-5470	73	15	|e0	|e0	NOUN
ejpam-5470	73	16	−	−	PROPN
ejpam-5470	73	17	e1|	e1|	NOUN
ejpam-5470	73	18	=	=	NOUN
ejpam-5470	73	19	1	1	NUM
ejpam-5470	73	20	.	.	PUNCT
ejpam-5470	74	1	thus	thus	ADV
ejpam-5470	74	2	p2r⊙l4	p2r⊙l4	NOUN
ejpam-5470	74	3	3,3	3,3	NUM
ejpam-5470	74	4	,	,	PUNCT
ejpam-5470	74	5	r	r	NOUN
ejpam-5470	74	6	≥	≥	NOUN
ejpam-5470	74	7	1	1	NUM
ejpam-5470	74	8	is	be	AUX
ejpam-5470	74	9	cordial	cordial	ADJ
ejpam-5470	74	10	.	.	PUNCT
ejpam-5470	75	1	subcase	subcase	PROPN
ejpam-5470	75	2	1.2	1.2	NUM
ejpam-5470	75	3	.	.	PUNCT
ejpam-5470	76	1	k	k	PROPN
ejpam-5470	76	2	is	be	AUX
ejpam-5470	76	3	odd	odd	ADJ
ejpam-5470	76	4	.	.	PUNCT
ejpam-5470	77	1	let	let	VERB
ejpam-5470	77	2	k=	k=	X
ejpam-5470	78	1	2r+1	2r+1	PROPN
ejpam-5470	78	2	where	where	SCONJ
ejpam-5470	78	3	r	r	NOUN
ejpam-5470	78	4	≥	≥	NOUN
ejpam-5470	78	5	0	0	NUM
ejpam-5470	78	6	.	.	PUNCT
ejpam-5470	79	1	then	then	ADV
ejpam-5470	79	2	take	take	VERB
ejpam-5470	79	3	the	the	DET
ejpam-5470	79	4	labeling	labeling	NOUN
ejpam-5470	80	1	[	[	X
ejpam-5470	80	2	m2r+1;00100	m2r+1;00100	NOUN
ejpam-5470	80	3	,	,	PUNCT
ejpam-5470	80	4	11011	11011	NUM
ejpam-5470	80	5	,	,	PUNCT
ejpam-5470	80	6	00100	00100	NUM
ejpam-5470	80	7	,	,	PUNCT
ejpam-5470	80	8	11011	11011	NUM
ejpam-5470	80	9	,	,	PUNCT
ejpam-5470	80	10	...	...	PUNCT
ejpam-5470	80	11	,	,	PUNCT
ejpam-5470	80	12	(	(	PUNCT
ejpam-5470	80	13	r−	r−	PROPN
ejpam-5470	80	14	times	time	NOUN
ejpam-5470	80	15	)	)	PUNCT
ejpam-5470	80	16	,	,	PUNCT
ejpam-5470	80	17	11100	11100	NUM
ejpam-5470	80	18	]	]	PUNCT
ejpam-5470	80	19	for	for	ADP
ejpam-5470	80	20	p2r+1⊙l4	p2r+1⊙l4	NOUN
ejpam-5470	80	21	3,3	3,3	NUM
ejpam-5470	80	22	.	.	PUNCT
ejpam-5470	81	1	therefore	therefore	ADV
ejpam-5470	81	2	x0	x0	PROPN
ejpam-5470	81	3	=	=	ADJ
ejpam-5470	81	4	r+1,x1	r+1,x1	ADV
ejpam-5470	81	5	=	=	ADJ
ejpam-5470	81	6	r	r	NOUN
ejpam-5470	81	7	,	,	PUNCT
ejpam-5470	81	8	a0=	a0=	PROPN
ejpam-5470	81	9	0,a1=	0,a1=	NUM
ejpam-5470	81	10	2r	2r	NUM
ejpam-5470	81	11	,	,	PUNCT
ejpam-5470	81	12	y0=	y0=	PROPN
ejpam-5470	81	13	4,y1=	4,y1=	NUM
ejpam-5470	81	14	1,b0=	1,b0=	NUM
ejpam-5470	81	15	2,b1=	2,b1=	NUM
ejpam-5470	81	16	4	4	NUM
ejpam-5470	81	17	,	,	PUNCT
ejpam-5470	81	18	y′0=	y′0=	ADJ
ejpam-5470	81	19	1,y′1=	1,y′1=	NUM
ejpam-5470	81	20	4,b′0=	4,b′0=	NUM
ejpam-5470	81	21	2,b′1=	2,b′1=	NUM
ejpam-5470	81	22	4,y∗0=	4,y∗0=	ADJ
ejpam-5470	81	23	2,y∗1=	2,y∗1=	NOUN
ejpam-5470	81	24	3,b∗0=	3,b∗0=	ADJ
ejpam-5470	81	25	4	4	NUM
ejpam-5470	81	26	and	and	CCONJ
ejpam-5470	81	27	b∗1=	b∗1=	PROPN
ejpam-5470	81	28	2	2	NUM
ejpam-5470	81	29	,	,	PUNCT
ejpam-5470	81	30	where	where	SCONJ
ejpam-5470	81	31	y∗i	y∗i	NUM
ejpam-5470	81	32	and	and	CCONJ
ejpam-5470	81	33	b∗i	b∗i	NUM
ejpam-5470	81	34	are	be	AUX
ejpam-5470	81	35	the	the	DET
ejpam-5470	81	36	numbers	number	NOUN
ejpam-5470	81	37	of	of	ADP
ejpam-5470	81	38	vertices	vertex	NOUN
ejpam-5470	81	39	and	and	CCONJ
ejpam-5470	81	40	edges	edge	NOUN
ejpam-5470	81	41	labelled	label	VERB
ejpam-5470	81	42	i	i	PRON
ejpam-5470	81	43	in	in	ADP
ejpam-5470	81	44	l4	l4	PROPN
ejpam-5470	81	45	3,3	3,3	NUM
ejpam-5470	81	46	that	that	PRON
ejpam-5470	81	47	are	be	AUX
ejpam-5470	81	48	connected	connect	VERB
ejpam-5470	81	49	to	to	ADP
ejpam-5470	81	50	the	the	DET
ejpam-5470	81	51	last	last	ADJ
ejpam-5470	81	52	zero	zero	NUM
ejpam-5470	81	53	in	in	ADP
ejpam-5470	81	54	p4r+3	p4r+3	PROPN
ejpam-5470	81	55	.	.	PUNCT
ejpam-5470	82	1	consequently	consequently	ADV
ejpam-5470	82	2	,	,	PUNCT
ejpam-5470	82	3	it	it	PRON
ejpam-5470	82	4	is	be	AUX
ejpam-5470	82	5	easy	easy	ADJ
ejpam-5470	82	6	to	to	PART
ejpam-5470	82	7	show	show	VERB
ejpam-5470	82	8	that	that	SCONJ
ejpam-5470	82	9	|v0	|v0	NOUN
ejpam-5470	82	10	−	−	NOUN
ejpam-5470	82	11	v1|	v1|	NOUN
ejpam-5470	82	12	=	=	SYM
ejpam-5470	82	13	0	0	NUM
ejpam-5470	82	14	and	and	CCONJ
ejpam-5470	82	15	|e0	|e0	NOUN
ejpam-5470	82	16	−	−	PROPN
ejpam-5470	82	17	e1|	e1|	NOUN
ejpam-5470	82	18	=	=	NOUN
ejpam-5470	82	19	1	1	NUM
ejpam-5470	82	20	.	.	PUNCT
ejpam-5470	82	21	thus	thus	ADV
ejpam-5470	82	22	p2r+1⊙l4	p2r+1⊙l4	NOUN
ejpam-5470	82	23	3,3	3,3	NUM
ejpam-5470	82	24	,	,	PUNCT
ejpam-5470	82	25	r	r	NOUN
ejpam-5470	82	26	≥	≥	NOUN
ejpam-5470	82	27	0	0	NUM
ejpam-5470	82	28	,	,	PUNCT
ejpam-5470	82	29	is	be	AUX
ejpam-5470	82	30	cordial	cordial	ADJ
ejpam-5470	82	31	and	and	CCONJ
ejpam-5470	82	32	the	the	DET
ejpam-5470	82	33	lemma	lemma	PROPN
ejpam-5470	82	34	follows	follow	VERB
ejpam-5470	82	35	.	.	PUNCT
ejpam-5470	83	1	case	case	NOUN
ejpam-5470	83	2	2	2	NUM
ejpam-5470	83	3	.	.	PUNCT
ejpam-5470	84	1	at	at	ADP
ejpam-5470	84	2	m	m	PROPN
ejpam-5470	84	3	≡	≡	PROPN
ejpam-5470	84	4	0(mod4	0(mod4	NUM
ejpam-5470	84	5	)	)	PUNCT
ejpam-5470	84	6	,	,	PUNCT
ejpam-5470	84	7	we	we	PRON
ejpam-5470	84	8	consider	consider	VERB
ejpam-5470	84	9	the	the	DET
ejpam-5470	84	10	following	follow	VERB
ejpam-5470	84	11	subcases	subcase	NOUN
ejpam-5470	84	12	.	.	PUNCT
ejpam-5470	85	1	subcase	subcase	PROPN
ejpam-5470	85	2	2.1	2.1	NUM
ejpam-5470	85	3	.	.	PUNCT
ejpam-5470	86	1	k	k	PROPN
ejpam-5470	86	2	≡	≡	PROPN
ejpam-5470	86	3	0(mod4	0(mod4	NUM
ejpam-5470	86	4	)	)	PUNCT
ejpam-5470	86	5	let	let	VERB
ejpam-5470	86	6	k=	k=	ADJ
ejpam-5470	86	7	4r	4r	NOUN
ejpam-5470	86	8	,	,	PUNCT
ejpam-5470	86	9	r	r	NOUN
ejpam-5470	86	10	≥	≥	NOUN
ejpam-5470	86	11	1	1	NUM
ejpam-5470	86	12	and	and	CCONJ
ejpam-5470	86	13	m=	m=	X
ejpam-5470	86	14	4	4	NUM
ejpam-5470	86	15	t	t	PROPN
ejpam-5470	86	16	,	,	PUNCT
ejpam-5470	86	17	t	t	PROPN
ejpam-5470	86	18	>	>	X
ejpam-5470	86	19	1	1	NUM
ejpam-5470	86	20	.	.	PUNCT
ejpam-5470	87	1	then	then	ADV
ejpam-5470	87	2	,	,	PUNCT
ejpam-5470	87	3	the	the	DET
ejpam-5470	87	4	labelling	labelling	NOUN
ejpam-5470	87	5	[	[	X
ejpam-5470	87	6	l4r;03	l4r;03	ADP
ejpam-5470	87	7	13m4t−4	13m4t−4	NUM
ejpam-5470	87	8	,	,	PUNCT
ejpam-5470	87	9	03	03	NUM
ejpam-5470	87	10	13m4t−4	13m4t−4	NUM
ejpam-5470	87	11	,	,	PUNCT
ejpam-5470	87	12	01l4	01l4	NUM
ejpam-5470	87	13	m	m	NOUN
ejpam-5470	87	14	′	′	ADJ
ejpam-5470	87	15	4t−4	4t−4	NOUN
ejpam-5470	87	16	,	,	PUNCT
ejpam-5470	87	17	01l4	01l4	NUM
ejpam-5470	87	18	m	m	VERB
ejpam-5470	87	19	′	′	ADJ
ejpam-5470	87	20	4t−4	4t−4	PROPN
ejpam-5470	87	21	,	,	PUNCT
ejpam-5470	87	22	...	...	PUNCT
ejpam-5470	87	23	,	,	PUNCT
ejpam-5470	87	24	(	(	PUNCT
ejpam-5470	87	25	r−times	r−time	NOUN
ejpam-5470	87	26	)	)	PUNCT
ejpam-5470	87	27	]	]	PUNCT
ejpam-5470	87	28	for	for	ADP
ejpam-5470	87	29	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	87	30	3,4	3,4	NUM
ejpam-5470	87	31	t	t	NOUN
ejpam-5470	87	32	can	can	AUX
ejpam-5470	87	33	be	be	AUX
ejpam-5470	87	34	applied	apply	VERB
ejpam-5470	87	35	.	.	PUNCT
ejpam-5470	88	1	therefore	therefore	ADV
ejpam-5470	88	2	x0	x0	PROPN
ejpam-5470	88	3	=	=	PROPN
ejpam-5470	88	4	x1=	x1=	PROPN
ejpam-5470	88	5	2r	2r	NUM
ejpam-5470	88	6	,	,	PUNCT
ejpam-5470	88	7	a0=	a0=	NOUN
ejpam-5470	88	8	2r	2r	NUM
ejpam-5470	88	9	,	,	PUNCT
ejpam-5470	88	10	a1=	a1=	PROPN
ejpam-5470	88	11	2r	2r	NUM
ejpam-5470	89	1	−	−	ADP
ejpam-5470	89	2	1,y0	1,y0	NUM
ejpam-5470	89	3	=	=	SYM
ejpam-5470	89	4	y1=	y1=	PROPN
ejpam-5470	89	5	2t+	2t+	NUM
ejpam-5470	89	6	1,b0=	1,b0=	PROPN
ejpam-5470	89	7	8t−	8t−	PROPN
ejpam-5470	89	8	3,b1=	3,b1=	NUM
ejpam-5470	89	9	8t−	8t−	PROPN
ejpam-5470	89	10	3,y′0	3,y′0	NUM
ejpam-5470	89	11	=	=	NOUN
ejpam-5470	89	12	y′1=	y′1=	NOUN
ejpam-5470	89	13	2t+	2t+	NUM
ejpam-5470	89	14	1,b′0=	1,b′0=	NUM
ejpam-5470	89	15	8t−	8t−	NUM
ejpam-5470	89	16	3	3	NUM
ejpam-5470	89	17	and	and	CCONJ
ejpam-5470	89	18	b′1=	b′1=	ADP
ejpam-5470	89	19	8	8	NUM
ejpam-5470	89	20	t	t	NOUN
ejpam-5470	89	21	−	−	NOUN
ejpam-5470	89	22	3	3	NUM
ejpam-5470	89	23	.	.	PUNCT
ejpam-5470	90	1	so	so	ADV
ejpam-5470	90	2	,	,	PUNCT
ejpam-5470	90	3	|v0	|v0	NOUN
ejpam-5470	90	4	−	−	NOUN
ejpam-5470	90	5	v1|	v1|	NOUN
ejpam-5470	90	6	=	=	SYM
ejpam-5470	90	7	0	0	NUM
ejpam-5470	90	8	and	and	CCONJ
ejpam-5470	90	9	|e0	|e0	NOUN
ejpam-5470	91	1	−	−	PROPN
ejpam-5470	91	2	e1|	e1|	NOUN
ejpam-5470	91	3	=	=	NOUN
ejpam-5470	91	4	1	1	X
ejpam-5470	91	5	.	.	X
ejpam-5470	92	1	for	for	ADP
ejpam-5470	92	2	the	the	DET
ejpam-5470	92	3	case	case	NOUN
ejpam-5470	92	4	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	92	5	3,4	3,4	NUM
ejpam-5470	92	6	,	,	PUNCT
ejpam-5470	92	7	the	the	DET
ejpam-5470	92	8	labeling	labeling	NOUN
ejpam-5470	92	9	[	[	X
ejpam-5470	92	10	l4r;03	l4r;03	ADP
ejpam-5470	92	11	13	13	NUM
ejpam-5470	92	12	,	,	PUNCT
ejpam-5470	92	13	03	03	NUM
ejpam-5470	92	14	13	13	NUM
ejpam-5470	92	15	,	,	PUNCT
ejpam-5470	92	16	01l4	01l4	NUM
ejpam-5470	92	17	,	,	PUNCT
ejpam-5470	92	18	01l4	01l4	NUM
ejpam-5470	92	19	,	,	PUNCT
ejpam-5470	92	20	...	...	PUNCT
ejpam-5470	92	21	,	,	PUNCT
ejpam-5470	92	22	(	(	PUNCT
ejpam-5470	92	23	r	r	NOUN
ejpam-5470	92	24	−	−	PROPN
ejpam-5470	92	25	times	time	NOUN
ejpam-5470	92	26	)	)	PUNCT
ejpam-5470	92	27	]	]	PUNCT
ejpam-5470	92	28	is	be	AUX
ejpam-5470	92	29	sufficient	sufficient	ADJ
ejpam-5470	92	30	and	and	CCONJ
ejpam-5470	92	31	thus	thus	ADV
ejpam-5470	92	32	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	92	33	3,4	3,4	NUM
ejpam-5470	92	34	t	t	NOUN
ejpam-5470	92	35	is	be	AUX
ejpam-5470	92	36	cordial	cordial	ADJ
ejpam-5470	92	37	.	.	PUNCT
ejpam-5470	93	1	subcase	subcase	PROPN
ejpam-5470	93	2	2.2.k	2.2.k	NUM
ejpam-5470	93	3	≡	≡	PROPN
ejpam-5470	93	4	1(mod4	1(mod4	NUM
ejpam-5470	93	5	)	)	PUNCT
ejpam-5470	93	6	let	let	VERB
ejpam-5470	93	7	k=	k=	X
ejpam-5470	93	8	4r+1,r	4r+1,r	NOUN
ejpam-5470	93	9	≥	≥	X
ejpam-5470	93	10	0	0	NUM
ejpam-5470	94	1	andm=	andm=	PROPN
ejpam-5470	94	2	4	4	NUM
ejpam-5470	94	3	t	t	PROPN
ejpam-5470	94	4	,	,	PUNCT
ejpam-5470	94	5	t	t	PROPN
ejpam-5470	94	6	>	>	X
ejpam-5470	94	7	1	1	NUM
ejpam-5470	94	8	.	.	PUNCT
ejpam-5470	95	1	then	then	ADV
ejpam-5470	95	2	,	,	PUNCT
ejpam-5470	95	3	the	the	DET
ejpam-5470	95	4	labelling	labelling	NOUN
ejpam-5470	95	5	[	[	X
ejpam-5470	95	6	l4r0;03	l4r0;03	ADJ
ejpam-5470	95	7	13m4t−4	13m4t−4	NUM
ejpam-5470	95	8	,	,	PUNCT
ejpam-5470	95	9	03	03	NUM
ejpam-5470	95	10	13m4t−4	13m4t−4	NUM
ejpam-5470	95	11	,	,	PUNCT
ejpam-5470	95	12	01l4	01l4	NUM
ejpam-5470	95	13	m	m	NOUN
ejpam-5470	95	14	′	′	ADJ
ejpam-5470	95	15	4t−4	4t−4	NOUN
ejpam-5470	95	16	,	,	PUNCT
ejpam-5470	95	17	01l4	01l4	NUM
ejpam-5470	95	18	m	m	VERB
ejpam-5470	95	19	′	′	ADJ
ejpam-5470	95	20	4t−4	4t−4	PROPN
ejpam-5470	95	21	,	,	PUNCT
ejpam-5470	95	22	...	...	PUNCT
ejpam-5470	95	23	,	,	PUNCT
ejpam-5470	95	24	(	(	PUNCT
ejpam-5470	95	25	r	r	NOUN
ejpam-5470	95	26	−	−	PROPN
ejpam-5470	95	27	times),03l3m4t−4	times),03l3m4t−4	PROPN
ejpam-5470	95	28	]	]	PUNCT
ejpam-5470	95	29	for	for	ADP
ejpam-5470	95	30	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	95	31	3,4	3,4	NUM
ejpam-5470	95	32	t	t	NOUN
ejpam-5470	95	33	is	be	AUX
ejpam-5470	95	34	considered	consider	VERB
ejpam-5470	95	35	.	.	PUNCT
ejpam-5470	96	1	therefore	therefore	ADV
ejpam-5470	96	2	x0=	x0=	PROPN
ejpam-5470	97	1	2r+1,x1=	2r+1,x1=	NUM
ejpam-5470	97	2	2r	2r	NUM
ejpam-5470	97	3	,	,	PUNCT
ejpam-5470	97	4	a0	a0	PROPN
ejpam-5470	97	5	=	=	PROPN
ejpam-5470	97	6	a1=	a1=	PROPN
ejpam-5470	97	7	2r	2r	NUM
ejpam-5470	97	8	,	,	PUNCT
ejpam-5470	97	9	y0	y0	PROPN
ejpam-5470	97	10	=	=	SYM
ejpam-5470	97	11	y1=	y1=	PROPN
ejpam-5470	97	12	2t+1,b0=	2t+1,b0=	NUM
ejpam-5470	97	13	8t−3,b1=	8t−3,b1=	NUM
ejpam-5470	97	14	8t−3,y′0	8t−3,y′0	NOUN
ejpam-5470	97	15	=	=	NOUN
ejpam-5470	97	16	y′1=	y′1=	ADP
ejpam-5470	97	17	2t+1,b′0=	2t+1,b′0=	NUM
ejpam-5470	97	18	8t−	8t−	NUM
ejpam-5470	97	19	3	3	NUM
ejpam-5470	97	20	and	and	CCONJ
ejpam-5470	97	21	b′1=	b′1=	ADP
ejpam-5470	97	22	8t−3	8t−3	NUM
ejpam-5470	97	23	.	.	PUNCT
ejpam-5470	98	1	hence	hence	ADV
ejpam-5470	98	2	,	,	PUNCT
ejpam-5470	98	3	|v0−v1|	|v0−v1|	NOUN
ejpam-5470	98	4	=	=	SYM
ejpam-5470	98	5	1	1	NUM
ejpam-5470	98	6	and	and	CCONJ
ejpam-5470	98	7	|e0−e1|	|e0−e1|	NOUN
ejpam-5470	98	8	=	=	NOUN
ejpam-5470	98	9	0	0	PROPN
ejpam-5470	98	10	.	.	PUNCT
ejpam-5470	99	1	for	for	ADP
ejpam-5470	99	2	the	the	DET
ejpam-5470	99	3	case	case	NOUN
ejpam-5470	99	4	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	99	5	3,4	3,4	NUM
ejpam-5470	99	6	,	,	PUNCT
ejpam-5470	99	7	the	the	DET
ejpam-5470	99	8	labeling	labeling	NOUN
ejpam-5470	99	9	[	[	X
ejpam-5470	99	10	l4r0;03	l4r0;03	ADJ
ejpam-5470	99	11	13	13	NUM
ejpam-5470	99	12	,	,	PUNCT
ejpam-5470	99	13	03	03	NUM
ejpam-5470	99	14	13	13	NUM
ejpam-5470	99	15	,	,	PUNCT
ejpam-5470	99	16	01l4	01l4	NUM
ejpam-5470	99	17	,	,	PUNCT
ejpam-5470	99	18	01l4	01l4	NUM
ejpam-5470	99	19	,	,	PUNCT
ejpam-5470	99	20	...	...	PUNCT
ejpam-5470	99	21	,	,	PUNCT
ejpam-5470	99	22	(	(	PUNCT
ejpam-5470	99	23	r	r	NOUN
ejpam-5470	99	24	−	−	PROPN
ejpam-5470	99	25	times	time	NOUN
ejpam-5470	99	26	)	)	PUNCT
ejpam-5470	99	27	,	,	PUNCT
ejpam-5470	99	28	1303	1303	NUM
ejpam-5470	99	29	]	]	PUNCT
ejpam-5470	99	30	is	be	AUX
ejpam-5470	99	31	sufficient	sufficient	ADJ
ejpam-5470	99	32	and	and	CCONJ
ejpam-5470	99	33	thus	thus	ADV
ejpam-5470	99	34	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	99	35	3,4	3,4	NUM
ejpam-5470	99	36	t	t	NOUN
ejpam-5470	99	37	is	be	AUX
ejpam-5470	99	38	cordial	cordial	ADJ
ejpam-5470	99	39	.	.	PUNCT
ejpam-5470	100	1	subcase	subcase	PROPN
ejpam-5470	100	2	2.3.k	2.3.k	NUM
ejpam-5470	100	3	≡	≡	PROPN
ejpam-5470	100	4	2(mod4	2(mod4	NUM
ejpam-5470	100	5	)	)	PUNCT
ejpam-5470	100	6	a.	a.	NOUN
ejpam-5470	100	7	abd	abd	PROPN
ejpam-5470	100	8	el	el	PROPN
ejpam-5470	100	9	-	-	PROPN
ejpam-5470	100	10	hay	hay	PROPN
ejpam-5470	100	11	et	et	PROPN
ejpam-5470	100	12	al	al	PROPN
ejpam-5470	100	13	.	.	PUNCT
ejpam-5470	100	14	/	/	SYM
ejpam-5470	100	15	eur	eur	PROPN
ejpam-5470	100	16	.	.	PUNCT
ejpam-5470	101	1	j.	j.	PROPN
ejpam-5470	101	2	pure	pure	PROPN
ejpam-5470	101	3	appl	appl	PROPN
ejpam-5470	101	4	.	.	PROPN
ejpam-5470	101	5	math	math	PROPN
ejpam-5470	101	6	,	,	PUNCT
ejpam-5470	101	7	18	18	NUM
ejpam-5470	101	8	(	(	PUNCT
ejpam-5470	101	9	1	1	NUM
ejpam-5470	101	10	)	)	PUNCT
ejpam-5470	101	11	(	(	PUNCT
ejpam-5470	101	12	2025	2025	NUM
ejpam-5470	101	13	)	)	PUNCT
ejpam-5470	101	14	,	,	PUNCT
ejpam-5470	101	15	5470	5470	NUM
ejpam-5470	101	16	4	4	NUM
ejpam-5470	101	17	of	of	ADP
ejpam-5470	101	18	14	14	NUM
ejpam-5470	101	19	let	let	VERB
ejpam-5470	101	20	k=	k=	PROPN
ejpam-5470	101	21	4r+2,r	4r+2,r	NUM
ejpam-5470	101	22	≥	≥	NOUN
ejpam-5470	101	23	0	0	NUM
ejpam-5470	101	24	andm=	andm=	PROPN
ejpam-5470	101	25	4	4	NUM
ejpam-5470	101	26	t	t	PROPN
ejpam-5470	101	27	,	,	PUNCT
ejpam-5470	101	28	t	t	PROPN
ejpam-5470	101	29	>	>	X
ejpam-5470	101	30	1	1	NUM
ejpam-5470	101	31	.	.	PUNCT
ejpam-5470	102	1	then	then	ADV
ejpam-5470	102	2	,	,	PUNCT
ejpam-5470	102	3	the	the	DET
ejpam-5470	102	4	labelling	labelling	NOUN
ejpam-5470	102	5	[	[	X
ejpam-5470	102	6	l4r10;03	l4r10;03	PROPN
ejpam-5470	102	7	13m4t−4	13m4t−4	NUM
ejpam-5470	102	8	,	,	PUNCT
ejpam-5470	102	9	03	03	NUM
ejpam-5470	102	10	13m4t−4	13m4t−4	NUM
ejpam-5470	102	11	,	,	PUNCT
ejpam-5470	102	12	01l4	01l4	NUM
ejpam-5470	102	13	m	m	NOUN
ejpam-5470	102	14	′	′	ADJ
ejpam-5470	102	15	4t−4	4t−4	NOUN
ejpam-5470	102	16	,	,	PUNCT
ejpam-5470	102	17	01l4	01l4	NUM
ejpam-5470	102	18	m	m	VERB
ejpam-5470	102	19	′	′	ADJ
ejpam-5470	102	20	4t−4	4t−4	PROPN
ejpam-5470	102	21	,	,	PUNCT
ejpam-5470	102	22	...	...	PUNCT
ejpam-5470	102	23	,	,	PUNCT
ejpam-5470	102	24	(	(	PUNCT
ejpam-5470	102	25	r−times	r−time	NOUN
ejpam-5470	102	26	)	)	PUNCT
ejpam-5470	102	27	,	,	PUNCT
ejpam-5470	102	28	01l4	01l4	NUM
ejpam-5470	102	29	m	m	VERB
ejpam-5470	102	30	′	′	ADJ
ejpam-5470	102	31	4t−4	4t−4	NOUN
ejpam-5470	102	32	,	,	PUNCT
ejpam-5470	102	33	03	03	NUM
ejpam-5470	102	34	13m4t−4	13m4t−4	NUM
ejpam-5470	102	35	]	]	PUNCT
ejpam-5470	102	36	for	for	ADP
ejpam-5470	102	37	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	102	38	3,4	3,4	NUM
ejpam-5470	102	39	t	t	NOUN
ejpam-5470	102	40	is	be	AUX
ejpam-5470	102	41	applied	apply	VERB
ejpam-5470	102	42	.	.	PUNCT
ejpam-5470	103	1	therefore	therefore	ADV
ejpam-5470	103	2	x0	x0	PROPN
ejpam-5470	103	3	=	=	PROPN
ejpam-5470	103	4	x1=	x1=	PROPN
ejpam-5470	103	5	2r+1,a0=	2r+1,a0=	NUM
ejpam-5470	103	6	2r+1,a1=	2r+1,a1=	NUM
ejpam-5470	103	7	2r	2r	NUM
ejpam-5470	103	8	,	,	PUNCT
ejpam-5470	103	9	y0	y0	NOUN
ejpam-5470	103	10	=	=	SYM
ejpam-5470	103	11	y1=	y1=	PROPN
ejpam-5470	103	12	2t+1,b0=	2t+1,b0=	NUM
ejpam-5470	103	13	8t−3,b1=	8t−3,b1=	NUM
ejpam-5470	103	14	8t−3,y′0	8t−3,y′0	NOUN
ejpam-5470	103	15	=	=	NOUN
ejpam-5470	103	16	y′1=	y′1=	NOUN
ejpam-5470	103	17	2t+	2t+	NUM
ejpam-5470	103	18	1,b′0=	1,b′0=	NUM
ejpam-5470	103	19	8t−3	8t−3	NUM
ejpam-5470	103	20	and	and	CCONJ
ejpam-5470	103	21	b′1=	b′1=	ADP
ejpam-5470	103	22	8t−3	8t−3	NUM
ejpam-5470	103	23	.	.	PUNCT
ejpam-5470	104	1	so	so	ADV
ejpam-5470	104	2	,	,	PUNCT
ejpam-5470	104	3	|v0−v1|	|v0−v1|	NUM
ejpam-5470	104	4	=	=	SYM
ejpam-5470	104	5	0	0	NUM
ejpam-5470	104	6	and	and	CCONJ
ejpam-5470	104	7	|e0−e1|	|e0−e1|	NOUN
ejpam-5470	104	8	=	=	NOUN
ejpam-5470	104	9	1	1	X
ejpam-5470	104	10	.	.	X
ejpam-5470	105	1	for	for	ADP
ejpam-5470	105	2	the	the	DET
ejpam-5470	105	3	case	case	NOUN
ejpam-5470	105	4	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	105	5	3,4	3,4	NUM
ejpam-5470	105	6	,	,	PUNCT
ejpam-5470	105	7	the	the	DET
ejpam-5470	105	8	labeling	labeling	NOUN
ejpam-5470	105	9	[	[	X
ejpam-5470	105	10	l4r10;03	l4r10;03	PROPN
ejpam-5470	105	11	13	13	NUM
ejpam-5470	105	12	,	,	PUNCT
ejpam-5470	105	13	03	03	NUM
ejpam-5470	105	14	13	13	NUM
ejpam-5470	105	15	,	,	PUNCT
ejpam-5470	105	16	01l4	01l4	NUM
ejpam-5470	105	17	,	,	PUNCT
ejpam-5470	105	18	01l4	01l4	NUM
ejpam-5470	105	19	,	,	PUNCT
ejpam-5470	105	20	...	...	PUNCT
ejpam-5470	105	21	,	,	PUNCT
ejpam-5470	105	22	(	(	PUNCT
ejpam-5470	105	23	r	r	NOUN
ejpam-5470	105	24	−	−	PROPN
ejpam-5470	105	25	times	time	NOUN
ejpam-5470	105	26	)	)	PUNCT
ejpam-5470	105	27	,	,	PUNCT
ejpam-5470	105	28	01l4	01l4	NUM
ejpam-5470	105	29	,	,	PUNCT
ejpam-5470	105	30	03	03	NUM
ejpam-5470	105	31	13	13	NUM
ejpam-5470	105	32	]	]	PUNCT
ejpam-5470	105	33	is	be	AUX
ejpam-5470	105	34	sufficient	sufficient	ADJ
ejpam-5470	105	35	and	and	CCONJ
ejpam-5470	105	36	thus	thus	ADV
ejpam-5470	105	37	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	105	38	3,4	3,4	NUM
ejpam-5470	105	39	t	t	NOUN
ejpam-5470	105	40	is	be	AUX
ejpam-5470	105	41	cordial	cordial	ADJ
ejpam-5470	105	42	.	.	PUNCT
ejpam-5470	106	1	subcase	subcase	PROPN
ejpam-5470	106	2	2.4.k	2.4.k	NUM
ejpam-5470	106	3	≡	≡	PROPN
ejpam-5470	106	4	3(mod4	3(mod4	NUM
ejpam-5470	106	5	)	)	PUNCT
ejpam-5470	106	6	let	let	VERB
ejpam-5470	106	7	k=	k=	X
ejpam-5470	106	8	4r+3,r	4r+3,r	NUM
ejpam-5470	106	9	≥	≥	NOUN
ejpam-5470	106	10	0	0	NUM
ejpam-5470	106	11	andm=	andm=	PROPN
ejpam-5470	106	12	4	4	NUM
ejpam-5470	106	13	t	t	PROPN
ejpam-5470	106	14	,	,	PUNCT
ejpam-5470	106	15	t	t	PROPN
ejpam-5470	106	16	>	>	X
ejpam-5470	106	17	1	1	NUM
ejpam-5470	106	18	.	.	PUNCT
ejpam-5470	107	1	then	then	ADV
ejpam-5470	107	2	,	,	PUNCT
ejpam-5470	107	3	one	one	PRON
ejpam-5470	107	4	can	can	AUX
ejpam-5470	107	5	select	select	VERB
ejpam-5470	107	6	the	the	DET
ejpam-5470	107	7	labelling	labelling	NOUN
ejpam-5470	107	8	[	[	X
ejpam-5470	107	9	l4r001;0313m4t−4	l4r001;0313m4t−4	PROPN
ejpam-5470	107	10	,	,	PUNCT
ejpam-5470	107	11	03	03	NUM
ejpam-5470	107	12	13m4t−4	13m4t−4	NUM
ejpam-5470	107	13	,	,	PUNCT
ejpam-5470	107	14	01l4	01l4	NUM
ejpam-5470	107	15	m	m	NOUN
ejpam-5470	107	16	′	′	ADJ
ejpam-5470	107	17	4t−4	4t−4	NOUN
ejpam-5470	107	18	,	,	PUNCT
ejpam-5470	107	19	01l4	01l4	NUM
ejpam-5470	107	20	m	m	VERB
ejpam-5470	107	21	′	′	ADJ
ejpam-5470	107	22	4t−4	4t−4	PROPN
ejpam-5470	107	23	,	,	PUNCT
ejpam-5470	107	24	...	...	PUNCT
ejpam-5470	107	25	,	,	PUNCT
ejpam-5470	107	26	(	(	PUNCT
ejpam-5470	107	27	r	r	NOUN
ejpam-5470	107	28	−	−	PROPN
ejpam-5470	107	29	times	time	NOUN
ejpam-5470	107	30	)	)	PUNCT
ejpam-5470	107	31	,	,	PUNCT
ejpam-5470	107	32	03	03	NUM
ejpam-5470	107	33	13m4t−4	13m4t−4	NUM
ejpam-5470	107	34	,	,	PUNCT
ejpam-5470	107	35	03	03	NUM
ejpam-5470	107	36	13m4t−4	13m4t−4	NUM
ejpam-5470	107	37	,	,	PUNCT
ejpam-5470	107	38	01l4	01l4	NUM
ejpam-5470	107	39	m	m	NOUN
ejpam-5470	107	40	′	′	ADJ
ejpam-5470	107	41	4t−4	4t−4	NOUN
ejpam-5470	107	42	]	]	PUNCT
ejpam-5470	107	43	for	for	ADP
ejpam-5470	107	44	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	107	45	3,4	3,4	NUM
ejpam-5470	107	46	t.	t.	NOUN
ejpam-5470	107	47	therefore	therefore	ADV
ejpam-5470	107	48	x0=	x0=	PUNCT
ejpam-5470	108	1	2r	2r	NUM
ejpam-5470	109	1	+	+	CCONJ
ejpam-5470	109	2	2,x1=	2,x1=	NUM
ejpam-5470	109	3	2r	2r	NUM
ejpam-5470	109	4	+	+	CCONJ
ejpam-5470	109	5	1,a0	1,a0	NUM
ejpam-5470	109	6	=	=	NOUN
ejpam-5470	109	7	a1=	a1=	ADJ
ejpam-5470	109	8	2r+1,y0	2r+1,y0	NOUN
ejpam-5470	109	9	=	=	SYM
ejpam-5470	109	10	y1=	y1=	NOUN
ejpam-5470	110	1	2t+1,b0=	2t+1,b0=	NUM
ejpam-5470	110	2	8t−3,b1=	8t−3,b1=	NUM
ejpam-5470	110	3	8t−3,y′0	8t−3,y′0	NOUN
ejpam-5470	110	4	=	=	NOUN
ejpam-5470	110	5	y′1=	y′1=	PROPN
ejpam-5470	110	6	2t+1,b′0=	2t+1,b′0=	NUM
ejpam-5470	110	7	8t−3	8t−3	NUM
ejpam-5470	110	8	and	and	CCONJ
ejpam-5470	110	9	b′1=	b′1=	ADP
ejpam-5470	110	10	8t−3	8t−3	NUM
ejpam-5470	110	11	.	.	PUNCT
ejpam-5470	111	1	hence	hence	ADV
ejpam-5470	111	2	,	,	PUNCT
ejpam-5470	111	3	one	one	PRON
ejpam-5470	111	4	can	can	AUX
ejpam-5470	111	5	easily	easily	ADV
ejpam-5470	111	6	show	show	VERB
ejpam-5470	111	7	that	that	SCONJ
ejpam-5470	111	8	|v0−v1|	|v0−v1|	NOUN
ejpam-5470	111	9	=	=	SYM
ejpam-5470	111	10	1	1	NUM
ejpam-5470	111	11	and	and	CCONJ
ejpam-5470	111	12	|e0−e1|	|e0−e1|	NOUN
ejpam-5470	111	13	=	=	NOUN
ejpam-5470	111	14	0	0	PROPN
ejpam-5470	111	15	.	.	PUNCT
ejpam-5470	112	1	for	for	ADP
ejpam-5470	112	2	the	the	DET
ejpam-5470	112	3	case	case	NOUN
ejpam-5470	112	4	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	112	5	3,4	3,4	NUM
ejpam-5470	112	6	,	,	PUNCT
ejpam-5470	112	7	the	the	DET
ejpam-5470	112	8	labeling	labeling	NOUN
ejpam-5470	112	9	[	[	X
ejpam-5470	112	10	l4r001;03	l4r001;03	PROPN
ejpam-5470	112	11	13	13	NUM
ejpam-5470	112	12	,	,	PUNCT
ejpam-5470	112	13	03	03	NUM
ejpam-5470	112	14	13	13	NUM
ejpam-5470	112	15	,	,	PUNCT
ejpam-5470	112	16	01l4	01l4	NUM
ejpam-5470	112	17	,	,	PUNCT
ejpam-5470	112	18	01l4	01l4	NUM
ejpam-5470	112	19	...	...	PUNCT
ejpam-5470	112	20	,	,	PUNCT
ejpam-5470	112	21	(	(	PUNCT
ejpam-5470	112	22	r	r	NOUN
ejpam-5470	112	23	−	−	PROPN
ejpam-5470	112	24	times	time	NOUN
ejpam-5470	112	25	)	)	PUNCT
ejpam-5470	112	26	]	]	PUNCT
ejpam-5470	112	27	is	be	AUX
ejpam-5470	112	28	sufficient	sufficient	ADJ
ejpam-5470	112	29	and	and	CCONJ
ejpam-5470	112	30	thus	thus	ADV
ejpam-5470	112	31	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	112	32	3,4	3,4	NUM
ejpam-5470	112	33	t	t	NOUN
ejpam-5470	112	34	is	be	AUX
ejpam-5470	112	35	cordial	cordial	ADJ
ejpam-5470	112	36	.	.	PUNCT
ejpam-5470	113	1	case	case	NOUN
ejpam-5470	113	2	3	3	X
ejpam-5470	113	3	.	.	PUNCT
ejpam-5470	114	1	at	at	ADP
ejpam-5470	114	2	m	m	PROPN
ejpam-5470	114	3	≡	≡	PROPN
ejpam-5470	114	4	1(mod4	1(mod4	NUM
ejpam-5470	114	5	)	)	PUNCT
ejpam-5470	114	6	,	,	PUNCT
ejpam-5470	114	7	we	we	PRON
ejpam-5470	114	8	consider	consider	VERB
ejpam-5470	114	9	the	the	DET
ejpam-5470	114	10	following	follow	VERB
ejpam-5470	114	11	subcases	subcase	NOUN
ejpam-5470	114	12	.	.	PUNCT
ejpam-5470	115	1	subcase	subcase	PROPN
ejpam-5470	115	2	3.1	3.1	NUM
ejpam-5470	115	3	.	.	PUNCT
ejpam-5470	116	1	k	k	PROPN
ejpam-5470	116	2	even	even	ADV
ejpam-5470	116	3	let	let	VERB
ejpam-5470	116	4	k=	k=	PRON
ejpam-5470	116	5	2r	2r	NUM
ejpam-5470	116	6	,	,	PUNCT
ejpam-5470	116	7	r	r	NOUN
ejpam-5470	116	8	≥	≥	NUM
ejpam-5470	116	9	1	1	NUM
ejpam-5470	116	10	andm=	andm=	PROPN
ejpam-5470	116	11	4t+1	4t+1	PROPN
ejpam-5470	116	12	,	,	PUNCT
ejpam-5470	116	13	t	t	PROPN
ejpam-5470	116	14	>	>	X
ejpam-5470	116	15	1	1	NUM
ejpam-5470	116	16	.	.	PUNCT
ejpam-5470	117	1	then	then	ADV
ejpam-5470	117	2	,	,	PUNCT
ejpam-5470	117	3	one	one	PRON
ejpam-5470	117	4	can	can	AUX
ejpam-5470	117	5	choose	choose	VERB
ejpam-5470	117	6	the	the	DET
ejpam-5470	117	7	labelling	labelling	NOUN
ejpam-5470	117	8	[	[	X
ejpam-5470	117	9	m2r;10	m2r;10	NOUN
ejpam-5470	117	10	13l	13l	NUM
ejpam-5470	117	11	′	′	NUM
ejpam-5470	117	12	4t−412	4t−412	NUM
ejpam-5470	117	13	,	,	PUNCT
ejpam-5470	117	14	10	10	NUM
ejpam-5470	117	15	13s4t−402	13s4t−402	NUM
ejpam-5470	117	16	,	,	PUNCT
ejpam-5470	117	17	...	...	PUNCT
ejpam-5470	117	18	,	,	PUNCT
ejpam-5470	117	19	(	(	PUNCT
ejpam-5470	117	20	r	r	NOUN
ejpam-5470	117	21	−	−	PROPN
ejpam-5470	117	22	times	time	NOUN
ejpam-5470	117	23	)	)	PUNCT
ejpam-5470	117	24	]	]	PUNCT
ejpam-5470	117	25	for	for	ADP
ejpam-5470	117	26	p2r⊙l4	p2r⊙l4	NOUN
ejpam-5470	117	27	3,4t+1	3,4t+1	NOUN
ejpam-5470	117	28	.	.	PUNCT
ejpam-5470	118	1	therefore	therefore	ADV
ejpam-5470	118	2	x0	x0	PROPN
ejpam-5470	118	3	=	=	PROPN
ejpam-5470	118	4	x1	x1	PROPN
ejpam-5470	118	5	=	=	SYM
ejpam-5470	118	6	r	r	NOUN
ejpam-5470	118	7	,	,	PUNCT
ejpam-5470	118	8	a0=	a0=	PROPN
ejpam-5470	118	9	0,a1=	0,a1=	NOUN
ejpam-5470	118	10	2r	2r	NUM
ejpam-5470	118	11	−	−	NOUN
ejpam-5470	118	12	1	1	NUM
ejpam-5470	118	13	,	,	PUNCT
ejpam-5470	118	14	y0=	y0=	NOUN
ejpam-5470	118	15	2	2	NUM
ejpam-5470	118	16	t	t	NOUN
ejpam-5470	118	17	+	+	NOUN
ejpam-5470	118	18	2,y1=	2,y1=	NUM
ejpam-5470	118	19	2	2	NUM
ejpam-5470	118	20	t	t	NOUN
ejpam-5470	118	21	+	+	NOUN
ejpam-5470	118	22	1,b0=	1,b0=	NUM
ejpam-5470	118	23	8	8	NUM
ejpam-5470	118	24	t	t	NOUN
ejpam-5470	118	25	−	−	NOUN
ejpam-5470	118	26	1,b1=	1,b1=	NUM
ejpam-5470	118	27	8	8	NUM
ejpam-5470	118	28	t	t	NOUN
ejpam-5470	118	29	−	−	NOUN
ejpam-5470	118	30	1,y′0=	1,y′0=	NUM
ejpam-5470	118	31	2	2	NUM
ejpam-5470	118	32	t	t	NOUN
ejpam-5470	118	33	+	+	NOUN
ejpam-5470	118	34	1,y′1=	1,y′1=	NUM
ejpam-5470	118	35	2	2	NUM
ejpam-5470	118	36	t	t	NOUN
ejpam-5470	118	37	+	+	NOUN
ejpam-5470	118	38	2,b′0=	2,b′0=	NUM
ejpam-5470	118	39	8	8	NUM
ejpam-5470	118	40	t	t	NOUN
ejpam-5470	118	41	−	−	NOUN
ejpam-5470	118	42	1	1	NUM
ejpam-5470	118	43	and	and	CCONJ
ejpam-5470	118	44	b′1=	b′1=	ADP
ejpam-5470	118	45	8t−	8t−	NUM
ejpam-5470	118	46	1	1	NUM
ejpam-5470	118	47	.	.	PUNCT
ejpam-5470	119	1	hence	hence	ADV
ejpam-5470	119	2	,	,	PUNCT
ejpam-5470	119	3	one	one	PRON
ejpam-5470	119	4	can	can	AUX
ejpam-5470	119	5	easily	easily	ADV
ejpam-5470	119	6	show	show	VERB
ejpam-5470	119	7	that	that	PRON
ejpam-5470	119	8	|v0−	|v0−	VERB
ejpam-5470	119	9	v1|	v1|	NOUN
ejpam-5470	119	10	=	=	PUNCT
ejpam-5470	119	11	0	0	NUM
ejpam-5470	119	12	and	and	CCONJ
ejpam-5470	119	13	|e0−	|e0−	ADJ
ejpam-5470	119	14	e1|	e1|	NOUN
ejpam-5470	119	15	=	=	PROPN
ejpam-5470	119	16	1	1	NUM
ejpam-5470	119	17	.	.	PUNCT
ejpam-5470	120	1	for	for	ADP
ejpam-5470	120	2	the	the	DET
ejpam-5470	120	3	special	special	ADJ
ejpam-5470	120	4	case	case	NOUN
ejpam-5470	120	5	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	120	6	3,5and	3,5and	NUM
ejpam-5470	120	7	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	120	8	3,5	3,5	NUM
ejpam-5470	120	9	,	,	PUNCT
ejpam-5470	120	10	the	the	DET
ejpam-5470	120	11	labeling	labeling	NOUN
ejpam-5470	120	12	[	[	X
ejpam-5470	120	13	l4r	l4r	X
ejpam-5470	120	14	;	;	PUNCT
ejpam-5470	120	15	1403	1403	NUM
ejpam-5470	120	16	,	,	PUNCT
ejpam-5470	120	17	1403	1403	NUM
ejpam-5470	120	18	,	,	PUNCT
ejpam-5470	120	19	04	04	NUM
ejpam-5470	120	20	13	13	NUM
ejpam-5470	120	21	,	,	PUNCT
ejpam-5470	120	22	04	04	NUM
ejpam-5470	120	23	13	13	NUM
ejpam-5470	120	24	,	,	PUNCT
ejpam-5470	120	25	...	...	PUNCT
ejpam-5470	120	26	,	,	PUNCT
ejpam-5470	120	27	(	(	PUNCT
ejpam-5470	120	28	r	r	NOUN
ejpam-5470	120	29	−	−	PROPN
ejpam-5470	120	30	times	time	NOUN
ejpam-5470	120	31	)	)	PUNCT
ejpam-5470	120	32	]	]	PUNCT
ejpam-5470	120	33	and	and	CCONJ
ejpam-5470	120	34	[	[	X
ejpam-5470	120	35	l4r01	l4r01	X
ejpam-5470	120	36	;	;	PUNCT
ejpam-5470	120	37	1403	1403	NUM
ejpam-5470	120	38	,	,	PUNCT
ejpam-5470	120	39	1403	1403	NUM
ejpam-5470	120	40	,	,	PUNCT
ejpam-5470	120	41	04	04	NUM
ejpam-5470	120	42	13	13	NUM
ejpam-5470	120	43	,	,	PUNCT
ejpam-5470	120	44	04	04	NUM
ejpam-5470	120	45	13	13	NUM
ejpam-5470	120	46	,	,	PUNCT
ejpam-5470	120	47	...	...	PUNCT
ejpam-5470	120	48	,	,	PUNCT
ejpam-5470	120	49	(	(	PUNCT
ejpam-5470	120	50	r−	r−	PROPN
ejpam-5470	120	51	times	time	NOUN
ejpam-5470	120	52	)	)	PUNCT
ejpam-5470	120	53	,	,	PUNCT
ejpam-5470	120	54	1403	1403	NUM
ejpam-5470	120	55	,	,	PUNCT
ejpam-5470	120	56	04	04	NUM
ejpam-5470	120	57	13	13	NUM
ejpam-5470	120	58	,	,	PUNCT
ejpam-5470	120	59	04	04	NUM
ejpam-5470	120	60	13	13	NUM
ejpam-5470	120	61	]	]	PUNCT
ejpam-5470	120	62	is	be	AUX
ejpam-5470	120	63	sufficient	sufficient	ADJ
ejpam-5470	120	64	and	and	CCONJ
ejpam-5470	120	65	thus	thus	ADV
ejpam-5470	120	66	p2r⊙l4	p2r⊙l4	ADP
ejpam-5470	120	67	3,4t+1	3,4t+1	NOUN
ejpam-5470	120	68	is	be	AUX
ejpam-5470	120	69	cordial	cordial	ADJ
ejpam-5470	120	70	.	.	PUNCT
ejpam-5470	121	1	subcase	subcase	PROPN
ejpam-5470	121	2	3.2	3.2	NUM
ejpam-5470	121	3	.	.	PUNCT
ejpam-5470	122	1	k	k	PROPN
ejpam-5470	122	2	odd	odd	ADJ
ejpam-5470	122	3	let	let	VERB
ejpam-5470	122	4	k=	k=	X
ejpam-5470	123	1	2r	2r	NUM
ejpam-5470	124	1	+	+	CCONJ
ejpam-5470	125	1	1,r	1,r	NUM
ejpam-5470	125	2	≥	≥	NOUN
ejpam-5470	125	3	1	1	NUM
ejpam-5470	125	4	and	and	CCONJ
ejpam-5470	125	5	m=	m=	X
ejpam-5470	125	6	4	4	NUM
ejpam-5470	125	7	t	t	NOUN
ejpam-5470	125	8	+	+	NOUN
ejpam-5470	125	9	1	1	NUM
ejpam-5470	125	10	,	,	PUNCT
ejpam-5470	125	11	t	t	PROPN
ejpam-5470	125	12	>	>	X
ejpam-5470	125	13	1	1	NUM
ejpam-5470	125	14	.	.	PUNCT
ejpam-5470	126	1	then	then	ADV
ejpam-5470	126	2	,	,	PUNCT
ejpam-5470	126	3	one	one	PRON
ejpam-5470	126	4	can	can	AUX
ejpam-5470	126	5	choose	choose	VERB
ejpam-5470	126	6	the	the	DET
ejpam-5470	126	7	labelling	labelling	NOUN
ejpam-5470	126	8	[	[	X
ejpam-5470	126	9	m2r+1;10	m2r+1;10	ADJ
ejpam-5470	126	10	13l	13l	NUM
ejpam-5470	126	11	′	′	NUM
ejpam-5470	126	12	4t−4	4t−4	NUM
ejpam-5470	126	13	12	12	NUM
ejpam-5470	126	14	,	,	PUNCT
ejpam-5470	126	15	10	10	NUM
ejpam-5470	126	16	13s4t−402	13s4t−402	NUM
ejpam-5470	126	17	,	,	PUNCT
ejpam-5470	126	18	...	...	PUNCT
ejpam-5470	126	19	,	,	PUNCT
ejpam-5470	126	20	(	(	PUNCT
ejpam-5470	126	21	r−times	r−time	NOUN
ejpam-5470	126	22	)	)	PUNCT
ejpam-5470	126	23	,	,	PUNCT
ejpam-5470	126	24	10	10	NUM
ejpam-5470	126	25	13s4t−402	13s4t−402	NUM
ejpam-5470	126	26	]	]	PUNCT
ejpam-5470	126	27	for	for	ADP
ejpam-5470	126	28	p2r+1⊙l4	p2r+1⊙l4	NOUN
ejpam-5470	126	29	3,4t+1	3,4t+1	NOUN
ejpam-5470	126	30	.	.	PUNCT
ejpam-5470	127	1	therefore	therefore	ADV
ejpam-5470	127	2	x0	x0	PROPN
ejpam-5470	127	3	=	=	ADJ
ejpam-5470	127	4	r+1,x1	r+1,x1	ADV
ejpam-5470	127	5	=	=	ADJ
ejpam-5470	127	6	r	r	NOUN
ejpam-5470	127	7	,	,	PUNCT
ejpam-5470	127	8	a0=	a0=	PROPN
ejpam-5470	127	9	0,a1=	0,a1=	NUM
ejpam-5470	127	10	2r	2r	NUM
ejpam-5470	127	11	,	,	PUNCT
ejpam-5470	127	12	y0=	y0=	PROPN
ejpam-5470	127	13	2t+2,y1=	2t+2,y1=	NUM
ejpam-5470	127	14	2t+1,b0=	2t+1,b0=	NUM
ejpam-5470	127	15	8t−1,b1=	8t−1,b1=	NUM
ejpam-5470	127	16	8t−1,y′0	8t−1,y′0	NOUN
ejpam-5470	127	17	=	=	NOUN
ejpam-5470	127	18	y”0=	y”0=	NOUN
ejpam-5470	127	19	2t+	2t+	NUM
ejpam-5470	127	20	1,y′1	1,y′1	NUM
ejpam-5470	127	21	=	=	NOUN
ejpam-5470	127	22	y”1=	y”1=	NOUN
ejpam-5470	127	23	2	2	NUM
ejpam-5470	127	24	t	t	NOUN
ejpam-5470	127	25	+	+	CCONJ
ejpam-5470	127	26	2,b′0	2,b′0	NUM
ejpam-5470	127	27	=	=	NOUN
ejpam-5470	127	28	b”0=	b”0=	NOUN
ejpam-5470	127	29	8	8	NUM
ejpam-5470	127	30	t	t	NOUN
ejpam-5470	127	31	−	−	NOUN
ejpam-5470	127	32	1	1	NUM
ejpam-5470	127	33	and	and	CCONJ
ejpam-5470	127	34	b′1	b′1	NOUN
ejpam-5470	127	35	=	=	SYM
ejpam-5470	127	36	b”1=	b”1=	NOUN
ejpam-5470	127	37	8	8	NUM
ejpam-5470	127	38	t	t	NOUN
ejpam-5470	127	39	−	−	NOUN
ejpam-5470	127	40	1	1	NUM
ejpam-5470	127	41	.	.	PUNCT
ejpam-5470	128	1	hence	hence	ADV
ejpam-5470	128	2	,	,	PUNCT
ejpam-5470	128	3	one	one	PRON
ejpam-5470	128	4	can	can	AUX
ejpam-5470	128	5	easily	easily	ADV
ejpam-5470	128	6	show	show	VERB
ejpam-5470	128	7	that	that	SCONJ
ejpam-5470	128	8	|v0−v1|	|v0−v1|	NOUN
ejpam-5470	128	9	=	=	SYM
ejpam-5470	128	10	0	0	NUM
ejpam-5470	128	11	and	and	CCONJ
ejpam-5470	128	12	|e0−e1|	|e0−e1|	NOUN
ejpam-5470	128	13	=	=	NOUN
ejpam-5470	128	14	1	1	X
ejpam-5470	128	15	.	.	X
ejpam-5470	129	1	for	for	ADP
ejpam-5470	129	2	the	the	DET
ejpam-5470	129	3	special	special	ADJ
ejpam-5470	129	4	case	case	NOUN
ejpam-5470	129	5	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	129	6	3,5and	3,5and	NUM
ejpam-5470	129	7	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	129	8	3,5	3,5	NUM
ejpam-5470	129	9	,	,	PUNCT
ejpam-5470	129	10	the	the	DET
ejpam-5470	129	11	labeling	labeling	NOUN
ejpam-5470	129	12	[	[	X
ejpam-5470	129	13	l4r0	l4r0	X
ejpam-5470	129	14	;	;	PUNCT
ejpam-5470	129	15	1403	1403	NUM
ejpam-5470	129	16	,	,	PUNCT
ejpam-5470	129	17	1403	1403	NUM
ejpam-5470	129	18	,	,	PUNCT
ejpam-5470	129	19	04	04	NUM
ejpam-5470	129	20	13	13	NUM
ejpam-5470	129	21	,	,	PUNCT
ejpam-5470	129	22	04	04	NUM
ejpam-5470	129	23	13	13	NUM
ejpam-5470	129	24	,	,	PUNCT
ejpam-5470	129	25	...	...	PUNCT
ejpam-5470	129	26	,	,	PUNCT
ejpam-5470	129	27	(	(	PUNCT
ejpam-5470	129	28	r−times),04	r−times),04	NOUN
ejpam-5470	129	29	13	13	NUM
ejpam-5470	129	30	]	]	PUNCT
ejpam-5470	129	31	and	and	CCONJ
ejpam-5470	129	32	[	[	X
ejpam-5470	129	33	l4r010	l4r010	NOUN
ejpam-5470	129	34	;	;	PUNCT
ejpam-5470	129	35	1403	1403	NUM
ejpam-5470	129	36	,	,	PUNCT
ejpam-5470	129	37	1403	1403	NUM
ejpam-5470	129	38	,	,	PUNCT
ejpam-5470	129	39	04	04	NUM
ejpam-5470	129	40	13	13	NUM
ejpam-5470	129	41	,	,	PUNCT
ejpam-5470	129	42	04	04	NUM
ejpam-5470	129	43	13	13	NUM
ejpam-5470	129	44	,	,	PUNCT
ejpam-5470	129	45	...	...	PUNCT
ejpam-5470	129	46	,	,	PUNCT
ejpam-5470	129	47	(	(	PUNCT
ejpam-5470	129	48	r−	r−	PROPN
ejpam-5470	129	49	times	time	NOUN
ejpam-5470	129	50	)	)	PUNCT
ejpam-5470	129	51	,	,	PUNCT
ejpam-5470	129	52	1403	1403	NUM
ejpam-5470	129	53	,	,	PUNCT
ejpam-5470	129	54	04	04	NUM
ejpam-5470	129	55	13	13	NUM
ejpam-5470	129	56	,	,	PUNCT
ejpam-5470	129	57	04	04	NUM
ejpam-5470	129	58	13	13	NUM
ejpam-5470	129	59	,	,	PUNCT
ejpam-5470	129	60	04	04	NUM
ejpam-5470	129	61	13	13	NUM
ejpam-5470	129	62	]	]	PUNCT
ejpam-5470	129	63	and	and	CCONJ
ejpam-5470	129	64	thus	thus	ADV
ejpam-5470	129	65	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	129	66	3,4t+1	3,4t+1	NOUN
ejpam-5470	129	67	is	be	AUX
ejpam-5470	129	68	cordial	cordial	ADJ
ejpam-5470	129	69	.	.	PUNCT
ejpam-5470	130	1	case	case	NOUN
ejpam-5470	130	2	4	4	NUM
ejpam-5470	130	3	.	.	PUNCT
ejpam-5470	131	1	at	at	ADP
ejpam-5470	131	2	m	m	PROPN
ejpam-5470	131	3	≡	≡	PROPN
ejpam-5470	131	4	2(mod4	2(mod4	NUM
ejpam-5470	131	5	)	)	PUNCT
ejpam-5470	131	6	,	,	PUNCT
ejpam-5470	131	7	we	we	PRON
ejpam-5470	131	8	consider	consider	VERB
ejpam-5470	131	9	the	the	DET
ejpam-5470	131	10	following	follow	VERB
ejpam-5470	131	11	subcases	subcase	NOUN
ejpam-5470	131	12	.	.	PUNCT
ejpam-5470	132	1	subcase	subcase	PROPN
ejpam-5470	132	2	4.1	4.1	NUM
ejpam-5470	132	3	.	.	PUNCT
ejpam-5470	133	1	k	k	PROPN
ejpam-5470	133	2	≡	≡	PROPN
ejpam-5470	133	3	0(mod4	0(mod4	NUM
ejpam-5470	133	4	)	)	PUNCT
ejpam-5470	133	5	let	let	VERB
ejpam-5470	133	6	k=	k=	ADJ
ejpam-5470	133	7	4r	4r	NOUN
ejpam-5470	133	8	,	,	PUNCT
ejpam-5470	133	9	r	r	NOUN
ejpam-5470	133	10	≥	≥	NOUN
ejpam-5470	133	11	1	1	NUM
ejpam-5470	133	12	and	and	CCONJ
ejpam-5470	133	13	m=	m=	VERB
ejpam-5470	133	14	4t+2	4t+2	PROPN
ejpam-5470	133	15	,	,	PUNCT
ejpam-5470	133	16	t	t	PROPN
ejpam-5470	133	17	>	>	X
ejpam-5470	133	18	1	1	NUM
ejpam-5470	133	19	.	.	PUNCT
ejpam-5470	134	1	then	then	ADV
ejpam-5470	134	2	,	,	PUNCT
ejpam-5470	134	3	the	the	DET
ejpam-5470	134	4	labelling	labelling	NOUN
ejpam-5470	134	5	[	[	X
ejpam-5470	134	6	l4r;010310	l4r;010310	NOUN
ejpam-5470	134	7	13m4t−6	13m4t−6	NUM
ejpam-5470	134	8	,	,	PUNCT
ejpam-5470	134	9	010310	010310	NUM
ejpam-5470	134	10	13m4t−6	13m4t−6	NUM
ejpam-5470	134	11	,	,	PUNCT
ejpam-5470	134	12	010310	010310	NUM
ejpam-5470	134	13	13m4t−6	13m4t−6	NUM
ejpam-5470	134	14	,	,	PUNCT
ejpam-5470	134	15	010310	010310	NUM
ejpam-5470	134	16	13m4t−6	13m4t−6	NUM
ejpam-5470	134	17	,	,	PUNCT
ejpam-5470	134	18	...	...	PUNCT
ejpam-5470	134	19	,	,	PUNCT
ejpam-5470	134	20	(	(	PUNCT
ejpam-5470	134	21	r	r	NOUN
ejpam-5470	134	22	−	−	PROPN
ejpam-5470	134	23	times	time	NOUN
ejpam-5470	134	24	)	)	PUNCT
ejpam-5470	134	25	]	]	PUNCT
ejpam-5470	134	26	for	for	ADP
ejpam-5470	134	27	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	134	28	3,4t+2	3,4t+2	NOUN
ejpam-5470	134	29	can	can	AUX
ejpam-5470	134	30	be	be	AUX
ejpam-5470	134	31	applied	apply	VERB
ejpam-5470	134	32	.	.	PUNCT
ejpam-5470	135	1	therefore	therefore	ADV
ejpam-5470	135	2	x0	x0	PROPN
ejpam-5470	135	3	=	=	PROPN
ejpam-5470	135	4	x1=	x1=	PROPN
ejpam-5470	135	5	2r	2r	NUM
ejpam-5470	135	6	,	,	PUNCT
ejpam-5470	135	7	a0=	a0=	PROPN
ejpam-5470	135	8	2r	2r	NUM
ejpam-5470	135	9	,	,	PUNCT
ejpam-5470	135	10	a1=	a1=	PROPN
ejpam-5470	135	11	2r−	2r−	PROPN
ejpam-5470	135	12	1,y0	1,y0	NUM
ejpam-5470	135	13	=	=	SYM
ejpam-5470	135	14	y1=	y1=	PROPN
ejpam-5470	135	15	2t+1,b0	2t+1,b0	NOUN
ejpam-5470	135	16	=	=	PUNCT
ejpam-5470	135	17	b1=	b1=	VERB
ejpam-5470	135	18	8t+1,y′0	8t+1,y′0	NOUN
ejpam-5470	135	19	=	=	SYM
ejpam-5470	135	20	y′1=	y′1=	NOUN
ejpam-5470	135	21	2t+	2t+	NUM
ejpam-5470	135	22	1,b′0=	1,b′0=	NUM
ejpam-5470	135	23	8	8	NUM
ejpam-5470	135	24	t	t	NOUN
ejpam-5470	135	25	+	+	CCONJ
ejpam-5470	135	26	1	1	NUM
ejpam-5470	135	27	and	and	CCONJ
ejpam-5470	135	28	b′1=	b′1=	ADP
ejpam-5470	135	29	8	8	NUM
ejpam-5470	135	30	t	t	NOUN
ejpam-5470	135	31	+	+	NOUN
ejpam-5470	135	32	1	1	X
ejpam-5470	135	33	.	.	PUNCT
ejpam-5470	136	1	so	so	ADV
ejpam-5470	136	2	,	,	PUNCT
ejpam-5470	136	3	|v0	|v0	NOUN
ejpam-5470	136	4	−	−	NOUN
ejpam-5470	136	5	v1|	v1|	NOUN
ejpam-5470	136	6	=	=	SYM
ejpam-5470	136	7	0	0	NUM
ejpam-5470	136	8	and	and	CCONJ
ejpam-5470	136	9	|e0	|e0	NOUN
ejpam-5470	137	1	−	−	PROPN
ejpam-5470	137	2	e1|	e1|	NOUN
ejpam-5470	137	3	=	=	NOUN
ejpam-5470	137	4	1	1	X
ejpam-5470	137	5	.	.	X
ejpam-5470	138	1	for	for	ADP
ejpam-5470	138	2	the	the	DET
ejpam-5470	138	3	case	case	NOUN
ejpam-5470	138	4	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	138	5	3,6	3,6	NUM
ejpam-5470	138	6	,	,	PUNCT
ejpam-5470	138	7	the	the	DET
ejpam-5470	138	8	labeling	labeling	NOUN
ejpam-5470	138	9	[	[	X
ejpam-5470	138	10	l4r;03	l4r;03	ADP
ejpam-5470	138	11	120	120	NUM
ejpam-5470	138	12	12	12	NUM
ejpam-5470	138	13	,	,	PUNCT
ejpam-5470	138	14	03	03	NUM
ejpam-5470	138	15	120	120	NUM
ejpam-5470	138	16	12	12	NUM
ejpam-5470	138	17	,	,	PUNCT
ejpam-5470	138	18	03	03	NUM
ejpam-5470	138	19	120	120	NUM
ejpam-5470	138	20	12	12	NUM
ejpam-5470	138	21	,	,	PUNCT
ejpam-5470	138	22	03	03	NUM
ejpam-5470	138	23	120	120	NUM
ejpam-5470	138	24	12	12	NUM
ejpam-5470	138	25	,	,	PUNCT
ejpam-5470	138	26	...	...	PUNCT
ejpam-5470	138	27	,	,	PUNCT
ejpam-5470	138	28	(	(	PUNCT
ejpam-5470	138	29	r	r	NOUN
ejpam-5470	138	30	−	−	PROPN
ejpam-5470	138	31	times	time	NOUN
ejpam-5470	138	32	)	)	PUNCT
ejpam-5470	138	33	]	]	PUNCT
ejpam-5470	138	34	is	be	AUX
ejpam-5470	138	35	sufficient	sufficient	ADJ
ejpam-5470	138	36	and	and	CCONJ
ejpam-5470	138	37	thus	thus	ADV
ejpam-5470	138	38	p4r⊙l4	p4r⊙l4	NOUN
ejpam-5470	138	39	3,4t+2	3,4t+2	NOUN
ejpam-5470	138	40	is	be	AUX
ejpam-5470	138	41	cordial	cordial	ADJ
ejpam-5470	138	42	.	.	PUNCT
ejpam-5470	139	1	subcase	subcase	PROPN
ejpam-5470	139	2	4.2.k	4.2.k	NUM
ejpam-5470	139	3	≡	≡	PROPN
ejpam-5470	139	4	1(mod4	1(mod4	NUM
ejpam-5470	139	5	)	)	PUNCT
ejpam-5470	139	6	let	let	VERB
ejpam-5470	139	7	k=	k=	X
ejpam-5470	139	8	4r+1,r	4r+1,r	NOUN
ejpam-5470	139	9	≥	≥	X
ejpam-5470	139	10	0	0	NUM
ejpam-5470	140	1	andm=	andm=	PROPN
ejpam-5470	140	2	4t+2	4t+2	PROPN
ejpam-5470	140	3	,	,	PUNCT
ejpam-5470	140	4	t	t	PROPN
ejpam-5470	140	5	>	>	X
ejpam-5470	140	6	1	1	NUM
ejpam-5470	140	7	.	.	PUNCT
ejpam-5470	141	1	then	then	ADV
ejpam-5470	141	2	,	,	PUNCT
ejpam-5470	141	3	the	the	DET
ejpam-5470	141	4	labelling	labelling	NOUN
ejpam-5470	141	5	[	[	X
ejpam-5470	141	6	l4r0;010310	l4r0;010310	NOUN
ejpam-5470	141	7	13m4t−6	13m4t−6	NUM
ejpam-5470	141	8	,	,	PUNCT
ejpam-5470	141	9	010310	010310	NUM
ejpam-5470	141	10	13m4t−6	13m4t−6	NUM
ejpam-5470	141	11	,	,	PUNCT
ejpam-5470	141	12	010310	010310	NUM
ejpam-5470	141	13	13m4t−6	13m4t−6	NUM
ejpam-5470	141	14	,	,	PUNCT
ejpam-5470	141	15	010310	010310	NUM
ejpam-5470	141	16	13m4t−6	13m4t−6	NUM
ejpam-5470	141	17	,	,	PUNCT
ejpam-5470	141	18	...	...	PUNCT
ejpam-5470	141	19	,	,	PUNCT
ejpam-5470	141	20	(	(	PUNCT
ejpam-5470	141	21	r−times	r−time	NOUN
ejpam-5470	141	22	)	)	PUNCT
ejpam-5470	141	23	,	,	PUNCT
ejpam-5470	141	24	010310	010310	NUM
ejpam-5470	141	25	13m4t−6	13m4t−6	NUM
ejpam-5470	141	26	]	]	PUNCT
ejpam-5470	141	27	for	for	ADP
ejpam-5470	141	28	p4r+1	p4r+1	PROPN
ejpam-5470	141	29	⊙l4	⊙l4	PUNCT
ejpam-5470	141	30	3,4t+2	3,4t+2	NOUN
ejpam-5470	141	31	is	be	AUX
ejpam-5470	141	32	considered	consider	VERB
ejpam-5470	141	33	.	.	PUNCT
ejpam-5470	142	1	therefore	therefore	ADV
ejpam-5470	142	2	x0=	x0=	PROPN
ejpam-5470	143	1	2r+1,x1=	2r+1,x1=	NUM
ejpam-5470	143	2	2r	2r	NUM
ejpam-5470	143	3	,	,	PUNCT
ejpam-5470	143	4	a0	a0	PROPN
ejpam-5470	143	5	=	=	PROPN
ejpam-5470	143	6	a1=	a1=	PROPN
ejpam-5470	143	7	2r	2r	NUM
ejpam-5470	143	8	,	,	PUNCT
ejpam-5470	143	9	y0	y0	PROPN
ejpam-5470	143	10	=	=	SYM
ejpam-5470	143	11	y1=	y1=	NOUN
ejpam-5470	143	12	2t+1,b0	2t+1,b0	NOUN
ejpam-5470	143	13	=	=	NUM
ejpam-5470	143	14	b1=	b1=	VERB
ejpam-5470	143	15	8t+1	8t+1	PROPN
ejpam-5470	143	16	,	,	PUNCT
ejpam-5470	143	17	y′0	y′0	PROPN
ejpam-5470	143	18	=	=	NOUN
ejpam-5470	143	19	y′1=	y′1=	PROPN
ejpam-5470	143	20	2t+	2t+	NUM
ejpam-5470	143	21	a.	a.	PROPN
ejpam-5470	143	22	abd	abd	PROPN
ejpam-5470	143	23	el	el	PROPN
ejpam-5470	143	24	-	-	PROPN
ejpam-5470	143	25	hay	hay	PROPN
ejpam-5470	143	26	et	et	PROPN
ejpam-5470	143	27	al	al	PROPN
ejpam-5470	143	28	.	.	PUNCT
ejpam-5470	143	29	/	/	SYM
ejpam-5470	143	30	eur	eur	PROPN
ejpam-5470	143	31	.	.	PUNCT
ejpam-5470	144	1	j.	j.	PROPN
ejpam-5470	144	2	pure	pure	PROPN
ejpam-5470	144	3	appl	appl	PROPN
ejpam-5470	144	4	.	.	PROPN
ejpam-5470	144	5	math	math	PROPN
ejpam-5470	144	6	,	,	PUNCT
ejpam-5470	144	7	18	18	NUM
ejpam-5470	144	8	(	(	PUNCT
ejpam-5470	144	9	1	1	NUM
ejpam-5470	144	10	)	)	PUNCT
ejpam-5470	144	11	(	(	PUNCT
ejpam-5470	144	12	2025	2025	NUM
ejpam-5470	144	13	)	)	PUNCT
ejpam-5470	144	14	,	,	PUNCT
ejpam-5470	144	15	5470	5470	NUM
ejpam-5470	144	16	5	5	NUM
ejpam-5470	144	17	of	of	ADP
ejpam-5470	144	18	14	14	NUM
ejpam-5470	144	19	1,b′0=	1,b′0=	NUM
ejpam-5470	144	20	8t+1	8t+1	PROPN
ejpam-5470	144	21	and	and	CCONJ
ejpam-5470	144	22	b′1=	b′1=	ADP
ejpam-5470	144	23	8t+1	8t+1	PROPN
ejpam-5470	144	24	.	.	PUNCT
ejpam-5470	145	1	hence	hence	ADV
ejpam-5470	145	2	,	,	PUNCT
ejpam-5470	145	3	|v0−v1|	|v0−v1|	NOUN
ejpam-5470	145	4	=	=	SYM
ejpam-5470	145	5	1	1	NUM
ejpam-5470	145	6	and	and	CCONJ
ejpam-5470	145	7	|e0−e1|	|e0−e1|	NOUN
ejpam-5470	145	8	=	=	NOUN
ejpam-5470	145	9	0	0	PROPN
ejpam-5470	145	10	.	.	PUNCT
ejpam-5470	146	1	for	for	ADP
ejpam-5470	146	2	the	the	DET
ejpam-5470	146	3	case	case	NOUN
ejpam-5470	146	4	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	146	5	3,6	3,6	NUM
ejpam-5470	146	6	,	,	PUNCT
ejpam-5470	146	7	the	the	DET
ejpam-5470	146	8	labeling	labeling	NOUN
ejpam-5470	146	9	[	[	X
ejpam-5470	146	10	l4r0;03	l4r0;03	ADV
ejpam-5470	146	11	120	120	NUM
ejpam-5470	146	12	12	12	NUM
ejpam-5470	146	13	,	,	PUNCT
ejpam-5470	146	14	03	03	NUM
ejpam-5470	146	15	120	120	NUM
ejpam-5470	146	16	12	12	NUM
ejpam-5470	146	17	,	,	PUNCT
ejpam-5470	146	18	03	03	NUM
ejpam-5470	146	19	120	120	NUM
ejpam-5470	146	20	12	12	NUM
ejpam-5470	146	21	,	,	PUNCT
ejpam-5470	146	22	03	03	NUM
ejpam-5470	146	23	120	120	NUM
ejpam-5470	146	24	12	12	NUM
ejpam-5470	146	25	,	,	PUNCT
ejpam-5470	146	26	...	...	PUNCT
ejpam-5470	146	27	,	,	PUNCT
ejpam-5470	146	28	(	(	PUNCT
ejpam-5470	146	29	r−	r−	NOUN
ejpam-5470	146	30	times),03	times),03	VERB
ejpam-5470	146	31	120	120	NUM
ejpam-5470	146	32	12	12	NUM
ejpam-5470	146	33	]	]	PUNCT
ejpam-5470	146	34	is	be	AUX
ejpam-5470	146	35	sufficient	sufficient	ADJ
ejpam-5470	146	36	and	and	CCONJ
ejpam-5470	146	37	thus	thus	ADV
ejpam-5470	146	38	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	146	39	3,4t+2	3,4t+2	NOUN
ejpam-5470	146	40	is	be	AUX
ejpam-5470	146	41	cordial	cordial	ADJ
ejpam-5470	146	42	.	.	PUNCT
ejpam-5470	147	1	subcase	subcase	PROPN
ejpam-5470	147	2	4.3.k	4.3.k	PROPN
ejpam-5470	147	3	≡	≡	PROPN
ejpam-5470	147	4	2(mod4	2(mod4	NUM
ejpam-5470	147	5	)	)	PUNCT
ejpam-5470	147	6	let	let	VERB
ejpam-5470	147	7	k=	k=	X
ejpam-5470	147	8	4r	4r	NOUN
ejpam-5470	147	9	+	+	CCONJ
ejpam-5470	147	10	2,r	2,r	NUM
ejpam-5470	147	11	≥	≥	NOUN
ejpam-5470	147	12	0	0	NUM
ejpam-5470	147	13	and	and	CCONJ
ejpam-5470	147	14	m=	m=	ADJ
ejpam-5470	147	15	4t+	4t+	PROPN
ejpam-5470	147	16	2	2	NUM
ejpam-5470	147	17	,	,	PUNCT
ejpam-5470	147	18	t	t	PROPN
ejpam-5470	147	19	>	>	X
ejpam-5470	147	20	1	1	NUM
ejpam-5470	147	21	.	.	PUNCT
ejpam-5470	148	1	then	then	ADV
ejpam-5470	148	2	,	,	PUNCT
ejpam-5470	148	3	the	the	DET
ejpam-5470	148	4	labelling	labelling	NOUN
ejpam-5470	148	5	[	[	X
ejpam-5470	148	6	l4r10;01031013m4t−6	l4r10;01031013m4t−6	PROPN
ejpam-5470	148	7	,	,	PUNCT
ejpam-5470	148	8	01031013m4t−6	01031013m4t−6	PROPN
ejpam-5470	148	9	,	,	PUNCT
ejpam-5470	148	10	01031013m4t−6	01031013m4t−6	PROPN
ejpam-5470	148	11	,	,	PUNCT
ejpam-5470	148	12	01031013m4t−6	01031013m4t−6	PROPN
ejpam-5470	148	13	,	,	PUNCT
ejpam-5470	148	14	...	...	PUNCT
ejpam-5470	148	15	,	,	PUNCT
ejpam-5470	148	16	(	(	PUNCT
ejpam-5470	148	17	r−times	r−time	NOUN
ejpam-5470	148	18	)	)	PUNCT
ejpam-5470	148	19	,	,	PUNCT
ejpam-5470	148	20	01031013m4t−6	01031013m4t−6	PROPN
ejpam-5470	148	21	,	,	PUNCT
ejpam-5470	148	22	01031013m4t−6	01031013m4t−6	PROPN
ejpam-5470	148	23	]	]	PUNCT
ejpam-5470	148	24	for	for	ADP
ejpam-5470	148	25	p4r+2	p4r+2	PROPN
ejpam-5470	148	26	⊙l4	⊙l4	X
ejpam-5470	148	27	3,4t+2	3,4t+2	NOUN
ejpam-5470	148	28	is	be	AUX
ejpam-5470	148	29	applied	apply	VERB
ejpam-5470	148	30	.	.	PUNCT
ejpam-5470	149	1	therefore	therefore	ADV
ejpam-5470	149	2	x0	x0	PROPN
ejpam-5470	149	3	=	=	PROPN
ejpam-5470	149	4	x1=	x1=	PROPN
ejpam-5470	149	5	2r	2r	NUM
ejpam-5470	150	1	+	+	CCONJ
ejpam-5470	151	1	1,a0=	1,a0=	NUM
ejpam-5470	151	2	2r	2r	NUM
ejpam-5470	151	3	+	+	CCONJ
ejpam-5470	151	4	1,a1=	1,a1=	NUM
ejpam-5470	151	5	2r	2r	NUM
ejpam-5470	151	6	,	,	PUNCT
ejpam-5470	151	7	y0	y0	PROPN
ejpam-5470	151	8	=	=	SYM
ejpam-5470	151	9	y1=	y1=	PROPN
ejpam-5470	151	10	2	2	NUM
ejpam-5470	151	11	t	t	NOUN
ejpam-5470	151	12	+	+	NOUN
ejpam-5470	151	13	1,b0	1,b0	NUM
ejpam-5470	151	14	=	=	NOUN
ejpam-5470	151	15	b1=	b1=	VERB
ejpam-5470	151	16	8t+1,y′0	8t+1,y′0	NOUN
ejpam-5470	151	17	=	=	SYM
ejpam-5470	151	18	y′1=	y′1=	ADP
ejpam-5470	151	19	2t+1,b′0=	2t+1,b′0=	NUM
ejpam-5470	151	20	8t+1	8t+1	PROPN
ejpam-5470	151	21	and	and	CCONJ
ejpam-5470	151	22	b′1=	b′1=	ADP
ejpam-5470	151	23	8t+1	8t+1	PROPN
ejpam-5470	151	24	.	.	PUNCT
ejpam-5470	152	1	so	so	ADV
ejpam-5470	152	2	,	,	PUNCT
ejpam-5470	152	3	|v0−v1|	|v0−v1|	NUM
ejpam-5470	152	4	=	=	SYM
ejpam-5470	152	5	0	0	NUM
ejpam-5470	152	6	and	and	CCONJ
ejpam-5470	152	7	|e0−e1|	|e0−e1|	NOUN
ejpam-5470	152	8	=	=	NOUN
ejpam-5470	152	9	1	1	X
ejpam-5470	152	10	.	.	X
ejpam-5470	153	1	for	for	ADP
ejpam-5470	153	2	the	the	DET
ejpam-5470	153	3	case	case	NOUN
ejpam-5470	153	4	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	153	5	3,6	3,6	NUM
ejpam-5470	153	6	,	,	PUNCT
ejpam-5470	153	7	the	the	DET
ejpam-5470	153	8	labeling	labeling	NOUN
ejpam-5470	153	9	[	[	X
ejpam-5470	153	10	l4r10;0312012	l4r10;0312012	NOUN
ejpam-5470	153	11	,	,	PUNCT
ejpam-5470	153	12	0312012	0312012	NUM
ejpam-5470	153	13	,	,	PUNCT
ejpam-5470	153	14	0312012	0312012	NUM
ejpam-5470	153	15	,	,	PUNCT
ejpam-5470	153	16	0312012	0312012	NUM
ejpam-5470	153	17	,	,	PUNCT
ejpam-5470	153	18	...	...	PUNCT
ejpam-5470	153	19	,	,	PUNCT
ejpam-5470	153	20	(	(	PUNCT
ejpam-5470	153	21	r	r	NOUN
ejpam-5470	153	22	−	−	PROPN
ejpam-5470	153	23	times),0312012	times),0312012	PROPN
ejpam-5470	153	24	,	,	PUNCT
ejpam-5470	153	25	0312012	0312012	NUM
ejpam-5470	153	26	]	]	PUNCT
ejpam-5470	153	27	is	be	AUX
ejpam-5470	153	28	sufficient	sufficient	ADJ
ejpam-5470	153	29	and	and	CCONJ
ejpam-5470	153	30	thus	thus	ADV
ejpam-5470	153	31	p4r+2⊙l4	p4r+2⊙l4	NUM
ejpam-5470	153	32	3,4t+2	3,4t+2	NOUN
ejpam-5470	153	33	is	be	AUX
ejpam-5470	153	34	cordial	cordial	ADJ
ejpam-5470	153	35	.	.	PUNCT
ejpam-5470	154	1	subcase	subcase	PROPN
ejpam-5470	154	2	4.4.k	4.4.k	NUM
ejpam-5470	154	3	≡	≡	PROPN
ejpam-5470	154	4	3(mod4	3(mod4	NUM
ejpam-5470	154	5	)	)	PUNCT
ejpam-5470	154	6	let	let	VERB
ejpam-5470	154	7	k=	k=	X
ejpam-5470	154	8	4r+3,r	4r+3,r	NUM
ejpam-5470	154	9	≥	≥	NOUN
ejpam-5470	154	10	0	0	NUM
ejpam-5470	154	11	andm=	andm=	PROPN
ejpam-5470	154	12	4t+2	4t+2	PROPN
ejpam-5470	154	13	,	,	PUNCT
ejpam-5470	154	14	t	t	PROPN
ejpam-5470	154	15	>	>	X
ejpam-5470	154	16	1	1	NUM
ejpam-5470	154	17	.	.	PUNCT
ejpam-5470	155	1	then	then	ADV
ejpam-5470	155	2	,	,	PUNCT
ejpam-5470	155	3	one	one	PRON
ejpam-5470	155	4	can	can	AUX
ejpam-5470	155	5	select	select	VERB
ejpam-5470	155	6	the	the	DET
ejpam-5470	155	7	labelling	labelling	NOUN
ejpam-5470	155	8	[	[	X
ejpam-5470	155	9	l4r001;010310	l4r001;010310	PROPN
ejpam-5470	155	10	13m4t−6	13m4t−6	PROPN
ejpam-5470	155	11	,	,	PUNCT
ejpam-5470	155	12	01031013m4t−6	01031013m4t−6	PROPN
ejpam-5470	155	13	,	,	PUNCT
ejpam-5470	155	14	010310	010310	NUM
ejpam-5470	155	15	13m4t−6	13m4t−6	NUM
ejpam-5470	155	16	,	,	PUNCT
ejpam-5470	155	17	010310	010310	NUM
ejpam-5470	155	18	13m4t−6	13m4t−6	NUM
ejpam-5470	155	19	,	,	PUNCT
ejpam-5470	155	20	...	...	PUNCT
ejpam-5470	155	21	,	,	PUNCT
ejpam-5470	155	22	(	(	PUNCT
ejpam-5470	155	23	r−times	r−time	NOUN
ejpam-5470	155	24	)	)	PUNCT
ejpam-5470	155	25	,	,	PUNCT
ejpam-5470	155	26	010310	010310	NUM
ejpam-5470	155	27	13m4t−6	13m4t−6	NUM
ejpam-5470	155	28	,	,	PUNCT
ejpam-5470	155	29	010310	010310	NUM
ejpam-5470	155	30	13m4t−6	13m4t−6	NUM
ejpam-5470	155	31	,	,	PUNCT
ejpam-5470	155	32	010310	010310	NUM
ejpam-5470	155	33	13m4t−6	13m4t−6	NUM
ejpam-5470	155	34	]	]	PUNCT
ejpam-5470	155	35	for	for	ADP
ejpam-5470	155	36	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	155	37	3,4t+2	3,4t+2	NOUN
ejpam-5470	155	38	.	.	PUNCT
ejpam-5470	156	1	therefore	therefore	ADV
ejpam-5470	156	2	x0=	x0=	PUNCT
ejpam-5470	156	3	2r+2,x1=	2r+2,x1=	NUM
ejpam-5470	156	4	2r+1,a0	2r+1,a0	NUM
ejpam-5470	156	5	=	=	VERB
ejpam-5470	156	6	a1=	a1=	ADJ
ejpam-5470	156	7	2r+	2r+	NUM
ejpam-5470	156	8	1,y0	1,y0	NUM
ejpam-5470	156	9	=	=	SYM
ejpam-5470	156	10	y1=	y1=	PROPN
ejpam-5470	156	11	2t+	2t+	NUM
ejpam-5470	156	12	1,b0	1,b0	NUM
ejpam-5470	156	13	=	=	SYM
ejpam-5470	156	14	b1=	b1=	VERB
ejpam-5470	156	15	8t+	8t+	NUM
ejpam-5470	156	16	1,y′0	1,y′0	NUM
ejpam-5470	156	17	=	=	NOUN
ejpam-5470	156	18	y′1=	y′1=	NOUN
ejpam-5470	156	19	2t+	2t+	NUM
ejpam-5470	156	20	1,b′0=	1,b′0=	NUM
ejpam-5470	156	21	8t+	8t+	NUM
ejpam-5470	156	22	1	1	NUM
ejpam-5470	156	23	and	and	CCONJ
ejpam-5470	156	24	b′1=	b′1=	ADP
ejpam-5470	156	25	8t+	8t+	NUM
ejpam-5470	156	26	1	1	NUM
ejpam-5470	156	27	.	.	PUNCT
ejpam-5470	157	1	hence	hence	ADV
ejpam-5470	157	2	,	,	PUNCT
ejpam-5470	157	3	one	one	PRON
ejpam-5470	157	4	can	can	AUX
ejpam-5470	157	5	easily	easily	ADV
ejpam-5470	157	6	show	show	VERB
ejpam-5470	157	7	that	that	SCONJ
ejpam-5470	157	8	|v0	|v0	NOUN
ejpam-5470	157	9	−	−	NOUN
ejpam-5470	157	10	v1|	v1|	NOUN
ejpam-5470	157	11	=	=	SYM
ejpam-5470	157	12	1	1	NUM
ejpam-5470	157	13	and	and	CCONJ
ejpam-5470	157	14	|e0	|e0	NOUN
ejpam-5470	157	15	−	−	PROPN
ejpam-5470	157	16	e1|	e1|	NOUN
ejpam-5470	157	17	=	=	NOUN
ejpam-5470	157	18	0	0	NUM
ejpam-5470	157	19	.	.	PUNCT
ejpam-5470	158	1	for	for	ADP
ejpam-5470	158	2	the	the	DET
ejpam-5470	158	3	case	case	NOUN
ejpam-5470	158	4	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	158	5	3,6	3,6	NUM
ejpam-5470	158	6	,	,	PUNCT
ejpam-5470	158	7	the	the	DET
ejpam-5470	158	8	labeling	labeling	NOUN
ejpam-5470	159	1	[	[	X
ejpam-5470	159	2	l4r001;03	l4r001;03	NOUN
ejpam-5470	159	3	120	120	NUM
ejpam-5470	159	4	12	12	NUM
ejpam-5470	159	5	,	,	PUNCT
ejpam-5470	159	6	03	03	NUM
ejpam-5470	159	7	120	120	NUM
ejpam-5470	159	8	12	12	NUM
ejpam-5470	159	9	,	,	PUNCT
ejpam-5470	159	10	03	03	NUM
ejpam-5470	159	11	120	120	NUM
ejpam-5470	159	12	12	12	NUM
ejpam-5470	159	13	,	,	PUNCT
ejpam-5470	159	14	03	03	NUM
ejpam-5470	159	15	120	120	NUM
ejpam-5470	159	16	12	12	NUM
ejpam-5470	159	17	,	,	PUNCT
ejpam-5470	159	18	...	...	PUNCT
ejpam-5470	159	19	,	,	PUNCT
ejpam-5470	159	20	(	(	PUNCT
ejpam-5470	159	21	r−times),03	r−times),03	X
ejpam-5470	159	22	120	120	NUM
ejpam-5470	159	23	12	12	NUM
ejpam-5470	159	24	,	,	PUNCT
ejpam-5470	159	25	03	03	NUM
ejpam-5470	159	26	120	120	NUM
ejpam-5470	159	27	12	12	NUM
ejpam-5470	159	28	,	,	PUNCT
ejpam-5470	159	29	03	03	NUM
ejpam-5470	159	30	120	120	NUM
ejpam-5470	159	31	12	12	NUM
ejpam-5470	159	32	]	]	PUNCT
ejpam-5470	159	33	is	be	AUX
ejpam-5470	159	34	sufficient	sufficient	ADJ
ejpam-5470	159	35	and	and	CCONJ
ejpam-5470	160	1	thus	thus	ADV
ejpam-5470	160	2	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	160	3	3,4t+2	3,4t+2	NOUN
ejpam-5470	160	4	is	be	AUX
ejpam-5470	160	5	cordial	cordial	ADJ
ejpam-5470	160	6	.	.	PUNCT
ejpam-5470	161	1	case	case	NOUN
ejpam-5470	161	2	5	5	NUM
ejpam-5470	161	3	.	.	PUNCT
ejpam-5470	162	1	at	at	ADP
ejpam-5470	162	2	m	m	PROPN
ejpam-5470	162	3	≡	≡	PROPN
ejpam-5470	162	4	3(mod4	3(mod4	NUM
ejpam-5470	162	5	)	)	PUNCT
ejpam-5470	162	6	,	,	PUNCT
ejpam-5470	162	7	we	we	PRON
ejpam-5470	162	8	consider	consider	VERB
ejpam-5470	162	9	the	the	DET
ejpam-5470	162	10	following	follow	VERB
ejpam-5470	162	11	subcases	subcase	NOUN
ejpam-5470	162	12	.	.	PUNCT
ejpam-5470	163	1	subcase	subcase	PROPN
ejpam-5470	163	2	5.1.k	5.1.k	PROPN
ejpam-5470	163	3	even	even	ADV
ejpam-5470	163	4	let	let	VERB
ejpam-5470	163	5	k=	k=	ADJ
ejpam-5470	163	6	4r	4r	NOUN
ejpam-5470	163	7	,	,	PUNCT
ejpam-5470	163	8	r	r	NOUN
ejpam-5470	163	9	≥	≥	NUM
ejpam-5470	163	10	1	1	NUM
ejpam-5470	163	11	andm=	andm=	NUM
ejpam-5470	163	12	4t+3	4t+3	PROPN
ejpam-5470	163	13	,	,	PUNCT
ejpam-5470	163	14	t	t	PROPN
ejpam-5470	163	15	≥	≥	NUM
ejpam-5470	163	16	1	1	NUM
ejpam-5470	163	17	.	.	PUNCT
ejpam-5470	164	1	then	then	ADV
ejpam-5470	164	2	,	,	PUNCT
ejpam-5470	164	3	the	the	DET
ejpam-5470	164	4	labelling	labelling	NOUN
ejpam-5470	164	5	[	[	X
ejpam-5470	164	6	m2r;010	m2r;010	ADJ
ejpam-5470	164	7	12l	12l	NOUN
ejpam-5470	164	8	′	′	NUM
ejpam-5470	164	9	4t0102	4t0102	NUM
ejpam-5470	164	10	,	,	PUNCT
ejpam-5470	164	11	010	010	NUM
ejpam-5470	164	12	12l	12l	NOUN
ejpam-5470	164	13	′	′	NUM
ejpam-5470	164	14	4t0102	4t0102	NUM
ejpam-5470	164	15	,	,	PUNCT
ejpam-5470	164	16	10102s	10102s	NUM
ejpam-5470	164	17	′	′	NUM
ejpam-5470	164	18	4t10	4t10	NOUN
ejpam-5470	164	19	12	12	NUM
ejpam-5470	164	20	,	,	PUNCT
ejpam-5470	164	21	10102s	10102s	NUM
ejpam-5470	164	22	′	′	NUM
ejpam-5470	164	23	4t10	4t10	NOUN
ejpam-5470	164	24	12	12	NUM
ejpam-5470	164	25	,	,	PUNCT
ejpam-5470	164	26	...	...	PUNCT
ejpam-5470	164	27	,	,	PUNCT
ejpam-5470	164	28	(	(	PUNCT
ejpam-5470	164	29	r	r	NOUN
ejpam-5470	164	30	−	−	PROPN
ejpam-5470	164	31	times	time	NOUN
ejpam-5470	164	32	)	)	PUNCT
ejpam-5470	164	33	]	]	PUNCT
ejpam-5470	164	34	for	for	ADP
ejpam-5470	164	35	p2r⊙l2	p2r⊙l2	PROPN
ejpam-5470	164	36	3,4t+3	3,4t+3	PROPN
ejpam-5470	164	37	can	can	AUX
ejpam-5470	164	38	be	be	AUX
ejpam-5470	164	39	applied	apply	VERB
ejpam-5470	164	40	.	.	PUNCT
ejpam-5470	165	1	therefore	therefore	ADV
ejpam-5470	165	2	x0	x0	PROPN
ejpam-5470	165	3	=	=	PROPN
ejpam-5470	165	4	x1	x1	PROPN
ejpam-5470	165	5	=	=	SYM
ejpam-5470	165	6	r	r	NOUN
ejpam-5470	165	7	,	,	PUNCT
ejpam-5470	165	8	a0=	a0=	PROPN
ejpam-5470	165	9	0,a1=	0,a1=	NUM
ejpam-5470	165	10	2r−1,y0=	2r−1,y0=	PROPN
ejpam-5470	165	11	2t+3,y1=	2t+3,y1=	NUM
ejpam-5470	165	12	2t+2,b0	2t+2,b0	NOUN
ejpam-5470	165	13	=	=	VERB
ejpam-5470	165	14	b1=	b1=	NOUN
ejpam-5470	165	15	8t+3,y′0=	8t+3,y′0=	NUM
ejpam-5470	165	16	2t+2,y′1=	2t+2,y′1=	NUM
ejpam-5470	165	17	2t+3,b′0=	2t+3,b′0=	NUM
ejpam-5470	165	18	8t+	8t+	NUM
ejpam-5470	165	19	3	3	NUM
ejpam-5470	165	20	and	and	CCONJ
ejpam-5470	165	21	b′1=	b′1=	ADP
ejpam-5470	165	22	8t+	8t+	NUM
ejpam-5470	165	23	4	4	NUM
ejpam-5470	165	24	.	.	PUNCT
ejpam-5470	165	25	hence	hence	ADV
ejpam-5470	165	26	,	,	PUNCT
ejpam-5470	165	27	|v0	|v0	NOUN
ejpam-5470	165	28	−	−	NOUN
ejpam-5470	165	29	v1|	v1|	NOUN
ejpam-5470	165	30	=	=	SYM
ejpam-5470	165	31	0	0	NUM
ejpam-5470	165	32	and	and	CCONJ
ejpam-5470	165	33	|e0	|e0	NOUN
ejpam-5470	166	1	−	−	PROPN
ejpam-5470	166	2	e1|	e1|	NOUN
ejpam-5470	166	3	=	=	NOUN
ejpam-5470	166	4	1	1	NUM
ejpam-5470	166	5	.	.	PUNCT
ejpam-5470	166	6	thus	thus	ADV
ejpam-5470	166	7	p2r⊙l2	p2r⊙l2	PROPN
ejpam-5470	166	8	3,4t+3	3,4t+3	PROPN
ejpam-5470	166	9	is	be	AUX
ejpam-5470	166	10	cordial	cordial	ADJ
ejpam-5470	166	11	.	.	PUNCT
ejpam-5470	167	1	subcase	subcase	PROPN
ejpam-5470	168	1	5.2.k	5.2.k	PROPN
ejpam-5470	168	2	odd	odd	ADJ
ejpam-5470	168	3	let	let	VERB
ejpam-5470	168	4	k=	k=	ADJ
ejpam-5470	168	5	4r	4r	NOUN
ejpam-5470	168	6	,	,	PUNCT
ejpam-5470	168	7	r	r	NOUN
ejpam-5470	168	8	≥	≥	NUM
ejpam-5470	168	9	1	1	NUM
ejpam-5470	168	10	andm=	andm=	NUM
ejpam-5470	168	11	4t+3	4t+3	PROPN
ejpam-5470	168	12	,	,	PUNCT
ejpam-5470	168	13	t	t	PROPN
ejpam-5470	168	14	≥	≥	NUM
ejpam-5470	168	15	1	1	NUM
ejpam-5470	168	16	.	.	PUNCT
ejpam-5470	169	1	then	then	ADV
ejpam-5470	169	2	,	,	PUNCT
ejpam-5470	169	3	the	the	DET
ejpam-5470	169	4	labelling	labelling	NOUN
ejpam-5470	169	5	[	[	X
ejpam-5470	169	6	m2r+1;010	m2r+1;010	ADJ
ejpam-5470	169	7	12l	12l	NOUN
ejpam-5470	169	8	′	′	NUM
ejpam-5470	169	9	4t0102	4t0102	NUM
ejpam-5470	169	10	,	,	PUNCT
ejpam-5470	169	11	010	010	NUM
ejpam-5470	169	12	12l	12l	NOUN
ejpam-5470	169	13	′	′	NUM
ejpam-5470	169	14	4t0102	4t0102	NUM
ejpam-5470	169	15	,	,	PUNCT
ejpam-5470	169	16	10102s	10102s	NUM
ejpam-5470	169	17	′	′	NUM
ejpam-5470	169	18	4t10	4t10	NOUN
ejpam-5470	169	19	12	12	NUM
ejpam-5470	169	20	,	,	PUNCT
ejpam-5470	169	21	10102s	10102s	NUM
ejpam-5470	169	22	′	′	NUM
ejpam-5470	169	23	4t10	4t10	NOUN
ejpam-5470	169	24	12	12	NUM
ejpam-5470	169	25	,	,	PUNCT
ejpam-5470	169	26	...	...	PUNCT
ejpam-5470	169	27	,	,	PUNCT
ejpam-5470	169	28	(	(	PUNCT
ejpam-5470	169	29	r	r	NOUN
ejpam-5470	169	30	−	−	PROPN
ejpam-5470	169	31	times	time	NOUN
ejpam-5470	169	32	)	)	PUNCT
ejpam-5470	169	33	,	,	PUNCT
ejpam-5470	169	34	10102s	10102s	NUM
ejpam-5470	169	35	′	′	NUM
ejpam-5470	169	36	4t10	4t10	NOUN
ejpam-5470	169	37	12	12	NUM
ejpam-5470	169	38	]	]	PUNCT
ejpam-5470	169	39	for	for	ADP
ejpam-5470	169	40	p2r+1⊙l2	p2r+1⊙l2	NOUN
ejpam-5470	169	41	3,4t+3	3,4t+3	NUM
ejpam-5470	169	42	can	can	AUX
ejpam-5470	169	43	be	be	AUX
ejpam-5470	169	44	applied	apply	VERB
ejpam-5470	169	45	.	.	PUNCT
ejpam-5470	170	1	therefore	therefore	ADV
ejpam-5470	170	2	x0	x0	PROPN
ejpam-5470	170	3	=	=	ADJ
ejpam-5470	170	4	r+1,x1	r+1,x1	ADV
ejpam-5470	170	5	=	=	ADJ
ejpam-5470	170	6	r	r	NOUN
ejpam-5470	170	7	,	,	PUNCT
ejpam-5470	170	8	a0=	a0=	PROPN
ejpam-5470	170	9	0,a1=	0,a1=	NUM
ejpam-5470	170	10	2r	2r	NUM
ejpam-5470	170	11	,	,	PUNCT
ejpam-5470	170	12	y0=	y0=	PROPN
ejpam-5470	170	13	2t+3,y1=	2t+3,y1=	NUM
ejpam-5470	170	14	2t+2,b0	2t+2,b0	NOUN
ejpam-5470	170	15	=	=	NOUN
ejpam-5470	170	16	b1=	b1=	VERB
ejpam-5470	170	17	8t+3,y′0	8t+3,y′0	NOUN
ejpam-5470	170	18	=	=	NOUN
ejpam-5470	170	19	y”0=	y”0=	NOUN
ejpam-5470	170	20	2t+	2t+	NUM
ejpam-5470	170	21	2,y′1	2,y′1	NUM
ejpam-5470	170	22	=	=	NOUN
ejpam-5470	170	23	y1”=	y1”=	NUM
ejpam-5470	170	24	2t+3,b′0	2t+3,b′0	NOUN
ejpam-5470	170	25	=	=	NOUN
ejpam-5470	170	26	b”0=	b”0=	NOUN
ejpam-5470	170	27	8t+3	8t+3	ADJ
ejpam-5470	170	28	and	and	CCONJ
ejpam-5470	170	29	b′1	b′1	NOUN
ejpam-5470	170	30	=	=	SYM
ejpam-5470	170	31	b”1=	b”1=	NOUN
ejpam-5470	170	32	8t+4	8t+4	PROPN
ejpam-5470	170	33	.	.	PUNCT
ejpam-5470	171	1	hence	hence	ADV
ejpam-5470	171	2	,	,	PUNCT
ejpam-5470	171	3	|v0−	|v0−	VERB
ejpam-5470	171	4	v1|	v1|	NOUN
ejpam-5470	171	5	=	=	SYM
ejpam-5470	171	6	1	1	NUM
ejpam-5470	171	7	and	and	CCONJ
ejpam-5470	171	8	|e0−	|e0−	NOUN
ejpam-5470	171	9	e1|	e1|	NOUN
ejpam-5470	171	10	=	=	PUNCT
ejpam-5470	171	11	0	0	NUM
ejpam-5470	171	12	.	.	PUNCT
ejpam-5470	172	1	thus	thus	ADV
ejpam-5470	172	2	p2r⊙l2	p2r⊙l2	PROPN
ejpam-5470	172	3	3,4t+3	3,4t+3	PROPN
ejpam-5470	172	4	is	be	AUX
ejpam-5470	172	5	cordial	cordial	ADJ
ejpam-5470	172	6	.	.	PUNCT
ejpam-5470	173	1	lemma	lemma	PROPN
ejpam-5470	173	2	2	2	NUM
ejpam-5470	173	3	.	.	NOUN
ejpam-5470	173	4	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	173	5	n	n	CCONJ
ejpam-5470	173	6	,	,	PUNCT
ejpam-5470	173	7	m	m	VERB
ejpam-5470	173	8	is	be	AUX
ejpam-5470	173	9	cordial	cordial	ADJ
ejpam-5470	173	10	for	for	ADP
ejpam-5470	173	11	all	all	DET
ejpam-5470	173	12	k	k	PROPN
ejpam-5470	173	13	≥	≥	NUM
ejpam-5470	173	14	1	1	NUM
ejpam-5470	173	15	and	and	CCONJ
ejpam-5470	173	16	m	m	PRON
ejpam-5470	173	17	>	>	X
ejpam-5470	173	18	6	6	NUM
ejpam-5470	173	19	except	except	SCONJ
ejpam-5470	173	20	at	at	ADP
ejpam-5470	173	21	m	m	PROPN
ejpam-5470	173	22	=	=	SYM
ejpam-5470	173	23	n	n	PROPN
ejpam-5470	173	24	=	=	SYM
ejpam-5470	173	25	7	7	X
ejpam-5470	173	26	.	.	PUNCT
ejpam-5470	174	1	proof	proof	NOUN
ejpam-5470	174	2	.	.	PUNCT
ejpam-5470	175	1	let	let	VERB
ejpam-5470	175	2	k	k	NOUN
ejpam-5470	175	3	=	=	PUNCT
ejpam-5470	175	4	4r	4r	NOUN
ejpam-5470	175	5	+	+	NUM
ejpam-5470	175	6	i′	i′	NOUN
ejpam-5470	175	7	(	(	PUNCT
ejpam-5470	175	8	i′	i′	NOUN
ejpam-5470	175	9	=	=	SYM
ejpam-5470	175	10	0	0	NUM
ejpam-5470	175	11	,	,	PUNCT
ejpam-5470	175	12	1	1	NUM
ejpam-5470	175	13	,	,	PUNCT
ejpam-5470	175	14	2	2	NUM
ejpam-5470	175	15	,	,	PUNCT
ejpam-5470	175	16	3	3	NUM
ejpam-5470	175	17	and	and	CCONJ
ejpam-5470	175	18	r	r	NOUN
ejpam-5470	175	19	≥	≥	NOUN
ejpam-5470	175	20	0	0	NUM
ejpam-5470	175	21	)	)	PUNCT
ejpam-5470	175	22	,	,	PUNCT
ejpam-5470	175	23	n=	n=	ADJ
ejpam-5470	175	24	4s	4s	NUM
ejpam-5470	175	25	+	+	CCONJ
ejpam-5470	175	26	i	i	PRON
ejpam-5470	175	27	and	and	CCONJ
ejpam-5470	175	28	m	m	VERB
ejpam-5470	175	29	=	=	NOUN
ejpam-5470	175	30	4	4	NUM
ejpam-5470	175	31	t	t	NOUN
ejpam-5470	175	32	+	+	X
ejpam-5470	175	33	j	j	PROPN
ejpam-5470	175	34	(	(	PUNCT
ejpam-5470	175	35	i	i	PROPN
ejpam-5470	175	36	,	,	PUNCT
ejpam-5470	175	37	j	j	PROPN
ejpam-5470	175	38	=	=	SYM
ejpam-5470	175	39	0	0	NUM
ejpam-5470	175	40	,	,	PUNCT
ejpam-5470	175	41	1	1	NUM
ejpam-5470	175	42	,	,	PUNCT
ejpam-5470	175	43	2	2	NUM
ejpam-5470	175	44	,	,	PUNCT
ejpam-5470	175	45	3	3	NUM
ejpam-5470	175	46	and	and	CCONJ
ejpam-5470	175	47	s	s	PROPN
ejpam-5470	175	48	,	,	PUNCT
ejpam-5470	175	49	t	t	PROPN
ejpam-5470	175	50	≥	≥	NUM
ejpam-5470	175	51	2	2	NUM
ejpam-5470	175	52	)	)	PUNCT
ejpam-5470	175	53	,	,	PUNCT
ejpam-5470	175	54	then	then	ADV
ejpam-5470	175	55	,	,	PUNCT
ejpam-5470	175	56	we	we	PRON
ejpam-5470	175	57	may	may	AUX
ejpam-5470	175	58	use	use	VERB
ejpam-5470	175	59	the	the	DET
ejpam-5470	175	60	labeling	labeling	NOUN
ejpam-5470	175	61	ai′	ai′	NOUN
ejpam-5470	175	62	or	or	CCONJ
ejpam-5470	175	63	aj′	aj′	NOUN
ejpam-5470	175	64	for	for	ADP
ejpam-5470	175	65	pk	pk	NOUN
ejpam-5470	175	66	as	as	SCONJ
ejpam-5470	175	67	given	give	VERB
ejpam-5470	175	68	in	in	ADP
ejpam-5470	175	69	table	table	NOUN
ejpam-5470	175	70	1	1	NUM
ejpam-5470	175	71	.	.	PUNCT
ejpam-5470	175	72	for	for	ADP
ejpam-5470	175	73	a	a	DET
ejpam-5470	175	74	given	give	VERB
ejpam-5470	175	75	value	value	NOUN
ejpam-5470	175	76	of	of	ADP
ejpam-5470	175	77	j	j	PROPN
ejpam-5470	175	78	with	with	ADP
ejpam-5470	175	79	0	0	NUM
ejpam-5470	175	80	≤	≤	NOUN
ejpam-5470	176	1	i	i	PRON
ejpam-5470	176	2	,	,	PUNCT
ejpam-5470	176	3	j	j	PROPN
ejpam-5470	176	4	≤	≤	PROPN
ejpam-5470	176	5	3	3	NUM
ejpam-5470	176	6	,	,	PUNCT
ejpam-5470	176	7	we	we	PRON
ejpam-5470	176	8	may	may	AUX
ejpam-5470	176	9	use	use	VERB
ejpam-5470	176	10	one	one	NUM
ejpam-5470	176	11	of	of	ADP
ejpam-5470	176	12	the	the	DET
ejpam-5470	176	13	labeling	labeling	NOUN
ejpam-5470	176	14	in	in	ADP
ejpam-5470	176	15	the	the	DET
ejpam-5470	176	16	set	set	NOUN
ejpam-5470	176	17	{	{	PUNCT
ejpam-5470	176	18	bij	bij	NOUN
ejpam-5470	176	19	,	,	PUNCT
ejpam-5470	176	20	b′	b′	NUM
ejpam-5470	176	21	ij	ij	NOUN
ejpam-5470	176	22	}	}	PUNCT
ejpam-5470	176	23	for	for	ADP
ejpam-5470	176	24	l4	l4	PROPN
ejpam-5470	176	25	n	n	CCONJ
ejpam-5470	176	26	,	,	PUNCT
ejpam-5470	176	27	m	m	PROPN
ejpam-5470	176	28	,	,	PUNCT
ejpam-5470	176	29	where	where	SCONJ
ejpam-5470	176	30	bij	bij	NOUN
ejpam-5470	176	31	and	and	CCONJ
ejpam-5470	176	32	b	b	NOUN
ejpam-5470	176	33	′	′	NUM
ejpam-5470	176	34	ij	ij	NOUN
ejpam-5470	176	35	are	be	AUX
ejpam-5470	176	36	the	the	DET
ejpam-5470	176	37	labeling	labeling	NOUN
ejpam-5470	176	38	of	of	ADP
ejpam-5470	176	39	l4	l4	PROPN
ejpam-5470	176	40	n	n	CCONJ
ejpam-5470	176	41	,	,	PUNCT
ejpam-5470	176	42	m	m	VERB
ejpam-5470	176	43	which	which	PRON
ejpam-5470	176	44	are	be	AUX
ejpam-5470	176	45	connected	connect	VERB
ejpam-5470	176	46	to	to	ADP
ejpam-5470	176	47	the	the	DET
ejpam-5470	176	48	vertices	vertex	NOUN
ejpam-5470	176	49	labeled	label	VERB
ejpam-5470	176	50	0	0	NUM
ejpam-5470	176	51	in	in	ADP
ejpam-5470	176	52	pk	pk	NOUN
ejpam-5470	176	53	,	,	PUNCT
ejpam-5470	176	54	while	while	SCONJ
ejpam-5470	176	55	bij	bij	NOUN
ejpam-5470	176	56	and	and	CCONJ
ejpam-5470	176	57	b′	b′	NUM
ejpam-5470	176	58	ij	ij	NOUN
ejpam-5470	176	59	are	be	AUX
ejpam-5470	176	60	the	the	DET
ejpam-5470	176	61	labeling	labeling	NOUN
ejpam-5470	176	62	of	of	ADP
ejpam-5470	176	63	l4	l4	PROPN
ejpam-5470	176	64	n	n	CCONJ
ejpam-5470	176	65	,	,	PUNCT
ejpam-5470	176	66	m	m	VERB
ejpam-5470	176	67	which	which	PRON
ejpam-5470	176	68	are	be	AUX
ejpam-5470	176	69	connected	connect	VERB
ejpam-5470	176	70	to	to	ADP
ejpam-5470	176	71	the	the	DET
ejpam-5470	176	72	vertices	vertex	NOUN
ejpam-5470	176	73	labeled	label	VERB
ejpam-5470	176	74	1	1	NUM
ejpam-5470	176	75	in	in	ADP
ejpam-5470	176	76	pk	pk	NOUN
ejpam-5470	176	77	as	as	SCONJ
ejpam-5470	176	78	given	give	VERB
ejpam-5470	176	79	in	in	ADP
ejpam-5470	176	80	table	table	NOUN
ejpam-5470	176	81	3.2	3.2	NUM
ejpam-5470	176	82	.	.	PUNCT
ejpam-5470	176	83	using	use	VERB
ejpam-5470	176	84	table	table	NOUN
ejpam-5470	176	85	3.3	3.3	NUM
ejpam-5470	176	86	and	and	CCONJ
ejpam-5470	176	87	the	the	DET
ejpam-5470	176	88	formulas	formula	NOUN
ejpam-5470	176	89	v0	v0	NOUN
ejpam-5470	176	90	−	−	PROPN
ejpam-5470	176	91	v1	v1	PROPN
ejpam-5470	176	92	=	=	SYM
ejpam-5470	176	93	(	(	PUNCT
ejpam-5470	176	94	x0	x0	PROPN
ejpam-5470	176	95	−	−	PROPN
ejpam-5470	176	96	x1	x1	PROPN
ejpam-5470	176	97	)	)	PUNCT
ejpam-5470	177	1	+	+	CCONJ
ejpam-5470	177	2	x0.(y0	x0.(y0	ADJ
ejpam-5470	177	3	−	−	PROPN
ejpam-5470	177	4	y1	y1	NOUN
ejpam-5470	177	5	)	)	PUNCT
ejpam-5470	177	6	+	+	CCONJ
ejpam-5470	178	1	x1.(y	x1.(y	NOUN
ejpam-5470	178	2	′	′	NOUN
ejpam-5470	178	3	0	0	NUM
ejpam-5470	179	1	−	−	NUM
ejpam-5470	179	2	y′1	y′1	X
ejpam-5470	179	3	)	)	PUNCT
ejpam-5470	179	4	and	and	CCONJ
ejpam-5470	179	5	e0	e0	PROPN
ejpam-5470	179	6	−	−	PROPN
ejpam-5470	179	7	e1	e1	PROPN
ejpam-5470	179	8	=	=	SYM
ejpam-5470	179	9	(	(	PUNCT
ejpam-5470	179	10	a0	a0	PROPN
ejpam-5470	179	11	−	−	PROPN
ejpam-5470	179	12	a1	a1	PROPN
ejpam-5470	179	13	)	)	PUNCT
ejpam-5470	179	14	+	+	CCONJ
ejpam-5470	179	15	x0.(b0	x0.(b0	PROPN
ejpam-5470	179	16	−	−	NOUN
ejpam-5470	179	17	b1	b1	NOUN
ejpam-5470	179	18	)	)	PUNCT
ejpam-5470	180	1	+	+	PUNCT
ejpam-5470	181	1	x1.(b	x1.(b	PROPN
ejpam-5470	181	2	′	′	NUM
ejpam-5470	181	3	0	0	NUM
ejpam-5470	181	4	−	−	NOUN
ejpam-5470	181	5	b′1	b′1	NOUN
ejpam-5470	181	6	)	)	PUNCT
ejpam-5470	182	1	+	+	CCONJ
ejpam-5470	182	2	x0.(y0	x0.(y0	ADJ
ejpam-5470	182	3	−	−	PROPN
ejpam-5470	182	4	y1	y1	NOUN
ejpam-5470	182	5	)	)	PUNCT
ejpam-5470	182	6	−	−	PROPN
ejpam-5470	183	1	x1.(y	x1.(y	NOUN
ejpam-5470	183	2	′	′	NUM
ejpam-5470	183	3	0	0	NUM
ejpam-5470	184	1	−	−	NUM
ejpam-5470	184	2	y′1	y′1	NOUN
ejpam-5470	184	3	)	)	PUNCT
ejpam-5470	184	4	,	,	PUNCT
ejpam-5470	184	5	we	we	PRON
ejpam-5470	184	6	can	can	AUX
ejpam-5470	184	7	compute	compute	VERB
ejpam-5470	184	8	the	the	DET
ejpam-5470	184	9	values	value	NOUN
ejpam-5470	184	10	shown	show	VERB
ejpam-5470	184	11	in	in	ADP
ejpam-5470	184	12	the	the	DET
ejpam-5470	184	13	last	last	ADJ
ejpam-5470	184	14	two	two	NUM
ejpam-5470	184	15	columns	column	NOUN
ejpam-5470	184	16	of	of	ADP
ejpam-5470	184	17	table	table	NOUN
ejpam-5470	184	18	3.3	3.3	NUM
ejpam-5470	184	19	.	.	PUNCT
ejpam-5470	185	1	we	we	PRON
ejpam-5470	185	2	see	see	VERB
ejpam-5470	185	3	that	that	SCONJ
ejpam-5470	185	4	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	185	5	n.m	n.m	NOUN
ejpam-5470	185	6	is	be	AUX
ejpam-5470	185	7	isomorphic	isomorphic	ADJ
ejpam-5470	185	8	to	to	ADP
ejpam-5470	185	9	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	185	10	m	m	PROPN
ejpam-5470	185	11	,	,	PUNCT
ejpam-5470	185	12	n.	n.	NOUN
ejpam-5470	185	13	since	since	SCONJ
ejpam-5470	185	14	all	all	PRON
ejpam-5470	185	15	of	of	ADP
ejpam-5470	185	16	these	these	DET
ejpam-5470	185	17	values	value	NOUN
ejpam-5470	185	18	are	be	AUX
ejpam-5470	185	19	1	1	NUM
ejpam-5470	185	20	or	or	CCONJ
ejpam-5470	185	21	0	0	NUM
ejpam-5470	185	22	,	,	PUNCT
ejpam-5470	185	23	the	the	DET
ejpam-5470	185	24	lemma	lemma	PROPN
ejpam-5470	185	25	follows	follow	VERB
ejpam-5470	185	26	.	.	PUNCT
ejpam-5470	186	1	a.	a.	PROPN
ejpam-5470	186	2	abd	abd	PROPN
ejpam-5470	186	3	el	el	PROPN
ejpam-5470	186	4	-	-	PROPN
ejpam-5470	186	5	hay	hay	PROPN
ejpam-5470	186	6	et	et	PROPN
ejpam-5470	186	7	al	al	PROPN
ejpam-5470	186	8	.	.	PUNCT
ejpam-5470	186	9	/	/	SYM
ejpam-5470	186	10	eur	eur	PROPN
ejpam-5470	186	11	.	.	PUNCT
ejpam-5470	187	1	j.	j.	PROPN
ejpam-5470	187	2	pure	pure	PROPN
ejpam-5470	187	3	appl	appl	PROPN
ejpam-5470	187	4	.	.	PROPN
ejpam-5470	187	5	math	math	PROPN
ejpam-5470	187	6	,	,	PUNCT
ejpam-5470	187	7	18	18	NUM
ejpam-5470	187	8	(	(	PUNCT
ejpam-5470	187	9	1	1	NUM
ejpam-5470	187	10	)	)	PUNCT
ejpam-5470	187	11	(	(	PUNCT
ejpam-5470	187	12	2025	2025	NUM
ejpam-5470	187	13	)	)	PUNCT
ejpam-5470	187	14	,	,	PUNCT
ejpam-5470	187	15	5470	5470	NUM
ejpam-5470	187	16	6	6	NUM
ejpam-5470	187	17	of	of	ADP
ejpam-5470	187	18	14	14	NUM
ejpam-5470	187	19	table	table	NOUN
ejpam-5470	187	20	3.1.labeling	3.1.labeling	PROPN
ejpam-5470	187	21	of	of	ADP
ejpam-5470	187	22	pk	pk	NOUN
ejpam-5470	187	23	k	k	NOUN
ejpam-5470	187	24	=	=	PUNCT
ejpam-5470	187	25	4r	4r	NOUN
ejpam-5470	187	26	+	+	NUM
ejpam-5470	187	27	i′	i′	NOUN
ejpam-5470	187	28	,	,	PUNCT
ejpam-5470	187	29	i′	i′	VERB
ejpam-5470	187	30	=	=	SYM
ejpam-5470	187	31	0	0	NUM
ejpam-5470	187	32	,	,	PUNCT
ejpam-5470	187	33	1	1	NUM
ejpam-5470	187	34	,	,	PUNCT
ejpam-5470	187	35	2	2	NUM
ejpam-5470	187	36	,	,	PUNCT
ejpam-5470	187	37	3	3	NUM
ejpam-5470	187	38	labeling	labeling	NOUN
ejpam-5470	187	39	of	of	ADP
ejpam-5470	187	40	pk	pk	NOUN
ejpam-5470	188	1	x0	x0	PROPN
ejpam-5470	188	2	x1	x1	PROPN
ejpam-5470	188	3	a0	a0	PROPN
ejpam-5470	188	4	a1	a1	PROPN
ejpam-5470	188	5	i′	i′	NOUN
ejpam-5470	188	6	=	=	SYM
ejpam-5470	188	7	0	0	NUM
ejpam-5470	188	8	a0	a0	NOUN
ejpam-5470	188	9	=	=	PUNCT
ejpam-5470	188	10	l4r	l4r	PROPN
ejpam-5470	188	11	a′	a′	NOUN
ejpam-5470	188	12	0	0	NUM
ejpam-5470	189	1	=	=	SYM
ejpam-5470	189	2	m4r	m4r	NOUN
ejpam-5470	189	3	2r	2r	NUM
ejpam-5470	189	4	2r	2r	NUM
ejpam-5470	189	5	2r	2r	NUM
ejpam-5470	189	6	2r	2r	NUM
ejpam-5470	189	7	2r	2r	NUM
ejpam-5470	189	8	0	0	NUM
ejpam-5470	190	1	2r	2r	NUM
ejpam-5470	190	2	−	−	NOUN
ejpam-5470	190	3	1	1	NUM
ejpam-5470	190	4	4r	4r	NUM
ejpam-5470	190	5	−	−	NOUN
ejpam-5470	190	6	1	1	NUM
ejpam-5470	191	1	i	i	NOUN
ejpam-5470	191	2	=	=	NOUN
ejpam-5470	191	3	1	1	NUM
ejpam-5470	191	4	a1	a1	NOUN
ejpam-5470	191	5	=	=	PUNCT
ejpam-5470	191	6	l4r0	l4r0	PROPN
ejpam-5470	191	7	a′	a′	PROPN
ejpam-5470	191	8	1	1	NUM
ejpam-5470	191	9	=	=	SYM
ejpam-5470	191	10	m4r+1	m4r+1	NOUN
ejpam-5470	191	11	2r	2r	NUM
ejpam-5470	192	1	+	+	CCONJ
ejpam-5470	192	2	1	1	NUM
ejpam-5470	192	3	2r	2r	NUM
ejpam-5470	192	4	+	+	CCONJ
ejpam-5470	192	5	1	1	NUM
ejpam-5470	192	6	2r	2r	NUM
ejpam-5470	192	7	2r	2r	NUM
ejpam-5470	193	1	2r	2r	NUM
ejpam-5470	193	2	0	0	PUNCT
ejpam-5470	194	1	2r	2r	NUM
ejpam-5470	194	2	4r	4r	NUM
ejpam-5470	194	3	i′	i′	NOUN
ejpam-5470	194	4	=	=	SYM
ejpam-5470	194	5	2	2	NUM
ejpam-5470	194	6	a2	a2	NOUN
ejpam-5470	194	7	=	=	SYM
ejpam-5470	194	8	l4r01	l4r01	PROPN
ejpam-5470	194	9	a′	a′	PROPN
ejpam-5470	194	10	2	2	NUM
ejpam-5470	194	11	=	=	SYM
ejpam-5470	194	12	m4r+2	m4r+2	NOUN
ejpam-5470	194	13	a′′	a′′	NOUN
ejpam-5470	194	14	2	2	NUM
ejpam-5470	194	15	=	=	SYM
ejpam-5470	194	16	l4r10	l4r10	NUM
ejpam-5470	194	17	2r	2r	NUM
ejpam-5470	194	18	+	+	CCONJ
ejpam-5470	194	19	1	1	NUM
ejpam-5470	194	20	2r	2r	NUM
ejpam-5470	194	21	+	+	CCONJ
ejpam-5470	194	22	1	1	NUM
ejpam-5470	194	23	2r	2r	NUM
ejpam-5470	194	24	+	+	CCONJ
ejpam-5470	194	25	1	1	NUM
ejpam-5470	194	26	2r	2r	NUM
ejpam-5470	194	27	+	+	CCONJ
ejpam-5470	194	28	1	1	NUM
ejpam-5470	194	29	2r	2r	NUM
ejpam-5470	194	30	+	+	CCONJ
ejpam-5470	194	31	1	1	NUM
ejpam-5470	194	32	2r	2r	NUM
ejpam-5470	194	33	+	+	CCONJ
ejpam-5470	194	34	1	1	NUM
ejpam-5470	194	35	2r	2r	NUM
ejpam-5470	194	36	0	0	NUM
ejpam-5470	195	1	2r	2r	NUM
ejpam-5470	196	1	+	+	CCONJ
ejpam-5470	196	2	1	1	NUM
ejpam-5470	196	3	2r	2r	NUM
ejpam-5470	196	4	+	+	CCONJ
ejpam-5470	196	5	1	1	NUM
ejpam-5470	196	6	4r	4r	NOUN
ejpam-5470	196	7	+	+	CCONJ
ejpam-5470	196	8	1	1	NUM
ejpam-5470	196	9	2r	2r	NUM
ejpam-5470	196	10	i′	i′	NOUN
ejpam-5470	196	11	=	=	SYM
ejpam-5470	196	12	3	3	NUM
ejpam-5470	196	13	a3	a3	NOUN
ejpam-5470	196	14	=	=	PUNCT
ejpam-5470	197	1	l4r001	l4r001	PROPN
ejpam-5470	197	2	a′	a′	PROPN
ejpam-5470	197	3	3	3	NUM
ejpam-5470	197	4	=	=	SYM
ejpam-5470	197	5	m4r+3	m4r+3	NOUN
ejpam-5470	197	6	a′′	a′′	NOUN
ejpam-5470	197	7	3	3	NUM
ejpam-5470	197	8	=	=	SYM
ejpam-5470	197	9	s4r100	s4r100	NOUN
ejpam-5470	197	10	2r	2r	NUM
ejpam-5470	198	1	+	+	CCONJ
ejpam-5470	198	2	2	2	NUM
ejpam-5470	198	3	2r	2r	NUM
ejpam-5470	198	4	+	+	CCONJ
ejpam-5470	198	5	2	2	NUM
ejpam-5470	198	6	2r	2r	NUM
ejpam-5470	198	7	+	+	CCONJ
ejpam-5470	198	8	2	2	NUM
ejpam-5470	198	9	2r	2r	NUM
ejpam-5470	198	10	+	+	CCONJ
ejpam-5470	198	11	1	1	NUM
ejpam-5470	198	12	2r	2r	NUM
ejpam-5470	198	13	+	+	CCONJ
ejpam-5470	198	14	1	1	NUM
ejpam-5470	198	15	2r	2r	NUM
ejpam-5470	198	16	+	+	CCONJ
ejpam-5470	198	17	1	1	NUM
ejpam-5470	198	18	2r	2r	NUM
ejpam-5470	198	19	+	+	CCONJ
ejpam-5470	198	20	1	1	NUM
ejpam-5470	198	21	0	0	NUM
ejpam-5470	198	22	2r	2r	NUM
ejpam-5470	199	1	+	+	CCONJ
ejpam-5470	199	2	1	1	NUM
ejpam-5470	199	3	2r	2r	NUM
ejpam-5470	199	4	+	+	CCONJ
ejpam-5470	199	5	1	1	NUM
ejpam-5470	199	6	4r	4r	NOUN
ejpam-5470	199	7	+	+	CCONJ
ejpam-5470	199	8	2	2	NUM
ejpam-5470	199	9	2r	2r	NUM
ejpam-5470	199	10	+	+	CCONJ
ejpam-5470	199	11	1	1	NUM
ejpam-5470	199	12	table	table	NOUN
ejpam-5470	199	13	3.2.labeling	3.2.labeling	NUM
ejpam-5470	199	14	of	of	ADP
ejpam-5470	199	15	l4	l4	PROPN
ejpam-5470	199	16	n	n	CCONJ
ejpam-5470	199	17	,	,	PUNCT
ejpam-5470	199	18	m	m	VERB
ejpam-5470	199	19	n	n	NOUN
ejpam-5470	199	20	=	=	SYM
ejpam-5470	199	21	4s+	4s+	NUM
ejpam-5470	200	1	i	i	PROPN
ejpam-5470	200	2	,	,	PUNCT
ejpam-5470	200	3	m	m	VERB
ejpam-5470	200	4	=	=	SYM
ejpam-5470	200	5	4t+	4t+	NUM
ejpam-5470	200	6	j	j	PROPN
ejpam-5470	200	7	,	,	PUNCT
ejpam-5470	200	8	i	i	PRON
ejpam-5470	200	9	,	,	PUNCT
ejpam-5470	200	10	j	j	PROPN
ejpam-5470	200	11	=	=	SYM
ejpam-5470	200	12	0	0	NUM
ejpam-5470	200	13	,	,	PUNCT
ejpam-5470	200	14	1	1	NUM
ejpam-5470	200	15	,	,	PUNCT
ejpam-5470	200	16	2	2	NUM
ejpam-5470	200	17	,	,	PUNCT
ejpam-5470	200	18	3	3	NUM
ejpam-5470	200	19	labeling	labeling	NOUN
ejpam-5470	200	20	of	of	ADP
ejpam-5470	200	21	l4	l4	PROPN
ejpam-5470	200	22	n	n	CCONJ
ejpam-5470	200	23	,	,	PUNCT
ejpam-5470	200	24	m	m	VERB
ejpam-5470	200	25	y0	y0	NOUN
ejpam-5470	200	26	y1	y1	NOUN
ejpam-5470	200	27	b0	b0	NOUN
ejpam-5470	200	28	b1	b1	NOUN
ejpam-5470	201	1	i	i	PROPN
ejpam-5470	201	2	,	,	PUNCT
ejpam-5470	201	3	j	j	PROPN
ejpam-5470	201	4	=	=	SYM
ejpam-5470	201	5	0	0	NUM
ejpam-5470	201	6	b00	b00	PROPN
ejpam-5470	201	7	=	=	PUNCT
ejpam-5470	201	8	s′	s′	VERB
ejpam-5470	201	9	4s12	4s12	NOUN
ejpam-5470	201	10	m	m	NOUN
ejpam-5470	201	11	′	′	NUM
ejpam-5470	202	1	4t−603	4t−603	NUM
ejpam-5470	202	2	2s+	2s+	NUM
ejpam-5470	202	3	2	2	NUM
ejpam-5470	202	4	t	t	NOUN
ejpam-5470	202	5	2s+	2s+	NUM
ejpam-5470	203	1	2t−	2t−	NOUN
ejpam-5470	203	2	1	1	NUM
ejpam-5470	203	3	8s+	8s+	NUM
ejpam-5470	203	4	8t−	8t−	NUM
ejpam-5470	203	5	9	9	NUM
ejpam-5470	203	6	8s+	8s+	NUM
ejpam-5470	203	7	8t−	8t−	NUM
ejpam-5470	203	8	9	9	NUM
ejpam-5470	203	9	i	i	PROPN
ejpam-5470	203	10	,	,	PUNCT
ejpam-5470	203	11	j	j	PROPN
ejpam-5470	203	12	=	=	SYM
ejpam-5470	203	13	0	0	NUM
ejpam-5470	203	14	b′	b′	NUM
ejpam-5470	203	15	00	00	NUM
ejpam-5470	203	16	=	=	SYM
ejpam-5470	203	17	l′	l′	VERB
ejpam-5470	203	18	4s02m4t−613	4s02m4t−613	NUM
ejpam-5470	203	19	2s+	2s+	NUM
ejpam-5470	204	1	2t−	2t−	SYM
ejpam-5470	204	2	1	1	NUM
ejpam-5470	204	3	2s+	2s+	NUM
ejpam-5470	204	4	2	2	NUM
ejpam-5470	204	5	t	t	NOUN
ejpam-5470	204	6	8s+	8s+	NUM
ejpam-5470	205	1	8t−	8t−	NUM
ejpam-5470	205	2	9	9	NUM
ejpam-5470	205	3	8s+	8s+	NUM
ejpam-5470	206	1	8t−	8t−	NUM
ejpam-5470	206	2	9	9	NUM
ejpam-5470	206	3	i	i	NOUN
ejpam-5470	206	4	=	=	PUNCT
ejpam-5470	206	5	0	0	PROPN
ejpam-5470	206	6	,	,	PUNCT
ejpam-5470	206	7	j	j	NOUN
ejpam-5470	206	8	=	=	SYM
ejpam-5470	206	9	1	1	NUM
ejpam-5470	206	10	b01	b01	NOUN
ejpam-5470	206	11	=	=	SYM
ejpam-5470	206	12	13m4s−603l4t−4013	13m4s−603l4t−4013	PROPN
ejpam-5470	206	13	2s+	2s+	NUM
ejpam-5470	207	1	2t−	2t−	NOUN
ejpam-5470	207	2	1	1	NUM
ejpam-5470	207	3	2s+	2s+	NUM
ejpam-5470	207	4	2t+	2t+	NUM
ejpam-5470	207	5	1	1	NUM
ejpam-5470	207	6	8s+	8s+	NUM
ejpam-5470	207	7	8t−	8t−	NUM
ejpam-5470	207	8	6	6	NUM
ejpam-5470	207	9	8s+	8s+	NUM
ejpam-5470	208	1	8t−	8t−	NUM
ejpam-5470	208	2	8	8	NUM
ejpam-5470	208	3	i	i	NOUN
ejpam-5470	208	4	=	=	NOUN
ejpam-5470	208	5	0	0	PROPN
ejpam-5470	208	6	,	,	PUNCT
ejpam-5470	208	7	j	j	NOUN
ejpam-5470	208	8	=	=	SYM
ejpam-5470	208	9	1	1	NUM
ejpam-5470	208	10	b01	b01	NOUN
ejpam-5470	208	11	=	=	SYM
ejpam-5470	208	12	03	03	NUM
ejpam-5470	208	13	m	m	VERB
ejpam-5470	208	14	′	′	NUM
ejpam-5470	208	15	4s−613s4t−4103	4s−613s4t−4103	NUM
ejpam-5470	208	16	2s+	2s+	NUM
ejpam-5470	208	17	2t+	2t+	NUM
ejpam-5470	208	18	1	1	NUM
ejpam-5470	208	19	2s+	2s+	NUM
ejpam-5470	208	20	2t−	2t−	NOUN
ejpam-5470	208	21	1	1	NUM
ejpam-5470	208	22	8s+	8s+	NUM
ejpam-5470	208	23	8t−	8t−	NUM
ejpam-5470	208	24	6	6	NUM
ejpam-5470	208	25	8s+	8s+	NUM
ejpam-5470	209	1	8t−	8t−	NUM
ejpam-5470	209	2	8	8	NUM
ejpam-5470	209	3	i	i	NOUN
ejpam-5470	209	4	=	=	NOUN
ejpam-5470	209	5	0	0	PROPN
ejpam-5470	209	6	,	,	PUNCT
ejpam-5470	209	7	j	j	PROPN
ejpam-5470	209	8	=	=	SYM
ejpam-5470	209	9	2	2	NUM
ejpam-5470	209	10	b02	b02	NOUN
ejpam-5470	209	11	=	=	PUNCT
ejpam-5470	209	12	s′	s′	PUNCT
ejpam-5470	209	13	4s013m4t−403	4s013m4t−403	NUM
ejpam-5470	209	14	2s+	2s+	NUM
ejpam-5470	209	15	2t+	2t+	NUM
ejpam-5470	209	16	1	1	NUM
ejpam-5470	209	17	2s+	2s+	NUM
ejpam-5470	209	18	2	2	NUM
ejpam-5470	209	19	t	t	NOUN
ejpam-5470	209	20	8s+	8s+	NUM
ejpam-5470	210	1	8t−	8t−	NUM
ejpam-5470	210	2	5	5	NUM
ejpam-5470	210	3	8s+	8s+	NUM
ejpam-5470	210	4	8t−	8t−	NUM
ejpam-5470	210	5	5	5	NUM
ejpam-5470	211	1	i	i	NOUN
ejpam-5470	211	2	=	=	NOUN
ejpam-5470	211	3	0	0	PROPN
ejpam-5470	211	4	,	,	PUNCT
ejpam-5470	211	5	j	j	NOUN
ejpam-5470	211	6	=	=	SYM
ejpam-5470	211	7	2	2	NUM
ejpam-5470	211	8	b′	b′	NUM
ejpam-5470	211	9	02	02	NUM
ejpam-5470	211	10	=	=	NUM
ejpam-5470	211	11	l′	l′	NOUN
ejpam-5470	211	12	4s103	4s103	NUM
ejpam-5470	211	13	m	m	NOUN
ejpam-5470	211	14	′	′	NUM
ejpam-5470	211	15	4t−413	4t−413	NUM
ejpam-5470	211	16	2s+	2s+	NUM
ejpam-5470	211	17	2	2	NUM
ejpam-5470	211	18	t	t	NOUN
ejpam-5470	211	19	2s+	2s+	NUM
ejpam-5470	211	20	2t+	2t+	NUM
ejpam-5470	211	21	1	1	NUM
ejpam-5470	211	22	8s+	8s+	NUM
ejpam-5470	211	23	8t−	8t−	NUM
ejpam-5470	211	24	5	5	NUM
ejpam-5470	211	25	8s+	8s+	NUM
ejpam-5470	212	1	8t−	8t−	NUM
ejpam-5470	212	2	5	5	NUM
ejpam-5470	213	1	i	i	NOUN
ejpam-5470	213	2	=	=	NOUN
ejpam-5470	213	3	0	0	PROPN
ejpam-5470	213	4	,	,	PUNCT
ejpam-5470	213	5	j	j	NOUN
ejpam-5470	213	6	=	=	SYM
ejpam-5470	213	7	3	3	NUM
ejpam-5470	213	8	b03	b03	NOUN
ejpam-5470	213	9	=	=	PUNCT
ejpam-5470	213	10	13m4s−603l	13m4s−603l	NUM
ejpam-5470	213	11	′	′	NOUN
ejpam-5470	213	12	4t−413010	4t−413010	NOUN
ejpam-5470	213	13	2s+	2s+	NUM
ejpam-5470	213	14	2	2	NUM
ejpam-5470	213	15	t	t	NOUN
ejpam-5470	213	16	2s+	2s+	NUM
ejpam-5470	213	17	2t+	2t+	NUM
ejpam-5470	213	18	2	2	NUM
ejpam-5470	213	19	8s+	8s+	NUM
ejpam-5470	213	20	8t−	8t−	NUM
ejpam-5470	213	21	2	2	NUM
ejpam-5470	213	22	8s+	8s+	NUM
ejpam-5470	214	1	8t−	8t−	NUM
ejpam-5470	214	2	4	4	NUM
ejpam-5470	214	3	i	i	NOUN
ejpam-5470	214	4	=	=	NOUN
ejpam-5470	214	5	0	0	PROPN
ejpam-5470	214	6	,	,	PUNCT
ejpam-5470	214	7	j	j	X
ejpam-5470	214	8	=	=	SYM
ejpam-5470	214	9	3	3	NUM
ejpam-5470	214	10	b′	b′	NUM
ejpam-5470	214	11	03	03	NUM
ejpam-5470	215	1	=	=	SYM
ejpam-5470	215	2	03	03	NUM
ejpam-5470	215	3	m	m	VERB
ejpam-5470	215	4	′	′	NUM
ejpam-5470	215	5	4s−613s	4s−613s	NUM
ejpam-5470	216	1	′	′	NUM
ejpam-5470	217	1	4t−403101	4t−403101	NOUN
ejpam-5470	217	2	2s+	2s+	NUM
ejpam-5470	217	3	2t+	2t+	NUM
ejpam-5470	217	4	2	2	NUM
ejpam-5470	217	5	2s+	2s+	NUM
ejpam-5470	217	6	2	2	NUM
ejpam-5470	217	7	t	t	NOUN
ejpam-5470	217	8	8s+	8s+	NUM
ejpam-5470	218	1	8t−	8t−	NUM
ejpam-5470	218	2	2	2	NUM
ejpam-5470	218	3	8s+	8s+	NUM
ejpam-5470	219	1	8t−	8t−	NUM
ejpam-5470	219	2	4	4	NUM
ejpam-5470	219	3	i	i	PROPN
ejpam-5470	219	4	,	,	PUNCT
ejpam-5470	219	5	j	j	PROPN
ejpam-5470	219	6	=	=	SYM
ejpam-5470	219	7	1	1	NUM
ejpam-5470	219	8	b11	b11	NOUN
ejpam-5470	219	9	=	=	SYM
ejpam-5470	219	10	l4s02l	l4s02l	PROPN
ejpam-5470	219	11	′	′	NOUN
ejpam-5470	219	12	4t−413	4t−413	NUM
ejpam-5470	219	13	2s+	2s+	NUM
ejpam-5470	219	14	2	2	NUM
ejpam-5470	219	15	t	t	NOUN
ejpam-5470	219	16	2s+	2s+	NUM
ejpam-5470	220	1	2t−	2t−	NOUN
ejpam-5470	220	2	1	1	NUM
ejpam-5470	220	3	8s+	8s+	NUM
ejpam-5470	220	4	8t−	8t−	NUM
ejpam-5470	220	5	5	5	NUM
ejpam-5470	220	6	8s+	8s+	NUM
ejpam-5470	220	7	8t−	8t−	NUM
ejpam-5470	220	8	5	5	NUM
ejpam-5470	220	9	i	i	PROPN
ejpam-5470	220	10	,	,	PUNCT
ejpam-5470	220	11	j	j	PROPN
ejpam-5470	220	12	=	=	SYM
ejpam-5470	220	13	1	1	NUM
ejpam-5470	220	14	b′	b′	NUM
ejpam-5470	220	15	11	11	NUM
ejpam-5470	220	16	=	=	SYM
ejpam-5470	221	1	s4s12s	s4s12s	ADJ
ejpam-5470	221	2	′	′	NUM
ejpam-5470	221	3	4t−403	4t−403	NUM
ejpam-5470	221	4	2s+	2s+	NUM
ejpam-5470	222	1	2t−	2t−	NOUN
ejpam-5470	222	2	1	1	NUM
ejpam-5470	222	3	2s+	2s+	NUM
ejpam-5470	222	4	2	2	NUM
ejpam-5470	222	5	t	t	NOUN
ejpam-5470	222	6	8s+	8s+	NUM
ejpam-5470	223	1	8t−	8t−	NUM
ejpam-5470	223	2	5	5	NUM
ejpam-5470	223	3	8s+	8s+	NUM
ejpam-5470	223	4	8t−	8t−	NUM
ejpam-5470	223	5	5	5	NUM
ejpam-5470	224	1	i	i	NOUN
ejpam-5470	224	2	=	=	NOUN
ejpam-5470	224	3	1	1	NUM
ejpam-5470	224	4	,	,	PUNCT
ejpam-5470	224	5	j	j	NOUN
ejpam-5470	224	6	=	=	SYM
ejpam-5470	224	7	2	2	NUM
ejpam-5470	224	8	b12	b12	NOUN
ejpam-5470	224	9	=	=	SYM
ejpam-5470	224	10	13l	13l	NUM
ejpam-5470	224	11	′	′	NUM
ejpam-5470	224	12	4s−4041013m4t−6	4s−4041013m4t−6	PROPN
ejpam-5470	225	1	2s+	2s+	NUM
ejpam-5470	225	2	2	2	NUM
ejpam-5470	225	3	t	t	NOUN
ejpam-5470	225	4	2s+	2s+	NUM
ejpam-5470	225	5	2t+	2t+	NUM
ejpam-5470	225	6	2	2	NUM
ejpam-5470	225	7	8s+	8s+	NUM
ejpam-5470	225	8	8t−	8t−	NUM
ejpam-5470	225	9	2	2	NUM
ejpam-5470	225	10	8s+	8s+	NUM
ejpam-5470	226	1	8t−	8t−	NUM
ejpam-5470	226	2	4	4	NUM
ejpam-5470	226	3	i	i	NOUN
ejpam-5470	226	4	=	=	NOUN
ejpam-5470	226	5	1	1	NUM
ejpam-5470	226	6	,	,	PUNCT
ejpam-5470	226	7	j	j	NOUN
ejpam-5470	226	8	=	=	SYM
ejpam-5470	226	9	2	2	NUM
ejpam-5470	226	10	b′	b′	NUM
ejpam-5470	226	11	12	12	NUM
ejpam-5470	226	12	=	=	SYM
ejpam-5470	226	13	03s	03	NOUN
ejpam-5470	226	14	′	′	NUM
ejpam-5470	227	1	4s−4140103	4s−4140103	NUM
ejpam-5470	227	2	m	m	NOUN
ejpam-5470	227	3	′	′	NUM
ejpam-5470	227	4	4t−6	4t−6	PROPN
ejpam-5470	228	1	2s+	2s+	NUM
ejpam-5470	228	2	2t+	2t+	NUM
ejpam-5470	228	3	2	2	NUM
ejpam-5470	228	4	2s+	2s+	NUM
ejpam-5470	228	5	2	2	NUM
ejpam-5470	228	6	t	t	NOUN
ejpam-5470	228	7	8s+	8s+	NUM
ejpam-5470	229	1	8t−	8t−	NUM
ejpam-5470	229	2	2	2	NUM
ejpam-5470	229	3	8s+	8s+	NUM
ejpam-5470	229	4	8t−	8t−	NUM
ejpam-5470	229	5	4	4	NUM
ejpam-5470	229	6	i	i	NOUN
ejpam-5470	229	7	=	=	NOUN
ejpam-5470	229	8	1	1	NUM
ejpam-5470	229	9	,	,	PUNCT
ejpam-5470	229	10	j	j	NOUN
ejpam-5470	229	11	=	=	SYM
ejpam-5470	229	12	3	3	NUM
ejpam-5470	229	13	b13	b13	NOUN
ejpam-5470	229	14	=	=	SYM
ejpam-5470	229	15	13l	13l	NUM
ejpam-5470	229	16	′	′	NUM
ejpam-5470	229	17	4s−40210l	4s−40210l	NUM
ejpam-5470	230	1	′	′	NUM
ejpam-5470	230	2	4t−4	4t−4	NOUN
ejpam-5470	230	3	2s+	2s+	NUM
ejpam-5470	230	4	2t+	2t+	NUM
ejpam-5470	230	5	1	1	NUM
ejpam-5470	230	6	2s+	2s+	NUM
ejpam-5470	230	7	2t+	2t+	NUM
ejpam-5470	230	8	2	2	NUM
ejpam-5470	230	9	8s+	8s+	NUM
ejpam-5470	230	10	8t−	8t−	NUM
ejpam-5470	230	11	1	1	NUM
ejpam-5470	230	12	8s+	8s+	NUM
ejpam-5470	231	1	8t−	8t−	NUM
ejpam-5470	231	2	1	1	NUM
ejpam-5470	231	3	i	i	NOUN
ejpam-5470	231	4	=	=	NOUN
ejpam-5470	231	5	1	1	NUM
ejpam-5470	231	6	,	,	PUNCT
ejpam-5470	231	7	j	j	NOUN
ejpam-5470	231	8	=	=	SYM
ejpam-5470	231	9	3	3	NUM
ejpam-5470	231	10	b′	b′	NUM
ejpam-5470	231	11	13	13	NUM
ejpam-5470	231	12	=	=	SYM
ejpam-5470	231	13	03s4s−41201s4t−4	03s4s−41201s4t−4	NOUN
ejpam-5470	231	14	2s+	2s+	NUM
ejpam-5470	231	15	2t+	2t+	NUM
ejpam-5470	231	16	2	2	NUM
ejpam-5470	231	17	2s+	2s+	NUM
ejpam-5470	231	18	2t+	2t+	NUM
ejpam-5470	231	19	1	1	NUM
ejpam-5470	231	20	8s+	8s+	NUM
ejpam-5470	231	21	8t−	8t−	NUM
ejpam-5470	231	22	1	1	NUM
ejpam-5470	231	23	8s+	8s+	NUM
ejpam-5470	231	24	8t−	8t−	NUM
ejpam-5470	231	25	1	1	NUM
ejpam-5470	231	26	i	i	PROPN
ejpam-5470	231	27	,	,	PUNCT
ejpam-5470	231	28	j	j	PROPN
ejpam-5470	231	29	=	=	SYM
ejpam-5470	231	30	2	2	NUM
ejpam-5470	231	31	b22	b22	PROPN
ejpam-5470	231	32	=	=	PUNCT
ejpam-5470	231	33	0313l	0313l	NUM
ejpam-5470	231	34	′	′	NUM
ejpam-5470	231	35	4s−4021013m4t−6	4s−4021013m4t−6	PROPN
ejpam-5470	231	36	2s+	2s+	NUM
ejpam-5470	231	37	2t+	2t+	NUM
ejpam-5470	231	38	1	1	NUM
ejpam-5470	231	39	2s+	2s+	NUM
ejpam-5470	231	40	2t+	2t+	NUM
ejpam-5470	231	41	2	2	NUM
ejpam-5470	231	42	8s+	8s+	NUM
ejpam-5470	231	43	8t−	8t−	NUM
ejpam-5470	231	44	1	1	NUM
ejpam-5470	231	45	8s+	8s+	NUM
ejpam-5470	231	46	8t−	8t−	NUM
ejpam-5470	231	47	1	1	NUM
ejpam-5470	231	48	i	i	PROPN
ejpam-5470	231	49	,	,	PUNCT
ejpam-5470	231	50	j	j	PROPN
ejpam-5470	231	51	=	=	SYM
ejpam-5470	231	52	2	2	NUM
ejpam-5470	231	53	b′	b′	NUM
ejpam-5470	231	54	22	22	NUM
ejpam-5470	231	55	=	=	SYM
ejpam-5470	231	56	1303s	1303s	NUM
ejpam-5470	231	57	′	′	NUM
ejpam-5470	231	58	4s−4120103	4s−4120103	NUM
ejpam-5470	231	59	m	m	VERB
ejpam-5470	231	60	′	′	NUM
ejpam-5470	231	61	4t−6	4t−6	PROPN
ejpam-5470	231	62	2s+	2s+	NUM
ejpam-5470	231	63	2t+	2t+	NUM
ejpam-5470	231	64	2	2	NUM
ejpam-5470	231	65	2s+	2s+	NUM
ejpam-5470	231	66	2t+	2t+	NUM
ejpam-5470	231	67	1	1	NUM
ejpam-5470	231	68	8s+	8s+	NUM
ejpam-5470	231	69	8t−	8t−	NUM
ejpam-5470	231	70	1	1	NUM
ejpam-5470	231	71	8s+	8s+	NUM
ejpam-5470	231	72	8t−	8t−	NUM
ejpam-5470	231	73	1	1	NUM
ejpam-5470	231	74	i	i	NOUN
ejpam-5470	231	75	=	=	NOUN
ejpam-5470	231	76	2	2	NUM
ejpam-5470	231	77	,	,	PUNCT
ejpam-5470	231	78	j	j	NOUN
ejpam-5470	231	79	=	=	SYM
ejpam-5470	231	80	3	3	NUM
ejpam-5470	231	81	b33	b33	NOUN
ejpam-5470	231	82	=	=	SYM
ejpam-5470	231	83	031013m4s−60l	031013m4s−60l	NOUN
ejpam-5470	231	84	′	′	NUM
ejpam-5470	232	1	4s−41	4s−41	NUM
ejpam-5470	232	2	2s+	2s+	NUM
ejpam-5470	232	3	2t+	2t+	NUM
ejpam-5470	232	4	2	2	NUM
ejpam-5470	232	5	2s+	2s+	NUM
ejpam-5470	232	6	2t+	2t+	NUM
ejpam-5470	232	7	2	2	NUM
ejpam-5470	232	8	8s+	8s+	NUM
ejpam-5470	232	9	8t+	8t+	NUM
ejpam-5470	232	10	1	1	NUM
ejpam-5470	232	11	8s+	8s+	NUM
ejpam-5470	232	12	8t+	8t+	NUM
ejpam-5470	232	13	1	1	NUM
ejpam-5470	232	14	i	i	NOUN
ejpam-5470	232	15	=	=	NOUN
ejpam-5470	232	16	2	2	NUM
ejpam-5470	232	17	,	,	PUNCT
ejpam-5470	232	18	j	j	NOUN
ejpam-5470	232	19	=	=	SYM
ejpam-5470	232	20	3	3	NUM
ejpam-5470	232	21	b33	b33	NOUN
ejpam-5470	232	22	=	=	PUNCT
ejpam-5470	232	23	130103	130103	NUM
ejpam-5470	232	24	m	m	NOUN
ejpam-5470	232	25	′	′	NUM
ejpam-5470	232	26	4s−61s	4s−61s	NUM
ejpam-5470	233	1	′	′	NUM
ejpam-5470	234	1	4s−40	4s−40	NOUN
ejpam-5470	235	1	2s+	2s+	NUM
ejpam-5470	235	2	2t+	2t+	NUM
ejpam-5470	235	3	2	2	NUM
ejpam-5470	235	4	2s+	2s+	NUM
ejpam-5470	235	5	2t+	2t+	NUM
ejpam-5470	235	6	2	2	NUM
ejpam-5470	235	7	8s+	8s+	NUM
ejpam-5470	235	8	8t+	8t+	NUM
ejpam-5470	235	9	1	1	NUM
ejpam-5470	235	10	8s+	8s+	NUM
ejpam-5470	235	11	8t+	8t+	NUM
ejpam-5470	235	12	1	1	NUM
ejpam-5470	235	13	i	i	PROPN
ejpam-5470	235	14	,	,	PUNCT
ejpam-5470	235	15	j	j	PROPN
ejpam-5470	235	16	=	=	SYM
ejpam-5470	235	17	3	3	NUM
ejpam-5470	235	18	b′	b′	NUM
ejpam-5470	235	19	33	33	NUM
ejpam-5470	235	20	=	=	SYM
ejpam-5470	235	21	02	02	NUM
ejpam-5470	235	22	m	m	NOUN
ejpam-5470	235	23	′	′	NUM
ejpam-5470	235	24	4s−213s	4s−213s	NOUN
ejpam-5470	235	25	′	′	NUM
ejpam-5470	236	1	4t−403101	4t−403101	NOUN
ejpam-5470	236	2	2s+	2s+	NUM
ejpam-5470	236	3	2t+	2t+	NUM
ejpam-5470	236	4	3	3	NUM
ejpam-5470	236	5	2s+	2s+	NUM
ejpam-5470	236	6	2t+	2t+	NUM
ejpam-5470	236	7	2	2	NUM
ejpam-5470	236	8	8s+	8s+	NUM
ejpam-5470	236	9	8t+	8t+	NUM
ejpam-5470	236	10	3	3	NUM
ejpam-5470	236	11	8s+	8s+	NUM
ejpam-5470	236	12	8t+	8t+	NUM
ejpam-5470	236	13	3	3	NUM
ejpam-5470	236	14	i	i	PROPN
ejpam-5470	236	15	,	,	PUNCT
ejpam-5470	236	16	j	j	PROPN
ejpam-5470	236	17	=	=	SYM
ejpam-5470	236	18	3	3	NUM
ejpam-5470	236	19	b33	b33	NOUN
ejpam-5470	236	20	=	=	NOUN
ejpam-5470	236	21	12m4s−203l	12m4s−203l	NOUN
ejpam-5470	236	22	′	′	NUM
ejpam-5470	236	23	4t−413010	4t−413010	NUM
ejpam-5470	236	24	2s+	2s+	NUM
ejpam-5470	236	25	2t+	2t+	NUM
ejpam-5470	236	26	2	2	NUM
ejpam-5470	236	27	2s+	2s+	NUM
ejpam-5470	236	28	2t+	2t+	NUM
ejpam-5470	236	29	3	3	NUM
ejpam-5470	236	30	8s+	8s+	NUM
ejpam-5470	236	31	8t+	8t+	NUM
ejpam-5470	236	32	3	3	NUM
ejpam-5470	236	33	8s+	8s+	NUM
ejpam-5470	236	34	8t+	8t+	NUM
ejpam-5470	236	35	3	3	NUM
ejpam-5470	236	36	a.	a.	NOUN
ejpam-5470	236	37	abd	abd	PROPN
ejpam-5470	236	38	el	el	PROPN
ejpam-5470	236	39	-	-	PROPN
ejpam-5470	236	40	hay	hay	PROPN
ejpam-5470	236	41	et	et	PROPN
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ejpam-5470	236	43	.	.	PUNCT
ejpam-5470	236	44	/	/	SYM
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ejpam-5470	236	46	.	.	PUNCT
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ejpam-5470	237	2	pure	pure	PROPN
ejpam-5470	237	3	appl	appl	PROPN
ejpam-5470	237	4	.	.	PROPN
ejpam-5470	237	5	math	math	PROPN
ejpam-5470	237	6	,	,	PUNCT
ejpam-5470	237	7	18	18	NUM
ejpam-5470	237	8	(	(	PUNCT
ejpam-5470	237	9	1	1	NUM
ejpam-5470	237	10	)	)	PUNCT
ejpam-5470	237	11	(	(	PUNCT
ejpam-5470	237	12	2025	2025	NUM
ejpam-5470	237	13	)	)	PUNCT
ejpam-5470	237	14	,	,	PUNCT
ejpam-5470	237	15	5470	5470	NUM
ejpam-5470	237	16	7	7	NUM
ejpam-5470	237	17	of	of	ADP
ejpam-5470	237	18	14	14	NUM
ejpam-5470	237	19	table	table	NOUN
ejpam-5470	237	20	3.3.labeling	3.3.labeling	NUM
ejpam-5470	237	21	of	of	ADP
ejpam-5470	237	22	pk	pk	PROPN
ejpam-5470	237	23	⊙	⊙	PROPN
ejpam-5470	237	24	l4	l4	PROPN
ejpam-5470	237	25	n	n	CCONJ
ejpam-5470	237	26	,	,	PUNCT
ejpam-5470	237	27	m	m	VERB
ejpam-5470	237	28	i	i	PRON
ejpam-5470	237	29	ij	ij	INTJ
ejpam-5470	237	30	pk	pk	PROPN
ejpam-5470	237	31	l4	l4	PROPN
ejpam-5470	237	32	n	n	CCONJ
ejpam-5470	237	33	,	,	PUNCT
ejpam-5470	237	34	m	m	PROPN
ejpam-5470	237	35	|v0	|v0	NOUN
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ejpam-5470	238	2	v1|	v1|	ADJ
ejpam-5470	238	3	|e0	|e0	NOUN
ejpam-5470	238	4	−	−	PROPN
ejpam-5470	238	5	e1|	e1|	NOUN
ejpam-5470	238	6	0	0	NUM
ejpam-5470	238	7	00	00	NUM
ejpam-5470	238	8	a′	a′	PROPN
ejpam-5470	238	9	0	0	NUM
ejpam-5470	238	10	b00	b00	PROPN
ejpam-5470	238	11	,	,	PUNCT
ejpam-5470	238	12	b	b	NOUN
ejpam-5470	238	13	′	′	NUM
ejpam-5470	238	14	00	00	NUM
ejpam-5470	238	15	,	,	PUNCT
ejpam-5470	238	16	b00	b00	NOUN
ejpam-5470	238	17	,	,	PUNCT
ejpam-5470	238	18	b	b	NOUN
ejpam-5470	238	19	′	′	NUM
ejpam-5470	238	20	00	00	NUM
ejpam-5470	238	21	0	0	NUM
ejpam-5470	238	22	1	1	NUM
ejpam-5470	238	23	1	1	NUM
ejpam-5470	238	24	00	00	NUM
ejpam-5470	238	25	a′	a′	PROPN
ejpam-5470	238	26	1	1	NUM
ejpam-5470	238	27	b00	b00	NOUN
ejpam-5470	238	28	,	,	PUNCT
ejpam-5470	238	29	b	b	NOUN
ejpam-5470	238	30	′	′	NUM
ejpam-5470	238	31	00	00	NUM
ejpam-5470	238	32	,	,	PUNCT
ejpam-5470	238	33	b00	b00	NOUN
ejpam-5470	238	34	,	,	PUNCT
ejpam-5470	238	35	b	b	NOUN
ejpam-5470	238	36	′	′	NOUN
ejpam-5470	238	37	00	00	NUM
ejpam-5470	238	38	,	,	PUNCT
ejpam-5470	238	39	...	...	PUNCT
ejpam-5470	238	40	,	,	PUNCT
ejpam-5470	238	41	b	b	X
ejpam-5470	238	42	′	′	NUM
ejpam-5470	238	43	00	00	NUM
ejpam-5470	238	44	0	0	NUM
ejpam-5470	238	45	1	1	NUM
ejpam-5470	238	46	2	2	NUM
ejpam-5470	238	47	00	00	NUM
ejpam-5470	238	48	a′	a′	PROPN
ejpam-5470	238	49	2	2	NUM
ejpam-5470	238	50	b00	b00	NOUN
ejpam-5470	238	51	,	,	PUNCT
ejpam-5470	238	52	b	b	NOUN
ejpam-5470	238	53	′	′	NUM
ejpam-5470	238	54	00	00	NUM
ejpam-5470	238	55	,	,	PUNCT
ejpam-5470	238	56	b00	b00	NOUN
ejpam-5470	238	57	,	,	PUNCT
ejpam-5470	238	58	b	b	NOUN
ejpam-5470	238	59	′	′	NOUN
ejpam-5470	238	60	00	00	NUM
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ejpam-5470	238	63	,	,	PUNCT
ejpam-5470	238	64	b00	b00	NOUN
ejpam-5470	238	65	,	,	PUNCT
ejpam-5470	238	66	b	b	NOUN
ejpam-5470	238	67	′	′	NUM
ejpam-5470	238	68	00	00	NUM
ejpam-5470	238	69	0	0	NUM
ejpam-5470	238	70	1	1	NUM
ejpam-5470	238	71	3	3	NUM
ejpam-5470	238	72	00	00	NUM
ejpam-5470	238	73	a′	a′	PROPN
ejpam-5470	238	74	3	3	NUM
ejpam-5470	238	75	b00	b00	NOUN
ejpam-5470	238	76	,	,	PUNCT
ejpam-5470	238	77	b	b	NOUN
ejpam-5470	238	78	′	′	NUM
ejpam-5470	238	79	00	00	NUM
ejpam-5470	238	80	,	,	PUNCT
ejpam-5470	238	81	b00	b00	NOUN
ejpam-5470	238	82	,	,	PUNCT
ejpam-5470	238	83	b	b	NOUN
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ejpam-5470	238	85	00	00	NUM
ejpam-5470	238	86	,	,	PUNCT
ejpam-5470	238	87	...	...	PUNCT
ejpam-5470	238	88	,	,	PUNCT
ejpam-5470	238	89	b00	b00	NOUN
ejpam-5470	238	90	,	,	PUNCT
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ejpam-5470	238	94	,	,	PUNCT
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ejpam-5470	238	96	′	′	NUM
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ejpam-5470	238	99	1	1	NUM
ejpam-5470	238	100	0	0	NUM
ejpam-5470	238	101	01	01	NUM
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ejpam-5470	238	103	b01	b01	NOUN
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ejpam-5470	238	108	′	′	NUM
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ejpam-5470	238	115	1	1	NUM
ejpam-5470	238	116	1	1	NUM
ejpam-5470	238	117	01	01	NUM
ejpam-5470	238	118	a1	a1	NOUN
ejpam-5470	238	119	b01	b01	NOUN
ejpam-5470	238	120	,	,	PUNCT
ejpam-5470	238	121	b01	b01	NOUN
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ejpam-5470	238	124	′	′	NUM
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ejpam-5470	238	130	,	,	PUNCT
ejpam-5470	238	131	...	...	PUNCT
ejpam-5470	238	132	,	,	PUNCT
ejpam-5470	238	133	b01	b01	NOUN
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ejpam-5470	238	136	2	2	NUM
ejpam-5470	238	137	01	01	NUM
ejpam-5470	238	138	a2	a2	PROPN
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ejpam-5470	238	140	,	,	PUNCT
ejpam-5470	238	141	b01	b01	NOUN
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ejpam-5470	238	144	′	′	NUM
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ejpam-5470	238	150	,	,	PUNCT
ejpam-5470	238	151	...	...	PUNCT
ejpam-5470	238	152	,	,	PUNCT
ejpam-5470	238	153	b01	b01	NOUN
ejpam-5470	238	154	,	,	PUNCT
ejpam-5470	238	155	b	b	NOUN
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ejpam-5470	238	159	1	1	NUM
ejpam-5470	238	160	3	3	NUM
ejpam-5470	238	161	01	01	NUM
ejpam-5470	238	162	a3	a3	NOUN
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ejpam-5470	238	168	′	′	NUM
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ejpam-5470	238	172	′	′	NOUN
ejpam-5470	238	173	01	01	NUM
ejpam-5470	238	174	,	,	PUNCT
ejpam-5470	238	175	...	...	PUNCT
ejpam-5470	238	176	,	,	PUNCT
ejpam-5470	238	177	b01	b01	NOUN
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ejpam-5470	238	179	b01	b01	NOUN
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ejpam-5470	238	181	b	b	NOUN
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ejpam-5470	238	188	a′	a′	PROPN
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ejpam-5470	238	193	′	′	NUM
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ejpam-5470	238	196	b02	b02	PROPN
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ejpam-5470	238	198	b	b	NOUN
ejpam-5470	238	199	′	′	NUM
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ejpam-5470	238	202	1	1	NUM
ejpam-5470	238	203	1	1	NUM
ejpam-5470	238	204	02	02	NUM
ejpam-5470	238	205	a′	a′	PROPN
ejpam-5470	238	206	1	1	NUM
ejpam-5470	238	207	b02	b02	PROPN
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ejpam-5470	238	209	b	b	NOUN
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ejpam-5470	238	633	b	b	NOUN
ejpam-5470	238	634	′	′	NOUN
ejpam-5470	238	635	13	13	NUM
ejpam-5470	238	636	,	,	PUNCT
ejpam-5470	238	637	b	b	NOUN
ejpam-5470	238	638	′	′	NOUN
ejpam-5470	238	639	13	13	NUM
ejpam-5470	238	640	0	0	NUM
ejpam-5470	238	641	1	1	NUM
ejpam-5470	238	642	a.	a.	NOUN
ejpam-5470	238	643	abd	abd	PROPN
ejpam-5470	238	644	el	el	PROPN
ejpam-5470	238	645	-	-	PROPN
ejpam-5470	238	646	hay	hay	PROPN
ejpam-5470	238	647	et	et	PROPN
ejpam-5470	238	648	al	al	PROPN
ejpam-5470	238	649	.	.	PUNCT
ejpam-5470	238	650	/	/	SYM
ejpam-5470	238	651	eur	eur	PROPN
ejpam-5470	238	652	.	.	PUNCT
ejpam-5470	239	1	j.	j.	PROPN
ejpam-5470	239	2	pure	pure	PROPN
ejpam-5470	239	3	appl	appl	PROPN
ejpam-5470	239	4	.	.	PROPN
ejpam-5470	239	5	math	math	PROPN
ejpam-5470	239	6	,	,	PUNCT
ejpam-5470	239	7	18	18	NUM
ejpam-5470	239	8	(	(	PUNCT
ejpam-5470	239	9	1	1	NUM
ejpam-5470	239	10	)	)	PUNCT
ejpam-5470	239	11	(	(	PUNCT
ejpam-5470	239	12	2025	2025	NUM
ejpam-5470	239	13	)	)	PUNCT
ejpam-5470	239	14	,	,	PUNCT
ejpam-5470	239	15	5470	5470	NUM
ejpam-5470	239	16	8	8	NUM
ejpam-5470	239	17	of	of	ADP
ejpam-5470	239	18	14	14	NUM
ejpam-5470	240	1	i	i	PRON
ejpam-5470	240	2	ij	ij	INTJ
ejpam-5470	240	3	pk	pk	PROPN
ejpam-5470	240	4	l4	l4	PROPN
ejpam-5470	240	5	n	n	CCONJ
ejpam-5470	240	6	,	,	PUNCT
ejpam-5470	240	7	m	m	PROPN
ejpam-5470	240	8	|v0	|v0	NOUN
ejpam-5470	240	9	−	−	ADJ
ejpam-5470	240	10	v1|	v1|	ADJ
ejpam-5470	240	11	|e0	|e0	NOUN
ejpam-5470	240	12	−	−	PROPN
ejpam-5470	240	13	e1|	e1|	NOUN
ejpam-5470	240	14	0	0	NUM
ejpam-5470	240	15	22	22	NUM
ejpam-5470	240	16	a′	a′	PROPN
ejpam-5470	240	17	0	0	NUM
ejpam-5470	240	18	b22	b22	PROPN
ejpam-5470	240	19	,	,	PUNCT
ejpam-5470	240	20	b	b	PROPN
ejpam-5470	240	21	′	′	NUM
ejpam-5470	240	22	22	22	NUM
ejpam-5470	240	23	,	,	PUNCT
ejpam-5470	240	24	b22	b22	PROPN
ejpam-5470	240	25	,	,	PUNCT
ejpam-5470	240	26	b	b	PROPN
ejpam-5470	240	27	′	′	NOUN
ejpam-5470	240	28	22	22	NUM
ejpam-5470	240	29	0	0	NUM
ejpam-5470	240	30	1	1	NUM
ejpam-5470	240	31	1	1	NUM
ejpam-5470	240	32	22	22	NUM
ejpam-5470	240	33	a′	a′	PROPN
ejpam-5470	240	34	1	1	NUM
ejpam-5470	240	35	b22	b22	PROPN
ejpam-5470	240	36	,	,	PUNCT
ejpam-5470	240	37	b	b	PROPN
ejpam-5470	240	38	′	′	NUM
ejpam-5470	240	39	22	22	NUM
ejpam-5470	240	40	,	,	PUNCT
ejpam-5470	240	41	b22	b22	PROPN
ejpam-5470	240	42	,	,	PUNCT
ejpam-5470	240	43	b	b	PROPN
ejpam-5470	240	44	′	′	NUM
ejpam-5470	240	45	22	22	NUM
ejpam-5470	240	46	,	,	PUNCT
ejpam-5470	240	47	...	...	PUNCT
ejpam-5470	240	48	,	,	PUNCT
ejpam-5470	240	49	b	b	X
ejpam-5470	240	50	′	′	NOUN
ejpam-5470	240	51	22	22	NUM
ejpam-5470	240	52	0	0	NUM
ejpam-5470	240	53	1	1	NUM
ejpam-5470	240	54	2	2	NUM
ejpam-5470	240	55	22	22	NUM
ejpam-5470	240	56	a′	a′	PROPN
ejpam-5470	240	57	2	2	NUM
ejpam-5470	240	58	b22	b22	PROPN
ejpam-5470	240	59	,	,	PUNCT
ejpam-5470	240	60	b	b	PROPN
ejpam-5470	240	61	′	′	NUM
ejpam-5470	240	62	22	22	NUM
ejpam-5470	240	63	,	,	PUNCT
ejpam-5470	240	64	b22	b22	PROPN
ejpam-5470	240	65	,	,	PUNCT
ejpam-5470	240	66	b	b	PROPN
ejpam-5470	240	67	′	′	NUM
ejpam-5470	240	68	22	22	NUM
ejpam-5470	240	69	,	,	PUNCT
ejpam-5470	240	70	...	...	PUNCT
ejpam-5470	240	71	,	,	PUNCT
ejpam-5470	240	72	b22	b22	PROPN
ejpam-5470	240	73	,	,	PUNCT
ejpam-5470	240	74	b	b	PROPN
ejpam-5470	240	75	′	′	NOUN
ejpam-5470	240	76	22	22	NUM
ejpam-5470	240	77	0	0	NUM
ejpam-5470	240	78	1	1	NUM
ejpam-5470	240	79	3	3	NUM
ejpam-5470	240	80	22	22	NUM
ejpam-5470	240	81	a′	a′	PROPN
ejpam-5470	240	82	3	3	NUM
ejpam-5470	240	83	b22	b22	PROPN
ejpam-5470	240	84	,	,	PUNCT
ejpam-5470	240	85	b	b	PROPN
ejpam-5470	240	86	′	′	NUM
ejpam-5470	240	87	22	22	NUM
ejpam-5470	240	88	,	,	PUNCT
ejpam-5470	240	89	b22	b22	PROPN
ejpam-5470	240	90	,	,	PUNCT
ejpam-5470	240	91	b	b	PROPN
ejpam-5470	240	92	′	′	NUM
ejpam-5470	240	93	22	22	NUM
ejpam-5470	240	94	,	,	PUNCT
ejpam-5470	240	95	...	...	PUNCT
ejpam-5470	240	96	,	,	PUNCT
ejpam-5470	240	97	b22	b22	PROPN
ejpam-5470	240	98	,	,	PUNCT
ejpam-5470	240	99	b	b	PROPN
ejpam-5470	240	100	′	′	NUM
ejpam-5470	240	101	22	22	NUM
ejpam-5470	240	102	,	,	PUNCT
ejpam-5470	240	103	b	b	NOUN
ejpam-5470	240	104	′	′	NOUN
ejpam-5470	240	105	22	22	NUM
ejpam-5470	240	106	0	0	NUM
ejpam-5470	240	107	1	1	NUM
ejpam-5470	240	108	0	0	NUM
ejpam-5470	240	109	23	23	NUM
ejpam-5470	240	110	a0	a0	PROPN
ejpam-5470	240	111	b23	b23	PROPN
ejpam-5470	240	112	,	,	PUNCT
ejpam-5470	240	113	b23	b23	PROPN
ejpam-5470	240	114	,	,	PUNCT
ejpam-5470	240	115	b	b	NOUN
ejpam-5470	240	116	′	′	NUM
ejpam-5470	240	117	23	23	NUM
ejpam-5470	240	118	,	,	PUNCT
ejpam-5470	240	119	b	b	NOUN
ejpam-5470	240	120	′	′	NOUN
ejpam-5470	240	121	23	23	NUM
ejpam-5470	240	122	0	0	NUM
ejpam-5470	240	123	1	1	NUM
ejpam-5470	240	124	1	1	NUM
ejpam-5470	240	125	23	23	NUM
ejpam-5470	240	126	a1	a1	NOUN
ejpam-5470	240	127	b23	b23	PROPN
ejpam-5470	240	128	,	,	PUNCT
ejpam-5470	240	129	b23	b23	PROPN
ejpam-5470	240	130	,	,	PUNCT
ejpam-5470	240	131	b	b	NOUN
ejpam-5470	240	132	′	′	NUM
ejpam-5470	240	133	23	23	NUM
ejpam-5470	240	134	,	,	PUNCT
ejpam-5470	240	135	b	b	NOUN
ejpam-5470	240	136	′	′	NOUN
ejpam-5470	240	137	23	23	NUM
ejpam-5470	240	138	,	,	PUNCT
ejpam-5470	240	139	...	...	PUNCT
ejpam-5470	240	140	,	,	PUNCT
ejpam-5470	240	141	b23	b23	PROPN
ejpam-5470	240	142	1	1	NUM
ejpam-5470	240	143	0	0	NUM
ejpam-5470	240	144	2	2	NUM
ejpam-5470	240	145	23	23	NUM
ejpam-5470	240	146	a2	a2	PROPN
ejpam-5470	240	147	b23	b23	PROPN
ejpam-5470	240	148	,	,	PUNCT
ejpam-5470	240	149	b23	b23	PROPN
ejpam-5470	240	150	,	,	PUNCT
ejpam-5470	240	151	b	b	NOUN
ejpam-5470	240	152	′	′	NUM
ejpam-5470	240	153	23	23	NUM
ejpam-5470	240	154	,	,	PUNCT
ejpam-5470	240	155	b	b	NOUN
ejpam-5470	240	156	′	′	NOUN
ejpam-5470	240	157	23	23	NUM
ejpam-5470	240	158	,	,	PUNCT
ejpam-5470	240	159	...	...	PUNCT
ejpam-5470	240	160	,	,	PUNCT
ejpam-5470	240	161	b23	b23	PROPN
ejpam-5470	240	162	,	,	PUNCT
ejpam-5470	240	163	b	b	NOUN
ejpam-5470	240	164	′	′	NOUN
ejpam-5470	240	165	23	23	NUM
ejpam-5470	240	166	0	0	NUM
ejpam-5470	240	167	1	1	NUM
ejpam-5470	240	168	3	3	NUM
ejpam-5470	240	169	23	23	NUM
ejpam-5470	240	170	a3	a3	NOUN
ejpam-5470	240	171	b23	b23	PROPN
ejpam-5470	240	172	,	,	PUNCT
ejpam-5470	240	173	b23	b23	PROPN
ejpam-5470	240	174	,	,	PUNCT
ejpam-5470	240	175	b	b	NOUN
ejpam-5470	240	176	′	′	NUM
ejpam-5470	240	177	23	23	NUM
ejpam-5470	240	178	,	,	PUNCT
ejpam-5470	240	179	b	b	NOUN
ejpam-5470	240	180	′	′	NOUN
ejpam-5470	240	181	23	23	NUM
ejpam-5470	240	182	,	,	PUNCT
ejpam-5470	240	183	...	...	PUNCT
ejpam-5470	240	184	,	,	PUNCT
ejpam-5470	240	185	b23	b23	PROPN
ejpam-5470	240	186	,	,	PUNCT
ejpam-5470	240	187	b23	b23	PROPN
ejpam-5470	240	188	,	,	PUNCT
ejpam-5470	240	189	b	b	NOUN
ejpam-5470	240	190	′	′	NOUN
ejpam-5470	240	191	23	23	NUM
ejpam-5470	240	192	1	1	NUM
ejpam-5470	240	193	0	0	NUM
ejpam-5470	240	194	0	0	NUM
ejpam-5470	240	195	33	33	NUM
ejpam-5470	240	196	a′	a′	NOUN
ejpam-5470	240	197	0	0	NUM
ejpam-5470	240	198	b33	b33	NOUN
ejpam-5470	240	199	,	,	PUNCT
ejpam-5470	240	200	b	b	NOUN
ejpam-5470	240	201	′	′	NUM
ejpam-5470	240	202	33	33	NUM
ejpam-5470	240	203	,	,	PUNCT
ejpam-5470	240	204	b33	b33	NUM
ejpam-5470	240	205	,	,	PUNCT
ejpam-5470	240	206	b	b	NOUN
ejpam-5470	240	207	′	′	NUM
ejpam-5470	241	1	33	33	NUM
ejpam-5470	241	2	0	0	NUM
ejpam-5470	241	3	1	1	NUM
ejpam-5470	241	4	1	1	NUM
ejpam-5470	241	5	33	33	NUM
ejpam-5470	241	6	a′	a′	NOUN
ejpam-5470	241	7	1	1	NUM
ejpam-5470	241	8	b33	b33	NOUN
ejpam-5470	241	9	,	,	PUNCT
ejpam-5470	241	10	b	b	NOUN
ejpam-5470	241	11	′	′	NUM
ejpam-5470	241	12	33	33	NUM
ejpam-5470	241	13	,	,	PUNCT
ejpam-5470	241	14	b33	b33	NUM
ejpam-5470	241	15	,	,	PUNCT
ejpam-5470	241	16	b	b	NOUN
ejpam-5470	241	17	′	′	NUM
ejpam-5470	241	18	33	33	NUM
ejpam-5470	241	19	,	,	PUNCT
ejpam-5470	241	20	...	...	PUNCT
ejpam-5470	241	21	,	,	PUNCT
ejpam-5470	241	22	b	b	X
ejpam-5470	241	23	′	′	NUM
ejpam-5470	242	1	33	33	NUM
ejpam-5470	242	2	0	0	NUM
ejpam-5470	242	3	1	1	NUM
ejpam-5470	242	4	2	2	NUM
ejpam-5470	242	5	33	33	NUM
ejpam-5470	242	6	a′	a′	ADJ
ejpam-5470	242	7	2	2	NUM
ejpam-5470	242	8	b33	b33	NOUN
ejpam-5470	242	9	,	,	PUNCT
ejpam-5470	242	10	b	b	NOUN
ejpam-5470	242	11	′	′	NUM
ejpam-5470	242	12	33	33	NUM
ejpam-5470	242	13	,	,	PUNCT
ejpam-5470	242	14	b33	b33	NUM
ejpam-5470	242	15	,	,	PUNCT
ejpam-5470	242	16	b	b	NOUN
ejpam-5470	242	17	′	′	NUM
ejpam-5470	242	18	33	33	NUM
ejpam-5470	242	19	,	,	PUNCT
ejpam-5470	242	20	...	...	PUNCT
ejpam-5470	242	21	,	,	PUNCT
ejpam-5470	242	22	b33	b33	PROPN
ejpam-5470	242	23	,	,	PUNCT
ejpam-5470	242	24	b	b	NOUN
ejpam-5470	242	25	′	′	NUM
ejpam-5470	242	26	33	33	NUM
ejpam-5470	242	27	0	0	NUM
ejpam-5470	242	28	1	1	NUM
ejpam-5470	242	29	3	3	NUM
ejpam-5470	242	30	33	33	NUM
ejpam-5470	242	31	a′	a′	NOUN
ejpam-5470	242	32	3	3	NUM
ejpam-5470	242	33	b33	b33	NOUN
ejpam-5470	242	34	,	,	PUNCT
ejpam-5470	242	35	b	b	NOUN
ejpam-5470	242	36	′	′	NUM
ejpam-5470	242	37	33	33	NUM
ejpam-5470	242	38	,	,	PUNCT
ejpam-5470	242	39	b33	b33	NUM
ejpam-5470	242	40	,	,	PUNCT
ejpam-5470	242	41	b	b	NOUN
ejpam-5470	242	42	′	′	NUM
ejpam-5470	242	43	33	33	NUM
ejpam-5470	242	44	,	,	PUNCT
ejpam-5470	242	45	...	...	PUNCT
ejpam-5470	242	46	,	,	PUNCT
ejpam-5470	242	47	b33	b33	PROPN
ejpam-5470	242	48	,	,	PUNCT
ejpam-5470	242	49	b	b	NOUN
ejpam-5470	242	50	′	′	NUM
ejpam-5470	242	51	33	33	NUM
ejpam-5470	242	52	,	,	PUNCT
ejpam-5470	242	53	b	b	NOUN
ejpam-5470	242	54	′	′	NUM
ejpam-5470	242	55	33	33	NUM
ejpam-5470	242	56	0	0	NUM
ejpam-5470	242	57	1	1	NUM
ejpam-5470	242	58	lemma	lemma	PROPN
ejpam-5470	242	59	3	3	NUM
ejpam-5470	242	60	.	.	PUNCT
ejpam-5470	242	61	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	242	62	4,m	4,m	PROPN
ejpam-5470	242	63	is	be	AUX
ejpam-5470	242	64	cordial	cordial	ADJ
ejpam-5470	242	65	for	for	ADP
ejpam-5470	242	66	all	all	PRON
ejpam-5470	242	67	k	k	PROPN
ejpam-5470	242	68	≥	≥	NUM
ejpam-5470	242	69	1	1	NUM
ejpam-5470	242	70	and	and	CCONJ
ejpam-5470	242	71	m	m	VERB
ejpam-5470	242	72	>	>	X
ejpam-5470	242	73	3	3	NUM
ejpam-5470	242	74	.	.	PUNCT
ejpam-5470	243	1	proof	proof	NOUN
ejpam-5470	243	2	.	.	PUNCT
ejpam-5470	244	1	we	we	PRON
ejpam-5470	244	2	need	need	VERB
ejpam-5470	244	3	to	to	PART
ejpam-5470	244	4	examine	examine	VERB
ejpam-5470	244	5	the	the	DET
ejpam-5470	244	6	following	follow	VERB
ejpam-5470	244	7	cases	case	NOUN
ejpam-5470	244	8	:	:	PUNCT
ejpam-5470	244	9	case	case	NOUN
ejpam-5470	244	10	1	1	NUM
ejpam-5470	244	11	.	.	PUNCT
ejpam-5470	245	1	at	at	ADP
ejpam-5470	245	2	m	m	PROPN
ejpam-5470	245	3	≡	≡	PROPN
ejpam-5470	245	4	0(mod4	0(mod4	NUM
ejpam-5470	245	5	)	)	PUNCT
ejpam-5470	245	6	,	,	PUNCT
ejpam-5470	245	7	we	we	PRON
ejpam-5470	245	8	consider	consider	VERB
ejpam-5470	245	9	the	the	DET
ejpam-5470	245	10	following	follow	VERB
ejpam-5470	245	11	sub	sub	NOUN
ejpam-5470	245	12	subcases	subcase	NOUN
ejpam-5470	245	13	.	.	PUNCT
ejpam-5470	246	1	subcase	subcase	PROPN
ejpam-5470	246	2	1.1.k	1.1.k	PROPN
ejpam-5470	246	3	≡	≡	PROPN
ejpam-5470	246	4	0(mod4	0(mod4	NUM
ejpam-5470	246	5	)	)	PUNCT
ejpam-5470	246	6	let	let	VERB
ejpam-5470	246	7	k=	k=	ADJ
ejpam-5470	246	8	4r	4r	NOUN
ejpam-5470	246	9	,	,	PUNCT
ejpam-5470	246	10	r	r	NOUN
ejpam-5470	246	11	≥	≥	NUM
ejpam-5470	246	12	1	1	NUM
ejpam-5470	246	13	andm=	andm=	NUM
ejpam-5470	246	14	4	4	NUM
ejpam-5470	246	15	t	t	PROPN
ejpam-5470	246	16	,	,	PUNCT
ejpam-5470	246	17	t	t	PROPN
ejpam-5470	246	18	>	>	X
ejpam-5470	246	19	1	1	NUM
ejpam-5470	246	20	.	.	PUNCT
ejpam-5470	247	1	then	then	ADV
ejpam-5470	247	2	,	,	PUNCT
ejpam-5470	247	3	the	the	DET
ejpam-5470	247	4	labelling	labelling	NOUN
ejpam-5470	247	5	[	[	X
ejpam-5470	247	6	l4r;0	l4r;0	NOUN
ejpam-5470	247	7	15m4t−603	15m4t−603	NUM
ejpam-5470	247	8	,	,	PUNCT
ejpam-5470	247	9	0	0	NUM
ejpam-5470	247	10	15m4t−603	15m4t−603	NUM
ejpam-5470	247	11	,	,	PUNCT
ejpam-5470	247	12	105	105	NUM
ejpam-5470	247	13	m	m	NOUN
ejpam-5470	247	14	′	′	NUM
ejpam-5470	247	15	4t−6	4t−6	PROPN
ejpam-5470	247	16	13	13	NUM
ejpam-5470	247	17	,	,	PUNCT
ejpam-5470	247	18	105	105	NUM
ejpam-5470	247	19	m	m	NOUN
ejpam-5470	247	20	′	′	NUM
ejpam-5470	247	21	4t−6	4t−6	PROPN
ejpam-5470	247	22	13	13	NUM
ejpam-5470	247	23	...	...	PUNCT
ejpam-5470	247	24	,	,	PUNCT
ejpam-5470	247	25	(	(	PUNCT
ejpam-5470	247	26	r−times	r−time	NOUN
ejpam-5470	247	27	)	)	PUNCT
ejpam-5470	247	28	]	]	PUNCT
ejpam-5470	247	29	for	for	ADP
ejpam-5470	247	30	p4r⊙	p4r⊙	PROPN
ejpam-5470	247	31	l4	l4	PROPN
ejpam-5470	247	32	4,4	4,4	PROPN
ejpam-5470	247	33	t	t	PROPN
ejpam-5470	247	34	is	be	AUX
ejpam-5470	247	35	applied	apply	VERB
ejpam-5470	247	36	.	.	PUNCT
ejpam-5470	248	1	therefore	therefore	ADV
ejpam-5470	248	2	x0	x0	PROPN
ejpam-5470	248	3	=	=	PROPN
ejpam-5470	248	4	x1=	x1=	PROPN
ejpam-5470	248	5	2r	2r	NUM
ejpam-5470	248	6	,	,	PUNCT
ejpam-5470	248	7	a0=	a0=	PROPN
ejpam-5470	248	8	2r	2r	NUM
ejpam-5470	248	9	,	,	PUNCT
ejpam-5470	248	10	a1=	a1=	PROPN
ejpam-5470	248	11	2r−	2r−	PROPN
ejpam-5470	248	12	1,y0=	1,y0=	NUM
ejpam-5470	248	13	2t+1,y1=	2t+1,y1=	NUM
ejpam-5470	248	14	2t+2,b0=	2t+2,b0=	NUM
ejpam-5470	248	15	8t−1,b1=	8t−1,b1=	PROPN
ejpam-5470	248	16	8t−2,y′0=	8t−2,y′0=	NUM
ejpam-5470	248	17	2t+2,y′1=	2t+2,y′1=	NUM
ejpam-5470	248	18	2t+1,b′0=	2t+1,b′0=	NUM
ejpam-5470	248	19	8t−1	8t−1	NUM
ejpam-5470	248	20	and	and	CCONJ
ejpam-5470	248	21	b′1=	b′1=	ADP
ejpam-5470	248	22	8t−2	8t−2	NUM
ejpam-5470	248	23	.	.	PUNCT
ejpam-5470	249	1	so	so	ADV
ejpam-5470	249	2	,	,	PUNCT
ejpam-5470	249	3	|v0−v1|	|v0−v1|	NUM
ejpam-5470	249	4	=	=	SYM
ejpam-5470	249	5	0	0	NUM
ejpam-5470	249	6	and	and	CCONJ
ejpam-5470	249	7	|e0−e1|	|e0−e1|	NOUN
ejpam-5470	249	8	=	=	NOUN
ejpam-5470	249	9	1	1	X
ejpam-5470	249	10	.	.	X
ejpam-5470	250	1	for	for	ADP
ejpam-5470	250	2	the	the	DET
ejpam-5470	250	3	case	case	NOUN
ejpam-5470	250	4	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	250	5	4,4	4,4	NUM
ejpam-5470	250	6	,	,	PUNCT
ejpam-5470	250	7	the	the	DET
ejpam-5470	250	8	labeling	labeling	NOUN
ejpam-5470	250	9	[	[	X
ejpam-5470	250	10	m4r;010103	m4r;010103	NOUN
ejpam-5470	250	11	,	,	PUNCT
ejpam-5470	250	12	1010	1010	NUM
ejpam-5470	250	13	13	13	NUM
ejpam-5470	250	14	,	,	PUNCT
ejpam-5470	250	15	010103	010103	NUM
ejpam-5470	250	16	,	,	PUNCT
ejpam-5470	250	17	1010	1010	NUM
ejpam-5470	250	18	13	13	NUM
ejpam-5470	250	19	,	,	PUNCT
ejpam-5470	250	20	...	...	PUNCT
ejpam-5470	250	21	,	,	PUNCT
ejpam-5470	250	22	(	(	PUNCT
ejpam-5470	250	23	r	r	NOUN
ejpam-5470	250	24	−	−	PROPN
ejpam-5470	250	25	times	time	NOUN
ejpam-5470	250	26	)	)	PUNCT
ejpam-5470	250	27	]	]	PUNCT
ejpam-5470	250	28	is	be	AUX
ejpam-5470	250	29	sufficient	sufficient	ADJ
ejpam-5470	250	30	and	and	CCONJ
ejpam-5470	250	31	thus	thus	ADV
ejpam-5470	250	32	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	250	33	4,4	4,4	PROPN
ejpam-5470	250	34	t	t	PROPN
ejpam-5470	250	35	is	be	AUX
ejpam-5470	250	36	cordial	cordial	ADJ
ejpam-5470	250	37	.	.	PUNCT
ejpam-5470	251	1	subcase	subcase	PROPN
ejpam-5470	251	2	1.2.k	1.2.k	NUM
ejpam-5470	251	3	≡	≡	PROPN
ejpam-5470	251	4	1(mod4	1(mod4	NUM
ejpam-5470	251	5	)	)	PUNCT
ejpam-5470	251	6	let	let	VERB
ejpam-5470	251	7	k=	k=	X
ejpam-5470	251	8	4r+1,r	4r+1,r	NOUN
ejpam-5470	251	9	≥	≥	X
ejpam-5470	251	10	0	0	NUM
ejpam-5470	252	1	andm=	andm=	PROPN
ejpam-5470	252	2	4	4	NUM
ejpam-5470	252	3	t	t	PROPN
ejpam-5470	252	4	,	,	PUNCT
ejpam-5470	252	5	t	t	PROPN
ejpam-5470	252	6	>	>	X
ejpam-5470	252	7	1	1	NUM
ejpam-5470	252	8	.	.	PUNCT
ejpam-5470	253	1	then	then	ADV
ejpam-5470	253	2	,	,	PUNCT
ejpam-5470	253	3	the	the	DET
ejpam-5470	253	4	labelling	labelling	NOUN
ejpam-5470	253	5	[	[	X
ejpam-5470	253	6	l4r0;015m4t−603	l4r0;015m4t−603	NOUN
ejpam-5470	253	7	,	,	PUNCT
ejpam-5470	253	8	015m4t−603	015m4t−603	PROPN
ejpam-5470	253	9	,	,	PUNCT
ejpam-5470	253	10	105	105	NUM
ejpam-5470	253	11	m	m	NOUN
ejpam-5470	253	12	′	′	NUM
ejpam-5470	253	13	4t−6	4t−6	PROPN
ejpam-5470	253	14	13	13	NUM
ejpam-5470	253	15	,	,	PUNCT
ejpam-5470	253	16	105	105	NUM
ejpam-5470	253	17	m	m	NOUN
ejpam-5470	253	18	′	′	NUM
ejpam-5470	253	19	4t−6	4t−6	PROPN
ejpam-5470	253	20	13	13	NUM
ejpam-5470	253	21	...	...	PUNCT
ejpam-5470	253	22	,	,	PUNCT
ejpam-5470	253	23	(	(	PUNCT
ejpam-5470	253	24	r−	r−	PROPN
ejpam-5470	253	25	times	time	NOUN
ejpam-5470	253	26	)	)	PUNCT
ejpam-5470	253	27	,	,	PUNCT
ejpam-5470	253	28	0	0	NUM
ejpam-5470	253	29	15m4t−603	15m4t−603	NUM
ejpam-5470	253	30	]	]	PUNCT
ejpam-5470	253	31	for	for	ADP
ejpam-5470	253	32	p4r+1⊙	p4r+1⊙	PROPN
ejpam-5470	253	33	l4	l4	PROPN
ejpam-5470	253	34	4,4	4,4	PROPN
ejpam-5470	253	35	t	t	PROPN
ejpam-5470	253	36	is	be	AUX
ejpam-5470	253	37	applied	apply	VERB
ejpam-5470	253	38	.	.	PUNCT
ejpam-5470	254	1	therefore	therefore	ADV
ejpam-5470	254	2	x0=	x0=	PUNCT
ejpam-5470	254	3	2r	2r	NUM
ejpam-5470	255	1	+	+	CCONJ
ejpam-5470	255	2	1,x1=	1,x1=	NUM
ejpam-5470	255	3	2r	2r	NUM
ejpam-5470	255	4	,	,	PUNCT
ejpam-5470	255	5	a0	a0	PROPN
ejpam-5470	255	6	=	=	PROPN
ejpam-5470	255	7	a1=	a1=	PROPN
ejpam-5470	255	8	2r	2r	NUM
ejpam-5470	255	9	,	,	PUNCT
ejpam-5470	255	10	y0=	y0=	PROPN
ejpam-5470	255	11	2	2	NUM
ejpam-5470	255	12	t	t	NOUN
ejpam-5470	255	13	+	+	NOUN
ejpam-5470	255	14	1,y1=	1,y1=	NUM
ejpam-5470	255	15	2	2	NUM
ejpam-5470	255	16	t	t	NOUN
ejpam-5470	255	17	+	+	CCONJ
ejpam-5470	255	18	2,b0=	2,b0=	NUM
ejpam-5470	255	19	8	8	NUM
ejpam-5470	255	20	t	t	NOUN
ejpam-5470	255	21	−	−	NOUN
ejpam-5470	255	22	1,b1=	1,b1=	NUM
ejpam-5470	255	23	8	8	NUM
ejpam-5470	255	24	t	t	NOUN
ejpam-5470	255	25	−	−	NOUN
ejpam-5470	255	26	2,y′0=	2,y′0=	NUM
ejpam-5470	255	27	2	2	NUM
ejpam-5470	255	28	t	t	NOUN
ejpam-5470	255	29	+	+	NOUN
ejpam-5470	255	30	2,y′1=	2,y′1=	NUM
ejpam-5470	255	31	2	2	NUM
ejpam-5470	255	32	t	t	NOUN
ejpam-5470	255	33	+	+	CCONJ
ejpam-5470	255	34	1,b′0=	1,b′0=	NUM
ejpam-5470	255	35	8	8	NUM
ejpam-5470	255	36	t	t	NOUN
ejpam-5470	255	37	−	−	NOUN
ejpam-5470	255	38	1	1	NUM
ejpam-5470	255	39	and	and	CCONJ
ejpam-5470	255	40	b′1=	b′1=	ADP
ejpam-5470	255	41	8	8	NUM
ejpam-5470	255	42	t	t	NOUN
ejpam-5470	255	43	−	−	NOUN
ejpam-5470	255	44	2	2	NUM
ejpam-5470	255	45	.	.	PUNCT
ejpam-5470	256	1	so	so	ADV
ejpam-5470	256	2	,	,	PUNCT
ejpam-5470	256	3	|v0	|v0	NOUN
ejpam-5470	256	4	−	−	NOUN
ejpam-5470	256	5	v1|	v1|	NOUN
ejpam-5470	256	6	=	=	SYM
ejpam-5470	256	7	0	0	NUM
ejpam-5470	256	8	and	and	CCONJ
ejpam-5470	256	9	|e0	|e0	NOUN
ejpam-5470	257	1	−	−	PROPN
ejpam-5470	257	2	e1|	e1|	NOUN
ejpam-5470	257	3	=	=	NOUN
ejpam-5470	257	4	0	0	NUM
ejpam-5470	257	5	.	.	PUNCT
ejpam-5470	258	1	for	for	ADP
ejpam-5470	258	2	the	the	DET
ejpam-5470	258	3	case	case	NOUN
ejpam-5470	258	4	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	258	5	4,4	4,4	NUM
ejpam-5470	258	6	,	,	PUNCT
ejpam-5470	258	7	the	the	DET
ejpam-5470	258	8	labeling	labeling	NOUN
ejpam-5470	258	9	[	[	X
ejpam-5470	258	10	m4r+1;010103	m4r+1;010103	PROPN
ejpam-5470	258	11	,	,	PUNCT
ejpam-5470	258	12	1010	1010	NUM
ejpam-5470	258	13	13	13	NUM
ejpam-5470	258	14	,	,	PUNCT
ejpam-5470	258	15	010103	010103	NUM
ejpam-5470	258	16	,	,	PUNCT
ejpam-5470	258	17	1010	1010	NUM
ejpam-5470	258	18	13	13	NUM
ejpam-5470	258	19	,	,	PUNCT
ejpam-5470	258	20	...	...	PUNCT
ejpam-5470	258	21	,	,	PUNCT
ejpam-5470	258	22	(	(	PUNCT
ejpam-5470	258	23	r	r	NOUN
ejpam-5470	258	24	−	−	PROPN
ejpam-5470	258	25	times	time	NOUN
ejpam-5470	258	26	)	)	PUNCT
ejpam-5470	258	27	,	,	PUNCT
ejpam-5470	258	28	1010	1010	NUM
ejpam-5470	258	29	13	13	NUM
ejpam-5470	258	30	]	]	PUNCT
ejpam-5470	258	31	is	be	AUX
ejpam-5470	258	32	sufficient	sufficient	ADJ
ejpam-5470	258	33	and	and	CCONJ
ejpam-5470	258	34	thus	thus	ADV
ejpam-5470	258	35	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	258	36	4,4	4,4	NUM
ejpam-5470	258	37	t	t	PROPN
ejpam-5470	258	38	is	be	AUX
ejpam-5470	258	39	cordial	cordial	ADJ
ejpam-5470	258	40	.	.	PUNCT
ejpam-5470	259	1	subcase	subcase	PROPN
ejpam-5470	259	2	1.3.k	1.3.k	PROPN
ejpam-5470	259	3	≡	≡	PROPN
ejpam-5470	259	4	2(mod4	2(mod4	NUM
ejpam-5470	259	5	)	)	PUNCT
ejpam-5470	259	6	let	let	VERB
ejpam-5470	259	7	k=	k=	PROPN
ejpam-5470	259	8	4r+2,r	4r+2,r	NUM
ejpam-5470	259	9	≥	≥	NOUN
ejpam-5470	259	10	0	0	NUM
ejpam-5470	259	11	andm=	andm=	PROPN
ejpam-5470	259	12	4	4	NUM
ejpam-5470	259	13	t	t	PROPN
ejpam-5470	259	14	,	,	PUNCT
ejpam-5470	259	15	t	t	PROPN
ejpam-5470	259	16	>	>	X
ejpam-5470	259	17	1	1	NUM
ejpam-5470	259	18	.	.	PUNCT
ejpam-5470	260	1	then	then	ADV
ejpam-5470	260	2	,	,	PUNCT
ejpam-5470	260	3	the	the	DET
ejpam-5470	260	4	labelling	labelling	NOUN
ejpam-5470	260	5	[	[	X
ejpam-5470	260	6	l4r10;0	l4r10;0	PROPN
ejpam-5470	260	7	15m4t−603	15m4t−603	NUM
ejpam-5470	260	8	,	,	PUNCT
ejpam-5470	260	9	0	0	NUM
ejpam-5470	260	10	15m4t−603	15m4t−603	NUM
ejpam-5470	260	11	,	,	PUNCT
ejpam-5470	260	12	105	105	NUM
ejpam-5470	260	13	m	m	NOUN
ejpam-5470	260	14	′	′	NUM
ejpam-5470	260	15	4t−6	4t−6	PROPN
ejpam-5470	260	16	13	13	NUM
ejpam-5470	260	17	,	,	PUNCT
ejpam-5470	260	18	105	105	NUM
ejpam-5470	260	19	m	m	NOUN
ejpam-5470	260	20	′	′	NUM
ejpam-5470	260	21	4t−6	4t−6	PROPN
ejpam-5470	260	22	13	13	NUM
ejpam-5470	260	23	...	...	PUNCT
ejpam-5470	260	24	,	,	PUNCT
ejpam-5470	260	25	(	(	PUNCT
ejpam-5470	260	26	r−times	r−time	NOUN
ejpam-5470	260	27	)	)	PUNCT
ejpam-5470	260	28	,	,	PUNCT
ejpam-5470	260	29	105	105	NUM
ejpam-5470	260	30	m	m	NOUN
ejpam-5470	260	31	′	′	NUM
ejpam-5470	260	32	4t−6	4t−6	PROPN
ejpam-5470	260	33	13	13	NUM
ejpam-5470	260	34	,	,	PUNCT
ejpam-5470	260	35	0	0	NUM
ejpam-5470	260	36	15m4t−603	15m4t−603	NUM
ejpam-5470	260	37	]	]	PUNCT
ejpam-5470	260	38	for	for	ADP
ejpam-5470	260	39	p4r+2	p4r+2	PROPN
ejpam-5470	260	40	⊙	⊙	PROPN
ejpam-5470	260	41	l4	l4	PROPN
ejpam-5470	260	42	4,4	4,4	PROPN
ejpam-5470	260	43	t	t	PROPN
ejpam-5470	260	44	is	be	AUX
ejpam-5470	260	45	applied	apply	VERB
ejpam-5470	260	46	.	.	PUNCT
ejpam-5470	261	1	therefore	therefore	ADV
ejpam-5470	261	2	x0	x0	PROPN
ejpam-5470	261	3	=	=	PROPN
ejpam-5470	261	4	x1=	x1=	PROPN
ejpam-5470	261	5	2r+1,a0=	2r+1,a0=	NUM
ejpam-5470	261	6	2r+1,a1=	2r+1,a1=	NUM
ejpam-5470	261	7	2r	2r	NUM
ejpam-5470	261	8	,	,	PUNCT
ejpam-5470	261	9	y0=	y0=	PROPN
ejpam-5470	261	10	2t+1,y1=	2t+1,y1=	NUM
ejpam-5470	261	11	2t+2,b0=	2t+2,b0=	NUM
ejpam-5470	261	12	8t−1,b1=	8t−1,b1=	PROPN
ejpam-5470	261	13	8t−	8t−	PROPN
ejpam-5470	261	14	2,y′0=	2,y′0=	NUM
ejpam-5470	261	15	2t+2,y′1=	2t+2,y′1=	NUM
ejpam-5470	261	16	2t+1,b′0=	2t+1,b′0=	NUM
ejpam-5470	261	17	8t−1	8t−1	NUM
ejpam-5470	261	18	and	and	CCONJ
ejpam-5470	261	19	b′1=	b′1=	ADP
ejpam-5470	261	20	8t−2	8t−2	NUM
ejpam-5470	261	21	.	.	PUNCT
ejpam-5470	262	1	so	so	ADV
ejpam-5470	262	2	,	,	PUNCT
ejpam-5470	262	3	|v0−v1|	|v0−v1|	NUM
ejpam-5470	262	4	=	=	SYM
ejpam-5470	262	5	0	0	NUM
ejpam-5470	262	6	and	and	CCONJ
ejpam-5470	262	7	|e0−e1|	|e0−e1|	NOUN
ejpam-5470	262	8	=	=	NOUN
ejpam-5470	262	9	1	1	X
ejpam-5470	262	10	.	.	X
ejpam-5470	263	1	for	for	ADP
ejpam-5470	263	2	the	the	DET
ejpam-5470	263	3	case	case	NOUN
ejpam-5470	263	4	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	263	5	4,4	4,4	NUM
ejpam-5470	263	6	,	,	PUNCT
ejpam-5470	263	7	the	the	DET
ejpam-5470	263	8	labeling	labeling	NOUN
ejpam-5470	263	9	[	[	X
ejpam-5470	263	10	m4r+2;010103	m4r+2;010103	X
ejpam-5470	263	11	,	,	PUNCT
ejpam-5470	263	12	1010	1010	NUM
ejpam-5470	263	13	13	13	NUM
ejpam-5470	263	14	,	,	PUNCT
ejpam-5470	263	15	010103	010103	NUM
ejpam-5470	263	16	,	,	PUNCT
ejpam-5470	263	17	1010	1010	NUM
ejpam-5470	263	18	13	13	NUM
ejpam-5470	263	19	,	,	PUNCT
ejpam-5470	263	20	...	...	PUNCT
ejpam-5470	263	21	,	,	PUNCT
ejpam-5470	263	22	(	(	PUNCT
ejpam-5470	263	23	r−times	r−time	NOUN
ejpam-5470	263	24	)	)	PUNCT
ejpam-5470	263	25	,	,	PUNCT
ejpam-5470	263	26	1010	1010	NUM
ejpam-5470	263	27	13	13	NUM
ejpam-5470	263	28	,	,	PUNCT
ejpam-5470	263	29	010103	010103	NUM
ejpam-5470	263	30	]	]	PUNCT
ejpam-5470	263	31	is	be	AUX
ejpam-5470	263	32	sufficient	sufficient	ADJ
ejpam-5470	263	33	and	and	CCONJ
ejpam-5470	263	34	thus	thus	ADV
ejpam-5470	263	35	p4r+2⊙l4	p4r+2⊙l4	NUM
ejpam-5470	263	36	4,4	4,4	NUM
ejpam-5470	263	37	t	t	NOUN
ejpam-5470	263	38	is	be	AUX
ejpam-5470	263	39	cordial	cordial	ADJ
ejpam-5470	263	40	.	.	PUNCT
ejpam-5470	264	1	subcase	subcase	PROPN
ejpam-5470	264	2	1.4.k	1.4.k	NUM
ejpam-5470	264	3	≡	≡	PROPN
ejpam-5470	264	4	3(mod4	3(mod4	NUM
ejpam-5470	264	5	)	)	PUNCT
ejpam-5470	264	6	let	let	VERB
ejpam-5470	264	7	k=	k=	X
ejpam-5470	264	8	4r+3,r	4r+3,r	NUM
ejpam-5470	264	9	≥	≥	NOUN
ejpam-5470	264	10	0	0	NUM
ejpam-5470	264	11	andm=	andm=	PROPN
ejpam-5470	264	12	4	4	NUM
ejpam-5470	264	13	t	t	PROPN
ejpam-5470	264	14	,	,	PUNCT
ejpam-5470	264	15	t	t	PROPN
ejpam-5470	264	16	>	>	X
ejpam-5470	264	17	1	1	NUM
ejpam-5470	264	18	.	.	PUNCT
ejpam-5470	265	1	then	then	ADV
ejpam-5470	265	2	,	,	PUNCT
ejpam-5470	265	3	the	the	DET
ejpam-5470	265	4	labelling	labelling	NOUN
ejpam-5470	265	5	[	[	X
ejpam-5470	265	6	l4r001;0	l4r001;0	ADJ
ejpam-5470	265	7	15m4t−603	15m4t−603	NUM
ejpam-5470	265	8	,	,	PUNCT
ejpam-5470	265	9	0	0	NUM
ejpam-5470	265	10	15m4t−603	15m4t−603	NUM
ejpam-5470	265	11	,	,	PUNCT
ejpam-5470	265	12	105	105	NUM
ejpam-5470	265	13	m	m	NOUN
ejpam-5470	265	14	′	′	NUM
ejpam-5470	265	15	4t−6	4t−6	PROPN
ejpam-5470	265	16	13	13	NUM
ejpam-5470	265	17	,	,	PUNCT
ejpam-5470	265	18	105	105	NUM
ejpam-5470	265	19	m	m	NOUN
ejpam-5470	265	20	′	′	NUM
ejpam-5470	265	21	4t−6	4t−6	PROPN
ejpam-5470	265	22	13	13	NUM
ejpam-5470	265	23	...	...	PUNCT
ejpam-5470	265	24	,	,	PUNCT
ejpam-5470	265	25	(	(	PUNCT
ejpam-5470	265	26	r−times	r−time	NOUN
ejpam-5470	265	27	)	)	PUNCT
ejpam-5470	265	28	,	,	PUNCT
ejpam-5470	265	29	0	0	NUM
ejpam-5470	265	30	15m4t−603	15m4t−603	NUM
ejpam-5470	265	31	,	,	PUNCT
ejpam-5470	265	32	0	0	NUM
ejpam-5470	265	33	15m4t−603	15m4t−603	NUM
ejpam-5470	265	34	,	,	PUNCT
ejpam-5470	265	35	105	105	NUM
ejpam-5470	265	36	m	m	NOUN
ejpam-5470	265	37	′	′	NUM
ejpam-5470	265	38	4t−6	4t−6	NUM
ejpam-5470	265	39	13	13	NUM
ejpam-5470	265	40	]	]	PUNCT
ejpam-5470	265	41	for	for	ADP
ejpam-5470	265	42	p4r+3⊙	p4r+3⊙	PROPN
ejpam-5470	265	43	l4	l4	PROPN
ejpam-5470	265	44	4,4	4,4	PROPN
ejpam-5470	265	45	t	t	PROPN
ejpam-5470	265	46	is	be	AUX
ejpam-5470	265	47	applied	apply	VERB
ejpam-5470	265	48	.	.	PUNCT
ejpam-5470	266	1	therefore	therefore	ADV
ejpam-5470	266	2	x0=	x0=	PUNCT
ejpam-5470	266	3	2r	2r	NUM
ejpam-5470	266	4	+	+	CCONJ
ejpam-5470	266	5	2,x1=	2,x1=	NUM
ejpam-5470	266	6	2r	2r	NUM
ejpam-5470	266	7	+	+	CCONJ
ejpam-5470	266	8	1,a0	1,a0	NUM
ejpam-5470	266	9	=	=	NOUN
ejpam-5470	266	10	a1=	a1=	PROPN
ejpam-5470	266	11	2r	2r	NUM
ejpam-5470	267	1	+	+	CCONJ
ejpam-5470	267	2	1,y0=	1,y0=	PROPN
ejpam-5470	267	3	2	2	NUM
ejpam-5470	267	4	t	t	NOUN
ejpam-5470	267	5	+	+	NOUN
ejpam-5470	267	6	1,y1=	1,y1=	NUM
ejpam-5470	267	7	2	2	NUM
ejpam-5470	267	8	t	t	NOUN
ejpam-5470	267	9	+	+	CCONJ
ejpam-5470	267	10	2,b0=	2,b0=	NUM
ejpam-5470	267	11	8t−	8t−	NUM
ejpam-5470	267	12	1,b1=	1,b1=	NUM
ejpam-5470	268	1	8t−	8t−	PROPN
ejpam-5470	268	2	2,y′0=	2,y′0=	NUM
ejpam-5470	268	3	2t+	2t+	NUM
ejpam-5470	268	4	2,y′1=	2,y′1=	NUM
ejpam-5470	268	5	2t+	2t+	NUM
ejpam-5470	268	6	1,b′0=	1,b′0=	NUM
ejpam-5470	268	7	8t−	8t−	NUM
ejpam-5470	268	8	1	1	NUM
ejpam-5470	268	9	and	and	CCONJ
ejpam-5470	268	10	b′1=	b′1=	ADP
ejpam-5470	268	11	8t−	8t−	PROPN
ejpam-5470	268	12	2	2	NUM
ejpam-5470	268	13	.	.	PUNCT
ejpam-5470	269	1	so	so	ADV
ejpam-5470	269	2	,	,	PUNCT
ejpam-5470	269	3	|v0	|v0	NOUN
ejpam-5470	269	4	−	−	NOUN
ejpam-5470	269	5	v1|	v1|	NOUN
ejpam-5470	269	6	=	=	SYM
ejpam-5470	269	7	0	0	NUM
ejpam-5470	269	8	a.	a.	PROPN
ejpam-5470	269	9	abd	abd	PROPN
ejpam-5470	269	10	el	el	PROPN
ejpam-5470	269	11	-	-	PROPN
ejpam-5470	269	12	hay	hay	PROPN
ejpam-5470	269	13	et	et	PROPN
ejpam-5470	269	14	al	al	PROPN
ejpam-5470	269	15	.	.	PUNCT
ejpam-5470	269	16	/	/	SYM
ejpam-5470	269	17	eur	eur	PROPN
ejpam-5470	269	18	.	.	PUNCT
ejpam-5470	270	1	j.	j.	PROPN
ejpam-5470	270	2	pure	pure	PROPN
ejpam-5470	270	3	appl	appl	PROPN
ejpam-5470	270	4	.	.	PROPN
ejpam-5470	270	5	math	math	PROPN
ejpam-5470	270	6	,	,	PUNCT
ejpam-5470	270	7	18	18	NUM
ejpam-5470	270	8	(	(	PUNCT
ejpam-5470	270	9	1	1	NUM
ejpam-5470	270	10	)	)	PUNCT
ejpam-5470	270	11	(	(	PUNCT
ejpam-5470	270	12	2025	2025	NUM
ejpam-5470	270	13	)	)	PUNCT
ejpam-5470	270	14	,	,	PUNCT
ejpam-5470	270	15	5470	5470	NUM
ejpam-5470	270	16	9	9	NUM
ejpam-5470	270	17	of	of	ADP
ejpam-5470	270	18	14	14	NUM
ejpam-5470	270	19	and	and	CCONJ
ejpam-5470	270	20	|e0	|e0	NOUN
ejpam-5470	270	21	−	−	PROPN
ejpam-5470	270	22	e1|	e1|	NOUN
ejpam-5470	270	23	=	=	NOUN
ejpam-5470	270	24	0	0	NUM
ejpam-5470	270	25	.	.	PUNCT
ejpam-5470	271	1	for	for	ADP
ejpam-5470	271	2	the	the	DET
ejpam-5470	271	3	case	case	NOUN
ejpam-5470	271	4	p4r+3⊙l4	p4r+3⊙l4	X
ejpam-5470	271	5	4,4	4,4	NUM
ejpam-5470	271	6	,	,	PUNCT
ejpam-5470	271	7	the	the	DET
ejpam-5470	271	8	labeling	labeling	NOUN
ejpam-5470	271	9	[	[	X
ejpam-5470	271	10	m4r+3;010103	m4r+3;010103	NOUN
ejpam-5470	271	11	,	,	PUNCT
ejpam-5470	271	12	1010	1010	NUM
ejpam-5470	271	13	13	13	NUM
ejpam-5470	271	14	,	,	PUNCT
ejpam-5470	271	15	010103	010103	NUM
ejpam-5470	271	16	,	,	PUNCT
ejpam-5470	271	17	1010	1010	NUM
ejpam-5470	271	18	13	13	NUM
ejpam-5470	271	19	,	,	PUNCT
ejpam-5470	271	20	...	...	PUNCT
ejpam-5470	271	21	,	,	PUNCT
ejpam-5470	271	22	(	(	PUNCT
ejpam-5470	271	23	r	r	NOUN
ejpam-5470	271	24	−	−	PROPN
ejpam-5470	271	25	times	time	NOUN
ejpam-5470	271	26	)	)	PUNCT
ejpam-5470	271	27	,	,	PUNCT
ejpam-5470	271	28	010103	010103	NUM
ejpam-5470	271	29	,	,	PUNCT
ejpam-5470	271	30	1010	1010	NUM
ejpam-5470	271	31	13	13	NUM
ejpam-5470	271	32	,	,	PUNCT
ejpam-5470	271	33	1010	1010	NUM
ejpam-5470	271	34	13	13	NUM
ejpam-5470	271	35	]	]	PUNCT
ejpam-5470	271	36	is	be	AUX
ejpam-5470	271	37	sufficient	sufficient	ADJ
ejpam-5470	271	38	and	and	CCONJ
ejpam-5470	271	39	thus	thus	ADV
ejpam-5470	271	40	p4r+3⊙l4	p4r+3⊙l4	X
ejpam-5470	271	41	4,4	4,4	NOUN
ejpam-5470	271	42	t	t	PROPN
ejpam-5470	271	43	is	be	AUX
ejpam-5470	271	44	cordial	cordial	ADJ
ejpam-5470	271	45	.	.	PUNCT
ejpam-5470	272	1	case	case	NOUN
ejpam-5470	272	2	2	2	NUM
ejpam-5470	272	3	.	.	PUNCT
ejpam-5470	273	1	at	at	ADP
ejpam-5470	273	2	m	m	PROPN
ejpam-5470	273	3	≡	≡	PROPN
ejpam-5470	273	4	1(mod4	1(mod4	NUM
ejpam-5470	273	5	)	)	PUNCT
ejpam-5470	273	6	,	,	PUNCT
ejpam-5470	273	7	we	we	PRON
ejpam-5470	273	8	consider	consider	VERB
ejpam-5470	273	9	the	the	DET
ejpam-5470	273	10	following	follow	VERB
ejpam-5470	273	11	subcases	subcase	NOUN
ejpam-5470	273	12	.	.	PUNCT
ejpam-5470	274	1	subcase	subcase	PROPN
ejpam-5470	274	2	2.1.k	2.1.k	NUM
ejpam-5470	274	3	≡	≡	PROPN
ejpam-5470	274	4	0(mod4	0(mod4	NUM
ejpam-5470	274	5	)	)	PUNCT
ejpam-5470	274	6	let	let	VERB
ejpam-5470	274	7	k=	k=	ADJ
ejpam-5470	274	8	4r	4r	NOUN
ejpam-5470	274	9	,	,	PUNCT
ejpam-5470	274	10	r	r	NOUN
ejpam-5470	274	11	≥	≥	NUM
ejpam-5470	274	12	1	1	NUM
ejpam-5470	274	13	andm=	andm=	PROPN
ejpam-5470	274	14	4t+1	4t+1	PROPN
ejpam-5470	274	15	,	,	PUNCT
ejpam-5470	274	16	t	t	PROPN
ejpam-5470	274	17	>	>	X
ejpam-5470	274	18	1	1	NUM
ejpam-5470	274	19	.	.	PUNCT
ejpam-5470	275	1	then	then	ADV
ejpam-5470	275	2	,	,	PUNCT
ejpam-5470	275	3	the	the	DET
ejpam-5470	275	4	labelling	labelling	NOUN
ejpam-5470	275	5	[	[	X
ejpam-5470	275	6	m4r;010	m4r;010	NOUN
ejpam-5470	275	7	12s	12	NOUN
ejpam-5470	275	8	′	′	NUM
ejpam-5470	275	9	4t−403	4t−403	NOUN
ejpam-5470	275	10	,	,	PUNCT
ejpam-5470	275	11	10102l	10102l	NUM
ejpam-5470	275	12	′	′	NUM
ejpam-5470	275	13	4	4	NUM
ejpam-5470	275	14	t	t	NOUN
ejpam-5470	275	15	13	13	NUM
ejpam-5470	275	16	,	,	PUNCT
ejpam-5470	275	17	010	010	NUM
ejpam-5470	275	18	12s	12	NOUN
ejpam-5470	275	19	′	′	NUM
ejpam-5470	275	20	4t−403	4t−403	NOUN
ejpam-5470	275	21	,	,	PUNCT
ejpam-5470	275	22	10102l	10102l	NUM
ejpam-5470	275	23	′	′	NUM
ejpam-5470	275	24	4	4	NUM
ejpam-5470	275	25	t	t	NOUN
ejpam-5470	275	26	13	13	NUM
ejpam-5470	275	27	,	,	PUNCT
ejpam-5470	275	28	...	...	PUNCT
ejpam-5470	275	29	,	,	PUNCT
ejpam-5470	275	30	(	(	PUNCT
ejpam-5470	275	31	r−times	r−time	NOUN
ejpam-5470	275	32	)	)	PUNCT
ejpam-5470	275	33	]	]	PUNCT
ejpam-5470	275	34	for	for	SCONJ
ejpam-5470	275	35	p4r⊙	p4r⊙	PROPN
ejpam-5470	275	36	l4	l4	PROPN
ejpam-5470	275	37	4,4t+1	4,4t+1	PROPN
ejpam-5470	275	38	is	be	AUX
ejpam-5470	275	39	applied	apply	VERB
ejpam-5470	275	40	.	.	PUNCT
ejpam-5470	276	1	therefore	therefore	ADV
ejpam-5470	276	2	x0	x0	PROPN
ejpam-5470	276	3	=	=	PROPN
ejpam-5470	276	4	x1=	x1=	PROPN
ejpam-5470	276	5	2r	2r	NUM
ejpam-5470	276	6	,	,	PUNCT
ejpam-5470	276	7	a0=	a0=	NOUN
ejpam-5470	276	8	0,a1=	0,a1=	NOUN
ejpam-5470	276	9	4r	4r	NOUN
ejpam-5470	276	10	−	−	NOUN
ejpam-5470	276	11	1,y0=	1,y0=	PROPN
ejpam-5470	276	12	2	2	NUM
ejpam-5470	276	13	t	t	NOUN
ejpam-5470	276	14	+	+	NOUN
ejpam-5470	276	15	3,y1=	3,y1=	NUM
ejpam-5470	276	16	2	2	NUM
ejpam-5470	276	17	t	t	NOUN
ejpam-5470	276	18	+	+	NOUN
ejpam-5470	276	19	1,b0=	1,b0=	NUM
ejpam-5470	276	20	8	8	NUM
ejpam-5470	276	21	t	t	NOUN
ejpam-5470	276	22	,	,	PUNCT
ejpam-5470	276	23	b1=	b1=	NOUN
ejpam-5470	276	24	8	8	NUM
ejpam-5470	276	25	t	t	NOUN
ejpam-5470	276	26	+	+	CCONJ
ejpam-5470	276	27	1,y′0=	1,y′0=	NUM
ejpam-5470	276	28	2	2	NUM
ejpam-5470	276	29	t	t	NOUN
ejpam-5470	276	30	+	+	NOUN
ejpam-5470	276	31	1,y′1=	1,y′1=	NUM
ejpam-5470	276	32	2	2	NUM
ejpam-5470	276	33	t	t	NOUN
ejpam-5470	276	34	+	+	CCONJ
ejpam-5470	276	35	3,b′0=	3,b′0=	NUM
ejpam-5470	276	36	8	8	NUM
ejpam-5470	276	37	t	t	NOUN
ejpam-5470	276	38	and	and	CCONJ
ejpam-5470	276	39	b′1=	b′1=	ADP
ejpam-5470	276	40	8	8	NUM
ejpam-5470	276	41	t	t	NOUN
ejpam-5470	276	42	+	+	NOUN
ejpam-5470	276	43	1	1	X
ejpam-5470	276	44	.	.	PUNCT
ejpam-5470	277	1	so	so	ADV
ejpam-5470	277	2	,	,	PUNCT
ejpam-5470	277	3	|v0	|v0	NOUN
ejpam-5470	277	4	−	−	NOUN
ejpam-5470	277	5	v1|	v1|	NOUN
ejpam-5470	277	6	=	=	SYM
ejpam-5470	277	7	0	0	NUM
ejpam-5470	277	8	and	and	CCONJ
ejpam-5470	277	9	|e0	|e0	NOUN
ejpam-5470	278	1	−	−	PROPN
ejpam-5470	278	2	e1|	e1|	NOUN
ejpam-5470	278	3	=	=	NOUN
ejpam-5470	278	4	1	1	X
ejpam-5470	278	5	.	.	X
ejpam-5470	279	1	for	for	ADP
ejpam-5470	279	2	the	the	DET
ejpam-5470	279	3	case	case	NOUN
ejpam-5470	279	4	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	279	5	4,5	4,5	NUM
ejpam-5470	279	6	,	,	PUNCT
ejpam-5470	279	7	the	the	DET
ejpam-5470	279	8	labeling	labeling	NOUN
ejpam-5470	279	9	[	[	X
ejpam-5470	279	10	m4r;03	m4r;03	PROPN
ejpam-5470	279	11	12021,03	12021,03	NUM
ejpam-5470	279	12	12021	12021	NUM
ejpam-5470	279	13	,	,	PUNCT
ejpam-5470	279	14	1302	1302	NUM
ejpam-5470	279	15	120	120	NUM
ejpam-5470	279	16	,	,	PUNCT
ejpam-5470	279	17	1302	1302	NUM
ejpam-5470	279	18	120	120	NUM
ejpam-5470	279	19	,	,	PUNCT
ejpam-5470	279	20	...	...	PUNCT
ejpam-5470	279	21	,	,	PUNCT
ejpam-5470	279	22	(	(	PUNCT
ejpam-5470	279	23	r	r	NOUN
ejpam-5470	279	24	−	−	PROPN
ejpam-5470	279	25	times	time	NOUN
ejpam-5470	279	26	)	)	PUNCT
ejpam-5470	279	27	]	]	PUNCT
ejpam-5470	279	28	is	be	AUX
ejpam-5470	279	29	sufficient	sufficient	ADJ
ejpam-5470	279	30	and	and	CCONJ
ejpam-5470	279	31	thus	thus	ADV
ejpam-5470	279	32	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	279	33	4,4t+1	4,4t+1	NOUN
ejpam-5470	279	34	is	be	AUX
ejpam-5470	279	35	cordial	cordial	ADJ
ejpam-5470	279	36	.	.	PUNCT
ejpam-5470	280	1	subcase	subcase	PROPN
ejpam-5470	280	2	2.2.k	2.2.k	NUM
ejpam-5470	280	3	≡	≡	PROPN
ejpam-5470	280	4	1(mod4	1(mod4	NUM
ejpam-5470	280	5	)	)	PUNCT
ejpam-5470	280	6	let	let	VERB
ejpam-5470	280	7	k=	k=	X
ejpam-5470	280	8	4r+1,r	4r+1,r	NOUN
ejpam-5470	280	9	≥	≥	X
ejpam-5470	280	10	0	0	NUM
ejpam-5470	281	1	andm=	andm=	PROPN
ejpam-5470	281	2	4t+1	4t+1	PROPN
ejpam-5470	281	3	,	,	PUNCT
ejpam-5470	281	4	t	t	PROPN
ejpam-5470	281	5	>	>	X
ejpam-5470	281	6	1	1	NUM
ejpam-5470	281	7	.	.	PUNCT
ejpam-5470	282	1	then	then	ADV
ejpam-5470	282	2	,	,	PUNCT
ejpam-5470	282	3	the	the	DET
ejpam-5470	282	4	labelling	labelling	NOUN
ejpam-5470	282	5	[	[	X
ejpam-5470	282	6	m4r+1;010	m4r+1;010	NOUN
ejpam-5470	282	7	12s	12	NOUN
ejpam-5470	282	8	′	′	NUM
ejpam-5470	282	9	4t−403	4t−403	NOUN
ejpam-5470	282	10	,	,	PUNCT
ejpam-5470	282	11	10102l	10102l	NUM
ejpam-5470	282	12	′	′	NUM
ejpam-5470	282	13	4	4	NUM
ejpam-5470	282	14	t	t	NOUN
ejpam-5470	282	15	13	13	NUM
ejpam-5470	282	16	,	,	PUNCT
ejpam-5470	282	17	010	010	NUM
ejpam-5470	282	18	12s	12	NOUN
ejpam-5470	282	19	′	′	NUM
ejpam-5470	282	20	4t−403	4t−403	NOUN
ejpam-5470	282	21	,	,	PUNCT
ejpam-5470	282	22	10102l	10102l	NUM
ejpam-5470	282	23	′	′	NUM
ejpam-5470	282	24	4	4	NUM
ejpam-5470	282	25	t	t	NOUN
ejpam-5470	282	26	13	13	NUM
ejpam-5470	282	27	,	,	PUNCT
ejpam-5470	282	28	...	...	PUNCT
ejpam-5470	282	29	,	,	PUNCT
ejpam-5470	282	30	(	(	PUNCT
ejpam-5470	282	31	r	r	NOUN
ejpam-5470	282	32	−	−	PROPN
ejpam-5470	282	33	times	time	NOUN
ejpam-5470	282	34	)	)	PUNCT
ejpam-5470	282	35	,	,	PUNCT
ejpam-5470	282	36	010	010	NUM
ejpam-5470	282	37	13l	13l	NUM
ejpam-5470	282	38	′	′	NUM
ejpam-5470	282	39	4t−403	4t−403	NUM
ejpam-5470	282	40	]	]	PUNCT
ejpam-5470	282	41	for	for	SCONJ
ejpam-5470	282	42	p4r+1⊙	p4r+1⊙	PROPN
ejpam-5470	282	43	l4	l4	PROPN
ejpam-5470	282	44	4,4t+1	4,4t+1	PROPN
ejpam-5470	282	45	is	be	AUX
ejpam-5470	282	46	applied	apply	VERB
ejpam-5470	282	47	.	.	PUNCT
ejpam-5470	283	1	therefore	therefore	ADV
ejpam-5470	283	2	x0=	x0=	PROPN
ejpam-5470	284	1	2r+1,x1=	2r+1,x1=	NUM
ejpam-5470	284	2	2r	2r	NUM
ejpam-5470	284	3	,	,	PUNCT
ejpam-5470	284	4	a0=	a0=	NOUN
ejpam-5470	284	5	0,a1=	0,a1=	NOUN
ejpam-5470	284	6	4r	4r	NOUN
ejpam-5470	284	7	,	,	PUNCT
ejpam-5470	284	8	y0=	y0=	PROPN
ejpam-5470	284	9	2t+3,y1=	2t+3,y1=	NUM
ejpam-5470	284	10	2t+1,b0=	2t+1,b0=	NUM
ejpam-5470	284	11	8	8	NUM
ejpam-5470	284	12	t	t	NOUN
ejpam-5470	284	13	,	,	PUNCT
ejpam-5470	284	14	b1=	b1=	PROPN
ejpam-5470	284	15	8t+1,y′0=	8t+1,y′0=	NUM
ejpam-5470	284	16	2t+	2t+	NUM
ejpam-5470	284	17	1,y′1=	1,y′1=	NUM
ejpam-5470	284	18	2t+3,b′0=	2t+3,b′0=	NUM
ejpam-5470	284	19	8	8	NUM
ejpam-5470	284	20	t	t	NOUN
ejpam-5470	284	21	,	,	PUNCT
ejpam-5470	284	22	b′1=	b′1=	ADP
ejpam-5470	284	23	8t+1,y”0=	8t+1,y”0=	NUM
ejpam-5470	284	24	2t+2,y”1=	2t+2,y”1=	NUM
ejpam-5470	284	25	2t+2,b”0=	2t+2,b”0=	NUM
ejpam-5470	284	26	8	8	NUM
ejpam-5470	284	27	t	t	NOUN
ejpam-5470	284	28	and	and	CCONJ
ejpam-5470	284	29	b”1=	b”1=	PROPN
ejpam-5470	284	30	8t+1	8t+1	PROPN
ejpam-5470	284	31	.	.	PUNCT
ejpam-5470	285	1	so	so	ADV
ejpam-5470	285	2	,	,	PUNCT
ejpam-5470	285	3	|v0−v1|	|v0−v1|	NUM
ejpam-5470	285	4	=	=	SYM
ejpam-5470	285	5	1	1	NUM
ejpam-5470	285	6	and	and	CCONJ
ejpam-5470	285	7	|e0	|e0	NOUN
ejpam-5470	286	1	−	−	PROPN
ejpam-5470	286	2	e1|	e1|	NOUN
ejpam-5470	286	3	=	=	NOUN
ejpam-5470	286	4	1	1	X
ejpam-5470	286	5	.	.	X
ejpam-5470	286	6	for	for	ADP
ejpam-5470	286	7	the	the	DET
ejpam-5470	286	8	case	case	NOUN
ejpam-5470	286	9	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	286	10	4,5	4,5	NUM
ejpam-5470	286	11	,	,	PUNCT
ejpam-5470	286	12	the	the	DET
ejpam-5470	286	13	labeling	labeling	NOUN
ejpam-5470	286	14	[	[	X
ejpam-5470	286	15	m4r;03	m4r;03	PROPN
ejpam-5470	286	16	12021,03	12021,03	NUM
ejpam-5470	286	17	12021	12021	NUM
ejpam-5470	286	18	,	,	PUNCT
ejpam-5470	286	19	1302	1302	NUM
ejpam-5470	286	20	120	120	NUM
ejpam-5470	286	21	,	,	PUNCT
ejpam-5470	286	22	1302	1302	NUM
ejpam-5470	286	23	120	120	NUM
ejpam-5470	286	24	,	,	PUNCT
ejpam-5470	286	25	...	...	PUNCT
ejpam-5470	286	26	,	,	PUNCT
ejpam-5470	286	27	(	(	PUNCT
ejpam-5470	286	28	r	r	NOUN
ejpam-5470	286	29	−	−	PROPN
ejpam-5470	286	30	times	time	NOUN
ejpam-5470	286	31	)	)	PUNCT
ejpam-5470	286	32	,	,	PUNCT
ejpam-5470	286	33	010	010	NUM
ejpam-5470	286	34	140	140	NUM
ejpam-5470	286	35	]	]	PUNCT
ejpam-5470	286	36	is	be	AUX
ejpam-5470	286	37	sufficient	sufficient	ADJ
ejpam-5470	286	38	and	and	CCONJ
ejpam-5470	286	39	thus	thus	ADV
ejpam-5470	286	40	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	286	41	4,4t+1	4,4t+1	NOUN
ejpam-5470	286	42	is	be	AUX
ejpam-5470	286	43	cordial	cordial	ADJ
ejpam-5470	286	44	.	.	PUNCT
ejpam-5470	287	1	subcase	subcase	PROPN
ejpam-5470	287	2	2.3.k	2.3.k	NUM
ejpam-5470	287	3	≡	≡	PROPN
ejpam-5470	287	4	2(mod4	2(mod4	NUM
ejpam-5470	287	5	)	)	PUNCT
ejpam-5470	287	6	let	let	VERB
ejpam-5470	287	7	k=	k=	PROPN
ejpam-5470	287	8	4r+2,r	4r+2,r	NUM
ejpam-5470	287	9	≥	≥	NOUN
ejpam-5470	287	10	0	0	NUM
ejpam-5470	287	11	andm=	andm=	PROPN
ejpam-5470	287	12	4	4	NUM
ejpam-5470	287	13	t	t	PROPN
ejpam-5470	287	14	,	,	PUNCT
ejpam-5470	287	15	t	t	PROPN
ejpam-5470	287	16	>	>	X
ejpam-5470	287	17	1	1	NUM
ejpam-5470	287	18	.	.	PUNCT
ejpam-5470	288	1	then	then	ADV
ejpam-5470	288	2	,	,	PUNCT
ejpam-5470	288	3	the	the	DET
ejpam-5470	288	4	labelling	labelling	NOUN
ejpam-5470	288	5	[	[	X
ejpam-5470	288	6	m4r+1;010	m4r+1;010	NOUN
ejpam-5470	288	7	12s	12	NOUN
ejpam-5470	288	8	′	′	NUM
ejpam-5470	288	9	4t−403	4t−403	NOUN
ejpam-5470	288	10	,	,	PUNCT
ejpam-5470	288	11	10102l	10102l	NUM
ejpam-5470	288	12	′	′	NUM
ejpam-5470	288	13	4	4	NUM
ejpam-5470	288	14	t	t	NOUN
ejpam-5470	288	15	13	13	NUM
ejpam-5470	288	16	,	,	PUNCT
ejpam-5470	288	17	010	010	NUM
ejpam-5470	288	18	12s	12	NOUN
ejpam-5470	288	19	′	′	NUM
ejpam-5470	288	20	4t−403	4t−403	NOUN
ejpam-5470	288	21	,	,	PUNCT
ejpam-5470	288	22	10102l	10102l	NUM
ejpam-5470	288	23	′	′	NUM
ejpam-5470	288	24	4	4	NUM
ejpam-5470	288	25	t	t	NOUN
ejpam-5470	288	26	13	13	NUM
ejpam-5470	288	27	,	,	PUNCT
ejpam-5470	288	28	...	...	PUNCT
ejpam-5470	288	29	,	,	PUNCT
ejpam-5470	288	30	(	(	PUNCT
ejpam-5470	288	31	r	r	NOUN
ejpam-5470	288	32	−	−	PROPN
ejpam-5470	288	33	times	time	NOUN
ejpam-5470	288	34	)	)	PUNCT
ejpam-5470	288	35	,	,	PUNCT
ejpam-5470	288	36	010	010	NUM
ejpam-5470	288	37	12s	12	NOUN
ejpam-5470	288	38	′	′	NUM
ejpam-5470	288	39	4t−403	4t−403	NOUN
ejpam-5470	288	40	,	,	PUNCT
ejpam-5470	288	41	10102l	10102l	NUM
ejpam-5470	288	42	′	′	NUM
ejpam-5470	288	43	4	4	NUM
ejpam-5470	288	44	t	t	NOUN
ejpam-5470	288	45	13	13	NUM
ejpam-5470	288	46	]	]	PUNCT
ejpam-5470	288	47	for	for	ADP
ejpam-5470	288	48	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	288	49	4,4	4,4	NUM
ejpam-5470	288	50	t	t	PROPN
ejpam-5470	288	51	is	be	AUX
ejpam-5470	288	52	applied	apply	VERB
ejpam-5470	288	53	.	.	PUNCT
ejpam-5470	289	1	therefore	therefore	ADV
ejpam-5470	289	2	x0	x0	PROPN
ejpam-5470	289	3	=	=	PROPN
ejpam-5470	289	4	x1=	x1=	PROPN
ejpam-5470	289	5	2r+1,a0=	2r+1,a0=	NUM
ejpam-5470	289	6	0,a1=	0,a1=	NUM
ejpam-5470	289	7	4r+1,y0=	4r+1,y0=	NUM
ejpam-5470	289	8	2t+3,y1=	2t+3,y1=	NUM
ejpam-5470	289	9	2t+1,b0=	2t+1,b0=	NUM
ejpam-5470	289	10	8	8	NUM
ejpam-5470	289	11	t	t	NOUN
ejpam-5470	289	12	,	,	PUNCT
ejpam-5470	289	13	b1=	b1=	PROPN
ejpam-5470	289	14	8t+	8t+	NUM
ejpam-5470	289	15	1,y′0=	1,y′0=	NUM
ejpam-5470	289	16	2t+1,y′1=	2t+1,y′1=	NUM
ejpam-5470	289	17	2t+3,b′0=	2t+3,b′0=	NUM
ejpam-5470	289	18	8	8	NUM
ejpam-5470	289	19	t	t	NOUN
ejpam-5470	289	20	and	and	CCONJ
ejpam-5470	289	21	b′1=	b′1=	ADP
ejpam-5470	289	22	8t+1	8t+1	PROPN
ejpam-5470	289	23	.	.	PUNCT
ejpam-5470	290	1	so	so	ADV
ejpam-5470	290	2	,	,	PUNCT
ejpam-5470	290	3	|v0	|v0	PROPN
ejpam-5470	290	4	−	−	NOUN
ejpam-5470	290	5	v1|	v1|	NOUN
ejpam-5470	290	6	=	=	SYM
ejpam-5470	290	7	0	0	NUM
ejpam-5470	290	8	and	and	CCONJ
ejpam-5470	290	9	|e0	|e0	NOUN
ejpam-5470	291	1	−	−	PROPN
ejpam-5470	291	2	e1|	e1|	NOUN
ejpam-5470	291	3	=	=	NOUN
ejpam-5470	291	4	1	1	X
ejpam-5470	291	5	.	.	X
ejpam-5470	291	6	for	for	ADP
ejpam-5470	291	7	the	the	DET
ejpam-5470	291	8	case	case	NOUN
ejpam-5470	291	9	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	291	10	4,5	4,5	NUM
ejpam-5470	291	11	,	,	PUNCT
ejpam-5470	291	12	the	the	DET
ejpam-5470	291	13	labeling	labeling	NOUN
ejpam-5470	292	1	[	[	X
ejpam-5470	292	2	l4r01;03	l4r01;03	PROPN
ejpam-5470	292	3	12021,03	12021,03	NUM
ejpam-5470	292	4	12021	12021	NUM
ejpam-5470	292	5	,	,	PUNCT
ejpam-5470	292	6	1302	1302	NUM
ejpam-5470	292	7	120	120	NUM
ejpam-5470	292	8	,	,	PUNCT
ejpam-5470	292	9	1302	1302	NUM
ejpam-5470	292	10	120	120	NUM
ejpam-5470	292	11	,	,	PUNCT
ejpam-5470	292	12	...	...	PUNCT
ejpam-5470	292	13	,	,	PUNCT
ejpam-5470	292	14	(	(	PUNCT
ejpam-5470	292	15	r−	r−	PROPN
ejpam-5470	292	16	times	time	NOUN
ejpam-5470	292	17	)	)	PUNCT
ejpam-5470	292	18	,	,	PUNCT
ejpam-5470	292	19	03	03	NUM
ejpam-5470	292	20	12021,03	12021,03	NUM
ejpam-5470	292	21	12021	12021	NUM
ejpam-5470	292	22	]	]	PUNCT
ejpam-5470	292	23	is	be	AUX
ejpam-5470	292	24	sufficient	sufficient	ADJ
ejpam-5470	292	25	and	and	CCONJ
ejpam-5470	292	26	thus	thus	ADV
ejpam-5470	292	27	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	292	28	4,4t+1	4,4t+1	NOUN
ejpam-5470	292	29	is	be	AUX
ejpam-5470	292	30	cordial	cordial	ADJ
ejpam-5470	292	31	.	.	PUNCT
ejpam-5470	293	1	subcase	subcase	PROPN
ejpam-5470	293	2	2.4.k	2.4.k	NUM
ejpam-5470	293	3	≡	≡	PROPN
ejpam-5470	293	4	3(mod4	3(mod4	NUM
ejpam-5470	293	5	)	)	PUNCT
ejpam-5470	293	6	let	let	VERB
ejpam-5470	293	7	k=	k=	X
ejpam-5470	293	8	4r+3,r	4r+3,r	NUM
ejpam-5470	293	9	≥	≥	NOUN
ejpam-5470	293	10	0	0	NUM
ejpam-5470	293	11	andm=	andm=	PROPN
ejpam-5470	293	12	4t+1	4t+1	PROPN
ejpam-5470	293	13	,	,	PUNCT
ejpam-5470	293	14	t	t	PROPN
ejpam-5470	293	15	>	>	X
ejpam-5470	293	16	1	1	NUM
ejpam-5470	293	17	.	.	PUNCT
ejpam-5470	294	1	then	then	ADV
ejpam-5470	294	2	,	,	PUNCT
ejpam-5470	294	3	the	the	DET
ejpam-5470	294	4	labelling	labelling	NOUN
ejpam-5470	294	5	[	[	X
ejpam-5470	294	6	m4r+1;010	m4r+1;010	NOUN
ejpam-5470	294	7	12s	12	NOUN
ejpam-5470	294	8	′	′	NUM
ejpam-5470	294	9	4t−403	4t−403	NOUN
ejpam-5470	294	10	,	,	PUNCT
ejpam-5470	294	11	10102l	10102l	NUM
ejpam-5470	294	12	′	′	NUM
ejpam-5470	294	13	4	4	NUM
ejpam-5470	294	14	t	t	NOUN
ejpam-5470	294	15	13	13	NUM
ejpam-5470	294	16	,	,	PUNCT
ejpam-5470	294	17	010	010	NUM
ejpam-5470	294	18	12s	12	NOUN
ejpam-5470	294	19	′	′	NUM
ejpam-5470	294	20	4t−403	4t−403	NOUN
ejpam-5470	294	21	,	,	PUNCT
ejpam-5470	294	22	10102l	10102l	NUM
ejpam-5470	294	23	′	′	NUM
ejpam-5470	294	24	4	4	NUM
ejpam-5470	294	25	t	t	NOUN
ejpam-5470	294	26	13	13	NUM
ejpam-5470	294	27	,	,	PUNCT
ejpam-5470	294	28	...	...	PUNCT
ejpam-5470	294	29	,	,	PUNCT
ejpam-5470	294	30	(	(	PUNCT
ejpam-5470	294	31	r	r	NOUN
ejpam-5470	294	32	−	−	PROPN
ejpam-5470	294	33	times	time	NOUN
ejpam-5470	294	34	)	)	PUNCT
ejpam-5470	294	35	,	,	PUNCT
ejpam-5470	294	36	010	010	NUM
ejpam-5470	294	37	13l	13l	NUM
ejpam-5470	294	38	′	′	NUM
ejpam-5470	294	39	4t−403	4t−403	NUM
ejpam-5470	294	40	]	]	PUNCT
ejpam-5470	294	41	for	for	ADP
ejpam-5470	294	42	p4r+3⊙	p4r+3⊙	PROPN
ejpam-5470	294	43	l4	l4	PROPN
ejpam-5470	294	44	4,4t+1	4,4t+1	PROPN
ejpam-5470	294	45	is	be	AUX
ejpam-5470	294	46	applied	apply	VERB
ejpam-5470	294	47	.	.	PUNCT
ejpam-5470	295	1	therefore	therefore	ADV
ejpam-5470	295	2	x0=	x0=	PUNCT
ejpam-5470	295	3	2r	2r	NUM
ejpam-5470	295	4	+	+	CCONJ
ejpam-5470	295	5	2,x1=	2,x1=	NUM
ejpam-5470	295	6	2r	2r	NUM
ejpam-5470	296	1	+	+	CCONJ
ejpam-5470	296	2	1,a0=	1,a0=	NUM
ejpam-5470	296	3	0,a1=	0,a1=	NOUN
ejpam-5470	296	4	4r	4r	NOUN
ejpam-5470	296	5	+	+	CCONJ
ejpam-5470	296	6	2,y0=	2,y0=	NUM
ejpam-5470	296	7	2t+	2t+	NUM
ejpam-5470	296	8	3,y1=	3,y1=	NUM
ejpam-5470	296	9	2t+	2t+	NUM
ejpam-5470	296	10	1,b0=	1,b0=	NUM
ejpam-5470	296	11	8	8	NUM
ejpam-5470	296	12	t	t	NOUN
ejpam-5470	296	13	,	,	PUNCT
ejpam-5470	296	14	b1=	b1=	PROPN
ejpam-5470	296	15	8t+	8t+	NUM
ejpam-5470	296	16	1,y′0=	1,y′0=	NUM
ejpam-5470	296	17	2t+1,y′1=	2t+1,y′1=	NUM
ejpam-5470	296	18	2t+3,b′0=	2t+3,b′0=	NUM
ejpam-5470	296	19	8	8	NUM
ejpam-5470	296	20	t	t	NOUN
ejpam-5470	296	21	,	,	PUNCT
ejpam-5470	296	22	b′1=	b′1=	ADP
ejpam-5470	296	23	8t+1,y”0=	8t+1,y”0=	NUM
ejpam-5470	296	24	2t+2,y”1=	2t+2,y”1=	NUM
ejpam-5470	296	25	2t+2,b”0=	2t+2,b”0=	NUM
ejpam-5470	296	26	8	8	NUM
ejpam-5470	296	27	t	t	NOUN
ejpam-5470	296	28	and	and	CCONJ
ejpam-5470	296	29	b”1=	b”1=	PROPN
ejpam-5470	296	30	8t+1	8t+1	PROPN
ejpam-5470	296	31	.	.	PUNCT
ejpam-5470	297	1	so	so	ADV
ejpam-5470	297	2	,	,	PUNCT
ejpam-5470	297	3	|v0−v1|	|v0−v1|	NUM
ejpam-5470	297	4	=	=	SYM
ejpam-5470	297	5	1	1	NUM
ejpam-5470	297	6	and	and	CCONJ
ejpam-5470	297	7	|e0−e1|	|e0−e1|	NOUN
ejpam-5470	297	8	=	=	NOUN
ejpam-5470	297	9	1	1	X
ejpam-5470	297	10	.	.	X
ejpam-5470	298	1	for	for	ADP
ejpam-5470	298	2	the	the	DET
ejpam-5470	298	3	case	case	NOUN
ejpam-5470	298	4	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	298	5	4,5	4,5	NUM
ejpam-5470	298	6	,	,	PUNCT
ejpam-5470	298	7	the	the	DET
ejpam-5470	298	8	labeling	labeling	NOUN
ejpam-5470	298	9	[	[	X
ejpam-5470	298	10	m4r;03	m4r;03	NUM
ejpam-5470	298	11	12021	12021	NUM
ejpam-5470	298	12	,	,	PUNCT
ejpam-5470	298	13	1302	1302	NUM
ejpam-5470	298	14	120	120	NUM
ejpam-5470	298	15	,	,	PUNCT
ejpam-5470	298	16	03	03	NUM
ejpam-5470	298	17	12021	12021	NUM
ejpam-5470	298	18	,	,	PUNCT
ejpam-5470	298	19	1302	1302	NUM
ejpam-5470	298	20	120	120	NUM
ejpam-5470	298	21	,	,	PUNCT
ejpam-5470	298	22	...	...	PUNCT
ejpam-5470	298	23	,	,	PUNCT
ejpam-5470	298	24	(	(	PUNCT
ejpam-5470	298	25	r−times),03	r−times),03	PROPN
ejpam-5470	298	26	12021	12021	NUM
ejpam-5470	298	27	,	,	PUNCT
ejpam-5470	298	28	1302	1302	NUM
ejpam-5470	298	29	120	120	NUM
ejpam-5470	298	30	,	,	PUNCT
ejpam-5470	298	31	010	010	NUM
ejpam-5470	298	32	140]is	140]is	NUM
ejpam-5470	298	33	sufficient	sufficient	ADJ
ejpam-5470	298	34	and	and	CCONJ
ejpam-5470	298	35	thus	thus	ADV
ejpam-5470	298	36	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	298	37	4,4t+1	4,4t+1	NOUN
ejpam-5470	298	38	is	be	AUX
ejpam-5470	298	39	cordial	cordial	ADJ
ejpam-5470	298	40	.	.	PUNCT
ejpam-5470	299	1	case	case	NOUN
ejpam-5470	299	2	3	3	X
ejpam-5470	299	3	.	.	PUNCT
ejpam-5470	300	1	at	at	ADP
ejpam-5470	300	2	m	m	PROPN
ejpam-5470	300	3	≡	≡	PROPN
ejpam-5470	300	4	2(mod4	2(mod4	NUM
ejpam-5470	300	5	)	)	PUNCT
ejpam-5470	300	6	,	,	PUNCT
ejpam-5470	300	7	we	we	PRON
ejpam-5470	300	8	consider	consider	VERB
ejpam-5470	300	9	the	the	DET
ejpam-5470	300	10	following	follow	VERB
ejpam-5470	300	11	sub	sub	NOUN
ejpam-5470	300	12	subcases	subcase	NOUN
ejpam-5470	300	13	.	.	PUNCT
ejpam-5470	301	1	subcase	subcase	PROPN
ejpam-5470	301	2	3.1.k	3.1.k	NUM
ejpam-5470	301	3	≡	≡	PROPN
ejpam-5470	301	4	0(mod4	0(mod4	NUM
ejpam-5470	301	5	)	)	PUNCT
ejpam-5470	301	6	let	let	VERB
ejpam-5470	301	7	k=	k=	ADJ
ejpam-5470	301	8	4r	4r	NOUN
ejpam-5470	301	9	,	,	PUNCT
ejpam-5470	301	10	r	r	NOUN
ejpam-5470	301	11	≥	≥	NUM
ejpam-5470	301	12	1	1	NUM
ejpam-5470	301	13	andm=	andm=	PROPN
ejpam-5470	301	14	4t+2	4t+2	PROPN
ejpam-5470	301	15	,	,	PUNCT
ejpam-5470	301	16	t	t	PROPN
ejpam-5470	301	17	>	>	X
ejpam-5470	301	18	1	1	NUM
ejpam-5470	301	19	.	.	PUNCT
ejpam-5470	302	1	then	then	ADV
ejpam-5470	302	2	,	,	PUNCT
ejpam-5470	302	3	the	the	DET
ejpam-5470	302	4	labelling	labelling	NOUN
ejpam-5470	302	5	[	[	X
ejpam-5470	302	6	l4r;0	l4r;0	ADP
ejpam-5470	302	7	15m4t−60310	15m4t−60310	NUM
ejpam-5470	302	8	,	,	PUNCT
ejpam-5470	302	9	0	0	NUM
ejpam-5470	302	10	15m4t−60310	15m4t−60310	NUM
ejpam-5470	302	11	,	,	PUNCT
ejpam-5470	302	12	105	105	NUM
ejpam-5470	302	13	m	m	NOUN
ejpam-5470	302	14	′	′	NUM
ejpam-5470	302	15	4t−6	4t−6	PROPN
ejpam-5470	302	16	1301	1301	NUM
ejpam-5470	302	17	,	,	PUNCT
ejpam-5470	302	18	105	105	NUM
ejpam-5470	302	19	m	m	NOUN
ejpam-5470	302	20	′	′	NUM
ejpam-5470	302	21	4t−6	4t−6	NUM
ejpam-5470	302	22	1301	1301	NUM
ejpam-5470	302	23	,	,	PUNCT
ejpam-5470	302	24	...	...	PUNCT
ejpam-5470	302	25	,	,	PUNCT
ejpam-5470	302	26	(	(	PUNCT
ejpam-5470	302	27	r−times	r−time	NOUN
ejpam-5470	302	28	)	)	PUNCT
ejpam-5470	302	29	]	]	PUNCT
ejpam-5470	302	30	for	for	ADP
ejpam-5470	302	31	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	302	32	4,4t+2	4,4t+2	PROPN
ejpam-5470	302	33	is	be	AUX
ejpam-5470	302	34	applied	apply	VERB
ejpam-5470	302	35	.	.	PUNCT
ejpam-5470	303	1	therefore	therefore	ADV
ejpam-5470	303	2	x0	x0	PROPN
ejpam-5470	303	3	=	=	PROPN
ejpam-5470	303	4	x1=	x1=	PROPN
ejpam-5470	303	5	2r	2r	NUM
ejpam-5470	303	6	,	,	PUNCT
ejpam-5470	303	7	a0=	a0=	PROPN
ejpam-5470	303	8	2r	2r	NUM
ejpam-5470	303	9	,	,	PUNCT
ejpam-5470	303	10	a1=	a1=	PROPN
ejpam-5470	303	11	2r−1,y0=	2r−1,y0=	PROPN
ejpam-5470	303	12	2t+2	2t+2	PROPN
ejpam-5470	303	13	,	,	PUNCT
ejpam-5470	303	14	y1=	y1=	PROPN
ejpam-5470	303	15	2t+3,b0=	2t+3,b0=	NUM
ejpam-5470	303	16	8t+3,b1=	8t+3,b1=	NUM
ejpam-5470	303	17	8t+2,y′0=	8t+2,y′0=	NUM
ejpam-5470	303	18	2t+3,y′1=	2t+3,y′1=	NUM
ejpam-5470	303	19	2t+2,b′0=	2t+2,b′0=	NUM
ejpam-5470	303	20	8t+3	8t+3	ADJ
ejpam-5470	303	21	and	and	CCONJ
ejpam-5470	303	22	b′1=	b′1=	ADP
ejpam-5470	303	23	8	8	NUM
ejpam-5470	303	24	t	t	NOUN
ejpam-5470	303	25	+	+	NOUN
ejpam-5470	303	26	2	2	X
ejpam-5470	303	27	.	.	PUNCT
ejpam-5470	304	1	so	so	ADV
ejpam-5470	304	2	,	,	PUNCT
ejpam-5470	304	3	|v0	|v0	NOUN
ejpam-5470	304	4	−	−	NOUN
ejpam-5470	304	5	v1|	v1|	NOUN
ejpam-5470	304	6	=	=	SYM
ejpam-5470	304	7	0	0	NUM
ejpam-5470	304	8	and	and	CCONJ
ejpam-5470	304	9	|e0	|e0	NOUN
ejpam-5470	305	1	−	−	PROPN
ejpam-5470	305	2	e1|	e1|	NOUN
ejpam-5470	305	3	=	=	NOUN
ejpam-5470	305	4	1	1	X
ejpam-5470	305	5	.	.	X
ejpam-5470	306	1	for	for	ADP
ejpam-5470	306	2	the	the	DET
ejpam-5470	306	3	case	case	NOUN
ejpam-5470	306	4	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	306	5	4,6	4,6	NUM
ejpam-5470	306	6	,	,	PUNCT
ejpam-5470	306	7	the	the	DET
ejpam-5470	306	8	labeling	labeling	NOUN
ejpam-5470	306	9	[	[	X
ejpam-5470	306	10	l4r;03	l4r;03	ADP
ejpam-5470	306	11	1402	1402	NUM
ejpam-5470	306	12	,	,	PUNCT
ejpam-5470	306	13	03	03	NUM
ejpam-5470	306	14	1402	1402	NUM
ejpam-5470	306	15	,	,	PUNCT
ejpam-5470	306	16	1304	1304	NUM
ejpam-5470	306	17	12	12	NUM
ejpam-5470	306	18	,	,	PUNCT
ejpam-5470	306	19	1304	1304	NUM
ejpam-5470	306	20	12	12	NUM
ejpam-5470	306	21	,	,	PUNCT
ejpam-5470	306	22	...	...	PUNCT
ejpam-5470	306	23	,	,	PUNCT
ejpam-5470	306	24	(	(	PUNCT
ejpam-5470	306	25	r−	r−	PROPN
ejpam-5470	306	26	times	time	NOUN
ejpam-5470	306	27	)	)	PUNCT
ejpam-5470	306	28	]	]	PUNCT
ejpam-5470	306	29	is	be	AUX
ejpam-5470	306	30	sufficient	sufficient	ADJ
ejpam-5470	306	31	and	and	CCONJ
ejpam-5470	306	32	thus	thus	ADV
ejpam-5470	306	33	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	306	34	4,4t+2	4,4t+2	NOUN
ejpam-5470	306	35	is	be	AUX
ejpam-5470	306	36	cordial	cordial	ADJ
ejpam-5470	306	37	.	.	PUNCT
ejpam-5470	307	1	subcase	subcase	PROPN
ejpam-5470	307	2	3.2.k	3.2.k	NUM
ejpam-5470	307	3	≡	≡	PROPN
ejpam-5470	307	4	1(mod4	1(mod4	NUM
ejpam-5470	307	5	)	)	PUNCT
ejpam-5470	307	6	a.	a.	PROPN
ejpam-5470	307	7	abd	abd	PROPN
ejpam-5470	307	8	el	el	PROPN
ejpam-5470	307	9	-	-	PROPN
ejpam-5470	307	10	hay	hay	PROPN
ejpam-5470	307	11	et	et	PROPN
ejpam-5470	307	12	al	al	PROPN
ejpam-5470	307	13	.	.	PUNCT
ejpam-5470	307	14	/	/	SYM
ejpam-5470	307	15	eur	eur	PROPN
ejpam-5470	307	16	.	.	PUNCT
ejpam-5470	308	1	j.	j.	PROPN
ejpam-5470	308	2	pure	pure	PROPN
ejpam-5470	308	3	appl	appl	PROPN
ejpam-5470	308	4	.	.	PROPN
ejpam-5470	308	5	math	math	PROPN
ejpam-5470	308	6	,	,	PUNCT
ejpam-5470	308	7	18	18	NUM
ejpam-5470	308	8	(	(	PUNCT
ejpam-5470	308	9	1	1	NUM
ejpam-5470	308	10	)	)	PUNCT
ejpam-5470	308	11	(	(	PUNCT
ejpam-5470	308	12	2025	2025	NUM
ejpam-5470	308	13	)	)	PUNCT
ejpam-5470	308	14	,	,	PUNCT
ejpam-5470	308	15	5470	5470	NUM
ejpam-5470	308	16	10	10	NUM
ejpam-5470	308	17	of	of	ADP
ejpam-5470	308	18	14	14	NUM
ejpam-5470	308	19	let	let	VERB
ejpam-5470	308	20	k=	k=	X
ejpam-5470	308	21	4r+1,r	4r+1,r	NOUN
ejpam-5470	308	22	≥	≥	X
ejpam-5470	308	23	0	0	NUM
ejpam-5470	308	24	andm=	andm=	PROPN
ejpam-5470	308	25	4t+2	4t+2	PROPN
ejpam-5470	308	26	,	,	PUNCT
ejpam-5470	308	27	t	t	PROPN
ejpam-5470	308	28	>	>	X
ejpam-5470	308	29	1	1	NUM
ejpam-5470	308	30	.	.	PUNCT
ejpam-5470	309	1	then	then	ADV
ejpam-5470	309	2	,	,	PUNCT
ejpam-5470	309	3	the	the	DET
ejpam-5470	309	4	labelling	labelling	NOUN
ejpam-5470	309	5	[	[	X
ejpam-5470	309	6	l4r0;015m4t−60310	l4r0;015m4t−60310	PROPN
ejpam-5470	309	7	,	,	PUNCT
ejpam-5470	309	8	015	015	NUM
ejpam-5470	309	9	m4t−60310	m4t−60310	PROPN
ejpam-5470	309	10	,	,	PUNCT
ejpam-5470	309	11	105	105	NUM
ejpam-5470	309	12	m	m	NOUN
ejpam-5470	309	13	′	′	NUM
ejpam-5470	310	1	4t−6	4t−6	PROPN
ejpam-5470	310	2	1301	1301	NUM
ejpam-5470	310	3	,	,	PUNCT
ejpam-5470	310	4	105	105	NUM
ejpam-5470	310	5	m	m	NOUN
ejpam-5470	310	6	′	′	NUM
ejpam-5470	311	1	4t−6	4t−6	NUM
ejpam-5470	311	2	1301	1301	NUM
ejpam-5470	311	3	,	,	PUNCT
ejpam-5470	311	4	...	...	PUNCT
ejpam-5470	311	5	,	,	PUNCT
ejpam-5470	311	6	(	(	PUNCT
ejpam-5470	311	7	r−times	r−time	NOUN
ejpam-5470	311	8	)	)	PUNCT
ejpam-5470	311	9	,	,	PUNCT
ejpam-5470	311	10	0	0	NUM
ejpam-5470	311	11	15m4t−60310	15m4t−60310	NUM
ejpam-5470	311	12	]	]	PUNCT
ejpam-5470	311	13	for	for	ADP
ejpam-5470	311	14	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	311	15	4,4t+2	4,4t+2	PROPN
ejpam-5470	311	16	is	be	AUX
ejpam-5470	311	17	applied	apply	VERB
ejpam-5470	311	18	.	.	PUNCT
ejpam-5470	312	1	therefore	therefore	ADV
ejpam-5470	312	2	x0=	x0=	PROPN
ejpam-5470	313	1	2r+1,x1=	2r+1,x1=	NUM
ejpam-5470	313	2	2r	2r	NUM
ejpam-5470	313	3	,	,	PUNCT
ejpam-5470	313	4	a0	a0	PROPN
ejpam-5470	313	5	=	=	PROPN
ejpam-5470	313	6	a1=	a1=	PROPN
ejpam-5470	313	7	2r	2r	NUM
ejpam-5470	313	8	,	,	PUNCT
ejpam-5470	313	9	y0=	y0=	PROPN
ejpam-5470	313	10	2t+2,y1=	2t+2,y1=	NUM
ejpam-5470	313	11	2t+3,b0=	2t+3,b0=	NUM
ejpam-5470	313	12	8t+3,b1=	8t+3,b1=	NUM
ejpam-5470	313	13	8t+2,y′0=	8t+2,y′0=	NUM
ejpam-5470	313	14	2t+	2t+	NUM
ejpam-5470	313	15	3,y′1=	3,y′1=	NUM
ejpam-5470	313	16	2	2	NUM
ejpam-5470	313	17	t	t	NOUN
ejpam-5470	313	18	+	+	NOUN
ejpam-5470	313	19	2,b′0=	2,b′0=	NUM
ejpam-5470	313	20	8	8	NUM
ejpam-5470	313	21	t	t	NOUN
ejpam-5470	313	22	+	+	CCONJ
ejpam-5470	313	23	3	3	NUM
ejpam-5470	313	24	and	and	CCONJ
ejpam-5470	313	25	b′1=	b′1=	ADP
ejpam-5470	313	26	8	8	NUM
ejpam-5470	313	27	t	t	NOUN
ejpam-5470	313	28	+	+	NOUN
ejpam-5470	313	29	2	2	X
ejpam-5470	313	30	.	.	PUNCT
ejpam-5470	314	1	so	so	ADV
ejpam-5470	314	2	,	,	PUNCT
ejpam-5470	314	3	|v0	|v0	NOUN
ejpam-5470	314	4	−	−	NOUN
ejpam-5470	314	5	v1|	v1|	NOUN
ejpam-5470	314	6	=	=	SYM
ejpam-5470	314	7	0	0	NUM
ejpam-5470	314	8	and	and	CCONJ
ejpam-5470	314	9	|e0	|e0	NOUN
ejpam-5470	315	1	−	−	PROPN
ejpam-5470	315	2	e1|	e1|	NOUN
ejpam-5470	315	3	=	=	NOUN
ejpam-5470	315	4	0	0	NUM
ejpam-5470	315	5	.	.	PUNCT
ejpam-5470	316	1	for	for	ADP
ejpam-5470	316	2	the	the	DET
ejpam-5470	316	3	case	case	NOUN
ejpam-5470	316	4	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	316	5	4,6	4,6	NUM
ejpam-5470	316	6	,	,	PUNCT
ejpam-5470	316	7	the	the	DET
ejpam-5470	316	8	labeling	labeling	NOUN
ejpam-5470	316	9	[	[	X
ejpam-5470	316	10	l4r0;03	l4r0;03	ADJ
ejpam-5470	316	11	1402	1402	NUM
ejpam-5470	316	12	,	,	PUNCT
ejpam-5470	316	13	03	03	NUM
ejpam-5470	316	14	1402	1402	NUM
ejpam-5470	316	15	,	,	PUNCT
ejpam-5470	316	16	1304	1304	NUM
ejpam-5470	316	17	12	12	NUM
ejpam-5470	316	18	,	,	PUNCT
ejpam-5470	316	19	1304	1304	NUM
ejpam-5470	316	20	12	12	NUM
ejpam-5470	316	21	,	,	PUNCT
ejpam-5470	316	22	...	...	PUNCT
ejpam-5470	316	23	,	,	PUNCT
ejpam-5470	316	24	(	(	PUNCT
ejpam-5470	316	25	r	r	NOUN
ejpam-5470	316	26	−	−	NOUN
ejpam-5470	316	27	times),03	times),03	NOUN
ejpam-5470	316	28	1402	1402	NUM
ejpam-5470	316	29	]	]	PUNCT
ejpam-5470	316	30	is	be	AUX
ejpam-5470	316	31	sufficient	sufficient	ADJ
ejpam-5470	316	32	and	and	CCONJ
ejpam-5470	316	33	thus	thus	ADV
ejpam-5470	316	34	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	316	35	4,4t+2	4,4t+2	NOUN
ejpam-5470	316	36	is	be	AUX
ejpam-5470	316	37	cordial	cordial	ADJ
ejpam-5470	316	38	.	.	PUNCT
ejpam-5470	317	1	subcase	subcase	PROPN
ejpam-5470	317	2	3.3.k	3.3.k	NUM
ejpam-5470	317	3	≡	≡	PROPN
ejpam-5470	317	4	2(mod4	2(mod4	NUM
ejpam-5470	317	5	)	)	PUNCT
ejpam-5470	317	6	let	let	VERB
ejpam-5470	317	7	k=	k=	PROPN
ejpam-5470	317	8	4r+2,r	4r+2,r	NUM
ejpam-5470	317	9	≥	≥	NOUN
ejpam-5470	317	10	0	0	NUM
ejpam-5470	318	1	andm=	andm=	PROPN
ejpam-5470	318	2	4t+2	4t+2	PROPN
ejpam-5470	318	3	,	,	PUNCT
ejpam-5470	318	4	t	t	PROPN
ejpam-5470	318	5	>	>	X
ejpam-5470	318	6	1	1	NUM
ejpam-5470	318	7	.	.	PUNCT
ejpam-5470	319	1	then	then	ADV
ejpam-5470	319	2	,	,	PUNCT
ejpam-5470	319	3	the	the	DET
ejpam-5470	319	4	labelling	labelling	NOUN
ejpam-5470	319	5	[	[	X
ejpam-5470	319	6	l4r10;015m4t−60310	l4r10;015m4t−60310	X
ejpam-5470	319	7	,	,	PUNCT
ejpam-5470	319	8	015m4t−60310	015m4t−60310	NOUN
ejpam-5470	319	9	,	,	PUNCT
ejpam-5470	319	10	105	105	NUM
ejpam-5470	319	11	m	m	NOUN
ejpam-5470	319	12	′	′	NUM
ejpam-5470	319	13	4t−6	4t−6	PROPN
ejpam-5470	319	14	1301	1301	NUM
ejpam-5470	319	15	,	,	PUNCT
ejpam-5470	319	16	105	105	NUM
ejpam-5470	319	17	m	m	NOUN
ejpam-5470	319	18	′	′	NUM
ejpam-5470	319	19	4t−6	4t−6	NUM
ejpam-5470	319	20	1301	1301	NUM
ejpam-5470	319	21	,	,	PUNCT
ejpam-5470	319	22	...	...	PUNCT
ejpam-5470	319	23	,	,	PUNCT
ejpam-5470	319	24	(	(	PUNCT
ejpam-5470	319	25	r−times	r−time	NOUN
ejpam-5470	319	26	)	)	PUNCT
ejpam-5470	319	27	,	,	PUNCT
ejpam-5470	319	28	105	105	NUM
ejpam-5470	319	29	m	m	NOUN
ejpam-5470	319	30	′	′	NUM
ejpam-5470	319	31	4t−6	4t−6	PROPN
ejpam-5470	319	32	1301	1301	NUM
ejpam-5470	319	33	,	,	PUNCT
ejpam-5470	319	34	0	0	NUM
ejpam-5470	319	35	15m4t−60310	15m4t−60310	NUM
ejpam-5470	319	36	]	]	PUNCT
ejpam-5470	319	37	for	for	ADP
ejpam-5470	319	38	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	319	39	4,4t+2	4,4t+2	NOUN
ejpam-5470	319	40	is	be	AUX
ejpam-5470	319	41	applied	apply	VERB
ejpam-5470	319	42	.	.	PUNCT
ejpam-5470	320	1	therefore	therefore	ADV
ejpam-5470	320	2	x0	x0	PROPN
ejpam-5470	320	3	=	=	PROPN
ejpam-5470	320	4	x1=	x1=	PROPN
ejpam-5470	320	5	2r	2r	NUM
ejpam-5470	321	1	+	+	CCONJ
ejpam-5470	322	1	1,a0=	1,a0=	NUM
ejpam-5470	322	2	2r	2r	NUM
ejpam-5470	322	3	+	+	CCONJ
ejpam-5470	322	4	1,a1=	1,a1=	NUM
ejpam-5470	322	5	2r	2r	NUM
ejpam-5470	322	6	,	,	PUNCT
ejpam-5470	322	7	y0=	y0=	PROPN
ejpam-5470	322	8	2	2	NUM
ejpam-5470	322	9	t	t	NOUN
ejpam-5470	322	10	+	+	NOUN
ejpam-5470	322	11	2,y1=	2,y1=	NUM
ejpam-5470	322	12	2	2	NUM
ejpam-5470	322	13	t	t	NOUN
ejpam-5470	322	14	+	+	NOUN
ejpam-5470	322	15	3,b0=	3,b0=	NUM
ejpam-5470	322	16	8	8	NUM
ejpam-5470	322	17	t	t	NOUN
ejpam-5470	322	18	+	+	NOUN
ejpam-5470	322	19	3,b1=	3,b1=	NUM
ejpam-5470	322	20	8t+2,y′0=	8t+2,y′0=	NUM
ejpam-5470	322	21	2t+3,y′1=	2t+3,y′1=	NUM
ejpam-5470	322	22	2t+2,b′0=	2t+2,b′0=	NUM
ejpam-5470	322	23	8t+3	8t+3	ADJ
ejpam-5470	322	24	and	and	CCONJ
ejpam-5470	322	25	b′1=	b′1=	ADP
ejpam-5470	322	26	8t+2	8t+2	PROPN
ejpam-5470	322	27	.	.	PUNCT
ejpam-5470	323	1	so	so	ADV
ejpam-5470	323	2	,	,	PUNCT
ejpam-5470	323	3	|v0−v1|	|v0−v1|	NUM
ejpam-5470	323	4	=	=	SYM
ejpam-5470	323	5	0	0	NUM
ejpam-5470	323	6	and	and	CCONJ
ejpam-5470	323	7	|e0−e1|	|e0−e1|	NOUN
ejpam-5470	323	8	=	=	NOUN
ejpam-5470	323	9	1	1	X
ejpam-5470	323	10	.	.	X
ejpam-5470	324	1	for	for	ADP
ejpam-5470	324	2	the	the	DET
ejpam-5470	324	3	case	case	NOUN
ejpam-5470	324	4	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	324	5	4,6	4,6	NUM
ejpam-5470	324	6	,	,	PUNCT
ejpam-5470	324	7	the	the	DET
ejpam-5470	324	8	labeling	labeling	NOUN
ejpam-5470	324	9	[	[	X
ejpam-5470	324	10	l4r01;03	l4r01;03	PROPN
ejpam-5470	324	11	1402	1402	NUM
ejpam-5470	324	12	,	,	PUNCT
ejpam-5470	324	13	03	03	NUM
ejpam-5470	324	14	1402	1402	NUM
ejpam-5470	324	15	,	,	PUNCT
ejpam-5470	324	16	1304	1304	NUM
ejpam-5470	324	17	12	12	NUM
ejpam-5470	324	18	,	,	PUNCT
ejpam-5470	324	19	1304	1304	NUM
ejpam-5470	324	20	12	12	NUM
ejpam-5470	324	21	,	,	PUNCT
ejpam-5470	324	22	...	...	PUNCT
ejpam-5470	324	23	,	,	PUNCT
ejpam-5470	324	24	(	(	PUNCT
ejpam-5470	324	25	r	r	NOUN
ejpam-5470	324	26	−	−	PROPN
ejpam-5470	324	27	times),03	times),03	NOUN
ejpam-5470	324	28	1402	1402	NUM
ejpam-5470	324	29	,	,	PUNCT
ejpam-5470	324	30	1304	1304	NUM
ejpam-5470	324	31	12	12	NUM
ejpam-5470	324	32	]	]	PUNCT
ejpam-5470	324	33	is	be	AUX
ejpam-5470	324	34	sufficient	sufficient	ADJ
ejpam-5470	324	35	and	and	CCONJ
ejpam-5470	324	36	thus	thus	ADV
ejpam-5470	324	37	p4r+2⊙l4	p4r+2⊙l4	NUM
ejpam-5470	324	38	4,4t+2	4,4t+2	NOUN
ejpam-5470	324	39	is	be	AUX
ejpam-5470	324	40	cordial	cordial	ADJ
ejpam-5470	324	41	.	.	PUNCT
ejpam-5470	325	1	subcase	subcase	PROPN
ejpam-5470	325	2	3.4.k	3.4.k	NUM
ejpam-5470	325	3	≡	≡	PROPN
ejpam-5470	325	4	3(mod4	3(mod4	NUM
ejpam-5470	325	5	)	)	PUNCT
ejpam-5470	325	6	let	let	VERB
ejpam-5470	325	7	k=	k=	ADJ
ejpam-5470	325	8	4r	4r	NOUN
ejpam-5470	326	1	+	+	CCONJ
ejpam-5470	326	2	3,r	3,r	NUM
ejpam-5470	326	3	≥	≥	NOUN
ejpam-5470	326	4	0	0	NUM
ejpam-5470	326	5	and	and	CCONJ
ejpam-5470	326	6	m=	m=	ADJ
ejpam-5470	326	7	4t+	4t+	PROPN
ejpam-5470	326	8	2	2	NUM
ejpam-5470	326	9	,	,	PUNCT
ejpam-5470	326	10	t	t	PROPN
ejpam-5470	326	11	>	>	X
ejpam-5470	326	12	1	1	NUM
ejpam-5470	326	13	.	.	PUNCT
ejpam-5470	327	1	then	then	ADV
ejpam-5470	327	2	,	,	PUNCT
ejpam-5470	327	3	the	the	DET
ejpam-5470	327	4	labelling	labelling	NOUN
ejpam-5470	327	5	[	[	X
ejpam-5470	327	6	l4r021;0	l4r021;0	NOUN
ejpam-5470	327	7	15m4t−60310	15m4t−60310	NUM
ejpam-5470	327	8	,	,	PUNCT
ejpam-5470	327	9	015m4t−60310	015m4t−60310	NOUN
ejpam-5470	327	10	,	,	PUNCT
ejpam-5470	327	11	105	105	NUM
ejpam-5470	327	12	m	m	NOUN
ejpam-5470	327	13	′	′	NUM
ejpam-5470	327	14	4t−6	4t−6	PROPN
ejpam-5470	327	15	1301	1301	NUM
ejpam-5470	327	16	,	,	PUNCT
ejpam-5470	327	17	105	105	NUM
ejpam-5470	327	18	m	m	NOUN
ejpam-5470	327	19	′	′	NUM
ejpam-5470	327	20	4t−6	4t−6	NUM
ejpam-5470	327	21	1301	1301	NUM
ejpam-5470	327	22	,	,	PUNCT
ejpam-5470	327	23	...	...	PUNCT
ejpam-5470	327	24	,	,	PUNCT
ejpam-5470	327	25	(	(	PUNCT
ejpam-5470	327	26	r−times	r−time	NOUN
ejpam-5470	327	27	)	)	PUNCT
ejpam-5470	327	28	,	,	PUNCT
ejpam-5470	327	29	0	0	NUM
ejpam-5470	327	30	15m4t−60310	15m4t−60310	NUM
ejpam-5470	327	31	,	,	PUNCT
ejpam-5470	327	32	0	0	NUM
ejpam-5470	327	33	15m4t−60310	15m4t−60310	NUM
ejpam-5470	327	34	,	,	PUNCT
ejpam-5470	327	35	105	105	NUM
ejpam-5470	327	36	m	m	NOUN
ejpam-5470	327	37	′	′	NUM
ejpam-5470	327	38	4t−6	4t−6	PROPN
ejpam-5470	327	39	1301	1301	NUM
ejpam-5470	327	40	]	]	PUNCT
ejpam-5470	327	41	for	for	ADP
ejpam-5470	327	42	p4r+3⊙	p4r+3⊙	PROPN
ejpam-5470	327	43	l4	l4	PROPN
ejpam-5470	327	44	4,4t+2	4,4t+2	PROPN
ejpam-5470	327	45	is	be	AUX
ejpam-5470	327	46	applied	apply	VERB
ejpam-5470	327	47	.	.	PUNCT
ejpam-5470	328	1	therefore	therefore	ADV
ejpam-5470	328	2	x0=	x0=	PUNCT
ejpam-5470	328	3	2r+2,x1=	2r+2,x1=	NUM
ejpam-5470	328	4	2r+1,a0	2r+1,a0	NUM
ejpam-5470	328	5	=	=	VERB
ejpam-5470	328	6	a1=	a1=	PROPN
ejpam-5470	328	7	2r+	2r+	NUM
ejpam-5470	328	8	1,y0=	1,y0=	NUM
ejpam-5470	328	9	2t+2,y1=	2t+2,y1=	NUM
ejpam-5470	328	10	2t+3,b0=	2t+3,b0=	NUM
ejpam-5470	328	11	8t+3,b1=	8t+3,b1=	NUM
ejpam-5470	328	12	8t+2,y′0=	8t+2,y′0=	NUM
ejpam-5470	328	13	2t+3,y′1=	2t+3,y′1=	NUM
ejpam-5470	328	14	2t+2,b′0=	2t+2,b′0=	NUM
ejpam-5470	328	15	8t+3	8t+3	ADJ
ejpam-5470	328	16	and	and	CCONJ
ejpam-5470	328	17	b′1=	b′1=	ADP
ejpam-5470	328	18	8t+2	8t+2	PROPN
ejpam-5470	328	19	.	.	PUNCT
ejpam-5470	329	1	so	so	ADV
ejpam-5470	329	2	,	,	PUNCT
ejpam-5470	329	3	|v0−v1|	|v0−v1|	NUM
ejpam-5470	329	4	=	=	SYM
ejpam-5470	329	5	1	1	NUM
ejpam-5470	329	6	and	and	CCONJ
ejpam-5470	329	7	|e0−e1|	|e0−e1|	NOUN
ejpam-5470	329	8	=	=	NOUN
ejpam-5470	329	9	0	0	PROPN
ejpam-5470	329	10	.	.	PUNCT
ejpam-5470	330	1	for	for	ADP
ejpam-5470	330	2	the	the	DET
ejpam-5470	330	3	case	case	NOUN
ejpam-5470	330	4	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	330	5	4,6	4,6	NUM
ejpam-5470	330	6	,	,	PUNCT
ejpam-5470	330	7	the	the	DET
ejpam-5470	330	8	labeling	labeling	NOUN
ejpam-5470	330	9	[	[	X
ejpam-5470	330	10	l4r001	l4r001	X
ejpam-5470	330	11	;	;	PUNCT
ejpam-5470	330	12	1304	1304	NUM
ejpam-5470	330	13	12	12	NUM
ejpam-5470	330	14	,	,	PUNCT
ejpam-5470	330	15	1304	1304	NUM
ejpam-5470	330	16	12	12	NUM
ejpam-5470	330	17	,	,	PUNCT
ejpam-5470	330	18	03	03	NUM
ejpam-5470	330	19	1402	1402	NUM
ejpam-5470	330	20	,	,	PUNCT
ejpam-5470	330	21	03	03	NUM
ejpam-5470	330	22	1402	1402	NUM
ejpam-5470	330	23	,	,	PUNCT
ejpam-5470	330	24	...	...	PUNCT
ejpam-5470	330	25	,	,	PUNCT
ejpam-5470	330	26	(	(	PUNCT
ejpam-5470	330	27	r−times	r−time	NOUN
ejpam-5470	330	28	)	)	PUNCT
ejpam-5470	330	29	,	,	PUNCT
ejpam-5470	330	30	1304	1304	NUM
ejpam-5470	330	31	12	12	NUM
ejpam-5470	330	32	,	,	PUNCT
ejpam-5470	330	33	1304	1304	NUM
ejpam-5470	330	34	12	12	NUM
ejpam-5470	330	35	,	,	PUNCT
ejpam-5470	330	36	03	03	NUM
ejpam-5470	330	37	1402	1402	NUM
ejpam-5470	330	38	]	]	PUNCT
ejpam-5470	330	39	is	be	AUX
ejpam-5470	330	40	sufficient	sufficient	ADJ
ejpam-5470	330	41	and	and	CCONJ
ejpam-5470	330	42	thus	thus	ADV
ejpam-5470	330	43	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	330	44	4,4t+2	4,4t+2	NOUN
ejpam-5470	330	45	is	be	AUX
ejpam-5470	330	46	cordial	cordial	ADJ
ejpam-5470	330	47	.	.	PUNCT
ejpam-5470	331	1	case	case	NOUN
ejpam-5470	331	2	4	4	NUM
ejpam-5470	331	3	.	.	PUNCT
ejpam-5470	332	1	at	at	ADP
ejpam-5470	332	2	m	m	PROPN
ejpam-5470	332	3	≡	≡	PROPN
ejpam-5470	332	4	3(mod4	3(mod4	NUM
ejpam-5470	332	5	)	)	PUNCT
ejpam-5470	332	6	,	,	PUNCT
ejpam-5470	332	7	we	we	PRON
ejpam-5470	332	8	consider	consider	VERB
ejpam-5470	332	9	the	the	DET
ejpam-5470	332	10	following	follow	VERB
ejpam-5470	332	11	sub	sub	NOUN
ejpam-5470	332	12	subcases	subcase	NOUN
ejpam-5470	332	13	.	.	PUNCT
ejpam-5470	333	1	subcase	subcase	PROPN
ejpam-5470	333	2	4.1.k	4.1.k	PROPN
ejpam-5470	333	3	is	be	AUX
ejpam-5470	333	4	even	even	ADV
ejpam-5470	333	5	.	.	PUNCT
ejpam-5470	334	1	let	let	VERB
ejpam-5470	334	2	k=	k=	PRON
ejpam-5470	334	3	2r	2r	NUM
ejpam-5470	334	4	,	,	PUNCT
ejpam-5470	335	1	r	r	NOUN
ejpam-5470	335	2	≥	≥	NUM
ejpam-5470	335	3	1	1	NUM
ejpam-5470	335	4	andm=	andm=	NUM
ejpam-5470	335	5	4t+3	4t+3	PROPN
ejpam-5470	335	6	,	,	PUNCT
ejpam-5470	335	7	t	t	PROPN
ejpam-5470	335	8	≥	≥	NUM
ejpam-5470	335	9	1	1	NUM
ejpam-5470	335	10	.	.	PUNCT
ejpam-5470	336	1	then	then	ADV
ejpam-5470	336	2	,	,	PUNCT
ejpam-5470	336	3	the	the	DET
ejpam-5470	336	4	labelling	labelling	NOUN
ejpam-5470	336	5	[	[	X
ejpam-5470	336	6	m2r;103	m2r;103	X
ejpam-5470	336	7	12l4t−40102	12l4t−40102	NUM
ejpam-5470	336	8	,	,	PUNCT
ejpam-5470	336	9	1010m4	1010m4	PROPN
ejpam-5470	336	10	t	t	PROPN
ejpam-5470	336	11	12	12	NUM
ejpam-5470	336	12	,	,	PUNCT
ejpam-5470	336	13	...	...	PUNCT
ejpam-5470	336	14	,	,	PUNCT
ejpam-5470	336	15	(	(	PUNCT
ejpam-5470	336	16	r−times	r−time	NOUN
ejpam-5470	336	17	)	)	PUNCT
ejpam-5470	336	18	]	]	PUNCT
ejpam-5470	336	19	for	for	ADP
ejpam-5470	336	20	p2r⊙	p2r⊙	PROPN
ejpam-5470	336	21	l4	l4	PROPN
ejpam-5470	336	22	4,4t+3	4,4t+3	PROPN
ejpam-5470	336	23	is	be	AUX
ejpam-5470	336	24	applied	apply	VERB
ejpam-5470	336	25	.	.	PUNCT
ejpam-5470	337	1	therefore	therefore	ADV
ejpam-5470	337	2	x0	x0	PROPN
ejpam-5470	337	3	=	=	PROPN
ejpam-5470	337	4	x1	x1	PROPN
ejpam-5470	337	5	=	=	SYM
ejpam-5470	337	6	r	r	NOUN
ejpam-5470	337	7	,	,	PUNCT
ejpam-5470	337	8	a0=	a0=	PROPN
ejpam-5470	337	9	0,a1=	0,a1=	NUM
ejpam-5470	337	10	2r−1,y0=	2r−1,y0=	PROPN
ejpam-5470	337	11	2t+	2t+	NUM
ejpam-5470	337	12	4,y1=	4,y1=	NUM
ejpam-5470	337	13	2t+2,b0=	2t+2,b0=	NUM
ejpam-5470	337	14	8t+5,b1=	8t+5,b1=	NUM
ejpam-5470	337	15	8t+4,y′0=	8t+4,y′0=	NUM
ejpam-5470	337	16	2t+2,y′1=	2t+2,y′1=	NUM
ejpam-5470	337	17	2t+4,b′0=	2t+4,b′0=	NUM
ejpam-5470	337	18	8t+3	8t+3	ADJ
ejpam-5470	337	19	and	and	CCONJ
ejpam-5470	337	20	b′1=	b′1=	ADP
ejpam-5470	337	21	8t+6	8t+6	NOUN
ejpam-5470	337	22	.	.	PUNCT
ejpam-5470	338	1	hence	hence	ADV
ejpam-5470	338	2	,	,	PUNCT
ejpam-5470	338	3	|v0	|v0	NOUN
ejpam-5470	338	4	−	−	NOUN
ejpam-5470	338	5	v1|	v1|	NOUN
ejpam-5470	338	6	=	=	SYM
ejpam-5470	338	7	0	0	NUM
ejpam-5470	338	8	and	and	CCONJ
ejpam-5470	338	9	|e0	|e0	NOUN
ejpam-5470	339	1	−	−	PROPN
ejpam-5470	339	2	e1|	e1|	NOUN
ejpam-5470	339	3	=	=	PUNCT
ejpam-5470	339	4	1	1	NUM
ejpam-5470	339	5	and	and	CCONJ
ejpam-5470	339	6	thus	thus	ADV
ejpam-5470	339	7	p2r⊙l4	p2r⊙l4	NOUN
ejpam-5470	339	8	4,4t+3	4,4t+3	VERB
ejpam-5470	339	9	is	be	AUX
ejpam-5470	339	10	cordial	cordial	ADJ
ejpam-5470	339	11	.	.	PUNCT
ejpam-5470	340	1	subcase	subcase	PROPN
ejpam-5470	340	2	4.2.k	4.2.k	PROPN
ejpam-5470	340	3	is	be	AUX
ejpam-5470	340	4	odd	odd	ADJ
ejpam-5470	340	5	.	.	PUNCT
ejpam-5470	341	1	let	let	VERB
ejpam-5470	341	2	k=	k=	X
ejpam-5470	341	3	2r+1,r	2r+1,r	ADJ
ejpam-5470	341	4	≥	≥	NOUN
ejpam-5470	341	5	0	0	NUM
ejpam-5470	341	6	and	and	CCONJ
ejpam-5470	341	7	m=	m=	VERB
ejpam-5470	341	8	4t+3	4t+3	PROPN
ejpam-5470	341	9	,	,	PUNCT
ejpam-5470	341	10	t	t	PROPN
ejpam-5470	341	11	≥	≥	NUM
ejpam-5470	341	12	1	1	NUM
ejpam-5470	341	13	.	.	PUNCT
ejpam-5470	342	1	then	then	ADV
ejpam-5470	342	2	,	,	PUNCT
ejpam-5470	342	3	the	the	DET
ejpam-5470	342	4	labelling	labelling	NOUN
ejpam-5470	342	5	[	[	X
ejpam-5470	342	6	m2r+1;103	m2r+1;103	NOUN
ejpam-5470	342	7	12l4t−40102	12l4t−40102	NUM
ejpam-5470	342	8	,	,	PUNCT
ejpam-5470	342	9	1010m4	1010m4	PROPN
ejpam-5470	342	10	t	t	PROPN
ejpam-5470	342	11	12	12	NUM
ejpam-5470	342	12	,	,	PUNCT
ejpam-5470	342	13	...	...	PUNCT
ejpam-5470	342	14	,	,	PUNCT
ejpam-5470	342	15	(	(	PUNCT
ejpam-5470	342	16	r	r	NOUN
ejpam-5470	342	17	−	−	PROPN
ejpam-5470	342	18	times	time	NOUN
ejpam-5470	342	19	)	)	PUNCT
ejpam-5470	342	20	,	,	PUNCT
ejpam-5470	342	21	103m4	103m4	NUM
ejpam-5470	342	22	t	t	NOUN
ejpam-5470	342	23	12	12	NUM
ejpam-5470	342	24	]	]	PUNCT
ejpam-5470	342	25	for	for	ADP
ejpam-5470	342	26	p2r+1⊙l4	p2r+1⊙l4	NOUN
ejpam-5470	342	27	4,4t+3	4,4t+3	VERB
ejpam-5470	342	28	is	be	AUX
ejpam-5470	342	29	applied	apply	VERB
ejpam-5470	342	30	.	.	PUNCT
ejpam-5470	343	1	therefore	therefore	ADV
ejpam-5470	343	2	x0	x0	PROPN
ejpam-5470	343	3	=	=	NOUN
ejpam-5470	343	4	r	r	NOUN
ejpam-5470	343	5	+	+	NOUN
ejpam-5470	343	6	1,x1	1,x1	NUM
ejpam-5470	343	7	=	=	SYM
ejpam-5470	343	8	r	r	NOUN
ejpam-5470	343	9	,	,	PUNCT
ejpam-5470	343	10	a0=	a0=	PROPN
ejpam-5470	343	11	0,a1=	0,a1=	NUM
ejpam-5470	343	12	2r	2r	NUM
ejpam-5470	343	13	,	,	PUNCT
ejpam-5470	343	14	y0=	y0=	PROPN
ejpam-5470	343	15	2	2	NUM
ejpam-5470	343	16	t	t	NOUN
ejpam-5470	343	17	+	+	NOUN
ejpam-5470	343	18	4,y1=	4,y1=	NUM
ejpam-5470	343	19	2	2	NUM
ejpam-5470	343	20	t	t	NOUN
ejpam-5470	343	21	+	+	CCONJ
ejpam-5470	343	22	2,b0=	2,b0=	NUM
ejpam-5470	343	23	8	8	NUM
ejpam-5470	343	24	t	t	NOUN
ejpam-5470	343	25	+	+	NOUN
ejpam-5470	343	26	5,b1=	5,b1=	NUM
ejpam-5470	343	27	8	8	NUM
ejpam-5470	343	28	t	t	NOUN
ejpam-5470	343	29	+	+	NOUN
ejpam-5470	343	30	4,y′0=	4,y′0=	NUM
ejpam-5470	343	31	2	2	NUM
ejpam-5470	343	32	t	t	NOUN
ejpam-5470	343	33	+	+	NOUN
ejpam-5470	343	34	2,y′1=	2,y′1=	NUM
ejpam-5470	343	35	2	2	NUM
ejpam-5470	343	36	t	t	NOUN
ejpam-5470	343	37	+	+	CCONJ
ejpam-5470	343	38	4,b′0=	4,b′0=	NUM
ejpam-5470	343	39	8t+3,b′1=	8t+3,b′1=	NUM
ejpam-5470	343	40	8t+6,y”0=	8t+6,y”0=	NUM
ejpam-5470	343	41	2t+3,y”1=	2t+3,y”1=	NUM
ejpam-5470	343	42	2t+3,b”0=	2t+3,b”0=	NUM
ejpam-5470	343	43	8t+4	8t+4	PROPN
ejpam-5470	343	44	and	and	CCONJ
ejpam-5470	343	45	b”1=	b”1=	PROPN
ejpam-5470	343	46	8t+5	8t+5	PROPN
ejpam-5470	343	47	.	.	PUNCT
ejpam-5470	344	1	hence	hence	ADV
ejpam-5470	344	2	,	,	PUNCT
ejpam-5470	344	3	|v0−v1|	|v0−v1|	NOUN
ejpam-5470	344	4	=	=	SYM
ejpam-5470	344	5	1	1	NUM
ejpam-5470	344	6	and	and	CCONJ
ejpam-5470	344	7	|e0	|e0	NOUN
ejpam-5470	345	1	−	−	PROPN
ejpam-5470	345	2	e1|	e1|	NOUN
ejpam-5470	345	3	=	=	NOUN
ejpam-5470	345	4	1	1	X
ejpam-5470	345	5	.	.	PUNCT
ejpam-5470	345	6	thus	thus	ADV
ejpam-5470	345	7	p2r+1⊙l4	p2r+1⊙l4	NOUN
ejpam-5470	345	8	4,4t+3	4,4t+3	VERB
ejpam-5470	345	9	is	be	AUX
ejpam-5470	345	10	cordial	cordial	ADJ
ejpam-5470	345	11	and	and	CCONJ
ejpam-5470	345	12	the	the	DET
ejpam-5470	345	13	lemma	lemma	PROPN
ejpam-5470	345	14	follows	follow	VERB
ejpam-5470	345	15	.	.	PUNCT
ejpam-5470	346	1	■	■	PUNCT
ejpam-5470	346	2	lemma	lemma	PROPN
ejpam-5470	346	3	4	4	NUM
ejpam-5470	346	4	.	.	PUNCT
ejpam-5470	346	5	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	346	6	5,m	5,m	PROPN
ejpam-5470	346	7	is	be	AUX
ejpam-5470	346	8	cordial	cordial	ADJ
ejpam-5470	346	9	for	for	ADP
ejpam-5470	346	10	all	all	PRON
ejpam-5470	346	11	k	k	PROPN
ejpam-5470	346	12	≥	≥	NUM
ejpam-5470	346	13	1	1	NUM
ejpam-5470	346	14	and	and	CCONJ
ejpam-5470	346	15	m	m	PROPN
ejpam-5470	346	16	≥	≥	NOUN
ejpam-5470	346	17	3	3	NUM
ejpam-5470	346	18	.	.	PUNCT
ejpam-5470	347	1	proof	proof	NOUN
ejpam-5470	347	2	.	.	PUNCT
ejpam-5470	348	1	we	we	PRON
ejpam-5470	348	2	need	need	VERB
ejpam-5470	348	3	to	to	PART
ejpam-5470	348	4	examine	examine	VERB
ejpam-5470	348	5	the	the	DET
ejpam-5470	348	6	following	follow	VERB
ejpam-5470	348	7	two	two	NUM
ejpam-5470	348	8	cases	case	NOUN
ejpam-5470	348	9	:	:	PUNCT
ejpam-5470	348	10	case	case	NOUN
ejpam-5470	348	11	1	1	NUM
ejpam-5470	348	12	.	.	PUNCT
ejpam-5470	349	1	at	at	ADP
ejpam-5470	349	2	m	m	PROPN
ejpam-5470	349	3	≡	≡	PROPN
ejpam-5470	349	4	0(mod4	0(mod4	NUM
ejpam-5470	349	5	)	)	PUNCT
ejpam-5470	349	6	,	,	PUNCT
ejpam-5470	349	7	i.e	i.e	X
ejpam-5470	349	8	m=	m=	X
ejpam-5470	349	9	4t	4t	NOUN
ejpam-5470	349	10	,	,	PUNCT
ejpam-5470	349	11	t	t	PROPN
ejpam-5470	349	12	≥	≥	NUM
ejpam-5470	349	13	1	1	NUM
ejpam-5470	349	14	.	.	PUNCT
ejpam-5470	350	1	we	we	PRON
ejpam-5470	350	2	see	see	VERB
ejpam-5470	350	3	that	that	DET
ejpam-5470	350	4	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	350	5	5,4	5,4	NUM
ejpam-5470	350	6	and	and	CCONJ
ejpam-5470	350	7	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	350	8	5,4t	5,4t	NUM
ejpam-5470	350	9	,	,	PUNCT
ejpam-5470	350	10	t	t	PROPN
ejpam-5470	350	11	≥	≥	NUM
ejpam-5470	350	12	1	1	NUM
ejpam-5470	350	13	are	be	AUX
ejpam-5470	350	14	cordial	cordial	ADJ
ejpam-5470	350	15	.	.	PUNCT
ejpam-5470	351	1	this	this	PRON
ejpam-5470	351	2	is	be	AUX
ejpam-5470	351	3	clear	clear	ADJ
ejpam-5470	351	4	since	since	SCONJ
ejpam-5470	351	5	these	these	DET
ejpam-5470	351	6	graphs	graph	NOUN
ejpam-5470	351	7	are	be	AUX
ejpam-5470	351	8	isomorphic	isomorphic	ADJ
ejpam-5470	351	9	to	to	ADP
ejpam-5470	351	10	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	351	11	4,5	4,5	NUM
ejpam-5470	351	12	and	and	CCONJ
ejpam-5470	351	13	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	351	14	4t,5	4t,5	NUM
ejpam-5470	351	15	respectively	respectively	ADV
ejpam-5470	351	16	.	.	PUNCT
ejpam-5470	352	1	so	so	ADV
ejpam-5470	352	2	,	,	PUNCT
ejpam-5470	352	3	by	by	ADP
ejpam-5470	352	4	lemma	lemma	PROPN
ejpam-5470	352	5	3	3	NUM
ejpam-5470	352	6	,	,	PUNCT
ejpam-5470	352	7	we	we	PRON
ejpam-5470	352	8	conclude	conclude	VERB
ejpam-5470	352	9	that	that	SCONJ
ejpam-5470	352	10	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	352	11	5,4	5,4	NUM
ejpam-5470	352	12	and	and	CCONJ
ejpam-5470	352	13	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	352	14	5,4	5,4	NUM
ejpam-5470	352	15	t	t	NOUN
ejpam-5470	352	16	are	be	AUX
ejpam-5470	352	17	cordial	cordial	ADJ
ejpam-5470	352	18	.	.	PUNCT
ejpam-5470	353	1	case	case	NOUN
ejpam-5470	353	2	2	2	NUM
ejpam-5470	353	3	.	.	PUNCT
ejpam-5470	354	1	at	at	ADP
ejpam-5470	354	2	m	m	PROPN
ejpam-5470	354	3	≡	≡	PROPN
ejpam-5470	354	4	1(mod4	1(mod4	NUM
ejpam-5470	354	5	)	)	PUNCT
ejpam-5470	354	6	,	,	PUNCT
ejpam-5470	354	7	we	we	PRON
ejpam-5470	354	8	consider	consider	VERB
ejpam-5470	354	9	the	the	DET
ejpam-5470	354	10	following	follow	VERB
ejpam-5470	354	11	subcases	subcase	NOUN
ejpam-5470	354	12	.	.	PUNCT
ejpam-5470	355	1	subcase	subcase	PROPN
ejpam-5470	355	2	2.1.k	2.1.k	NUM
ejpam-5470	355	3	≡	≡	PROPN
ejpam-5470	355	4	0(mod4	0(mod4	NUM
ejpam-5470	355	5	)	)	PUNCT
ejpam-5470	355	6	let	let	VERB
ejpam-5470	355	7	k=	k=	ADJ
ejpam-5470	355	8	4r	4r	NOUN
ejpam-5470	355	9	,	,	PUNCT
ejpam-5470	355	10	r	r	NOUN
ejpam-5470	355	11	≥	≥	NUM
ejpam-5470	355	12	1	1	NUM
ejpam-5470	355	13	andm=	andm=	PROPN
ejpam-5470	355	14	4t+1	4t+1	PROPN
ejpam-5470	355	15	,	,	PUNCT
ejpam-5470	355	16	t	t	PROPN
ejpam-5470	355	17	>	>	X
ejpam-5470	355	18	1	1	NUM
ejpam-5470	355	19	.	.	PUNCT
ejpam-5470	356	1	then	then	ADV
ejpam-5470	356	2	,	,	PUNCT
ejpam-5470	356	3	the	the	DET
ejpam-5470	356	4	labelling	labelling	NOUN
ejpam-5470	356	5	[	[	X
ejpam-5470	356	6	l4r;014m4t−4031	l4r;014m4t−4031	PROPN
ejpam-5470	356	7	,	,	PUNCT
ejpam-5470	356	8	0	0	NUM
ejpam-5470	356	9	14m4t−4031	14m4t−4031	NUM
ejpam-5470	356	10	,	,	PUNCT
ejpam-5470	356	11	a.	a.	PROPN
ejpam-5470	356	12	abd	abd	PROPN
ejpam-5470	356	13	el	el	PROPN
ejpam-5470	356	14	-	-	PROPN
ejpam-5470	356	15	hay	hay	PROPN
ejpam-5470	356	16	et	et	PROPN
ejpam-5470	356	17	al	al	PROPN
ejpam-5470	356	18	.	.	PUNCT
ejpam-5470	356	19	/	/	SYM
ejpam-5470	356	20	eur	eur	PROPN
ejpam-5470	356	21	.	.	PUNCT
ejpam-5470	357	1	j.	j.	PROPN
ejpam-5470	357	2	pure	pure	PROPN
ejpam-5470	357	3	appl	appl	PROPN
ejpam-5470	357	4	.	.	PROPN
ejpam-5470	357	5	math	math	PROPN
ejpam-5470	357	6	,	,	PUNCT
ejpam-5470	357	7	18	18	NUM
ejpam-5470	357	8	(	(	PUNCT
ejpam-5470	357	9	1	1	NUM
ejpam-5470	357	10	)	)	PUNCT
ejpam-5470	357	11	(	(	PUNCT
ejpam-5470	357	12	2025	2025	NUM
ejpam-5470	357	13	)	)	PUNCT
ejpam-5470	357	14	,	,	PUNCT
ejpam-5470	357	15	5470	5470	NUM
ejpam-5470	357	16	11	11	NUM
ejpam-5470	357	17	of	of	ADP
ejpam-5470	357	18	14	14	NUM
ejpam-5470	357	19	104	104	NUM
ejpam-5470	357	20	m	m	NOUN
ejpam-5470	357	21	′	′	NUM
ejpam-5470	357	22	4t−4	4t−4	NUM
ejpam-5470	357	23	130	130	NUM
ejpam-5470	357	24	,	,	PUNCT
ejpam-5470	357	25	104	104	NUM
ejpam-5470	357	26	m	m	NOUN
ejpam-5470	357	27	′	′	NUM
ejpam-5470	357	28	4t−4	4t−4	NUM
ejpam-5470	357	29	130	130	NUM
ejpam-5470	357	30	,	,	PUNCT
ejpam-5470	357	31	...	...	PUNCT
ejpam-5470	357	32	,	,	PUNCT
ejpam-5470	357	33	(	(	PUNCT
ejpam-5470	357	34	r−times	r−time	NOUN
ejpam-5470	357	35	)	)	PUNCT
ejpam-5470	357	36	]	]	PUNCT
ejpam-5470	357	37	for	for	SCONJ
ejpam-5470	357	38	p4r⊙	p4r⊙	PROPN
ejpam-5470	357	39	l4	l4	PROPN
ejpam-5470	357	40	5,4t+1	5,4t+1	PROPN
ejpam-5470	357	41	is	be	AUX
ejpam-5470	357	42	applied	apply	VERB
ejpam-5470	357	43	.	.	PUNCT
ejpam-5470	358	1	therefore	therefore	ADV
ejpam-5470	358	2	x0	x0	PROPN
ejpam-5470	358	3	=	=	PROPN
ejpam-5470	358	4	x1=	x1=	PROPN
ejpam-5470	358	5	2r	2r	NUM
ejpam-5470	358	6	,	,	PUNCT
ejpam-5470	358	7	a0=	a0=	PROPN
ejpam-5470	358	8	2r	2r	NUM
ejpam-5470	358	9	,	,	PUNCT
ejpam-5470	358	10	a1=	a1=	PROPN
ejpam-5470	358	11	2r−1,y0=	2r−1,y0=	PROPN
ejpam-5470	358	12	2t+2,y1=	2t+2,y1=	NUM
ejpam-5470	358	13	2t+3,b0=	2t+3,b0=	NUM
ejpam-5470	358	14	8t−3,b1=	8t−3,b1=	NUM
ejpam-5470	358	15	8t+2,y′0=	8t+2,y′0=	NUM
ejpam-5470	358	16	2t+3,y′1=	2t+3,y′1=	NUM
ejpam-5470	358	17	2t+2,b′0=	2t+2,b′0=	NUM
ejpam-5470	358	18	8t+3	8t+3	ADJ
ejpam-5470	358	19	and	and	CCONJ
ejpam-5470	358	20	b′1=	b′1=	ADP
ejpam-5470	358	21	8	8	NUM
ejpam-5470	358	22	t	t	NOUN
ejpam-5470	358	23	+	+	NOUN
ejpam-5470	358	24	2	2	X
ejpam-5470	358	25	.	.	PUNCT
ejpam-5470	359	1	so	so	ADV
ejpam-5470	359	2	,	,	PUNCT
ejpam-5470	359	3	|v0	|v0	NOUN
ejpam-5470	359	4	−	−	NOUN
ejpam-5470	359	5	v1|	v1|	NOUN
ejpam-5470	359	6	=	=	SYM
ejpam-5470	359	7	0	0	NUM
ejpam-5470	359	8	and	and	CCONJ
ejpam-5470	359	9	|e0	|e0	NOUN
ejpam-5470	360	1	−	−	PROPN
ejpam-5470	360	2	e1|	e1|	NOUN
ejpam-5470	360	3	=	=	NOUN
ejpam-5470	360	4	1	1	X
ejpam-5470	360	5	.	.	X
ejpam-5470	361	1	for	for	ADP
ejpam-5470	361	2	the	the	DET
ejpam-5470	361	3	case	case	NOUN
ejpam-5470	361	4	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	361	5	5,5	5,5	NUM
ejpam-5470	361	6	,	,	PUNCT
ejpam-5470	361	7	the	the	DET
ejpam-5470	361	8	labeling	labeling	NOUN
ejpam-5470	361	9	[	[	X
ejpam-5470	361	10	m4r;105	m4r;105	NOUN
ejpam-5470	361	11	13	13	NUM
ejpam-5470	361	12	,	,	PUNCT
ejpam-5470	361	13	0	0	NUM
ejpam-5470	361	14	1503105	1503105	NUM
ejpam-5470	361	15	,	,	PUNCT
ejpam-5470	361	16	13	13	NUM
ejpam-5470	361	17	,	,	PUNCT
ejpam-5470	361	18	0	0	NUM
ejpam-5470	361	19	1503	1503	NUM
ejpam-5470	361	20	,	,	PUNCT
ejpam-5470	361	21	...	...	PUNCT
ejpam-5470	361	22	,	,	PUNCT
ejpam-5470	361	23	(	(	PUNCT
ejpam-5470	361	24	r−	r−	PROPN
ejpam-5470	361	25	times	time	NOUN
ejpam-5470	361	26	)	)	PUNCT
ejpam-5470	361	27	]	]	PUNCT
ejpam-5470	361	28	is	be	AUX
ejpam-5470	361	29	sufficient	sufficient	ADJ
ejpam-5470	361	30	and	and	CCONJ
ejpam-5470	361	31	thus	thus	ADV
ejpam-5470	361	32	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	361	33	5,4t+1	5,4t+1	PROPN
ejpam-5470	361	34	is	be	AUX
ejpam-5470	361	35	cordial	cordial	ADJ
ejpam-5470	361	36	.	.	PUNCT
ejpam-5470	362	1	subcase	subcase	PROPN
ejpam-5470	362	2	2.2.k	2.2.k	NUM
ejpam-5470	362	3	≡	≡	PROPN
ejpam-5470	362	4	1(mod4	1(mod4	NUM
ejpam-5470	362	5	)	)	PUNCT
ejpam-5470	362	6	let	let	VERB
ejpam-5470	362	7	k=	k=	X
ejpam-5470	362	8	4r+1,r	4r+1,r	NOUN
ejpam-5470	362	9	≥	≥	X
ejpam-5470	362	10	0	0	NUM
ejpam-5470	363	1	andm=	andm=	PROPN
ejpam-5470	363	2	4t+1	4t+1	PROPN
ejpam-5470	363	3	,	,	PUNCT
ejpam-5470	363	4	t	t	PROPN
ejpam-5470	363	5	>	>	X
ejpam-5470	363	6	1	1	NUM
ejpam-5470	363	7	.	.	PUNCT
ejpam-5470	364	1	then	then	ADV
ejpam-5470	364	2	,	,	PUNCT
ejpam-5470	364	3	the	the	DET
ejpam-5470	364	4	labelling	labelling	NOUN
ejpam-5470	364	5	[	[	X
ejpam-5470	364	6	l4r0;0	l4r0;0	PROPN
ejpam-5470	364	7	14m4t−4031	14m4t−4031	NUM
ejpam-5470	364	8	,	,	PUNCT
ejpam-5470	364	9	0	0	NUM
ejpam-5470	364	10	14m4t−4031	14m4t−4031	NUM
ejpam-5470	364	11	,	,	PUNCT
ejpam-5470	364	12	104	104	NUM
ejpam-5470	364	13	m	m	NOUN
ejpam-5470	364	14	′	′	NUM
ejpam-5470	364	15	4t−4	4t−4	NUM
ejpam-5470	364	16	130	130	NUM
ejpam-5470	364	17	,	,	PUNCT
ejpam-5470	364	18	104	104	NUM
ejpam-5470	364	19	m	m	NOUN
ejpam-5470	364	20	′	′	NUM
ejpam-5470	364	21	4t−4	4t−4	NUM
ejpam-5470	364	22	130	130	NUM
ejpam-5470	364	23	,	,	PUNCT
ejpam-5470	364	24	...	...	PUNCT
ejpam-5470	364	25	,	,	PUNCT
ejpam-5470	364	26	(	(	PUNCT
ejpam-5470	364	27	r	r	NOUN
ejpam-5470	364	28	−	−	PROPN
ejpam-5470	364	29	times	time	NOUN
ejpam-5470	364	30	)	)	PUNCT
ejpam-5470	364	31	,	,	PUNCT
ejpam-5470	364	32	0	0	NUM
ejpam-5470	364	33	14m4t−4031	14m4t−4031	NUM
ejpam-5470	364	34	]	]	PUNCT
ejpam-5470	364	35	for	for	ADP
ejpam-5470	364	36	p4r+1⊙	p4r+1⊙	PROPN
ejpam-5470	364	37	l4	l4	PROPN
ejpam-5470	364	38	5,4t+1	5,4t+1	PROPN
ejpam-5470	364	39	is	be	AUX
ejpam-5470	364	40	applied	apply	VERB
ejpam-5470	364	41	.	.	PUNCT
ejpam-5470	365	1	therefore	therefore	ADV
ejpam-5470	365	2	x0=	x0=	PROPN
ejpam-5470	366	1	2r+1,x1=	2r+1,x1=	NUM
ejpam-5470	366	2	2r	2r	NUM
ejpam-5470	366	3	,	,	PUNCT
ejpam-5470	366	4	a0	a0	PROPN
ejpam-5470	366	5	=	=	PROPN
ejpam-5470	366	6	a1=	a1=	PROPN
ejpam-5470	366	7	2r	2r	NUM
ejpam-5470	366	8	,	,	PUNCT
ejpam-5470	366	9	y0=	y0=	PROPN
ejpam-5470	366	10	2t+2,y1=	2t+2,y1=	PROPN
ejpam-5470	366	11	2t+3,b0=	2t+3,b0=	NUM
ejpam-5470	366	12	8t−3,b1=	8t−3,b1=	NUM
ejpam-5470	366	13	8t+2,y′0=	8t+2,y′0=	NUM
ejpam-5470	366	14	2t+	2t+	NUM
ejpam-5470	366	15	3,y′1=	3,y′1=	NUM
ejpam-5470	366	16	2	2	NUM
ejpam-5470	366	17	t	t	NOUN
ejpam-5470	366	18	+	+	NOUN
ejpam-5470	366	19	2,b′0=	2,b′0=	NUM
ejpam-5470	366	20	8	8	NUM
ejpam-5470	366	21	t	t	NOUN
ejpam-5470	366	22	+	+	CCONJ
ejpam-5470	366	23	3	3	NUM
ejpam-5470	366	24	and	and	CCONJ
ejpam-5470	366	25	b′1=	b′1=	ADP
ejpam-5470	366	26	8	8	NUM
ejpam-5470	366	27	t	t	NOUN
ejpam-5470	366	28	+	+	NOUN
ejpam-5470	366	29	2	2	X
ejpam-5470	366	30	.	.	PUNCT
ejpam-5470	367	1	so	so	ADV
ejpam-5470	367	2	,	,	PUNCT
ejpam-5470	367	3	|v0	|v0	NOUN
ejpam-5470	367	4	−	−	NOUN
ejpam-5470	367	5	v1|	v1|	NOUN
ejpam-5470	367	6	=	=	SYM
ejpam-5470	367	7	0	0	NUM
ejpam-5470	367	8	and	and	CCONJ
ejpam-5470	367	9	|e0	|e0	NOUN
ejpam-5470	368	1	−	−	PROPN
ejpam-5470	368	2	e1|	e1|	NOUN
ejpam-5470	368	3	=	=	NOUN
ejpam-5470	368	4	0	0	NUM
ejpam-5470	368	5	.	.	PUNCT
ejpam-5470	369	1	for	for	ADP
ejpam-5470	369	2	the	the	DET
ejpam-5470	369	3	case	case	NOUN
ejpam-5470	369	4	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	369	5	5,5	5,5	NUM
ejpam-5470	369	6	,	,	PUNCT
ejpam-5470	369	7	the	the	DET
ejpam-5470	369	8	labeling	labeling	NOUN
ejpam-5470	369	9	[	[	X
ejpam-5470	369	10	m4r+1;105	m4r+1;105	ADJ
ejpam-5470	369	11	13	13	NUM
ejpam-5470	369	12	,	,	PUNCT
ejpam-5470	369	13	0	0	NUM
ejpam-5470	369	14	1503	1503	NUM
ejpam-5470	369	15	,	,	PUNCT
ejpam-5470	369	16	105	105	NUM
ejpam-5470	369	17	13	13	NUM
ejpam-5470	369	18	,	,	PUNCT
ejpam-5470	369	19	0	0	NUM
ejpam-5470	369	20	1503	1503	NUM
ejpam-5470	369	21	,	,	PUNCT
ejpam-5470	369	22	...	...	PUNCT
ejpam-5470	369	23	,	,	PUNCT
ejpam-5470	369	24	(	(	PUNCT
ejpam-5470	369	25	r−times	r−time	NOUN
ejpam-5470	369	26	)	)	PUNCT
ejpam-5470	369	27	,	,	PUNCT
ejpam-5470	369	28	0	0	NUM
ejpam-5470	369	29	1503	1503	NUM
ejpam-5470	369	30	]	]	PUNCT
ejpam-5470	369	31	is	be	AUX
ejpam-5470	369	32	sufficient	sufficient	ADJ
ejpam-5470	369	33	and	and	CCONJ
ejpam-5470	369	34	thus	thus	ADV
ejpam-5470	369	35	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	369	36	5,4t+1	5,4t+1	PROPN
ejpam-5470	369	37	is	be	AUX
ejpam-5470	369	38	cordial	cordial	ADJ
ejpam-5470	369	39	.	.	PUNCT
ejpam-5470	370	1	subcase	subcase	PROPN
ejpam-5470	370	2	2.3.k	2.3.k	NUM
ejpam-5470	370	3	≡	≡	PROPN
ejpam-5470	370	4	2(mod4	2(mod4	NUM
ejpam-5470	370	5	)	)	PUNCT
ejpam-5470	370	6	let	let	VERB
ejpam-5470	370	7	k=	k=	PROPN
ejpam-5470	370	8	4r+2,r	4r+2,r	NUM
ejpam-5470	370	9	≥	≥	NOUN
ejpam-5470	370	10	0	0	NUM
ejpam-5470	370	11	andm=	andm=	PROPN
ejpam-5470	370	12	4t+1	4t+1	PROPN
ejpam-5470	370	13	,	,	PUNCT
ejpam-5470	370	14	t	t	PROPN
ejpam-5470	370	15	>	>	X
ejpam-5470	370	16	1	1	NUM
ejpam-5470	370	17	.	.	PUNCT
ejpam-5470	371	1	then	then	ADV
ejpam-5470	371	2	,	,	PUNCT
ejpam-5470	371	3	the	the	DET
ejpam-5470	371	4	labelling	labelling	NOUN
ejpam-5470	371	5	[	[	X
ejpam-5470	371	6	l4r01;0	l4r01;0	PROPN
ejpam-5470	371	7	14m4t−4031	14m4t−4031	NUM
ejpam-5470	371	8	,	,	PUNCT
ejpam-5470	371	9	0	0	NUM
ejpam-5470	371	10	14m4t−4031	14m4t−4031	NUM
ejpam-5470	371	11	,	,	PUNCT
ejpam-5470	371	12	104	104	NUM
ejpam-5470	371	13	m	m	NOUN
ejpam-5470	371	14	′	′	NUM
ejpam-5470	371	15	4t−4	4t−4	NUM
ejpam-5470	371	16	130	130	NUM
ejpam-5470	371	17	,	,	PUNCT
ejpam-5470	371	18	104	104	NUM
ejpam-5470	371	19	m	m	NOUN
ejpam-5470	371	20	′	′	NUM
ejpam-5470	371	21	4t−4	4t−4	NUM
ejpam-5470	371	22	130	130	NUM
ejpam-5470	371	23	,	,	PUNCT
ejpam-5470	371	24	...	...	PUNCT
ejpam-5470	371	25	,	,	PUNCT
ejpam-5470	371	26	(	(	PUNCT
ejpam-5470	371	27	r−times	r−time	NOUN
ejpam-5470	371	28	)	)	PUNCT
ejpam-5470	371	29	,	,	PUNCT
ejpam-5470	371	30	0	0	NUM
ejpam-5470	371	31	14m4t−4031	14m4t−4031	NUM
ejpam-5470	371	32	,	,	PUNCT
ejpam-5470	371	33	104	104	NUM
ejpam-5470	371	34	m	m	NOUN
ejpam-5470	371	35	′	′	NUM
ejpam-5470	371	36	4t−4	4t−4	NUM
ejpam-5470	371	37	130	130	NUM
ejpam-5470	371	38	]	]	PUNCT
ejpam-5470	371	39	for	for	ADP
ejpam-5470	371	40	p4r+2⊙	p4r+2⊙	PROPN
ejpam-5470	371	41	l4	l4	PROPN
ejpam-5470	371	42	5,4t+1	5,4t+1	PROPN
ejpam-5470	371	43	is	be	AUX
ejpam-5470	371	44	applied	apply	VERB
ejpam-5470	371	45	.	.	PUNCT
ejpam-5470	372	1	therefore	therefore	ADV
ejpam-5470	372	2	x0	x0	PROPN
ejpam-5470	372	3	=	=	PROPN
ejpam-5470	372	4	x1=	x1=	PROPN
ejpam-5470	372	5	2r	2r	NUM
ejpam-5470	373	1	+	+	CCONJ
ejpam-5470	373	2	1,a0=	1,a0=	NUM
ejpam-5470	373	3	2r	2r	NUM
ejpam-5470	373	4	,	,	PUNCT
ejpam-5470	373	5	a1=	a1=	PROPN
ejpam-5470	373	6	2r	2r	NUM
ejpam-5470	374	1	+	+	CCONJ
ejpam-5470	375	1	1,y0=	1,y0=	PROPN
ejpam-5470	375	2	2	2	NUM
ejpam-5470	375	3	t	t	NOUN
ejpam-5470	375	4	+	+	NOUN
ejpam-5470	375	5	2,y1=	2,y1=	NUM
ejpam-5470	375	6	2	2	NUM
ejpam-5470	375	7	t	t	NOUN
ejpam-5470	375	8	+	+	NOUN
ejpam-5470	375	9	3,b0=	3,b0=	NUM
ejpam-5470	375	10	8	8	NUM
ejpam-5470	375	11	t	t	NOUN
ejpam-5470	375	12	−	−	NOUN
ejpam-5470	375	13	3,b1=	3,b1=	NUM
ejpam-5470	375	14	8t+	8t+	NUM
ejpam-5470	375	15	2,y′0=	2,y′0=	NUM
ejpam-5470	375	16	2t+	2t+	NUM
ejpam-5470	375	17	3,y′1=	3,y′1=	NUM
ejpam-5470	375	18	2t+	2t+	NUM
ejpam-5470	375	19	2,b′0=	2,b′0=	NUM
ejpam-5470	375	20	8t+	8t+	NUM
ejpam-5470	375	21	3	3	NUM
ejpam-5470	375	22	and	and	CCONJ
ejpam-5470	375	23	b′1=	b′1=	ADP
ejpam-5470	375	24	8t+	8t+	NUM
ejpam-5470	375	25	2	2	NUM
ejpam-5470	375	26	.	.	PUNCT
ejpam-5470	376	1	so	so	ADV
ejpam-5470	376	2	,	,	PUNCT
ejpam-5470	376	3	|v0	|v0	NOUN
ejpam-5470	376	4	−	−	NOUN
ejpam-5470	376	5	v1|	v1|	NOUN
ejpam-5470	376	6	=	=	SYM
ejpam-5470	376	7	0	0	NUM
ejpam-5470	376	8	and	and	CCONJ
ejpam-5470	376	9	|e0	|e0	NOUN
ejpam-5470	377	1	−	−	PROPN
ejpam-5470	377	2	e1|	e1|	NOUN
ejpam-5470	377	3	=	=	NOUN
ejpam-5470	377	4	1	1	X
ejpam-5470	377	5	.	.	X
ejpam-5470	378	1	for	for	ADP
ejpam-5470	378	2	the	the	DET
ejpam-5470	378	3	case	case	NOUN
ejpam-5470	378	4	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	378	5	5,5	5,5	NUM
ejpam-5470	378	6	,	,	PUNCT
ejpam-5470	378	7	the	the	DET
ejpam-5470	378	8	labeling	labeling	NOUN
ejpam-5470	378	9	[	[	X
ejpam-5470	378	10	m4r+2;105	m4r+2;105	NOUN
ejpam-5470	378	11	13	13	NUM
ejpam-5470	378	12	,	,	PUNCT
ejpam-5470	378	13	0	0	NUM
ejpam-5470	378	14	1503	1503	NUM
ejpam-5470	378	15	,	,	PUNCT
ejpam-5470	378	16	105	105	NUM
ejpam-5470	378	17	13	13	NUM
ejpam-5470	378	18	,	,	PUNCT
ejpam-5470	378	19	0	0	NUM
ejpam-5470	378	20	1503	1503	NUM
ejpam-5470	378	21	,	,	PUNCT
ejpam-5470	378	22	...	...	PUNCT
ejpam-5470	378	23	,	,	PUNCT
ejpam-5470	378	24	(	(	PUNCT
ejpam-5470	378	25	r−	r−	PROPN
ejpam-5470	378	26	times	time	NOUN
ejpam-5470	378	27	)	)	PUNCT
ejpam-5470	378	28	,	,	PUNCT
ejpam-5470	378	29	105	105	NUM
ejpam-5470	378	30	13	13	NUM
ejpam-5470	378	31	,	,	PUNCT
ejpam-5470	378	32	0	0	NUM
ejpam-5470	378	33	1503	1503	NUM
ejpam-5470	378	34	]	]	PUNCT
ejpam-5470	378	35	is	be	AUX
ejpam-5470	378	36	sufficient	sufficient	ADJ
ejpam-5470	378	37	and	and	CCONJ
ejpam-5470	378	38	thus	thus	ADV
ejpam-5470	378	39	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	378	40	5,4t+1	5,4t+1	NOUN
ejpam-5470	378	41	is	be	AUX
ejpam-5470	378	42	cordial	cordial	ADJ
ejpam-5470	378	43	.	.	PUNCT
ejpam-5470	379	1	subcase	subcase	PROPN
ejpam-5470	379	2	2.4.k	2.4.k	NUM
ejpam-5470	379	3	≡	≡	PROPN
ejpam-5470	379	4	3(mod4	3(mod4	NUM
ejpam-5470	379	5	)	)	PUNCT
ejpam-5470	379	6	let	let	VERB
ejpam-5470	379	7	k=	k=	X
ejpam-5470	379	8	4r+3,r	4r+3,r	NUM
ejpam-5470	379	9	≥	≥	NOUN
ejpam-5470	379	10	0	0	NUM
ejpam-5470	379	11	andm=	andm=	PROPN
ejpam-5470	379	12	4t+1	4t+1	PROPN
ejpam-5470	379	13	,	,	PUNCT
ejpam-5470	379	14	t	t	PROPN
ejpam-5470	379	15	>	>	X
ejpam-5470	379	16	1	1	NUM
ejpam-5470	379	17	.	.	PUNCT
ejpam-5470	380	1	then	then	ADV
ejpam-5470	380	2	,	,	PUNCT
ejpam-5470	380	3	the	the	DET
ejpam-5470	380	4	labelling	labelling	NOUN
ejpam-5470	380	5	[	[	X
ejpam-5470	380	6	l4r001;0	l4r001;0	NOUN
ejpam-5470	380	7	14m4t−4031	14m4t−4031	NUM
ejpam-5470	380	8	,	,	PUNCT
ejpam-5470	380	9	0	0	NUM
ejpam-5470	380	10	14m4t−4031	14m4t−4031	NUM
ejpam-5470	380	11	,	,	PUNCT
ejpam-5470	380	12	104	104	NUM
ejpam-5470	380	13	m	m	NOUN
ejpam-5470	380	14	′	′	NUM
ejpam-5470	380	15	4t−4	4t−4	NUM
ejpam-5470	380	16	130	130	NUM
ejpam-5470	380	17	,	,	PUNCT
ejpam-5470	380	18	104	104	NUM
ejpam-5470	380	19	m	m	NOUN
ejpam-5470	380	20	′	′	NUM
ejpam-5470	380	21	4t−4	4t−4	NUM
ejpam-5470	380	22	130	130	NUM
ejpam-5470	380	23	,	,	PUNCT
ejpam-5470	380	24	...	...	PUNCT
ejpam-5470	380	25	,	,	PUNCT
ejpam-5470	380	26	(	(	PUNCT
ejpam-5470	380	27	r−times	r−time	NOUN
ejpam-5470	380	28	)	)	PUNCT
ejpam-5470	380	29	,	,	PUNCT
ejpam-5470	380	30	014m4t−4031	014m4t−4031	NOUN
ejpam-5470	380	31	,	,	PUNCT
ejpam-5470	380	32	0	0	NUM
ejpam-5470	380	33	14m4t−4031	14m4t−4031	NUM
ejpam-5470	380	34	,	,	PUNCT
ejpam-5470	380	35	104	104	NUM
ejpam-5470	380	36	m	m	NOUN
ejpam-5470	380	37	′	′	NUM
ejpam-5470	380	38	4t−4	4t−4	NUM
ejpam-5470	380	39	130	130	NUM
ejpam-5470	380	40	]	]	PUNCT
ejpam-5470	380	41	for	for	ADP
ejpam-5470	380	42	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	380	43	5,4t+1	5,4t+1	PRON
ejpam-5470	380	44	is	be	AUX
ejpam-5470	380	45	applied	apply	VERB
ejpam-5470	380	46	.	.	PUNCT
ejpam-5470	381	1	therefore	therefore	ADV
ejpam-5470	381	2	x0=	x0=	PROPN
ejpam-5470	381	3	2r+2,x1=	2r+2,x1=	NUM
ejpam-5470	381	4	2r+	2r+	NUM
ejpam-5470	382	1	1,a0	1,a0	NUM
ejpam-5470	382	2	=	=	NOUN
ejpam-5470	382	3	a1=	a1=	PROPN
ejpam-5470	382	4	2r+1,y0=	2r+1,y0=	NUM
ejpam-5470	382	5	2t+2,y1=	2t+2,y1=	NUM
ejpam-5470	382	6	2t+3,b0=	2t+3,b0=	NUM
ejpam-5470	382	7	8t−3,b1=	8t−3,b1=	NUM
ejpam-5470	382	8	8t+2,y′0=	8t+2,y′0=	NUM
ejpam-5470	382	9	2t+3,y′1=	2t+3,y′1=	NUM
ejpam-5470	382	10	2t+2,b′0=	2t+2,b′0=	NUM
ejpam-5470	382	11	8t+3	8t+3	ADJ
ejpam-5470	382	12	and	and	CCONJ
ejpam-5470	382	13	b′1=	b′1=	ADP
ejpam-5470	382	14	8t+	8t+	NUM
ejpam-5470	382	15	2	2	NUM
ejpam-5470	382	16	.	.	PUNCT
ejpam-5470	383	1	so	so	ADV
ejpam-5470	383	2	,	,	PUNCT
ejpam-5470	383	3	|v0	|v0	NOUN
ejpam-5470	383	4	−	−	NOUN
ejpam-5470	383	5	v1|	v1|	NOUN
ejpam-5470	383	6	=	=	SYM
ejpam-5470	383	7	0	0	NUM
ejpam-5470	383	8	and	and	CCONJ
ejpam-5470	383	9	|e0	|e0	NOUN
ejpam-5470	384	1	−	−	PROPN
ejpam-5470	384	2	e1|	e1|	NOUN
ejpam-5470	384	3	=	=	NOUN
ejpam-5470	384	4	0	0	NUM
ejpam-5470	384	5	.	.	PUNCT
ejpam-5470	385	1	for	for	ADP
ejpam-5470	385	2	the	the	DET
ejpam-5470	385	3	case	case	NOUN
ejpam-5470	385	4	p4r+3⊙l4	p4r+3⊙l4	VERB
ejpam-5470	385	5	5,5	5,5	NUM
ejpam-5470	385	6	,	,	PUNCT
ejpam-5470	385	7	the	the	DET
ejpam-5470	385	8	labeling	labeling	NOUN
ejpam-5470	385	9	[	[	X
ejpam-5470	385	10	m4r+3;105	m4r+3;105	NOUN
ejpam-5470	385	11	13	13	NUM
ejpam-5470	385	12	,	,	PUNCT
ejpam-5470	385	13	0	0	NUM
ejpam-5470	385	14	1503	1503	NUM
ejpam-5470	385	15	,	,	PUNCT
ejpam-5470	385	16	105	105	NUM
ejpam-5470	385	17	13	13	NUM
ejpam-5470	385	18	,	,	PUNCT
ejpam-5470	385	19	0	0	NUM
ejpam-5470	385	20	1503	1503	NUM
ejpam-5470	385	21	,	,	PUNCT
ejpam-5470	385	22	...	...	PUNCT
ejpam-5470	385	23	,	,	PUNCT
ejpam-5470	385	24	(	(	PUNCT
ejpam-5470	385	25	r−	r−	PROPN
ejpam-5470	385	26	times	time	NOUN
ejpam-5470	385	27	)	)	PUNCT
ejpam-5470	385	28	,	,	PUNCT
ejpam-5470	385	29	0	0	NUM
ejpam-5470	385	30	1503	1503	NUM
ejpam-5470	385	31	,	,	PUNCT
ejpam-5470	385	32	105	105	NUM
ejpam-5470	385	33	13	13	NUM
ejpam-5470	385	34	,	,	PUNCT
ejpam-5470	385	35	0	0	NUM
ejpam-5470	385	36	1503	1503	NUM
ejpam-5470	385	37	]	]	PUNCT
ejpam-5470	385	38	is	be	AUX
ejpam-5470	385	39	sufficient	sufficient	ADJ
ejpam-5470	385	40	and	and	CCONJ
ejpam-5470	385	41	thus	thus	ADV
ejpam-5470	385	42	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	385	43	5,4t+1	5,4t+1	PRON
ejpam-5470	385	44	is	be	AUX
ejpam-5470	385	45	cordial	cordial	ADJ
ejpam-5470	385	46	.	.	PUNCT
ejpam-5470	386	1	case	case	NOUN
ejpam-5470	386	2	3	3	X
ejpam-5470	386	3	.	.	PUNCT
ejpam-5470	387	1	at	at	ADP
ejpam-5470	387	2	m	m	PROPN
ejpam-5470	387	3	≡	≡	PROPN
ejpam-5470	387	4	2(mod4	2(mod4	NUM
ejpam-5470	387	5	)	)	PUNCT
ejpam-5470	387	6	,	,	PUNCT
ejpam-5470	387	7	we	we	PRON
ejpam-5470	387	8	consider	consider	VERB
ejpam-5470	387	9	the	the	DET
ejpam-5470	387	10	following	follow	VERB
ejpam-5470	387	11	sub	sub	NOUN
ejpam-5470	387	12	subcases	subcase	NOUN
ejpam-5470	387	13	.	.	PUNCT
ejpam-5470	388	1	subcase	subcase	PROPN
ejpam-5470	388	2	3.1.k	3.1.k	NUM
ejpam-5470	388	3	is	be	AUX
ejpam-5470	388	4	even	even	ADV
ejpam-5470	388	5	.	.	PUNCT
ejpam-5470	389	1	let	let	VERB
ejpam-5470	389	2	k=	k=	PRON
ejpam-5470	389	3	2r	2r	NUM
ejpam-5470	389	4	,	,	PUNCT
ejpam-5470	390	1	r	r	NOUN
ejpam-5470	390	2	≥	≥	NOUN
ejpam-5470	390	3	1	1	NUM
ejpam-5470	390	4	and	and	CCONJ
ejpam-5470	390	5	m=	m=	X
ejpam-5470	390	6	4	4	NUM
ejpam-5470	390	7	t	t	NOUN
ejpam-5470	390	8	+	+	CCONJ
ejpam-5470	390	9	2	2	NUM
ejpam-5470	390	10	,	,	PUNCT
ejpam-5470	390	11	t	t	PROPN
ejpam-5470	390	12	>	>	X
ejpam-5470	390	13	1	1	NUM
ejpam-5470	390	14	.	.	PUNCT
ejpam-5470	391	1	then	then	ADV
ejpam-5470	391	2	,	,	PUNCT
ejpam-5470	391	3	the	the	DET
ejpam-5470	391	4	labelling	labelling	NOUN
ejpam-5470	391	5	[	[	X
ejpam-5470	391	6	m2r;03	m2r;03	NUM
ejpam-5470	391	7	140103	140103	NUM
ejpam-5470	391	8	m	m	NOUN
ejpam-5470	391	9	′	′	NUM
ejpam-5470	391	10	4t−6	4t−6	PROPN
ejpam-5470	391	11	,	,	PUNCT
ejpam-5470	391	12	13040	13040	NUM
ejpam-5470	391	13	13m4t−6	13m4t−6	NUM
ejpam-5470	391	14	,	,	PUNCT
ejpam-5470	391	15	...	...	PUNCT
ejpam-5470	391	16	,	,	PUNCT
ejpam-5470	391	17	(	(	PUNCT
ejpam-5470	391	18	r	r	NOUN
ejpam-5470	391	19	−	−	PROPN
ejpam-5470	391	20	times	time	NOUN
ejpam-5470	391	21	)	)	PUNCT
ejpam-5470	391	22	]	]	PUNCT
ejpam-5470	391	23	for	for	ADP
ejpam-5470	391	24	p2r⊙	p2r⊙	PROPN
ejpam-5470	391	25	l4	l4	PROPN
ejpam-5470	391	26	5,4t+2	5,4t+2	PROPN
ejpam-5470	391	27	is	be	AUX
ejpam-5470	391	28	applied	apply	VERB
ejpam-5470	391	29	.	.	PUNCT
ejpam-5470	392	1	therefore	therefore	ADV
ejpam-5470	392	2	x0	x0	PROPN
ejpam-5470	392	3	=	=	PROPN
ejpam-5470	392	4	x1	x1	PROPN
ejpam-5470	392	5	=	=	SYM
ejpam-5470	392	6	r	r	NOUN
ejpam-5470	392	7	,	,	PUNCT
ejpam-5470	392	8	a0=	a0=	PROPN
ejpam-5470	392	9	0,a1=	0,a1=	NOUN
ejpam-5470	392	10	2r	2r	NUM
ejpam-5470	392	11	−	−	NOUN
ejpam-5470	392	12	1,y0=	1,y0=	PROPN
ejpam-5470	392	13	2	2	NUM
ejpam-5470	392	14	t	t	NOUN
ejpam-5470	392	15	+	+	NOUN
ejpam-5470	392	16	4,y1=	4,y1=	NUM
ejpam-5470	392	17	2	2	NUM
ejpam-5470	392	18	t	t	NOUN
ejpam-5470	392	19	+	+	CCONJ
ejpam-5470	392	20	2,b0=	2,b0=	NUM
ejpam-5470	392	21	8	8	NUM
ejpam-5470	392	22	t	t	NOUN
ejpam-5470	392	23	+	+	NOUN
ejpam-5470	392	24	4,b1=	4,b1=	NUM
ejpam-5470	392	25	8	8	NUM
ejpam-5470	392	26	t	t	NOUN
ejpam-5470	392	27	+	+	NOUN
ejpam-5470	392	28	5,y′0=	5,y′0=	NUM
ejpam-5470	392	29	2	2	NUM
ejpam-5470	392	30	t	t	NOUN
ejpam-5470	392	31	+	+	NOUN
ejpam-5470	392	32	2,y′1=	2,y′1=	NUM
ejpam-5470	392	33	2	2	NUM
ejpam-5470	392	34	t	t	NOUN
ejpam-5470	392	35	+	+	CCONJ
ejpam-5470	392	36	4,b′0=	4,b′0=	NUM
ejpam-5470	392	37	8	8	NUM
ejpam-5470	392	38	t	t	NOUN
ejpam-5470	392	39	+	+	CCONJ
ejpam-5470	392	40	4	4	NUM
ejpam-5470	392	41	and	and	CCONJ
ejpam-5470	392	42	b′1=	b′1=	ADP
ejpam-5470	392	43	8	8	NUM
ejpam-5470	392	44	t	t	NOUN
ejpam-5470	392	45	+	+	NOUN
ejpam-5470	392	46	5	5	NUM
ejpam-5470	392	47	.	.	PUNCT
ejpam-5470	393	1	so	so	ADV
ejpam-5470	393	2	,	,	PUNCT
ejpam-5470	393	3	|v0	|v0	NOUN
ejpam-5470	393	4	−	−	NOUN
ejpam-5470	393	5	v1|	v1|	NOUN
ejpam-5470	393	6	=	=	SYM
ejpam-5470	393	7	0	0	NUM
ejpam-5470	393	8	and	and	CCONJ
ejpam-5470	393	9	|e0	|e0	NOUN
ejpam-5470	394	1	−	−	PROPN
ejpam-5470	394	2	e1|	e1|	NOUN
ejpam-5470	394	3	=	=	NOUN
ejpam-5470	394	4	1	1	X
ejpam-5470	394	5	.	.	X
ejpam-5470	395	1	for	for	ADP
ejpam-5470	395	2	the	the	DET
ejpam-5470	395	3	case	case	NOUN
ejpam-5470	395	4	p2r⊙l4	p2r⊙l4	NOUN
ejpam-5470	395	5	5,6	5,6	NUM
ejpam-5470	395	6	,	,	PUNCT
ejpam-5470	395	7	the	the	DET
ejpam-5470	395	8	labeling	labeling	NOUN
ejpam-5470	395	9	[	[	X
ejpam-5470	395	10	m2r;03	m2r;03	NUM
ejpam-5470	395	11	1304	1304	NUM
ejpam-5470	395	12	,	,	PUNCT
ejpam-5470	395	13	1303	1303	NUM
ejpam-5470	395	14	14	14	NUM
ejpam-5470	395	15	,	,	PUNCT
ejpam-5470	395	16	...	...	PUNCT
ejpam-5470	395	17	,	,	PUNCT
ejpam-5470	395	18	(	(	PUNCT
ejpam-5470	395	19	r	r	NOUN
ejpam-5470	395	20	−	−	PROPN
ejpam-5470	395	21	times	time	NOUN
ejpam-5470	395	22	)	)	PUNCT
ejpam-5470	395	23	]	]	PUNCT
ejpam-5470	395	24	is	be	AUX
ejpam-5470	395	25	sufficient	sufficient	ADJ
ejpam-5470	395	26	and	and	CCONJ
ejpam-5470	395	27	thus	thus	ADV
ejpam-5470	395	28	p2r⊙l4	p2r⊙l4	NOUN
ejpam-5470	395	29	5,4t+2	5,4t+2	NOUN
ejpam-5470	395	30	is	be	AUX
ejpam-5470	395	31	cordial	cordial	ADJ
ejpam-5470	395	32	.	.	PUNCT
ejpam-5470	396	1	subcase	subcase	PROPN
ejpam-5470	396	2	3.2.k	3.2.k	NUM
ejpam-5470	396	3	is	be	AUX
ejpam-5470	396	4	odd	odd	ADJ
ejpam-5470	396	5	.	.	PUNCT
ejpam-5470	397	1	let	let	VERB
ejpam-5470	397	2	k=	k=	X
ejpam-5470	398	1	2r	2r	NUM
ejpam-5470	399	1	+	+	CCONJ
ejpam-5470	399	2	1,r	1,r	NUM
ejpam-5470	399	3	≥	≥	NOUN
ejpam-5470	399	4	0	0	NUM
ejpam-5470	399	5	and	and	CCONJ
ejpam-5470	399	6	m=	m=	ADJ
ejpam-5470	399	7	4t+	4t+	PROPN
ejpam-5470	399	8	2	2	NUM
ejpam-5470	399	9	,	,	PUNCT
ejpam-5470	399	10	t	t	PROPN
ejpam-5470	399	11	>	>	X
ejpam-5470	399	12	1	1	NUM
ejpam-5470	399	13	.	.	PUNCT
ejpam-5470	400	1	then	then	ADV
ejpam-5470	400	2	,	,	PUNCT
ejpam-5470	400	3	the	the	DET
ejpam-5470	400	4	labelling	labelling	NOUN
ejpam-5470	400	5	[	[	X
ejpam-5470	400	6	m2r+1;03	m2r+1;03	NOUN
ejpam-5470	400	7	140103	140103	NUM
ejpam-5470	400	8	m	m	NOUN
ejpam-5470	400	9	′	′	NUM
ejpam-5470	400	10	4t−6	4t−6	PROPN
ejpam-5470	400	11	,	,	PUNCT
ejpam-5470	400	12	13040	13040	NUM
ejpam-5470	400	13	13m4t−6	13m4t−6	NUM
ejpam-5470	400	14	,	,	PUNCT
ejpam-5470	400	15	...	...	PUNCT
ejpam-5470	400	16	,	,	PUNCT
ejpam-5470	400	17	(	(	PUNCT
ejpam-5470	400	18	r	r	NOUN
ejpam-5470	400	19	−	−	PROPN
ejpam-5470	400	20	times	time	NOUN
ejpam-5470	400	21	)	)	PUNCT
ejpam-5470	400	22	,	,	PUNCT
ejpam-5470	400	23	103l4	103l4	NUM
ejpam-5470	400	24	t	t	NOUN
ejpam-5470	400	25	12	12	NUM
ejpam-5470	400	26	]	]	PUNCT
ejpam-5470	400	27	for	for	ADP
ejpam-5470	400	28	p2r+1⊙l4	p2r+1⊙l4	NOUN
ejpam-5470	400	29	5,4t+2	5,4t+2	NOUN
ejpam-5470	400	30	is	be	AUX
ejpam-5470	400	31	applied	apply	VERB
ejpam-5470	400	32	.	.	PUNCT
ejpam-5470	401	1	therefore	therefore	ADV
ejpam-5470	401	2	x0	x0	PROPN
ejpam-5470	401	3	=	=	ADJ
ejpam-5470	401	4	r+1,x1	r+1,x1	ADV
ejpam-5470	401	5	=	=	ADJ
ejpam-5470	401	6	r	r	NOUN
ejpam-5470	401	7	,	,	PUNCT
ejpam-5470	401	8	a0=	a0=	PROPN
ejpam-5470	401	9	0,a1=	0,a1=	NUM
ejpam-5470	401	10	2r	2r	NUM
ejpam-5470	401	11	,	,	PUNCT
ejpam-5470	401	12	y0=	y0=	PROPN
ejpam-5470	401	13	2t+4,y1=	2t+4,y1=	NUM
ejpam-5470	401	14	2t+2,b0=	2t+2,b0=	NUM
ejpam-5470	401	15	8t+4,b1=	8t+4,b1=	NUM
ejpam-5470	401	16	8t+	8t+	NUM
ejpam-5470	401	17	5,y′0=	5,y′0=	NUM
ejpam-5470	401	18	2t+2,y′1=	2t+2,y′1=	NUM
ejpam-5470	401	19	2t+4,b′0=	2t+4,b′0=	NUM
ejpam-5470	401	20	8t+4,b′1=	8t+4,b′1=	NUM
ejpam-5470	401	21	8t+5,y”0=	8t+5,y”0=	NUM
ejpam-5470	401	22	2t+3,y”1=	2t+3,y”1=	NUM
ejpam-5470	401	23	2t+3,b”0=	2t+3,b”0=	NUM
ejpam-5470	401	24	8t+5	8t+5	PROPN
ejpam-5470	401	25	and	and	CCONJ
ejpam-5470	401	26	b”1=	b”1=	PROPN
ejpam-5470	401	27	8t+4	8t+4	PROPN
ejpam-5470	401	28	.	.	PUNCT
ejpam-5470	402	1	so	so	ADV
ejpam-5470	402	2	,	,	PUNCT
ejpam-5470	402	3	|v0	|v0	PROPN
ejpam-5470	402	4	−	−	NOUN
ejpam-5470	402	5	v1|	v1|	NOUN
ejpam-5470	402	6	=	=	SYM
ejpam-5470	402	7	1	1	NUM
ejpam-5470	402	8	and	and	CCONJ
ejpam-5470	402	9	|e0	|e0	NOUN
ejpam-5470	402	10	−	−	PROPN
ejpam-5470	402	11	e1|	e1|	NOUN
ejpam-5470	402	12	=	=	NOUN
ejpam-5470	402	13	1	1	X
ejpam-5470	402	14	.	.	X
ejpam-5470	402	15	for	for	ADP
ejpam-5470	402	16	the	the	DET
ejpam-5470	402	17	case	case	NOUN
ejpam-5470	402	18	p2r+1⊙l4	p2r+1⊙l4	NOUN
ejpam-5470	402	19	5,6	5,6	NUM
ejpam-5470	402	20	,	,	PUNCT
ejpam-5470	402	21	the	the	DET
ejpam-5470	402	22	labeling	labeling	NOUN
ejpam-5470	402	23	[	[	X
ejpam-5470	402	24	m2r+1;03	m2r+1;03	NOUN
ejpam-5470	402	25	1304	1304	NUM
ejpam-5470	402	26	,	,	PUNCT
ejpam-5470	402	27	1303	1303	NUM
ejpam-5470	402	28	14	14	NUM
ejpam-5470	402	29	,	,	PUNCT
ejpam-5470	402	30	...	...	PUNCT
ejpam-5470	402	31	,	,	PUNCT
ejpam-5470	402	32	(	(	PUNCT
ejpam-5470	402	33	r	r	NOUN
ejpam-5470	402	34	−	−	PROPN
ejpam-5470	402	35	times	time	NOUN
ejpam-5470	402	36	)	)	PUNCT
ejpam-5470	402	37	,	,	PUNCT
ejpam-5470	402	38	105	105	NUM
ejpam-5470	402	39	14	14	NUM
ejpam-5470	402	40	]	]	PUNCT
ejpam-5470	402	41	is	be	AUX
ejpam-5470	402	42	sufficient	sufficient	ADJ
ejpam-5470	402	43	and	and	CCONJ
ejpam-5470	402	44	thus	thus	ADV
ejpam-5470	402	45	p2r+1⊙l4	p2r+1⊙l4	NOUN
ejpam-5470	402	46	5,4t+2	5,4t+2	NOUN
ejpam-5470	402	47	is	be	AUX
ejpam-5470	402	48	cordial	cordial	ADJ
ejpam-5470	402	49	.	.	PUNCT
ejpam-5470	403	1	case	case	NOUN
ejpam-5470	403	2	4	4	NUM
ejpam-5470	403	3	.	.	PUNCT
ejpam-5470	404	1	at	at	ADP
ejpam-5470	404	2	m	m	PROPN
ejpam-5470	404	3	≡	≡	PROPN
ejpam-5470	404	4	3(mod4	3(mod4	NUM
ejpam-5470	404	5	)	)	PUNCT
ejpam-5470	404	6	,	,	PUNCT
ejpam-5470	404	7	we	we	PRON
ejpam-5470	404	8	consider	consider	VERB
ejpam-5470	404	9	the	the	DET
ejpam-5470	404	10	following	follow	VERB
ejpam-5470	404	11	sub	sub	NOUN
ejpam-5470	404	12	subcases	subcase	NOUN
ejpam-5470	404	13	.	.	PUNCT
ejpam-5470	405	1	subcase	subcase	PROPN
ejpam-5470	405	2	4.1.k	4.1.k	PROPN
ejpam-5470	405	3	≡	≡	PROPN
ejpam-5470	405	4	0(mod4	0(mod4	NUM
ejpam-5470	405	5	)	)	PUNCT
ejpam-5470	405	6	let	let	VERB
ejpam-5470	405	7	k=	k=	ADJ
ejpam-5470	405	8	4r	4r	NOUN
ejpam-5470	405	9	,	,	PUNCT
ejpam-5470	405	10	r	r	NOUN
ejpam-5470	405	11	≥	≥	NOUN
ejpam-5470	405	12	1	1	NUM
ejpam-5470	405	13	and	and	CCONJ
ejpam-5470	405	14	m=	m=	X
ejpam-5470	405	15	4	4	NUM
ejpam-5470	405	16	t	t	NOUN
ejpam-5470	405	17	+	+	NOUN
ejpam-5470	405	18	3	3	NUM
ejpam-5470	405	19	,	,	PUNCT
ejpam-5470	405	20	t	t	PROPN
ejpam-5470	405	21	≥	≥	NUM
ejpam-5470	405	22	1	1	NUM
ejpam-5470	405	23	.	.	PUNCT
ejpam-5470	406	1	then	then	ADV
ejpam-5470	406	2	,	,	PUNCT
ejpam-5470	406	3	the	the	DET
ejpam-5470	406	4	labelling	labelling	NOUN
ejpam-5470	406	5	[	[	X
ejpam-5470	406	6	l4r;0	l4r;0	NOUN
ejpam-5470	406	7	14	14	NUM
ejpam-5470	406	8	m	m	NOUN
ejpam-5470	406	9	′	′	NUM
ejpam-5470	406	10	4t02	4t02	NOUN
ejpam-5470	406	11	,	,	PUNCT
ejpam-5470	406	12	0	0	NUM
ejpam-5470	406	13	14	14	NUM
ejpam-5470	406	14	a.	a.	NOUN
ejpam-5470	406	15	abd	abd	PROPN
ejpam-5470	406	16	el	el	PROPN
ejpam-5470	406	17	-	-	PROPN
ejpam-5470	406	18	hay	hay	PROPN
ejpam-5470	406	19	et	et	PROPN
ejpam-5470	406	20	al	al	PROPN
ejpam-5470	406	21	.	.	PUNCT
ejpam-5470	406	22	/	/	SYM
ejpam-5470	406	23	eur	eur	PROPN
ejpam-5470	406	24	.	.	PUNCT
ejpam-5470	407	1	j.	j.	PROPN
ejpam-5470	407	2	pure	pure	PROPN
ejpam-5470	407	3	appl	appl	PROPN
ejpam-5470	407	4	.	.	PROPN
ejpam-5470	407	5	math	math	PROPN
ejpam-5470	407	6	,	,	PUNCT
ejpam-5470	407	7	18	18	NUM
ejpam-5470	407	8	(	(	PUNCT
ejpam-5470	407	9	1	1	NUM
ejpam-5470	407	10	)	)	PUNCT
ejpam-5470	407	11	(	(	PUNCT
ejpam-5470	407	12	2025	2025	NUM
ejpam-5470	407	13	)	)	PUNCT
ejpam-5470	407	14	,	,	PUNCT
ejpam-5470	407	15	5470	5470	NUM
ejpam-5470	407	16	12	12	NUM
ejpam-5470	407	17	of	of	ADP
ejpam-5470	407	18	14	14	NUM
ejpam-5470	407	19	m	m	NOUN
ejpam-5470	407	20	′	′	NUM
ejpam-5470	407	21	4t02	4t02	NOUN
ejpam-5470	407	22	,	,	PUNCT
ejpam-5470	407	23	104m4	104m4	NUM
ejpam-5470	407	24	t	t	NOUN
ejpam-5470	407	25	12	12	NUM
ejpam-5470	407	26	,	,	PUNCT
ejpam-5470	407	27	104m4	104m4	NUM
ejpam-5470	407	28	t	t	NOUN
ejpam-5470	407	29	12	12	NUM
ejpam-5470	407	30	,	,	PUNCT
ejpam-5470	407	31	...	...	PUNCT
ejpam-5470	407	32	,	,	PUNCT
ejpam-5470	407	33	(	(	PUNCT
ejpam-5470	407	34	r−times	r−time	NOUN
ejpam-5470	407	35	)	)	PUNCT
ejpam-5470	407	36	]	]	PUNCT
ejpam-5470	407	37	for	for	SCONJ
ejpam-5470	407	38	p4r⊙	p4r⊙	PROPN
ejpam-5470	407	39	l4	l4	PROPN
ejpam-5470	407	40	5,4t+3	5,4t+3	PROPN
ejpam-5470	407	41	is	be	AUX
ejpam-5470	407	42	applied	apply	VERB
ejpam-5470	407	43	.	.	PUNCT
ejpam-5470	408	1	therefore	therefore	ADV
ejpam-5470	408	2	x0	x0	PROPN
ejpam-5470	408	3	=	=	PROPN
ejpam-5470	408	4	x1=	x1=	PROPN
ejpam-5470	408	5	2r	2r	NUM
ejpam-5470	408	6	,	,	PUNCT
ejpam-5470	408	7	a0=	a0=	PROPN
ejpam-5470	408	8	2r	2r	NUM
ejpam-5470	408	9	,	,	PUNCT
ejpam-5470	408	10	a1=	a1=	PROPN
ejpam-5470	408	11	2r−1,y0=	2r−1,y0=	PROPN
ejpam-5470	408	12	2t+3,y1=	2t+3,y1=	NUM
ejpam-5470	409	1	2t+4,b0=	2t+4,b0=	NUM
ejpam-5470	409	2	8t+7,b1=	8t+7,b1=	NUM
ejpam-5470	409	3	8t+6,y′0=	8t+6,y′0=	NUM
ejpam-5470	409	4	2t+4,y′1=	2t+4,y′1=	NUM
ejpam-5470	409	5	2t+3,b′0=	2t+3,b′0=	NUM
ejpam-5470	409	6	8t+7	8t+7	NOUN
ejpam-5470	409	7	and	and	CCONJ
ejpam-5470	409	8	b′1=	b′1=	ADP
ejpam-5470	409	9	8t+	8t+	NUM
ejpam-5470	409	10	6	6	NUM
ejpam-5470	409	11	.	.	PUNCT
ejpam-5470	410	1	so	so	ADV
ejpam-5470	410	2	,	,	PUNCT
ejpam-5470	410	3	|v0	|v0	NOUN
ejpam-5470	410	4	−	−	NOUN
ejpam-5470	410	5	v1|	v1|	NOUN
ejpam-5470	410	6	=	=	SYM
ejpam-5470	410	7	0	0	NUM
ejpam-5470	410	8	and	and	CCONJ
ejpam-5470	410	9	|e0	|e0	NOUN
ejpam-5470	411	1	−	−	PROPN
ejpam-5470	411	2	e1|	e1|	NOUN
ejpam-5470	411	3	=	=	NOUN
ejpam-5470	411	4	1	1	NUM
ejpam-5470	411	5	.	.	PUNCT
ejpam-5470	411	6	thus	thus	ADV
ejpam-5470	411	7	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	411	8	5,4t+3	5,4t+3	NOUN
ejpam-5470	411	9	is	be	AUX
ejpam-5470	411	10	cordial	cordial	ADJ
ejpam-5470	411	11	.	.	PUNCT
ejpam-5470	412	1	subcase	subcase	PROPN
ejpam-5470	412	2	4.2.k	4.2.k	NUM
ejpam-5470	412	3	≡	≡	PROPN
ejpam-5470	412	4	1(mod4	1(mod4	NUM
ejpam-5470	412	5	)	)	PUNCT
ejpam-5470	412	6	let	let	VERB
ejpam-5470	412	7	k=	k=	X
ejpam-5470	412	8	4r+1,r	4r+1,r	NOUN
ejpam-5470	412	9	≥	≥	X
ejpam-5470	412	10	0	0	NUM
ejpam-5470	413	1	andm=	andm=	NUM
ejpam-5470	413	2	4t+3	4t+3	PROPN
ejpam-5470	413	3	,	,	PUNCT
ejpam-5470	413	4	t	t	PROPN
ejpam-5470	413	5	≥	≥	NUM
ejpam-5470	413	6	1	1	NUM
ejpam-5470	413	7	.	.	PUNCT
ejpam-5470	414	1	then	then	ADV
ejpam-5470	414	2	,	,	PUNCT
ejpam-5470	414	3	the	the	DET
ejpam-5470	414	4	labelling	labelling	NOUN
ejpam-5470	414	5	[	[	X
ejpam-5470	414	6	l4r0;0	l4r0;0	NUM
ejpam-5470	414	7	14	14	NUM
ejpam-5470	414	8	m	m	NOUN
ejpam-5470	414	9	′	′	NUM
ejpam-5470	414	10	4t02	4t02	NOUN
ejpam-5470	414	11	,	,	PUNCT
ejpam-5470	414	12	0	0	NUM
ejpam-5470	414	13	14	14	NUM
ejpam-5470	414	14	m	m	NOUN
ejpam-5470	414	15	′	′	NUM
ejpam-5470	414	16	4t02	4t02	NOUN
ejpam-5470	414	17	,	,	PUNCT
ejpam-5470	414	18	104m4	104m4	NUM
ejpam-5470	414	19	t	t	NOUN
ejpam-5470	414	20	12	12	NUM
ejpam-5470	414	21	,	,	PUNCT
ejpam-5470	414	22	104m4	104m4	NUM
ejpam-5470	414	23	t	t	NOUN
ejpam-5470	414	24	12	12	NUM
ejpam-5470	414	25	,	,	PUNCT
ejpam-5470	414	26	...	...	PUNCT
ejpam-5470	414	27	,	,	PUNCT
ejpam-5470	414	28	(	(	PUNCT
ejpam-5470	414	29	r	r	NOUN
ejpam-5470	414	30	−	−	PROPN
ejpam-5470	414	31	times	time	NOUN
ejpam-5470	414	32	)	)	PUNCT
ejpam-5470	414	33	,	,	PUNCT
ejpam-5470	414	34	0	0	NUM
ejpam-5470	414	35	14	14	NUM
ejpam-5470	414	36	m	m	NOUN
ejpam-5470	414	37	′	′	NUM
ejpam-5470	414	38	4t02	4t02	NOUN
ejpam-5470	414	39	]	]	PUNCT
ejpam-5470	414	40	for	for	ADP
ejpam-5470	414	41	p4r+1⊙	p4r+1⊙	PROPN
ejpam-5470	414	42	l4	l4	PROPN
ejpam-5470	414	43	5,4t+3	5,4t+3	PROPN
ejpam-5470	414	44	is	be	AUX
ejpam-5470	414	45	applied	apply	VERB
ejpam-5470	414	46	.	.	PUNCT
ejpam-5470	415	1	therefore	therefore	ADV
ejpam-5470	415	2	x0=	x0=	PROPN
ejpam-5470	416	1	2r+1,x1=	2r+1,x1=	NUM
ejpam-5470	416	2	2r	2r	NUM
ejpam-5470	416	3	,	,	PUNCT
ejpam-5470	416	4	a0	a0	PROPN
ejpam-5470	416	5	=	=	SYM
ejpam-5470	416	6	a1=2r	a1=2r	PROPN
ejpam-5470	416	7	,	,	PUNCT
ejpam-5470	416	8	y0=	y0=	PROPN
ejpam-5470	416	9	2t+3,y1=	2t+3,y1=	NUM
ejpam-5470	416	10	2t+4,b0=	2t+4,b0=	NUM
ejpam-5470	416	11	8t+7,b1=	8t+7,b1=	NUM
ejpam-5470	416	12	8t+6,y′0=	8t+6,y′0=	NUM
ejpam-5470	416	13	2t+4,y′1=	2t+4,y′1=	NUM
ejpam-5470	416	14	2t+	2t+	NUM
ejpam-5470	416	15	3,b′0=	3,b′0=	NUM
ejpam-5470	416	16	8	8	NUM
ejpam-5470	416	17	t	t	NOUN
ejpam-5470	416	18	+	+	CCONJ
ejpam-5470	416	19	7	7	NUM
ejpam-5470	416	20	and	and	CCONJ
ejpam-5470	416	21	b′1=	b′1=	ADP
ejpam-5470	416	22	8	8	NUM
ejpam-5470	416	23	t	t	NOUN
ejpam-5470	416	24	+	+	NOUN
ejpam-5470	416	25	6	6	NUM
ejpam-5470	416	26	.	.	PUNCT
ejpam-5470	417	1	so	so	ADV
ejpam-5470	417	2	,	,	PUNCT
ejpam-5470	417	3	|v0	|v0	NOUN
ejpam-5470	417	4	−	−	NOUN
ejpam-5470	417	5	v1|	v1|	NOUN
ejpam-5470	417	6	=	=	SYM
ejpam-5470	417	7	0	0	NUM
ejpam-5470	417	8	and	and	CCONJ
ejpam-5470	417	9	|e0	|e0	NOUN
ejpam-5470	418	1	−	−	PROPN
ejpam-5470	418	2	e1|	e1|	NOUN
ejpam-5470	418	3	=	=	NOUN
ejpam-5470	418	4	0	0	NUM
ejpam-5470	418	5	.	.	PUNCT
ejpam-5470	419	1	thus	thus	ADV
ejpam-5470	419	2	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	419	3	5,4t+3	5,4t+3	NOUN
ejpam-5470	419	4	is	be	AUX
ejpam-5470	419	5	cordial	cordial	ADJ
ejpam-5470	419	6	.	.	PUNCT
ejpam-5470	420	1	subcase	subcase	PROPN
ejpam-5470	420	2	4.3.k	4.3.k	PROPN
ejpam-5470	420	3	≡	≡	PROPN
ejpam-5470	420	4	2(mod4	2(mod4	NUM
ejpam-5470	420	5	)	)	PUNCT
ejpam-5470	420	6	let	let	VERB
ejpam-5470	420	7	k=	k=	PROPN
ejpam-5470	420	8	4r+2,r	4r+2,r	NUM
ejpam-5470	420	9	≥	≥	NOUN
ejpam-5470	420	10	0	0	NUM
ejpam-5470	421	1	andm=	andm=	NUM
ejpam-5470	421	2	4t+3	4t+3	PROPN
ejpam-5470	421	3	,	,	PUNCT
ejpam-5470	421	4	t	t	PROPN
ejpam-5470	421	5	≥	≥	NUM
ejpam-5470	421	6	1	1	NUM
ejpam-5470	421	7	.	.	PUNCT
ejpam-5470	422	1	then	then	ADV
ejpam-5470	422	2	,	,	PUNCT
ejpam-5470	422	3	the	the	DET
ejpam-5470	422	4	labelling	labelling	NOUN
ejpam-5470	422	5	[	[	X
ejpam-5470	422	6	l4r01;0	l4r01;0	PROPN
ejpam-5470	422	7	14	14	NUM
ejpam-5470	422	8	m	m	NOUN
ejpam-5470	422	9	′	′	NUM
ejpam-5470	422	10	4t02	4t02	NOUN
ejpam-5470	422	11	,	,	PUNCT
ejpam-5470	422	12	014	014	NUM
ejpam-5470	422	13	m	m	VERB
ejpam-5470	422	14	′	′	NUM
ejpam-5470	422	15	4t02	4t02	NOUN
ejpam-5470	422	16	,	,	PUNCT
ejpam-5470	422	17	104m4	104m4	NUM
ejpam-5470	422	18	t	t	NOUN
ejpam-5470	422	19	12	12	NUM
ejpam-5470	422	20	,	,	PUNCT
ejpam-5470	422	21	104m4	104m4	NUM
ejpam-5470	422	22	t	t	NOUN
ejpam-5470	422	23	12	12	NUM
ejpam-5470	422	24	,	,	PUNCT
ejpam-5470	422	25	...	...	PUNCT
ejpam-5470	422	26	,	,	PUNCT
ejpam-5470	422	27	(	(	PUNCT
ejpam-5470	422	28	r	r	NOUN
ejpam-5470	422	29	−	−	PROPN
ejpam-5470	422	30	times	time	NOUN
ejpam-5470	422	31	)	)	PUNCT
ejpam-5470	422	32	,	,	PUNCT
ejpam-5470	422	33	0	0	NUM
ejpam-5470	422	34	14	14	NUM
ejpam-5470	422	35	m	m	VERB
ejpam-5470	422	36	′	′	NUM
ejpam-5470	422	37	4t02	4t02	NOUN
ejpam-5470	422	38	,	,	PUNCT
ejpam-5470	422	39	104m4	104m4	NUM
ejpam-5470	422	40	t	t	NOUN
ejpam-5470	422	41	12	12	NUM
ejpam-5470	422	42	]	]	PUNCT
ejpam-5470	422	43	for	for	ADP
ejpam-5470	422	44	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	422	45	5,4t+3	5,4t+3	NOUN
ejpam-5470	422	46	is	be	AUX
ejpam-5470	422	47	applied	apply	VERB
ejpam-5470	422	48	.	.	PUNCT
ejpam-5470	423	1	therefore	therefore	ADV
ejpam-5470	423	2	x0	x0	PROPN
ejpam-5470	423	3	=	=	PROPN
ejpam-5470	423	4	x1=	x1=	PROPN
ejpam-5470	423	5	2r	2r	NUM
ejpam-5470	424	1	+	+	CCONJ
ejpam-5470	424	2	1,a0=	1,a0=	NUM
ejpam-5470	424	3	2r	2r	NUM
ejpam-5470	424	4	,	,	PUNCT
ejpam-5470	424	5	a1=	a1=	PROPN
ejpam-5470	424	6	2r	2r	NUM
ejpam-5470	425	1	+	+	CCONJ
ejpam-5470	425	2	1,y0=	1,y0=	PROPN
ejpam-5470	425	3	2	2	NUM
ejpam-5470	425	4	t	t	NOUN
ejpam-5470	425	5	+	+	NOUN
ejpam-5470	425	6	3,y1=	3,y1=	NUM
ejpam-5470	425	7	2	2	NUM
ejpam-5470	425	8	t	t	NOUN
ejpam-5470	425	9	+	+	NOUN
ejpam-5470	425	10	4,b0=	4,b0=	NUM
ejpam-5470	425	11	8	8	NUM
ejpam-5470	425	12	t	t	NOUN
ejpam-5470	425	13	+	+	CCONJ
ejpam-5470	425	14	7,b1=	7,b1=	NUM
ejpam-5470	425	15	8	8	NUM
ejpam-5470	425	16	t	t	NOUN
ejpam-5470	425	17	+	+	NOUN
ejpam-5470	425	18	6,y′0=	6,y′0=	NUM
ejpam-5470	425	19	2t+4,y′1=	2t+4,y′1=	NUM
ejpam-5470	425	20	2t+3,b′0=	2t+3,b′0=	NUM
ejpam-5470	425	21	8t+7	8t+7	NOUN
ejpam-5470	425	22	and	and	CCONJ
ejpam-5470	425	23	b′1=	b′1=	ADP
ejpam-5470	425	24	8t+6	8t+6	NOUN
ejpam-5470	425	25	.	.	PUNCT
ejpam-5470	426	1	so	so	ADV
ejpam-5470	426	2	,	,	PUNCT
ejpam-5470	426	3	|v0−v1|	|v0−v1|	NUM
ejpam-5470	426	4	=	=	SYM
ejpam-5470	426	5	0	0	NUM
ejpam-5470	426	6	and	and	CCONJ
ejpam-5470	426	7	|e0−	|e0−	ADJ
ejpam-5470	426	8	e1|	e1|	NOUN
ejpam-5470	426	9	=	=	NOUN
ejpam-5470	426	10	1	1	X
ejpam-5470	426	11	.	.	PUNCT
ejpam-5470	426	12	thus	thus	ADV
ejpam-5470	426	13	p4r+2⊙l4	p4r+2⊙l4	NUM
ejpam-5470	426	14	5,4t+3	5,4t+3	NOUN
ejpam-5470	426	15	is	be	AUX
ejpam-5470	426	16	cordial	cordial	ADJ
ejpam-5470	426	17	.	.	PUNCT
ejpam-5470	427	1	subcase	subcase	PROPN
ejpam-5470	427	2	4.4.k	4.4.k	NUM
ejpam-5470	427	3	≡	≡	PROPN
ejpam-5470	427	4	3(mod4	3(mod4	NUM
ejpam-5470	427	5	)	)	PUNCT
ejpam-5470	427	6	let	let	VERB
ejpam-5470	427	7	k=	k=	X
ejpam-5470	427	8	4r+3,r	4r+3,r	NUM
ejpam-5470	427	9	≥	≥	NOUN
ejpam-5470	427	10	0	0	NUM
ejpam-5470	428	1	andm=	andm=	NUM
ejpam-5470	428	2	4t+3	4t+3	PROPN
ejpam-5470	428	3	,	,	PUNCT
ejpam-5470	428	4	t	t	PROPN
ejpam-5470	428	5	≥	≥	NUM
ejpam-5470	428	6	1	1	NUM
ejpam-5470	428	7	.	.	PUNCT
ejpam-5470	429	1	then	then	ADV
ejpam-5470	429	2	,	,	PUNCT
ejpam-5470	429	3	the	the	DET
ejpam-5470	429	4	labelling	labelling	NOUN
ejpam-5470	429	5	[	[	X
ejpam-5470	429	6	l4r001;0	l4r001;0	ADJ
ejpam-5470	429	7	14	14	NUM
ejpam-5470	429	8	m	m	NOUN
ejpam-5470	429	9	′	′	NUM
ejpam-5470	429	10	4t02	4t02	NOUN
ejpam-5470	429	11	,	,	PUNCT
ejpam-5470	429	12	014	014	NUM
ejpam-5470	429	13	m	m	VERB
ejpam-5470	429	14	′	′	NUM
ejpam-5470	429	15	4t02	4t02	NOUN
ejpam-5470	429	16	,	,	PUNCT
ejpam-5470	429	17	104m4	104m4	NUM
ejpam-5470	429	18	t	t	NOUN
ejpam-5470	429	19	12	12	NUM
ejpam-5470	429	20	,	,	PUNCT
ejpam-5470	429	21	104m4	104m4	NUM
ejpam-5470	429	22	t	t	NOUN
ejpam-5470	429	23	12	12	NUM
ejpam-5470	429	24	,	,	PUNCT
ejpam-5470	429	25	...	...	PUNCT
ejpam-5470	429	26	,	,	PUNCT
ejpam-5470	429	27	(	(	PUNCT
ejpam-5470	429	28	r	r	NOUN
ejpam-5470	429	29	−	−	PROPN
ejpam-5470	429	30	times	time	NOUN
ejpam-5470	429	31	)	)	PUNCT
ejpam-5470	429	32	,	,	PUNCT
ejpam-5470	429	33	0	0	NUM
ejpam-5470	429	34	14	14	NUM
ejpam-5470	429	35	m	m	NOUN
ejpam-5470	429	36	′	′	NUM
ejpam-5470	429	37	4t02	4t02	NOUN
ejpam-5470	429	38	,	,	PUNCT
ejpam-5470	429	39	0	0	NUM
ejpam-5470	429	40	14	14	NUM
ejpam-5470	429	41	m	m	NOUN
ejpam-5470	429	42	′	′	NUM
ejpam-5470	429	43	4t02	4t02	NOUN
ejpam-5470	429	44	,	,	PUNCT
ejpam-5470	429	45	104m4	104m4	NUM
ejpam-5470	429	46	t	t	NOUN
ejpam-5470	429	47	12	12	NUM
ejpam-5470	429	48	]	]	PUNCT
ejpam-5470	429	49	for	for	ADP
ejpam-5470	429	50	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	429	51	5,4t+3	5,4t+3	NOUN
ejpam-5470	429	52	is	be	AUX
ejpam-5470	429	53	applied	apply	VERB
ejpam-5470	429	54	.	.	PUNCT
ejpam-5470	430	1	therefore	therefore	ADV
ejpam-5470	430	2	x0	x0	PROPN
ejpam-5470	430	3	=	=	X
ejpam-5470	430	4	x1=	x1=	PROPN
ejpam-5470	430	5	2r+1,a0	2r+1,a0	NUM
ejpam-5470	430	6	=	=	VERB
ejpam-5470	430	7	a1=	a1=	PROPN
ejpam-5470	430	8	2r+1,y0=	2r+1,y0=	NUM
ejpam-5470	430	9	2t+3,y1=	2t+3,y1=	NUM
ejpam-5470	430	10	2t+4,b0=	2t+4,b0=	NUM
ejpam-5470	430	11	8t+7,b1=	8t+7,b1=	NUM
ejpam-5470	430	12	8t+	8t+	NUM
ejpam-5470	430	13	6,y′0=	6,y′0=	NUM
ejpam-5470	430	14	2t+4,y′1=	2t+4,y′1=	NUM
ejpam-5470	430	15	2t+3,b′0=	2t+3,b′0=	NUM
ejpam-5470	430	16	8t+7	8t+7	NOUN
ejpam-5470	430	17	and	and	CCONJ
ejpam-5470	430	18	b′1=	b′1=	ADP
ejpam-5470	430	19	8t+6	8t+6	NOUN
ejpam-5470	430	20	.	.	PUNCT
ejpam-5470	431	1	so	so	ADV
ejpam-5470	431	2	,	,	PUNCT
ejpam-5470	431	3	|v0−	|v0−	VERB
ejpam-5470	431	4	v1|	v1|	NOUN
ejpam-5470	431	5	=	=	SYM
ejpam-5470	431	6	1	1	NUM
ejpam-5470	431	7	and	and	CCONJ
ejpam-5470	431	8	|e0−	|e0−	NOUN
ejpam-5470	431	9	e1|	e1|	NOUN
ejpam-5470	431	10	=	=	NOUN
ejpam-5470	431	11	0	0	NUM
ejpam-5470	431	12	.	.	PUNCT
ejpam-5470	431	13	thus	thus	ADV
ejpam-5470	431	14	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	431	15	5,4t+3	5,4t+3	NOUN
ejpam-5470	431	16	is	be	AUX
ejpam-5470	431	17	cordial	cordial	ADJ
ejpam-5470	431	18	and	and	CCONJ
ejpam-5470	431	19	the	the	DET
ejpam-5470	431	20	lemma	lemma	PROPN
ejpam-5470	431	21	follows	follow	VERB
ejpam-5470	431	22	.	.	PUNCT
ejpam-5470	432	1	■	■	PUNCT
ejpam-5470	432	2	lemma	lemma	PROPN
ejpam-5470	432	3	5	5	NUM
ejpam-5470	432	4	.	.	PUNCT
ejpam-5470	432	5	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	432	6	6,m	6,m	NOUN
ejpam-5470	432	7	;	;	PUNCT
ejpam-5470	432	8	is	be	AUX
ejpam-5470	432	9	cordial	cordial	ADJ
ejpam-5470	432	10	for	for	ADP
ejpam-5470	432	11	all	all	DET
ejpam-5470	432	12	m	m	PROPN
ejpam-5470	432	13	,	,	PUNCT
ejpam-5470	432	14	k.	k.	PROPN
ejpam-5470	432	15	proof	proof	PROPN
ejpam-5470	432	16	.	.	PUNCT
ejpam-5470	433	1	let	let	VERB
ejpam-5470	433	2	n	n	NOUN
ejpam-5470	433	3	=	=	SYM
ejpam-5470	433	4	6	6	NUM
ejpam-5470	433	5	,	,	PUNCT
ejpam-5470	433	6	then	then	ADV
ejpam-5470	433	7	we	we	PRON
ejpam-5470	433	8	need	need	VERB
ejpam-5470	433	9	to	to	PART
ejpam-5470	433	10	examine	examine	VERB
ejpam-5470	433	11	the	the	DET
ejpam-5470	433	12	following	follow	VERB
ejpam-5470	433	13	cases	case	NOUN
ejpam-5470	433	14	:	:	PUNCT
ejpam-5470	433	15	case	case	NOUN
ejpam-5470	433	16	1	1	NUM
ejpam-5470	433	17	.	.	PUNCT
ejpam-5470	434	1	at	at	ADP
ejpam-5470	434	2	m	m	PROPN
ejpam-5470	434	3	≡	≡	PROPN
ejpam-5470	434	4	0(mod4	0(mod4	NUM
ejpam-5470	434	5	)	)	PUNCT
ejpam-5470	434	6	,	,	PUNCT
ejpam-5470	434	7	i.e	i.e	X
ejpam-5470	434	8	m=	m=	X
ejpam-5470	434	9	4t	4t	NOUN
ejpam-5470	434	10	,	,	PUNCT
ejpam-5470	434	11	t	t	PROPN
ejpam-5470	434	12	≥	≥	NUM
ejpam-5470	434	13	1	1	NUM
ejpam-5470	434	14	.	.	PUNCT
ejpam-5470	435	1	we	we	PRON
ejpam-5470	435	2	see	see	VERB
ejpam-5470	435	3	that	that	DET
ejpam-5470	435	4	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	435	5	6,4	6,4	NUM
ejpam-5470	435	6	and	and	CCONJ
ejpam-5470	435	7	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	435	8	6,4t	6,4t	PROPN
ejpam-5470	435	9	,	,	PUNCT
ejpam-5470	435	10	t	t	PROPN
ejpam-5470	435	11	≥	≥	NUM
ejpam-5470	435	12	1	1	NUM
ejpam-5470	435	13	are	be	AUX
ejpam-5470	435	14	cordial	cordial	ADJ
ejpam-5470	435	15	.	.	PUNCT
ejpam-5470	436	1	this	this	PRON
ejpam-5470	436	2	is	be	AUX
ejpam-5470	436	3	clear	clear	ADJ
ejpam-5470	436	4	since	since	SCONJ
ejpam-5470	436	5	these	these	DET
ejpam-5470	436	6	graphs	graph	NOUN
ejpam-5470	436	7	are	be	AUX
ejpam-5470	436	8	isomorphic	isomorphic	ADJ
ejpam-5470	436	9	to	to	ADP
ejpam-5470	436	10	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	436	11	4,6	4,6	NUM
ejpam-5470	436	12	and	and	CCONJ
ejpam-5470	436	13	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	436	14	4t,6	4t,6	NUM
ejpam-5470	436	15	respectively	respectively	ADV
ejpam-5470	436	16	.	.	PUNCT
ejpam-5470	437	1	so	so	ADV
ejpam-5470	437	2	,	,	PUNCT
ejpam-5470	437	3	by	by	ADP
ejpam-5470	437	4	lemma	lemma	PROPN
ejpam-5470	437	5	3	3	NUM
ejpam-5470	437	6	,	,	PUNCT
ejpam-5470	437	7	we	we	PRON
ejpam-5470	437	8	conclude	conclude	VERB
ejpam-5470	437	9	that	that	SCONJ
ejpam-5470	437	10	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	437	11	6,4	6,4	NUM
ejpam-5470	437	12	and	and	CCONJ
ejpam-5470	437	13	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	437	14	6,4	6,4	NUM
ejpam-5470	437	15	t	t	NOUN
ejpam-5470	437	16	are	be	AUX
ejpam-5470	437	17	cordial	cordial	ADJ
ejpam-5470	437	18	.	.	PUNCT
ejpam-5470	438	1	case	case	NOUN
ejpam-5470	438	2	2	2	NUM
ejpam-5470	438	3	.	.	PUNCT
ejpam-5470	439	1	at	at	ADP
ejpam-5470	439	2	m	m	PROPN
ejpam-5470	439	3	≡	≡	PROPN
ejpam-5470	439	4	1(mod4	1(mod4	NUM
ejpam-5470	439	5	)	)	PUNCT
ejpam-5470	439	6	,	,	PUNCT
ejpam-5470	439	7	i.e	i.e	PROPN
ejpam-5470	439	8	m=	m=	X
ejpam-5470	439	9	4t+	4t+	NUM
ejpam-5470	439	10	1,t	1,t	NUM
ejpam-5470	439	11	≥	≥	NOUN
ejpam-5470	439	12	1	1	NUM
ejpam-5470	439	13	.	.	PUNCT
ejpam-5470	440	1	we	we	PRON
ejpam-5470	440	2	see	see	VERB
ejpam-5470	440	3	that	that	PRON
ejpam-5470	440	4	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	440	5	6,5	6,5	NUM
ejpam-5470	440	6	and	and	CCONJ
ejpam-5470	440	7	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	440	8	6,4t+1,t	6,4t+1,t	NUM
ejpam-5470	440	9	≥	≥	NOUN
ejpam-5470	440	10	1	1	NUM
ejpam-5470	440	11	are	be	AUX
ejpam-5470	440	12	cordial	cordial	ADJ
ejpam-5470	440	13	.	.	PUNCT
ejpam-5470	441	1	this	this	PRON
ejpam-5470	441	2	is	be	AUX
ejpam-5470	441	3	clear	clear	ADJ
ejpam-5470	441	4	since	since	SCONJ
ejpam-5470	441	5	these	these	DET
ejpam-5470	441	6	graphs	graph	NOUN
ejpam-5470	441	7	are	be	AUX
ejpam-5470	441	8	isomorphic	isomorphic	ADJ
ejpam-5470	441	9	to	to	ADP
ejpam-5470	441	10	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	441	11	5,6	5,6	NUM
ejpam-5470	441	12	and	and	CCONJ
ejpam-5470	441	13	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	441	14	4t+1,6	4t+1,6	NOUN
ejpam-5470	441	15	respectively	respectively	ADV
ejpam-5470	441	16	.	.	PUNCT
ejpam-5470	442	1	so	so	ADV
ejpam-5470	442	2	,	,	PUNCT
ejpam-5470	442	3	by	by	ADP
ejpam-5470	442	4	lemma	lemma	PROPN
ejpam-5470	442	5	4	4	NUM
ejpam-5470	442	6	,	,	PUNCT
ejpam-5470	442	7	we	we	PRON
ejpam-5470	442	8	conclude	conclude	VERB
ejpam-5470	442	9	that	that	SCONJ
ejpam-5470	442	10	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	442	11	6,5	6,5	NUM
ejpam-5470	442	12	and	and	CCONJ
ejpam-5470	442	13	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	442	14	6,4t+1	6,4t+1	PROPN
ejpam-5470	442	15	are	be	AUX
ejpam-5470	442	16	cordial	cordial	ADJ
ejpam-5470	442	17	.	.	PUNCT
ejpam-5470	443	1	case	case	NOUN
ejpam-5470	443	2	3	3	X
ejpam-5470	443	3	.	.	PUNCT
ejpam-5470	444	1	at	at	ADP
ejpam-5470	444	2	m	m	PROPN
ejpam-5470	444	3	≡	≡	PROPN
ejpam-5470	444	4	2(mod4	2(mod4	NUM
ejpam-5470	444	5	)	)	PUNCT
ejpam-5470	444	6	,	,	PUNCT
ejpam-5470	444	7	we	we	PRON
ejpam-5470	444	8	need	need	VERB
ejpam-5470	444	9	to	to	PART
ejpam-5470	444	10	examine	examine	VERB
ejpam-5470	444	11	the	the	DET
ejpam-5470	444	12	following	follow	VERB
ejpam-5470	444	13	two	two	NUM
ejpam-5470	444	14	subcases	subcase	NOUN
ejpam-5470	444	15	:	:	PUNCT
ejpam-5470	444	16	subcase	subcase	NOUN
ejpam-5470	444	17	3.1.k	3.1.k	NUM
ejpam-5470	444	18	even	even	ADV
ejpam-5470	444	19	let	let	VERB
ejpam-5470	444	20	k=	k=	PRON
ejpam-5470	444	21	2r	2r	NUM
ejpam-5470	444	22	,	,	PUNCT
ejpam-5470	445	1	r	r	NOUN
ejpam-5470	445	2	≥	≥	NUM
ejpam-5470	445	3	1	1	NUM
ejpam-5470	445	4	andm=	andm=	NUM
ejpam-5470	445	5	4t+3	4t+3	PROPN
ejpam-5470	445	6	,	,	PUNCT
ejpam-5470	445	7	t	t	PROPN
ejpam-5470	445	8	≥	≥	NUM
ejpam-5470	445	9	1	1	NUM
ejpam-5470	445	10	.	.	PUNCT
ejpam-5470	446	1	then	then	ADV
ejpam-5470	446	2	,	,	PUNCT
ejpam-5470	446	3	the	the	DET
ejpam-5470	446	4	labelling	labelling	NOUN
ejpam-5470	446	5	[	[	X
ejpam-5470	446	6	m2r	m2r	NOUN
ejpam-5470	446	7	;	;	PUNCT
ejpam-5470	446	8	1205m4	1205m4	NOUN
ejpam-5470	446	9	t	t	NOUN
ejpam-5470	446	10	1201	1201	NUM
ejpam-5470	446	11	,	,	PUNCT
ejpam-5470	446	12	1205m4	1205m4	NOUN
ejpam-5470	446	13	t	t	NOUN
ejpam-5470	446	14	1201	1201	NUM
ejpam-5470	446	15	,	,	PUNCT
ejpam-5470	446	16	02	02	NUM
ejpam-5470	446	17	15	15	NUM
ejpam-5470	446	18	m	m	NOUN
ejpam-5470	446	19	′	′	NUM
ejpam-5470	446	20	4t0210,02	4t0210,02	NUM
ejpam-5470	446	21	15	15	NUM
ejpam-5470	446	22	m	m	NOUN
ejpam-5470	446	23	′	′	NUM
ejpam-5470	446	24	4t0210	4t0210	PROPN
ejpam-5470	446	25	,	,	PUNCT
ejpam-5470	446	26	...	...	PUNCT
ejpam-5470	446	27	,	,	PUNCT
ejpam-5470	446	28	(	(	PUNCT
ejpam-5470	446	29	r−times	r−time	NOUN
ejpam-5470	446	30	)	)	PUNCT
ejpam-5470	446	31	]	]	PUNCT
ejpam-5470	446	32	for	for	ADP
ejpam-5470	446	33	p2r⊙l4	p2r⊙l4	NOUN
ejpam-5470	446	34	6,4t+2	6,4t+2	NOUN
ejpam-5470	446	35	is	be	AUX
ejpam-5470	446	36	applied	apply	VERB
ejpam-5470	446	37	.	.	PUNCT
ejpam-5470	447	1	therefore	therefore	ADV
ejpam-5470	447	2	x0	x0	PROPN
ejpam-5470	447	3	=	=	PROPN
ejpam-5470	447	4	x1	x1	PROPN
ejpam-5470	447	5	=	=	SYM
ejpam-5470	447	6	r	r	NOUN
ejpam-5470	447	7	,	,	PUNCT
ejpam-5470	447	8	a0=	a0=	PROPN
ejpam-5470	447	9	0,a1=	0,a1=	NOUN
ejpam-5470	447	10	2r−	2r−	PROPN
ejpam-5470	447	11	1,y0=	1,y0=	NUM
ejpam-5470	447	12	2t+4,y1=	2t+4,y1=	NUM
ejpam-5470	447	13	2t+3,b0	2t+3,b0	NOUN
ejpam-5470	447	14	=	=	VERB
ejpam-5470	447	15	b1=	b1=	NOUN
ejpam-5470	447	16	8t+7,y′0=	8t+7,y′0=	NUM
ejpam-5470	447	17	2t+3,y′1=	2t+3,y′1=	NUM
ejpam-5470	447	18	2t+4,b′0=	2t+4,b′0=	NUM
ejpam-5470	447	19	8t+7	8t+7	NOUN
ejpam-5470	447	20	and	and	CCONJ
ejpam-5470	447	21	b′1=	b′1=	ADP
ejpam-5470	447	22	8t+	8t+	NUM
ejpam-5470	447	23	7	7	NUM
ejpam-5470	447	24	.	.	PUNCT
ejpam-5470	448	1	so	so	ADV
ejpam-5470	448	2	,	,	PUNCT
ejpam-5470	448	3	|v0	|v0	NOUN
ejpam-5470	448	4	−	−	NOUN
ejpam-5470	448	5	v1|	v1|	NOUN
ejpam-5470	448	6	=	=	SYM
ejpam-5470	448	7	0	0	NUM
ejpam-5470	448	8	and	and	CCONJ
ejpam-5470	448	9	|e0	|e0	NOUN
ejpam-5470	449	1	−	−	PROPN
ejpam-5470	449	2	e1|	e1|	NOUN
ejpam-5470	449	3	=	=	NOUN
ejpam-5470	449	4	1	1	NUM
ejpam-5470	449	5	.	.	PUNCT
ejpam-5470	449	6	thus	thus	ADV
ejpam-5470	449	7	p2r⊙l4	p2r⊙l4	NOUN
ejpam-5470	449	8	6,4t+2	6,4t+2	NOUN
ejpam-5470	449	9	is	be	AUX
ejpam-5470	449	10	cordial	cordial	ADJ
ejpam-5470	449	11	.	.	PUNCT
ejpam-5470	450	1	subcase	subcase	PROPN
ejpam-5470	450	2	3.2.k	3.2.k	NUM
ejpam-5470	450	3	odd	odd	ADJ
ejpam-5470	450	4	let	let	VERB
ejpam-5470	450	5	k=	k=	X
ejpam-5470	451	1	2r	2r	NUM
ejpam-5470	452	1	+	+	CCONJ
ejpam-5470	452	2	1,r	1,r	NUM
ejpam-5470	452	3	≥	≥	NOUN
ejpam-5470	452	4	0	0	NUM
ejpam-5470	452	5	and	and	CCONJ
ejpam-5470	452	6	m=	m=	ADJ
ejpam-5470	452	7	4t+	4t+	PROPN
ejpam-5470	452	8	3	3	NUM
ejpam-5470	452	9	,	,	PUNCT
ejpam-5470	452	10	t	t	PROPN
ejpam-5470	452	11	≥	≥	NUM
ejpam-5470	452	12	1	1	NUM
ejpam-5470	452	13	.	.	PUNCT
ejpam-5470	453	1	then	then	ADV
ejpam-5470	453	2	,	,	PUNCT
ejpam-5470	453	3	the	the	DET
ejpam-5470	453	4	labelling	labelling	NOUN
ejpam-5470	453	5	[	[	X
ejpam-5470	453	6	m2r+1	m2r+1	X
ejpam-5470	453	7	;	;	PUNCT
ejpam-5470	453	8	1205m4	1205m4	NOUN
ejpam-5470	453	9	t	t	NOUN
ejpam-5470	453	10	1201	1201	NUM
ejpam-5470	453	11	,	,	PUNCT
ejpam-5470	453	12	1205m4	1205m4	NOUN
ejpam-5470	453	13	t	t	NOUN
ejpam-5470	453	14	1201	1201	NUM
ejpam-5470	453	15	,	,	PUNCT
ejpam-5470	453	16	02	02	NUM
ejpam-5470	453	17	15	15	NUM
ejpam-5470	453	18	m	m	NOUN
ejpam-5470	453	19	′	′	NUM
ejpam-5470	453	20	4t0210,02	4t0210,02	NUM
ejpam-5470	453	21	15	15	NUM
ejpam-5470	453	22	m	m	NOUN
ejpam-5470	453	23	′	′	NUM
ejpam-5470	453	24	4t0210	4t0210	PROPN
ejpam-5470	453	25	,	,	PUNCT
ejpam-5470	453	26	...	...	PUNCT
ejpam-5470	453	27	,	,	PUNCT
ejpam-5470	453	28	(	(	PUNCT
ejpam-5470	453	29	r−times),02	r−times),02	PROPN
ejpam-5470	453	30	15	15	NUM
ejpam-5470	453	31	m	m	NOUN
ejpam-5470	453	32	′	′	NUM
ejpam-5470	453	33	4t0210	4t0210	PROPN
ejpam-5470	453	34	]	]	PUNCT
ejpam-5470	453	35	for	for	ADP
ejpam-5470	453	36	p2r+1⊙l4	p2r+1⊙l4	NOUN
ejpam-5470	453	37	5,4t+3	5,4t+3	NOUN
ejpam-5470	453	38	is	be	AUX
ejpam-5470	453	39	applied	apply	VERB
ejpam-5470	453	40	.	.	PUNCT
ejpam-5470	454	1	therefore	therefore	ADV
ejpam-5470	454	2	x0	x0	PROPN
ejpam-5470	454	3	=	=	NOUN
ejpam-5470	454	4	r	r	NOUN
ejpam-5470	454	5	+	+	NOUN
ejpam-5470	454	6	1,x1	1,x1	NUM
ejpam-5470	454	7	=	=	SYM
ejpam-5470	454	8	r	r	NOUN
ejpam-5470	454	9	,	,	PUNCT
ejpam-5470	454	10	a0=	a0=	PROPN
ejpam-5470	454	11	0,a1=	0,a1=	NUM
ejpam-5470	454	12	2r	2r	NUM
ejpam-5470	454	13	,	,	PUNCT
ejpam-5470	454	14	y0=	y0=	PROPN
ejpam-5470	454	15	2	2	NUM
ejpam-5470	454	16	t	t	NOUN
ejpam-5470	454	17	+	+	NOUN
ejpam-5470	454	18	4,y1=2	4,y1=2	PROPN
ejpam-5470	454	19	t	t	NOUN
ejpam-5470	454	20	+	+	NOUN
ejpam-5470	454	21	3,b0	3,b0	NUM
ejpam-5470	454	22	=	=	SYM
ejpam-5470	454	23	b1=	b1=	NOUN
ejpam-5470	454	24	8	8	NUM
ejpam-5470	454	25	t	t	NOUN
ejpam-5470	454	26	+	+	CCONJ
ejpam-5470	454	27	7,y′0	7,y′0	NOUN
ejpam-5470	454	28	=	=	NOUN
ejpam-5470	454	29	y”0=	y”0=	ADP
ejpam-5470	454	30	2	2	NUM
ejpam-5470	454	31	t	t	NOUN
ejpam-5470	454	32	+	+	NOUN
ejpam-5470	454	33	4,y′1	4,y′1	NUM
ejpam-5470	454	34	=	=	NOUN
ejpam-5470	454	35	y”1=	y”1=	NOUN
ejpam-5470	454	36	2	2	NUM
ejpam-5470	454	37	t	t	NOUN
ejpam-5470	454	38	+	+	NOUN
ejpam-5470	454	39	3,b′0	3,b′0	NUM
ejpam-5470	454	40	=	=	NOUN
ejpam-5470	454	41	b”0=	b”0=	NOUN
ejpam-5470	454	42	8	8	NUM
ejpam-5470	454	43	t	t	NOUN
ejpam-5470	454	44	+	+	CCONJ
ejpam-5470	454	45	7	7	NUM
ejpam-5470	454	46	and	and	CCONJ
ejpam-5470	454	47	b′1	b′1	NOUN
ejpam-5470	454	48	=	=	SYM
ejpam-5470	454	49	b”1=	b”1=	NOUN
ejpam-5470	454	50	8	8	NUM
ejpam-5470	454	51	t	t	NOUN
ejpam-5470	454	52	+	+	NOUN
ejpam-5470	454	53	7	7	X
ejpam-5470	454	54	.	.	PUNCT
ejpam-5470	455	1	so	so	ADV
ejpam-5470	455	2	,	,	PUNCT
ejpam-5470	455	3	|v0	|v0	NOUN
ejpam-5470	455	4	−	−	NOUN
ejpam-5470	455	5	v1|	v1|	NOUN
ejpam-5470	455	6	=	=	SYM
ejpam-5470	455	7	0	0	NUM
ejpam-5470	455	8	and	and	CCONJ
ejpam-5470	455	9	a.	a.	PROPN
ejpam-5470	455	10	abd	abd	PROPN
ejpam-5470	455	11	el	el	PROPN
ejpam-5470	455	12	-	-	PROPN
ejpam-5470	455	13	hay	hay	PROPN
ejpam-5470	455	14	et	et	PROPN
ejpam-5470	455	15	al	al	PROPN
ejpam-5470	455	16	.	.	PUNCT
ejpam-5470	455	17	/	/	SYM
ejpam-5470	455	18	eur	eur	PROPN
ejpam-5470	455	19	.	.	PUNCT
ejpam-5470	456	1	j.	j.	PROPN
ejpam-5470	456	2	pure	pure	PROPN
ejpam-5470	456	3	appl	appl	PROPN
ejpam-5470	456	4	.	.	PROPN
ejpam-5470	456	5	math	math	PROPN
ejpam-5470	456	6	,	,	PUNCT
ejpam-5470	456	7	18	18	NUM
ejpam-5470	456	8	(	(	PUNCT
ejpam-5470	456	9	1	1	NUM
ejpam-5470	456	10	)	)	PUNCT
ejpam-5470	456	11	(	(	PUNCT
ejpam-5470	456	12	2025	2025	NUM
ejpam-5470	456	13	)	)	PUNCT
ejpam-5470	456	14	,	,	PUNCT
ejpam-5470	456	15	5470	5470	NUM
ejpam-5470	456	16	13	13	NUM
ejpam-5470	456	17	of	of	ADP
ejpam-5470	456	18	14	14	NUM
ejpam-5470	456	19	|e0	|e0	NOUN
ejpam-5470	456	20	−	−	NOUN
ejpam-5470	456	21	e1|	e1|	NOUN
ejpam-5470	456	22	=	=	NOUN
ejpam-5470	456	23	0	0	NUM
ejpam-5470	456	24	.	.	PUNCT
ejpam-5470	457	1	thus	thus	ADV
ejpam-5470	457	2	p2r+1⊙l4	p2r+1⊙l4	NOUN
ejpam-5470	457	3	6,4t+3	6,4t+3	VERB
ejpam-5470	457	4	is	be	AUX
ejpam-5470	457	5	cordial	cordial	ADJ
ejpam-5470	457	6	.	.	PUNCT
ejpam-5470	458	1	case	case	NOUN
ejpam-5470	458	2	4	4	NUM
ejpam-5470	458	3	.	.	PUNCT
ejpam-5470	459	1	at	at	ADP
ejpam-5470	459	2	m	m	PROPN
ejpam-5470	459	3	≡	≡	PROPN
ejpam-5470	459	4	3(mod4	3(mod4	NUM
ejpam-5470	459	5	)	)	PUNCT
ejpam-5470	459	6	,	,	PUNCT
ejpam-5470	459	7	we	we	PRON
ejpam-5470	459	8	need	need	VERB
ejpam-5470	459	9	to	to	PART
ejpam-5470	459	10	examine	examine	VERB
ejpam-5470	459	11	the	the	DET
ejpam-5470	459	12	following	follow	VERB
ejpam-5470	459	13	subcases	subcase	NOUN
ejpam-5470	459	14	:	:	PUNCT
ejpam-5470	459	15	subcase	subcase	VERB
ejpam-5470	459	16	4.1	4.1	NUM
ejpam-5470	459	17	.	.	PUNCT
ejpam-5470	460	1	at	at	ADP
ejpam-5470	460	2	k	k	PROPN
ejpam-5470	460	3	≡	≡	PROPN
ejpam-5470	460	4	0(mod4	0(mod4	NUM
ejpam-5470	460	5	)	)	PUNCT
ejpam-5470	460	6	.	.	PUNCT
ejpam-5470	461	1	let	let	VERB
ejpam-5470	461	2	k=	k=	ADJ
ejpam-5470	461	3	4r	4r	NOUN
ejpam-5470	461	4	,	,	PUNCT
ejpam-5470	461	5	r	r	NOUN
ejpam-5470	461	6	≥	≥	NOUN
ejpam-5470	461	7	1	1	NUM
ejpam-5470	461	8	.	.	PUNCT
ejpam-5470	462	1	then	then	ADV
ejpam-5470	462	2	,	,	PUNCT
ejpam-5470	462	3	the	the	DET
ejpam-5470	462	4	labeling	labeling	NOUN
ejpam-5470	462	5	[	[	X
ejpam-5470	462	6	l4r;s403m4t0	l4r;s403m4t0	NOUN
ejpam-5470	462	7	,	,	PUNCT
ejpam-5470	462	8	s403m4t0	s403m4t0	PROPN
ejpam-5470	462	9	,	,	PUNCT
ejpam-5470	462	10	s403m4t0	s403m4t0	PROPN
ejpam-5470	462	11	,	,	PUNCT
ejpam-5470	462	12	s403m4t0	s403m4t0	PROPN
ejpam-5470	462	13	,	,	PUNCT
ejpam-5470	462	14	...	...	PUNCT
ejpam-5470	462	15	,	,	PUNCT
ejpam-5470	462	16	(	(	PUNCT
ejpam-5470	462	17	r−	r−	NOUN
ejpam-5470	462	18	time	time	NOUN
ejpam-5470	462	19	)	)	PUNCT
ejpam-5470	462	20	]	]	PUNCT
ejpam-5470	462	21	for	for	ADP
ejpam-5470	462	22	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	462	23	6,4t+3	6,4t+3	VERB
ejpam-5470	462	24	is	be	AUX
ejpam-5470	462	25	applied	apply	VERB
ejpam-5470	462	26	.	.	PUNCT
ejpam-5470	463	1	therefore	therefore	ADV
ejpam-5470	463	2	x0	x0	PROPN
ejpam-5470	463	3	=	=	PROPN
ejpam-5470	463	4	x1=	x1=	PROPN
ejpam-5470	463	5	2r	2r	NUM
ejpam-5470	463	6	,	,	PUNCT
ejpam-5470	463	7	a0=	a0=	NOUN
ejpam-5470	463	8	2r	2r	NUM
ejpam-5470	463	9	,	,	PUNCT
ejpam-5470	463	10	a1=	a1=	PROPN
ejpam-5470	463	11	2r	2r	NUM
ejpam-5470	464	1	−	−	ADP
ejpam-5470	464	2	1,y0	1,y0	NUM
ejpam-5470	464	3	=	=	SYM
ejpam-5470	464	4	y1=	y1=	PROPN
ejpam-5470	464	5	2	2	NUM
ejpam-5470	464	6	t	t	NOUN
ejpam-5470	464	7	+	+	NOUN
ejpam-5470	464	8	4,b0	4,b0	NUM
ejpam-5470	464	9	=	=	NOUN
ejpam-5470	464	10	b1=	b1=	VERB
ejpam-5470	464	11	8t+	8t+	NUM
ejpam-5470	464	12	9,y′0	9,y′0	NOUN
ejpam-5470	464	13	=	=	NOUN
ejpam-5470	464	14	y′1=	y′1=	NOUN
ejpam-5470	464	15	2t+	2t+	NUM
ejpam-5470	464	16	4	4	NUM
ejpam-5470	464	17	and	and	CCONJ
ejpam-5470	464	18	b′0	b′0	VERB
ejpam-5470	464	19	=	=	NOUN
ejpam-5470	464	20	b′1=	b′1=	ADP
ejpam-5470	464	21	8t+	8t+	NUM
ejpam-5470	464	22	9	9	NUM
ejpam-5470	464	23	.	.	PUNCT
ejpam-5470	465	1	consequently	consequently	ADV
ejpam-5470	465	2	,	,	PUNCT
ejpam-5470	465	3	it	it	PRON
ejpam-5470	465	4	is	be	AUX
ejpam-5470	465	5	easy	easy	ADJ
ejpam-5470	465	6	to	to	PART
ejpam-5470	465	7	show	show	VERB
ejpam-5470	465	8	that	that	SCONJ
ejpam-5470	465	9	|v0	|v0	NOUN
ejpam-5470	465	10	−	−	NOUN
ejpam-5470	465	11	v1|	v1|	NOUN
ejpam-5470	465	12	=	=	SYM
ejpam-5470	465	13	0	0	NUM
ejpam-5470	465	14	and	and	CCONJ
ejpam-5470	465	15	|e0	|e0	NOUN
ejpam-5470	465	16	−	−	PROPN
ejpam-5470	465	17	e1|	e1|	NOUN
ejpam-5470	465	18	=	=	NOUN
ejpam-5470	465	19	1	1	NUM
ejpam-5470	465	20	.	.	PUNCT
ejpam-5470	465	21	thus	thus	ADV
ejpam-5470	465	22	p4r⊙l4	p4r⊙l4	PROPN
ejpam-5470	465	23	6,4t+3	6,4t+3	VERB
ejpam-5470	465	24	,	,	PUNCT
ejpam-5470	465	25	is	be	AUX
ejpam-5470	465	26	cordial	cordial	ADJ
ejpam-5470	465	27	.	.	PUNCT
ejpam-5470	466	1	subcase	subcase	PROPN
ejpam-5470	466	2	4.2	4.2	NUM
ejpam-5470	466	3	.	.	PUNCT
ejpam-5470	467	1	at	at	ADP
ejpam-5470	467	2	k	k	PROPN
ejpam-5470	467	3	≡	≡	PROPN
ejpam-5470	467	4	1(mod4	1(mod4	NUM
ejpam-5470	467	5	)	)	PUNCT
ejpam-5470	467	6	.	.	PUNCT
ejpam-5470	468	1	let	let	VERB
ejpam-5470	468	2	k=	k=	PROPN
ejpam-5470	469	1	4r+1	4r+1	PROPN
ejpam-5470	469	2	,	,	PUNCT
ejpam-5470	469	3	r	r	NOUN
ejpam-5470	469	4	≥	≥	NOUN
ejpam-5470	469	5	0	0	NUM
ejpam-5470	469	6	.	.	PUNCT
ejpam-5470	470	1	then	then	ADV
ejpam-5470	470	2	one	one	PRON
ejpam-5470	470	3	can	can	AUX
ejpam-5470	470	4	choose	choose	VERB
ejpam-5470	470	5	the	the	DET
ejpam-5470	470	6	labeling	labeling	NOUN
ejpam-5470	470	7	[	[	X
ejpam-5470	470	8	l4r0;s403m4t0	l4r0;s403m4t0	PROPN
ejpam-5470	470	9	,	,	PUNCT
ejpam-5470	470	10	s403m4t0	s403m4t0	PROPN
ejpam-5470	470	11	,	,	PUNCT
ejpam-5470	470	12	s403m4t0	s403m4t0	PROPN
ejpam-5470	470	13	,	,	PUNCT
ejpam-5470	470	14	s403m4t0	s403m4t0	PROPN
ejpam-5470	470	15	,	,	PUNCT
ejpam-5470	470	16	...	...	PUNCT
ejpam-5470	470	17	,	,	PUNCT
ejpam-5470	470	18	(	(	PUNCT
ejpam-5470	470	19	r−time),s403m4t0	r−time),s403m4t0	X
ejpam-5470	470	20	]	]	PUNCT
ejpam-5470	470	21	for	for	ADP
ejpam-5470	470	22	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	470	23	6,4t+3	6,4t+3	VERB
ejpam-5470	470	24	.	.	PUNCT
ejpam-5470	471	1	therefore	therefore	ADV
ejpam-5470	471	2	x0=	x0=	PROPN
ejpam-5470	472	1	2r+1,x1=	2r+1,x1=	NUM
ejpam-5470	472	2	2r	2r	NUM
ejpam-5470	472	3	,	,	PUNCT
ejpam-5470	472	4	a0	a0	PROPN
ejpam-5470	472	5	=	=	PROPN
ejpam-5470	472	6	a1=	a1=	PROPN
ejpam-5470	472	7	2r	2r	NUM
ejpam-5470	472	8	,	,	PUNCT
ejpam-5470	472	9	y0	y0	PROPN
ejpam-5470	472	10	=	=	SYM
ejpam-5470	472	11	y1=	y1=	PROPN
ejpam-5470	472	12	2	2	NUM
ejpam-5470	472	13	t	t	NOUN
ejpam-5470	472	14	+	+	NOUN
ejpam-5470	472	15	4,b0	4,b0	NUM
ejpam-5470	472	16	=	=	NOUN
ejpam-5470	472	17	b1=	b1=	VERB
ejpam-5470	472	18	8	8	NUM
ejpam-5470	472	19	t	t	NOUN
ejpam-5470	472	20	+	+	NOUN
ejpam-5470	472	21	9,y′0	9,y′0	NOUN
ejpam-5470	472	22	=	=	NOUN
ejpam-5470	472	23	y′1=	y′1=	ADP
ejpam-5470	472	24	2	2	NUM
ejpam-5470	472	25	t	t	NOUN
ejpam-5470	472	26	+	+	CCONJ
ejpam-5470	472	27	4	4	NUM
ejpam-5470	472	28	and	and	CCONJ
ejpam-5470	472	29	b′0	b′0	VERB
ejpam-5470	472	30	=	=	NOUN
ejpam-5470	472	31	b′1=	b′1=	ADP
ejpam-5470	472	32	8	8	NUM
ejpam-5470	472	33	t	t	NOUN
ejpam-5470	472	34	+	+	NOUN
ejpam-5470	472	35	9	9	NUM
ejpam-5470	472	36	.	.	PUNCT
ejpam-5470	473	1	so	so	ADV
ejpam-5470	473	2	,	,	PUNCT
ejpam-5470	473	3	|v0	|v0	NOUN
ejpam-5470	473	4	−	−	NOUN
ejpam-5470	473	5	v1|	v1|	NOUN
ejpam-5470	473	6	=	=	SYM
ejpam-5470	473	7	1	1	NUM
ejpam-5470	473	8	and	and	CCONJ
ejpam-5470	473	9	|e0	|e0	NOUN
ejpam-5470	473	10	−	−	PROPN
ejpam-5470	473	11	e1|	e1|	NOUN
ejpam-5470	473	12	=	=	NOUN
ejpam-5470	473	13	0	0	NUM
ejpam-5470	473	14	.	.	PUNCT
ejpam-5470	474	1	thus	thus	ADV
ejpam-5470	474	2	p4r+1⊙l4	p4r+1⊙l4	NOUN
ejpam-5470	474	3	6,4t+3	6,4t+3	VERB
ejpam-5470	474	4	,	,	PUNCT
ejpam-5470	474	5	is	be	AUX
ejpam-5470	474	6	cordial	cordial	ADJ
ejpam-5470	474	7	.	.	PUNCT
ejpam-5470	475	1	subcase	subcase	PROPN
ejpam-5470	475	2	4.3	4.3	NUM
ejpam-5470	475	3	.	.	PUNCT
ejpam-5470	476	1	at	at	ADP
ejpam-5470	476	2	k	k	PROPN
ejpam-5470	476	3	≡	≡	PROPN
ejpam-5470	476	4	2(mod4	2(mod4	NUM
ejpam-5470	476	5	)	)	PUNCT
ejpam-5470	476	6	.	.	PUNCT
ejpam-5470	477	1	let	let	VERB
ejpam-5470	477	2	k=	k=	X
ejpam-5470	478	1	4r+2	4r+2	PROPN
ejpam-5470	478	2	,	,	PUNCT
ejpam-5470	478	3	r	r	NOUN
ejpam-5470	478	4	≥	≥	NOUN
ejpam-5470	478	5	0	0	NUM
ejpam-5470	478	6	.	.	PUNCT
ejpam-5470	479	1	then	then	ADV
ejpam-5470	479	2	one	one	PRON
ejpam-5470	479	3	can	can	AUX
ejpam-5470	479	4	take	take	VERB
ejpam-5470	479	5	the	the	DET
ejpam-5470	479	6	labeling	labeling	NOUN
ejpam-5470	479	7	[	[	X
ejpam-5470	479	8	l4r10;s403m4t0	l4r10;s403m4t0	ADJ
ejpam-5470	479	9	,	,	PUNCT
ejpam-5470	479	10	s403m4t0	s403m4t0	PROPN
ejpam-5470	479	11	,	,	PUNCT
ejpam-5470	479	12	s403m4t0	s403m4t0	PROPN
ejpam-5470	479	13	,	,	PUNCT
ejpam-5470	479	14	s403m4t0	s403m4t0	PROPN
ejpam-5470	479	15	,	,	PUNCT
ejpam-5470	479	16	...	...	PUNCT
ejpam-5470	479	17	,	,	PUNCT
ejpam-5470	479	18	(	(	PUNCT
ejpam-5470	479	19	r	r	NOUN
ejpam-5470	479	20	−	−	NOUN
ejpam-5470	479	21	time),s403m4t0	time),s403m4t0	NOUN
ejpam-5470	479	22	,	,	PUNCT
ejpam-5470	479	23	s403m4t0	s403m4t0	PROPN
ejpam-5470	479	24	]	]	PUNCT
ejpam-5470	479	25	for	for	ADP
ejpam-5470	479	26	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	479	27	6,4t+3	6,4t+3	VERB
ejpam-5470	479	28	.	.	PUNCT
ejpam-5470	480	1	therefore	therefore	ADV
ejpam-5470	480	2	x0	x0	PROPN
ejpam-5470	480	3	=	=	PROPN
ejpam-5470	480	4	x1=	x1=	PROPN
ejpam-5470	480	5	2r	2r	NUM
ejpam-5470	481	1	+	+	CCONJ
ejpam-5470	481	2	1,a0=	1,a0=	NUM
ejpam-5470	481	3	2r+1,a1=	2r+1,a1=	NUM
ejpam-5470	481	4	2r	2r	NUM
ejpam-5470	481	5	,	,	PUNCT
ejpam-5470	481	6	y0	y0	NOUN
ejpam-5470	481	7	=	=	SYM
ejpam-5470	481	8	y1=	y1=	NOUN
ejpam-5470	481	9	2t+4,b0	2t+4,b0	NOUN
ejpam-5470	481	10	=	=	NOUN
ejpam-5470	481	11	b1=	b1=	NOUN
ejpam-5470	481	12	8t+9,y′0	8t+9,y′0	NOUN
ejpam-5470	481	13	=	=	SYM
ejpam-5470	481	14	y′1=	y′1=	X
ejpam-5470	481	15	2t+4	2t+4	PROPN
ejpam-5470	481	16	and	and	CCONJ
ejpam-5470	481	17	b′0	b′0	VERB
ejpam-5470	481	18	=	=	SYM
ejpam-5470	481	19	b′1=	b′1=	ADP
ejpam-5470	481	20	8t+9	8t+9	NUM
ejpam-5470	481	21	.	.	PUNCT
ejpam-5470	482	1	hence	hence	ADV
ejpam-5470	482	2	,	,	PUNCT
ejpam-5470	482	3	|v0	|v0	NOUN
ejpam-5470	482	4	−	−	NOUN
ejpam-5470	482	5	v1|	v1|	NOUN
ejpam-5470	482	6	=	=	SYM
ejpam-5470	482	7	0	0	NUM
ejpam-5470	482	8	and	and	CCONJ
ejpam-5470	482	9	|e0	|e0	NOUN
ejpam-5470	483	1	−	−	PROPN
ejpam-5470	483	2	e1|	e1|	NOUN
ejpam-5470	483	3	=	=	NOUN
ejpam-5470	483	4	1	1	NUM
ejpam-5470	483	5	.	.	PUNCT
ejpam-5470	483	6	thus	thus	ADV
ejpam-5470	483	7	p4r+2⊙l4	p4r+2⊙l4	NOUN
ejpam-5470	483	8	6,4t+3	6,4t+3	VERB
ejpam-5470	483	9	,	,	PUNCT
ejpam-5470	483	10	is	be	AUX
ejpam-5470	483	11	cordial	cordial	ADJ
ejpam-5470	483	12	.	.	PUNCT
ejpam-5470	484	1	subcase	subcase	PROPN
ejpam-5470	484	2	4.4	4.4	NUM
ejpam-5470	484	3	.	.	PUNCT
ejpam-5470	485	1	at	at	ADP
ejpam-5470	485	2	k	k	PROPN
ejpam-5470	485	3	≡	≡	PROPN
ejpam-5470	485	4	3(mod4	3(mod4	NUM
ejpam-5470	485	5	)	)	PUNCT
ejpam-5470	485	6	.	.	PUNCT
ejpam-5470	486	1	let	let	VERB
ejpam-5470	486	2	k=	k=	ADJ
ejpam-5470	487	1	4r+3	4r+3	ADJ
ejpam-5470	487	2	,	,	PUNCT
ejpam-5470	487	3	r	r	NOUN
ejpam-5470	487	4	≥	≥	NOUN
ejpam-5470	487	5	0	0	NUM
ejpam-5470	487	6	.	.	PUNCT
ejpam-5470	488	1	then	then	ADV
ejpam-5470	488	2	one	one	PRON
ejpam-5470	488	3	can	can	AUX
ejpam-5470	488	4	select	select	VERB
ejpam-5470	488	5	the	the	DET
ejpam-5470	488	6	labeling	labeling	NOUN
ejpam-5470	488	7	[	[	X
ejpam-5470	488	8	l4r001;s403m4t0	l4r001;s403m4t0	X
ejpam-5470	488	9	,	,	PUNCT
ejpam-5470	488	10	s403m4t0	s403m4t0	PROPN
ejpam-5470	488	11	,	,	PUNCT
ejpam-5470	488	12	s403m4t0	s403m4t0	PROPN
ejpam-5470	488	13	,	,	PUNCT
ejpam-5470	488	14	s403m4t0	s403m4t0	PROPN
ejpam-5470	488	15	,	,	PUNCT
ejpam-5470	488	16	...	...	PUNCT
ejpam-5470	488	17	,	,	PUNCT
ejpam-5470	488	18	(	(	PUNCT
ejpam-5470	488	19	r−time),s403m4t0	r−time),s403m4t0	ADV
ejpam-5470	488	20	,	,	PUNCT
ejpam-5470	488	21	s403m4t0	s403m4t0	PROPN
ejpam-5470	488	22	,	,	PUNCT
ejpam-5470	488	23	s403m4t0	s403m4t0	PROPN
ejpam-5470	488	24	]	]	PUNCT
ejpam-5470	488	25	for	for	ADP
ejpam-5470	488	26	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	488	27	6,4t+3	6,4t+3	VERB
ejpam-5470	488	28	.	.	PUNCT
ejpam-5470	489	1	therefore	therefore	ADV
ejpam-5470	489	2	x0=	x0=	PROPN
ejpam-5470	489	3	2r+	2r+	NUM
ejpam-5470	489	4	2,x1=	2,x1=	NUM
ejpam-5470	489	5	2r+1,a0	2r+1,a0	NUM
ejpam-5470	489	6	=	=	NOUN
ejpam-5470	489	7	a1=	a1=	NOUN
ejpam-5470	489	8	2r+1,y0	2r+1,y0	NOUN
ejpam-5470	489	9	=	=	SYM
ejpam-5470	489	10	y1=	y1=	PROPN
ejpam-5470	489	11	2t+4,b0	2t+4,b0	NOUN
ejpam-5470	489	12	=	=	NOUN
ejpam-5470	489	13	b1=	b1=	NOUN
ejpam-5470	489	14	8t+9,y′0	8t+9,y′0	NOUN
ejpam-5470	489	15	=	=	SYM
ejpam-5470	489	16	y′1=	y′1=	X
ejpam-5470	489	17	2t+4	2t+4	PROPN
ejpam-5470	489	18	and	and	CCONJ
ejpam-5470	489	19	b′0	b′0	VERB
ejpam-5470	489	20	=	=	SYM
ejpam-5470	489	21	b′1=	b′1=	ADP
ejpam-5470	489	22	8t+9	8t+9	NUM
ejpam-5470	489	23	.	.	PUNCT
ejpam-5470	490	1	consequently	consequently	ADV
ejpam-5470	490	2	,	,	PUNCT
ejpam-5470	490	3	it	it	PRON
ejpam-5470	490	4	is	be	AUX
ejpam-5470	490	5	easy	easy	ADJ
ejpam-5470	490	6	to	to	PART
ejpam-5470	490	7	show	show	VERB
ejpam-5470	490	8	that	that	SCONJ
ejpam-5470	490	9	|v0	|v0	NOUN
ejpam-5470	490	10	−	−	NOUN
ejpam-5470	490	11	v1|	v1|	NOUN
ejpam-5470	490	12	=	=	SYM
ejpam-5470	490	13	1	1	NUM
ejpam-5470	490	14	and	and	CCONJ
ejpam-5470	490	15	|e0	|e0	NOUN
ejpam-5470	491	1	−	−	PROPN
ejpam-5470	491	2	e1|	e1|	NOUN
ejpam-5470	491	3	=	=	NOUN
ejpam-5470	491	4	0	0	NUM
ejpam-5470	491	5	.	.	PUNCT
ejpam-5470	491	6	thus	thus	ADV
ejpam-5470	491	7	p4r+3⊙l4	p4r+3⊙l4	NOUN
ejpam-5470	491	8	6,4t+3	6,4t+3	VERB
ejpam-5470	491	9	,	,	PUNCT
ejpam-5470	491	10	is	be	AUX
ejpam-5470	491	11	cordial	cordial	ADJ
ejpam-5470	491	12	and	and	CCONJ
ejpam-5470	491	13	the	the	DET
ejpam-5470	491	14	lemma	lemma	PROPN
ejpam-5470	491	15	follows	follow	VERB
ejpam-5470	491	16	.	.	PUNCT
ejpam-5470	492	1	■	■	PUNCT
ejpam-5470	492	2	4	4	X
ejpam-5470	492	3	.	.	X
ejpam-5470	492	4	conclusion	conclusion	NOUN
ejpam-5470	492	5	we	we	PRON
ejpam-5470	492	6	proved	prove	VERB
ejpam-5470	492	7	that	that	SCONJ
ejpam-5470	492	8	the	the	DET
ejpam-5470	492	9	corona	corona	PROPN
ejpam-5470	492	10	pk⊙l4	pk⊙l4	NOUN
ejpam-5470	492	11	n	n	CCONJ
ejpam-5470	492	12	,	,	PUNCT
ejpam-5470	492	13	m	m	VERB
ejpam-5470	492	14	between	between	ADP
ejpam-5470	492	15	paths	path	NOUN
ejpam-5470	492	16	pk	pk	NOUN
ejpam-5470	492	17	and	and	CCONJ
ejpam-5470	492	18	fourth	fourth	ADJ
ejpam-5470	492	19	power	power	NOUN
ejpam-5470	492	20	of	of	ADP
ejpam-5470	492	21	lemniscate	lemniscate	PROPN
ejpam-5470	492	22	graphs	graphs	PROPN
ejpam-5470	492	23	l4	l4	PROPN
ejpam-5470	492	24	n	n	CCONJ
ejpam-5470	492	25	,	,	PUNCT
ejpam-5470	492	26	m	m	VERB
ejpam-5470	492	27	is	be	AUX
ejpam-5470	492	28	cordial	cordial	ADJ
ejpam-5470	492	29	for	for	ADP
ejpam-5470	492	30	al	al	PROPN
ejpam-5470	492	31	k	k	PROPN
ejpam-5470	492	32	≥	≥	PROPN
ejpam-5470	492	33	1	1	NUM
ejpam-5470	492	34	,	,	PUNCT
ejpam-5470	492	35	n	n	CCONJ
ejpam-5470	492	36	,	,	PUNCT
ejpam-5470	492	37	m	m	VERB
ejpam-5470	492	38	≥	≥	NOUN
ejpam-5470	492	39	3	3	NUM
ejpam-5470	492	40	.	.	PUNCT
ejpam-5470	493	1	in	in	ADP
ejpam-5470	493	2	the	the	DET
ejpam-5470	493	3	future	future	NOUN
ejpam-5470	493	4	,	,	PUNCT
ejpam-5470	493	5	we	we	PRON
ejpam-5470	493	6	will	will	AUX
ejpam-5470	493	7	apply	apply	VERB
ejpam-5470	493	8	cordial	cordial	ADJ
ejpam-5470	493	9	labeling	labeling	NOUN
ejpam-5470	493	10	to	to	ADP
ejpam-5470	493	11	other	other	ADJ
ejpam-5470	493	12	types	type	NOUN
ejpam-5470	493	13	of	of	ADP
ejpam-5470	493	14	graphs	graph	NOUN
ejpam-5470	493	15	.	.	PUNCT
ejpam-5470	494	1	acknowledgements	acknowledgement	NOUN
ejpam-5470	494	2	the	the	DET
ejpam-5470	494	3	researchers	researcher	NOUN
ejpam-5470	494	4	would	would	AUX
ejpam-5470	494	5	like	like	VERB
ejpam-5470	494	6	to	to	PART
ejpam-5470	494	7	thank	thank	VERB
ejpam-5470	494	8	the	the	DET
ejpam-5470	494	9	deanship	deanship	NOUN
ejpam-5470	494	10	of	of	ADP
ejpam-5470	494	11	graduate	graduate	NOUN
ejpam-5470	494	12	studies	study	NOUN
ejpam-5470	494	13	and	and	CCONJ
ejpam-5470	494	14	scientific	scientific	ADJ
ejpam-5470	494	15	research	research	NOUN
ejpam-5470	494	16	at	at	ADP
ejpam-5470	494	17	qassim	qassim	PROPN
ejpam-5470	494	18	university	university	PROPN
ejpam-5470	494	19	for	for	ADP
ejpam-5470	494	20	financial	financial	ADJ
ejpam-5470	494	21	support	support	NOUN
ejpam-5470	494	22	(	(	PUNCT
ejpam-5470	494	23	qu	qu	NOUN
ejpam-5470	494	24	-	-	NOUN
ejpam-5470	494	25	apc-2024	apc-2024	NOUN
ejpam-5470	494	26	-	-	PUNCT
ejpam-5470	494	27	9/1	9/1	NUM
ejpam-5470	494	28	)	)	PUNCT
ejpam-5470	494	29	data	datum	NOUN
ejpam-5470	494	30	availability	availability	NOUN
ejpam-5470	494	31	statement	statement	NOUN
ejpam-5470	494	32	all	all	DET
ejpam-5470	494	33	data	datum	NOUN
ejpam-5470	494	34	generated	generate	VERB
ejpam-5470	494	35	or	or	CCONJ
ejpam-5470	494	36	analyzed	analyze	VERB
ejpam-5470	494	37	during	during	ADP
ejpam-5470	494	38	this	this	DET
ejpam-5470	494	39	study	study	NOUN
ejpam-5470	494	40	are	be	AUX
ejpam-5470	494	41	included	include	VERB
ejpam-5470	494	42	in	in	ADP
ejpam-5470	494	43	this	this	DET
ejpam-5470	494	44	published	publish	VERB
ejpam-5470	494	45	article	article	NOUN
ejpam-5470	494	46	.	.	PUNCT
ejpam-5470	495	1	references	reference	NOUN
ejpam-5470	495	2	[	[	X
ejpam-5470	495	3	1	1	NUM
ejpam-5470	495	4	]	]	PUNCT
ejpam-5470	495	5	b.	b.	PROPN
ejpam-5470	495	6	d.	d.	PROPN
ejpam-5470	495	7	acharya	acharya	PROPN
ejpam-5470	495	8	and	and	CCONJ
ejpam-5470	495	9	s.	s.	PROPN
ejpam-5470	495	10	m.	m.	PROPN
ejpam-5470	495	11	hegde	hegde	PROPN
ejpam-5470	495	12	.	.	PUNCT
ejpam-5470	496	1	arithmetic	arithmetic	ADJ
ejpam-5470	496	2	graphs	graph	NOUN
ejpam-5470	496	3	.	.	PUNCT
ejpam-5470	497	1	j.	j.	PROPN
ejpam-5470	497	2	graph	graph	PROPN
ejpam-5470	497	3	theory	theory	NOUN
ejpam-5470	497	4	,	,	PUNCT
ejpam-5470	497	5	14(3):275–299	14(3):275–299	PROPN
ejpam-5470	497	6	,	,	PUNCT
ejpam-5470	497	7	1990	1990	NUM
ejpam-5470	497	8	.	.	PUNCT
ejpam-5470	498	1	a.	a.	PROPN
ejpam-5470	498	2	abd	abd	PROPN
ejpam-5470	498	3	el	el	PROPN
ejpam-5470	498	4	-	-	PROPN
ejpam-5470	498	5	hay	hay	PROPN
ejpam-5470	498	6	et	et	PROPN
ejpam-5470	498	7	al	al	PROPN
ejpam-5470	498	8	.	.	PUNCT
ejpam-5470	498	9	/	/	SYM
ejpam-5470	498	10	eur	eur	PROPN
ejpam-5470	498	11	.	.	PUNCT
ejpam-5470	499	1	j.	j.	PROPN
ejpam-5470	499	2	pure	pure	PROPN
ejpam-5470	499	3	appl	appl	PROPN
ejpam-5470	499	4	.	.	PROPN
ejpam-5470	499	5	math	math	PROPN
ejpam-5470	499	6	,	,	PUNCT
ejpam-5470	499	7	18	18	NUM
ejpam-5470	499	8	(	(	PUNCT
ejpam-5470	499	9	1	1	NUM
ejpam-5470	499	10	)	)	PUNCT
ejpam-5470	499	11	(	(	PUNCT
ejpam-5470	499	12	2025	2025	NUM
ejpam-5470	499	13	)	)	PUNCT
ejpam-5470	499	14	,	,	PUNCT
ejpam-5470	499	15	5470	5470	NUM
ejpam-5470	499	16	14	14	NUM
ejpam-5470	499	17	of	of	ADP
ejpam-5470	499	18	14	14	NUM
ejpam-5470	499	19	[	[	X
ejpam-5470	499	20	2	2	NUM
ejpam-5470	499	21	]	]	PUNCT
ejpam-5470	499	22	k.	k.	PROPN
ejpam-5470	499	23	a.	a.	PROPN
ejpam-5470	499	24	alsatami	alsatami	PROPN
ejpam-5470	499	25	,	,	PUNCT
ejpam-5470	499	26	y.	y.	PROPN
ejpam-5470	499	27	algrawani	algrawani	PROPN
ejpam-5470	499	28	,	,	PUNCT
ejpam-5470	499	29	and	and	CCONJ
ejpam-5470	499	30	a.	a.	PROPN
ejpam-5470	499	31	abd	abd	PROPN
ejpam-5470	499	32	el	el	PROPN
ejpam-5470	499	33	-	-	PROPN
ejpam-5470	499	34	hay	hay	PROPN
ejpam-5470	499	35	.	.	PUNCT
ejpam-5470	500	1	a	a	DET
ejpam-5470	500	2	novel	novel	ADJ
ejpam-5470	500	3	problem	problem	NOUN
ejpam-5470	500	4	and	and	CCONJ
ejpam-5470	500	5	algorithm	algorithm	NOUN
ejpam-5470	500	6	for	for	ADP
ejpam-5470	500	7	solving	solve	VERB
ejpam-5470	500	8	permuted	permute	VERB
ejpam-5470	500	9	cordial	cordial	ADJ
ejpam-5470	500	10	labeling	labeling	NOUN
ejpam-5470	500	11	of	of	ADP
ejpam-5470	500	12	corona	corona	NOUN
ejpam-5470	500	13	product	product	NOUN
ejpam-5470	500	14	between	between	ADP
ejpam-5470	500	15	two	two	NUM
ejpam-5470	500	16	graphs	graph	NOUN
ejpam-5470	500	17	.	.	PUNCT
ejpam-5470	501	1	mathematical	mathematical	ADJ
ejpam-5470	501	2	models	model	NOUN
ejpam-5470	501	3	in	in	ADP
ejpam-5470	501	4	engineering	engineering	NOUN
ejpam-5470	501	5	,	,	PUNCT
ejpam-5470	501	6	11(1):1–11	11(1):1–11	NUM
ejpam-5470	501	7	,	,	PUNCT
ejpam-5470	501	8	2025	2025	NUM
ejpam-5470	501	9	.	.	PUNCT
ejpam-5470	502	1	[	[	X
ejpam-5470	502	2	3	3	NUM
ejpam-5470	502	3	]	]	X
ejpam-5470	502	4	i.	i.	PROPN
ejpam-5470	502	5	cahit	cahit	PROPN
ejpam-5470	502	6	.	.	PUNCT
ejpam-5470	503	1	cordial	cordial	ADJ
ejpam-5470	503	2	graphs	graph	NOUN
ejpam-5470	503	3	:	:	PUNCT
ejpam-5470	503	4	a	a	DET
ejpam-5470	503	5	weaker	weak	ADJ
ejpam-5470	503	6	version	version	NOUN
ejpam-5470	503	7	of	of	ADP
ejpam-5470	503	8	graceful	graceful	ADJ
ejpam-5470	503	9	and	and	CCONJ
ejpam-5470	503	10	harmonious	harmonious	ADJ
ejpam-5470	503	11	graphs	graph	NOUN
ejpam-5470	503	12	.	.	PUNCT
ejpam-5470	504	1	ars	ar	NOUN
ejpam-5470	504	2	combinatoria	combinatoria	PROPN
ejpam-5470	504	3	,	,	PUNCT
ejpam-5470	504	4	23:201–207	23:201–207	PROPN
ejpam-5470	504	5	,	,	PUNCT
ejpam-5470	504	6	1987	1987	NUM
ejpam-5470	504	7	.	.	PUNCT
ejpam-5470	505	1	[	[	X
ejpam-5470	505	2	4	4	NUM
ejpam-5470	505	3	]	]	X
ejpam-5470	505	4	i.	i.	PROPN
ejpam-5470	505	5	cahit	cahit	PROPN
ejpam-5470	505	6	.	.	PUNCT
ejpam-5470	506	1	on	on	ADP
ejpam-5470	506	2	cordial	cordial	ADJ
ejpam-5470	506	3	and	and	CCONJ
ejpam-5470	506	4	3	3	NUM
ejpam-5470	506	5	-	-	PUNCT
ejpam-5470	506	6	equitable	equitable	ADJ
ejpam-5470	506	7	labeling	labeling	NOUN
ejpam-5470	506	8	of	of	ADP
ejpam-5470	506	9	graphs	graph	NOUN
ejpam-5470	506	10	.	.	PUNCT
ejpam-5470	507	1	utilities	utility	NOUN
ejpam-5470	507	2	math	math	PROPN
ejpam-5470	507	3	.	.	PUNCT
ejpam-5470	507	4	,	,	PUNCT
ejpam-5470	507	5	37	37	NUM
ejpam-5470	507	6	,	,	PUNCT
ejpam-5470	507	7	1990	1990	NUM
ejpam-5470	507	8	.	.	PUNCT
ejpam-5470	508	1	[	[	X
ejpam-5470	508	2	5	5	NUM
ejpam-5470	508	3	]	]	PUNCT
ejpam-5470	508	4	i.	i.	NOUN
ejpam-5470	508	5	cahit	cahit	PROPN
ejpam-5470	508	6	.	.	PUNCT
ejpam-5470	509	1	recent	recent	ADJ
ejpam-5470	509	2	results	result	NOUN
ejpam-5470	509	3	and	and	CCONJ
ejpam-5470	509	4	open	open	ADJ
ejpam-5470	509	5	problems	problem	NOUN
ejpam-5470	509	6	on	on	ADP
ejpam-5470	509	7	cordial	cordial	ADJ
ejpam-5470	509	8	graphs	graph	NOUN
ejpam-5470	509	9	.	.	PUNCT
ejpam-5470	510	1	contemporary	contemporary	ADJ
ejpam-5470	510	2	methods	method	NOUN
ejpam-5470	510	3	in	in	ADP
ejpam-5470	510	4	graph	graph	NOUN
ejpam-5470	510	5	theory	theory	NOUN
ejpam-5470	510	6	,	,	PUNCT
ejpam-5470	510	7	pages	page	NOUN
ejpam-5470	510	8	209–230	209–230	NUM
ejpam-5470	510	9	,	,	PUNCT
ejpam-5470	510	10	1990	1990	NUM
ejpam-5470	510	11	.	.	PUNCT
ejpam-5470	511	1	[	[	X
ejpam-5470	511	2	6	6	NUM
ejpam-5470	511	3	]	]	PUNCT
ejpam-5470	511	4	a.	a.	NOUN
ejpam-5470	511	5	abd	abd	PROPN
ejpam-5470	511	6	el	el	PROPN
ejpam-5470	511	7	-	-	PROPN
ejpam-5470	511	8	hay	hay	PROPN
ejpam-5470	511	9	and	and	CCONJ
ejpam-5470	511	10	a.	a.	NOUN
ejpam-5470	511	11	elrokh	elrokh	PROPN
ejpam-5470	511	12	.	.	PUNCT
ejpam-5470	512	1	total	total	ADJ
ejpam-5470	512	2	cordial	cordial	ADJ
ejpam-5470	512	3	labeling	labeling	NOUN
ejpam-5470	512	4	of	of	ADP
ejpam-5470	512	5	corona	corona	NOUN
ejpam-5470	512	6	product	product	NOUN
ejpam-5470	512	7	of	of	ADP
ejpam-5470	512	8	paths	path	NOUN
ejpam-5470	512	9	and	and	CCONJ
ejpam-5470	512	10	second	second	ADJ
ejpam-5470	512	11	power	power	NOUN
ejpam-5470	512	12	of	of	ADP
ejpam-5470	512	13	fan	fan	NOUN
ejpam-5470	512	14	graph	graph	NOUN
ejpam-5470	512	15	.	.	PUNCT
ejpam-5470	513	1	turkish	turkish	ADJ
ejpam-5470	513	2	journal	journal	NOUN
ejpam-5470	513	3	of	of	ADP
ejpam-5470	513	4	computer	computer	NOUN
ejpam-5470	513	5	and	and	CCONJ
ejpam-5470	513	6	mathematics	mathematics	PROPN
ejpam-5470	513	7	education	education	NOUN
ejpam-5470	513	8	(	(	PUNCT
ejpam-5470	513	9	turcomat	turcomat	NOUN
ejpam-5470	513	10	)	)	PUNCT
ejpam-5470	513	11	,	,	PUNCT
ejpam-5470	513	12	13(3):681–690	13(3):681–690	PROPN
ejpam-5470	513	13	,	,	PUNCT
ejpam-5470	513	14	2022	2022	NUM
ejpam-5470	513	15	.	.	PUNCT
ejpam-5470	514	1	[	[	X
ejpam-5470	514	2	7	7	NUM
ejpam-5470	514	3	]	]	PUNCT
ejpam-5470	514	4	a.	a.	NOUN
ejpam-5470	514	5	elrokh	elrokh	NOUN
ejpam-5470	514	6	,	,	PUNCT
ejpam-5470	514	7	m.	m.	NOUN
ejpam-5470	514	8	m.	m.	PROPN
ejpam-5470	514	9	ali	ali	PROPN
ejpam-5470	514	10	al	al	PROPN
ejpam-5470	514	11	-	-	PUNCT
ejpam-5470	514	12	shamiri	shamiri	PROPN
ejpam-5470	514	13	,	,	PUNCT
ejpam-5470	514	14	m.	m.	NOUN
ejpam-5470	514	15	m.	m.	PROPN
ejpam-5470	514	16	a.	a.	PROPN
ejpam-5470	514	17	almazah	almazah	PROPN
ejpam-5470	514	18	,	,	PUNCT
ejpam-5470	514	19	and	and	CCONJ
ejpam-5470	514	20	a.	a.	PROPN
ejpam-5470	514	21	abd	abd	PROPN
ejpam-5470	514	22	el	el	PROPN
ejpam-5470	514	23	-	-	PROPN
ejpam-5470	514	24	hay	hay	PROPN
ejpam-5470	514	25	.	.	PUNCT
ejpam-5470	515	1	a	a	DET
ejpam-5470	515	2	novel	novel	ADJ
ejpam-5470	515	3	problem	problem	NOUN
ejpam-5470	515	4	for	for	ADP
ejpam-5470	515	5	solving	solve	VERB
ejpam-5470	515	6	permuted	permute	VERB
ejpam-5470	515	7	cordial	cordial	ADJ
ejpam-5470	515	8	labeling	labeling	NOUN
ejpam-5470	515	9	of	of	ADP
ejpam-5470	515	10	graphs	graph	NOUN
ejpam-5470	515	11	.	.	PUNCT
ejpam-5470	516	1	symmetry	symmetry	NOUN
ejpam-5470	516	2	,	,	PUNCT
ejpam-5470	516	3	15(4):825	15(4):825	PROPN
ejpam-5470	516	4	,	,	PUNCT
ejpam-5470	516	5	2023	2023	NUM
ejpam-5470	516	6	.	.	PUNCT
ejpam-5470	517	1	[	[	X
ejpam-5470	517	2	8	8	NUM
ejpam-5470	517	3	]	]	PUNCT
ejpam-5470	517	4	a.	a.	NOUN
ejpam-5470	517	5	elrokh	elrokh	NOUN
ejpam-5470	517	6	,	,	PUNCT
ejpam-5470	517	7	m.	m.	NOUN
ejpam-5470	517	8	m.	m.	PROPN
ejpam-5470	517	9	ali	ali	PROPN
ejpam-5470	517	10	al	al	PROPN
ejpam-5470	517	11	-	-	PUNCT
ejpam-5470	517	12	shamiri	shamiri	PROPN
ejpam-5470	517	13	,	,	PUNCT
ejpam-5470	517	14	and	and	CCONJ
ejpam-5470	517	15	a.	a.	PROPN
ejpam-5470	517	16	abd	abd	PROPN
ejpam-5470	517	17	el	el	PROPN
ejpam-5470	517	18	-	-	PROPN
ejpam-5470	517	19	hay	hay	PROPN
ejpam-5470	517	20	.	.	PUNCT
ejpam-5470	518	1	a	a	DET
ejpam-5470	518	2	novel	novel	ADJ
ejpam-5470	518	3	problem	problem	NOUN
ejpam-5470	518	4	to	to	PART
ejpam-5470	518	5	solve	solve	VERB
ejpam-5470	518	6	the	the	DET
ejpam-5470	518	7	logically	logically	ADV
ejpam-5470	518	8	labeling	labeling	NOUN
ejpam-5470	518	9	of	of	ADP
ejpam-5470	518	10	corona	corona	NOUN
ejpam-5470	518	11	between	between	ADP
ejpam-5470	518	12	paths	path	NOUN
ejpam-5470	518	13	and	and	CCONJ
ejpam-5470	518	14	cycles	cycle	NOUN
ejpam-5470	518	15	.	.	PUNCT
ejpam-5470	519	1	journal	journal	NOUN
ejpam-5470	519	2	of	of	ADP
ejpam-5470	519	3	mathematics	mathematic	NOUN
ejpam-5470	519	4	,	,	PUNCT
ejpam-5470	519	5	2022:11	2022:11	NUM
ejpam-5470	519	6	pages	page	NOUN
ejpam-5470	519	7	,	,	PUNCT
ejpam-5470	519	8	2022	2022	NUM
ejpam-5470	519	9	.	.	PUNCT
ejpam-5470	520	1	[	[	X
ejpam-5470	520	2	9	9	NUM
ejpam-5470	520	3	]	]	PUNCT
ejpam-5470	520	4	a.	a.	NOUN
ejpam-5470	520	5	elrokh	elrokh	NOUN
ejpam-5470	520	6	,	,	PUNCT
ejpam-5470	520	7	m.	m.	NOUN
ejpam-5470	520	8	m.	m.	PROPN
ejpam-5470	520	9	ali	ali	PROPN
ejpam-5470	520	10	al	al	PROPN
ejpam-5470	520	11	-	-	PUNCT
ejpam-5470	520	12	shamiri	shamiri	PROPN
ejpam-5470	520	13	,	,	PUNCT
ejpam-5470	520	14	and	and	CCONJ
ejpam-5470	520	15	a.	a.	PROPN
ejpam-5470	520	16	abd	abd	PROPN
ejpam-5470	520	17	el	el	PROPN
ejpam-5470	520	18	-	-	PROPN
ejpam-5470	520	19	hay	hay	PROPN
ejpam-5470	520	20	.	.	PUNCT
ejpam-5470	521	1	a	a	DET
ejpam-5470	521	2	novel	novel	ADJ
ejpam-5470	521	3	radio	radio	NOUN
ejpam-5470	521	4	geometric	geometric	ADJ
ejpam-5470	521	5	mean	mean	NOUN
ejpam-5470	521	6	algorithm	algorithm	NOUN
ejpam-5470	521	7	for	for	ADP
ejpam-5470	521	8	a	a	DET
ejpam-5470	521	9	graph	graph	NOUN
ejpam-5470	521	10	.	.	PUNCT
ejpam-5470	521	11	symmetry	symmetry	NOUN
ejpam-5470	521	12	,	,	PUNCT
ejpam-5470	521	13	15(3):570	15(3):570	NOUN
ejpam-5470	521	14	,	,	PUNCT
ejpam-5470	521	15	2023	2023	NUM
ejpam-5470	521	16	.	.	PUNCT
ejpam-5470	522	1	[	[	X
ejpam-5470	522	2	10	10	NUM
ejpam-5470	522	3	]	]	PUNCT
ejpam-5470	522	4	a.	a.	NOUN
ejpam-5470	522	5	elrokh	elrokh	NOUN
ejpam-5470	522	6	,	,	PUNCT
ejpam-5470	522	7	y.	y.	PROPN
ejpam-5470	522	8	elmshtaye	elmshtaye	VERB
ejpam-5470	522	9	,	,	PUNCT
ejpam-5470	522	10	and	and	CCONJ
ejpam-5470	523	1	a.	a.	PROPN
ejpam-5470	523	2	abd	abd	PROPN
ejpam-5470	523	3	el	el	PROPN
ejpam-5470	523	4	-	-	PROPN
ejpam-5470	523	5	hay	hay	PROPN
ejpam-5470	523	6	.	.	PUNCT
ejpam-5470	524	1	the	the	DET
ejpam-5470	524	2	cordiality	cordiality	NOUN
ejpam-5470	524	3	of	of	ADP
ejpam-5470	524	4	cone	cone	NOUN
ejpam-5470	524	5	and	and	CCONJ
ejpam-5470	524	6	lemniscate	lemniscate	PROPN
ejpam-5470	524	7	graphs	graph	NOUN
ejpam-5470	524	8	.	.	PUNCT
ejpam-5470	525	1	applied	apply	VERB
ejpam-5470	525	2	mathematics	mathematics	PROPN
ejpam-5470	525	3	&	&	CCONJ
ejpam-5470	525	4	information	information	NOUN
ejpam-5470	525	5	sciences	sciences	PROPN
ejpam-5470	525	6	,	,	PUNCT
ejpam-5470	525	7	16:1027–1034	16:1027–1034	NUM
ejpam-5470	525	8	,	,	PUNCT
ejpam-5470	525	9	2022	2022	NUM
ejpam-5470	525	10	.	.	PUNCT
ejpam-5470	526	1	[	[	X
ejpam-5470	526	2	11	11	NUM
ejpam-5470	526	3	]	]	PUNCT
ejpam-5470	526	4	a.	a.	NOUN
ejpam-5470	526	5	elrokh	elrokh	NOUN
ejpam-5470	526	6	,	,	PUNCT
ejpam-5470	526	7	r.	r.	PROPN
ejpam-5470	526	8	ismail	ismail	PROPN
ejpam-5470	526	9	,	,	PUNCT
ejpam-5470	526	10	a.	a.	PROPN
ejpam-5470	526	11	abd	abd	PROPN
ejpam-5470	526	12	el	el	PROPN
ejpam-5470	526	13	-	-	PROPN
ejpam-5470	526	14	hay	hay	PROPN
ejpam-5470	526	15	,	,	PUNCT
ejpam-5470	526	16	and	and	CCONJ
ejpam-5470	526	17	y.	y.	PROPN
ejpam-5470	526	18	elmshtaye	elmshtaye	PROPN
ejpam-5470	526	19	.	.	PUNCT
ejpam-5470	527	1	on	on	ADP
ejpam-5470	527	2	cubic	cubic	ADJ
ejpam-5470	527	3	roots	root	NOUN
ejpam-5470	527	4	cordial	cordial	ADJ
ejpam-5470	527	5	labeling	labeling	NOUN
ejpam-5470	527	6	for	for	ADP
ejpam-5470	527	7	some	some	DET
ejpam-5470	527	8	graphs	graph	NOUN
ejpam-5470	527	9	.	.	PUNCT
ejpam-5470	528	1	symmetry	symmetry	NOUN
ejpam-5470	528	2	,	,	PUNCT
ejpam-5470	528	3	15(5):990	15(5):990	NOUN
ejpam-5470	528	4	,	,	PUNCT
ejpam-5470	528	5	2023	2023	NUM
ejpam-5470	528	6	.	.	PUNCT
ejpam-5470	529	1	[	[	X
ejpam-5470	529	2	12	12	NUM
ejpam-5470	529	3	]	]	PUNCT
ejpam-5470	529	4	a.	a.	NOUN
ejpam-5470	529	5	elrokh	elrokh	NOUN
ejpam-5470	529	6	and	and	CCONJ
ejpam-5470	529	7	a.	a.	NOUN
ejpam-5470	529	8	rabie	rabie	PROPN
ejpam-5470	529	9	.	.	PUNCT
ejpam-5470	530	1	the	the	DET
ejpam-5470	530	2	cordiality	cordiality	NOUN
ejpam-5470	530	3	of	of	ADP
ejpam-5470	530	4	the	the	DET
ejpam-5470	530	5	sum	sum	NOUN
ejpam-5470	530	6	and	and	CCONJ
ejpam-5470	530	7	union	union	NOUN
ejpam-5470	530	8	of	of	ADP
ejpam-5470	530	9	two	two	NUM
ejpam-5470	530	10	fourth	fourth	ADJ
ejpam-5470	530	11	power	power	NOUN
ejpam-5470	530	12	of	of	ADP
ejpam-5470	530	13	paths	path	NOUN
ejpam-5470	530	14	and	and	CCONJ
ejpam-5470	530	15	cycles	cycle	NOUN
ejpam-5470	530	16	.	.	PUNCT
ejpam-5470	531	1	j	j	PROPN
ejpam-5470	531	2	egypt	egypt	PROPN
ejpam-5470	531	3	math	math	PROPN
ejpam-5470	531	4	soc	soc	PROPN
ejpam-5470	531	5	,	,	PUNCT
ejpam-5470	531	6	29:3	29:3	NUM
ejpam-5470	531	7	,	,	PUNCT
ejpam-5470	531	8	2021	2021	NUM
ejpam-5470	531	9	.	.	PUNCT
ejpam-5470	532	1	[	[	X
ejpam-5470	532	2	13	13	NUM
ejpam-5470	532	3	]	]	PUNCT
ejpam-5470	532	4	j.	j.	PROPN
ejpam-5470	532	5	a.	a.	PROPN
ejpam-5470	532	6	gallian	gallian	PROPN
ejpam-5470	532	7	.	.	PUNCT
ejpam-5470	533	1	a	a	DET
ejpam-5470	533	2	dynamic	dynamic	ADJ
ejpam-5470	533	3	survey	survey	NOUN
ejpam-5470	533	4	of	of	ADP
ejpam-5470	533	5	graph	graph	NOUN
ejpam-5470	533	6	labeling	labeling	NOUN
ejpam-5470	533	7	.	.	PUNCT
ejpam-5470	534	1	the	the	DET
ejpam-5470	534	2	electronic	electronic	ADJ
ejpam-5470	534	3	journal	journal	NOUN
ejpam-5470	534	4	of	of	ADP
ejpam-5470	534	5	combinatorics	combinatoric	NOUN
ejpam-5470	534	6	,	,	PUNCT
ejpam-5470	534	7	17	17	NUM
ejpam-5470	534	8	,	,	PUNCT
ejpam-5470	534	9	2010	2010	NUM
ejpam-5470	534	10	.	.	PUNCT
ejpam-5470	535	1	ds6	ds6	NOUN
ejpam-5470	535	2	.	.	PUNCT
ejpam-5470	536	1	[	[	X
ejpam-5470	536	2	14	14	NUM
ejpam-5470	536	3	]	]	PUNCT
ejpam-5470	536	4	m.	m.	PROPN
ejpam-5470	536	5	hovey	hovey	PROPN
ejpam-5470	536	6	.	.	PUNCT
ejpam-5470	537	1	a	a	DET
ejpam-5470	537	2	-	-	PUNCT
ejpam-5470	537	3	cordial	cordial	ADJ
ejpam-5470	537	4	graphs	graph	NOUN
ejpam-5470	537	5	.	.	PUNCT
ejpam-5470	538	1	discrete	discrete	ADJ
ejpam-5470	538	2	mathematics	mathematic	NOUN
ejpam-5470	538	3	,	,	PUNCT
ejpam-5470	538	4	93:183–194	93:183–194	PROPN
ejpam-5470	538	5	,	,	PUNCT
ejpam-5470	538	6	1991	1991	NUM
ejpam-5470	538	7	.	.	PUNCT
ejpam-5470	539	1	[	[	X
ejpam-5470	539	2	15	15	NUM
ejpam-5470	539	3	]	]	X
ejpam-5470	539	4	s.	s.	PROPN
ejpam-5470	539	5	nada	nada	PROPN
ejpam-5470	539	6	,	,	PUNCT
ejpam-5470	539	7	a.	a.	NOUN
ejpam-5470	539	8	elrokh	elrokh	NOUN
ejpam-5470	539	9	,	,	PUNCT
ejpam-5470	539	10	and	and	CCONJ
ejpam-5470	539	11	a.	a.	PROPN
ejpam-5470	539	12	abd	abd	PROPN
ejpam-5470	539	13	el	el	PROPN
ejpam-5470	539	14	-	-	PROPN
ejpam-5470	539	15	hay	hay	PROPN
ejpam-5470	539	16	.	.	PUNCT
ejpam-5470	540	1	on	on	ADP
ejpam-5470	540	2	signed	sign	VERB
ejpam-5470	540	3	product	product	NOUN
ejpam-5470	540	4	cordial	cordial	ADJ
ejpam-5470	540	5	of	of	ADP
ejpam-5470	540	6	cone	cone	NOUN
ejpam-5470	540	7	graph	graph	NOUN
ejpam-5470	540	8	and	and	CCONJ
ejpam-5470	540	9	its	its	PRON
ejpam-5470	540	10	second	second	ADJ
ejpam-5470	540	11	power	power	NOUN
ejpam-5470	540	12	.	.	PUNCT
ejpam-5470	541	1	turkish	turkish	ADJ
ejpam-5470	541	2	journal	journal	NOUN
ejpam-5470	541	3	of	of	ADP
ejpam-5470	541	4	computer	computer	NOUN
ejpam-5470	541	5	and	and	CCONJ
ejpam-5470	541	6	mathematics	mathematics	PROPN
ejpam-5470	541	7	education	education	NOUN
ejpam-5470	541	8	(	(	PUNCT
ejpam-5470	541	9	turcomat	turcomat	NOUN
ejpam-5470	541	10	)	)	PUNCT
ejpam-5470	541	11	,	,	PUNCT
ejpam-5470	541	12	13(3):597–606	13(3):597–606	NUM
ejpam-5470	541	13	,	,	PUNCT
ejpam-5470	541	14	2022	2022	NUM
ejpam-5470	541	15	.	.	PUNCT
ejpam-5470	542	1	[	[	X
ejpam-5470	542	2	16	16	NUM
ejpam-5470	542	3	]	]	PUNCT
ejpam-5470	542	4	a.	a.	PROPN
ejpam-5470	542	5	rosa	rosa	PROPN
ejpam-5470	542	6	.	.	PUNCT
ejpam-5470	543	1	on	on	ADP
ejpam-5470	543	2	certain	certain	ADJ
ejpam-5470	543	3	valuations	valuation	NOUN
ejpam-5470	543	4	of	of	ADP
ejpam-5470	543	5	the	the	DET
ejpam-5470	543	6	vertices	vertex	NOUN
ejpam-5470	543	7	of	of	ADP
ejpam-5470	543	8	a	a	DET
ejpam-5470	543	9	graph	graph	NOUN
ejpam-5470	543	10	.	.	PUNCT
ejpam-5470	544	1	in	in	ADP
ejpam-5470	544	2	theory	theory	NOUN
ejpam-5470	544	3	of	of	ADP
ejpam-5470	544	4	graphs	graph	NOUN
ejpam-5470	544	5	(	(	PUNCT
ejpam-5470	544	6	internat	internat	PROPN
ejpam-5470	544	7	symposium	symposium	PROPN
ejpam-5470	544	8	,	,	PUNCT
ejpam-5470	544	9	rome	rome	PROPN
ejpam-5470	544	10	,	,	PUNCT
ejpam-5470	544	11	july	july	PROPN
ejpam-5470	544	12	1966	1966	NUM
ejpam-5470	544	13	)	)	PUNCT
ejpam-5470	544	14	,	,	PUNCT
ejpam-5470	544	15	pages	page	NOUN
ejpam-5470	544	16	349–355	349–355	NUM
ejpam-5470	544	17	.	.	PUNCT
ejpam-5470	545	1	gordon	gordon	PROPN
ejpam-5470	545	2	and	and	CCONJ
ejpam-5470	545	3	breach	breach	PROPN
ejpam-5470	545	4	,	,	PUNCT
ejpam-5470	545	5	n.y	n.y	PROPN
ejpam-5470	545	6	.	.	PROPN
ejpam-5470	545	7	and	and	CCONJ
ejpam-5470	545	8	dunod	dunod	PROPN
ejpam-5470	545	9	paris	paris	PROPN
ejpam-5470	545	10	,	,	PUNCT
ejpam-5470	545	11	1967	1967	NUM
ejpam-5470	545	12	.	.	PUNCT
ejpam-5470	546	1	[	[	X
ejpam-5470	546	2	17	17	NUM
ejpam-5470	546	3	]	]	PUNCT
ejpam-5470	546	4	m.	m.	NOUN
ejpam-5470	546	5	a.	a.	PROPN
ejpam-5470	546	6	seoud	seoud	PROPN
ejpam-5470	546	7	,	,	PUNCT
ejpam-5470	546	8	a.	a.	NOUN
ejpam-5470	546	9	t.	t.	PROPN
ejpam-5470	546	10	diab	diab	PROPN
ejpam-5470	546	11	,	,	PUNCT
ejpam-5470	546	12	and	and	CCONJ
ejpam-5470	546	13	e.	e.	PROPN
ejpam-5470	546	14	a.	a.	PROPN
ejpam-5470	546	15	elsahawi	elsahawi	PROPN
ejpam-5470	546	16	.	.	PUNCT
ejpam-5470	547	1	on	on	ADP
ejpam-5470	547	2	strongly	strongly	ADV
ejpam-5470	547	3	-	-	PUNCT
ejpam-5470	547	4	c	c	NOUN
ejpam-5470	547	5	harmonious	harmonious	ADJ
ejpam-5470	547	6	,	,	PUNCT
ejpam-5470	547	7	relatively	relatively	ADV
ejpam-5470	547	8	prime	prime	ADJ
ejpam-5470	547	9	,	,	PUNCT
ejpam-5470	547	10	odd	odd	ADJ
ejpam-5470	547	11	graceful	graceful	ADJ
ejpam-5470	547	12	and	and	CCONJ
ejpam-5470	547	13	cordial	cordial	ADJ
ejpam-5470	547	14	graphs	graph	NOUN
ejpam-5470	547	15	.	.	PUNCT
ejpam-5470	548	1	proc	proc	NOUN
ejpam-5470	548	2	.	.	PUNCT
ejpam-5470	549	1	math	math	NOUN
ejpam-5470	549	2	.	.	PUNCT
ejpam-5470	550	1	phys	phy	NOUN
ejpam-5470	550	2	.	.	PUNCT
ejpam-5470	551	1	soc	soc	PROPN
ejpam-5470	551	2	.	.	PUNCT
ejpam-5470	552	1	egypt	egypt	PROPN
ejpam-5470	552	2	,	,	PUNCT
ejpam-5470	552	3	(	(	PUNCT
ejpam-5470	552	4	73):33–55	73):33–55	NUM
ejpam-5470	552	5	,	,	PUNCT
ejpam-5470	552	6	1998	1998	NUM
ejpam-5470	552	7	.	.	PUNCT