id	sid	tid	token	lemma	pos
ejpam-62	1	1	european	european	PROPN
ejpam-62	1	2	journal	journal	PROPN
ejpam-62	1	3	of	of	ADP
ejpam-62	1	4	pure	pure	ADJ
ejpam-62	1	5	and	and	CCONJ
ejpam-62	1	6	applied	apply	VERB
ejpam-62	1	7	mathematics	mathematic	NOUN
ejpam-62	1	8	vol	vol	NOUN
ejpam-62	1	9	.	.	PROPN
ejpam-62	2	1	1	1	NUM
ejpam-62	2	2	,	,	PUNCT
ejpam-62	2	3	no	no	INTJ
ejpam-62	2	4	.	.	NOUN
ejpam-62	2	5	3	3	NUM
ejpam-62	2	6	,	,	PUNCT
ejpam-62	2	7	2008	2008	NUM
ejpam-62	2	8	,	,	PUNCT
ejpam-62	2	9	(	(	PUNCT
ejpam-62	2	10	10	10	NUM
ejpam-62	2	11	-	-	SYM
ejpam-62	2	12	20	20	NUM
ejpam-62	2	13	)	)	PUNCT
ejpam-62	2	14	issn	issn	PROPN
ejpam-62	2	15	1307	1307	NUM
ejpam-62	2	16	-	-	SYM
ejpam-62	2	17	5543	5543	NUM
ejpam-62	3	1	–	–	PUNCT
ejpam-62	3	2	www.ejpam.com	www.ejpam.com	X
ejpam-62	3	3	score	score	VERB
ejpam-62	3	4	sequences	sequence	NOUN
ejpam-62	3	5	in	in	ADP
ejpam-62	3	6	oriented	orient	VERB
ejpam-62	3	7	k	k	ADJ
ejpam-62	3	8	-	-	PUNCT
ejpam-62	3	9	hypergraphs	hypergraphs	PROPN
ejpam-62	3	10	s.	s.	PROPN
ejpam-62	3	11	pirzada1,∗	pirzada1,∗	PROPN
ejpam-62	3	12	,	,	PUNCT
ejpam-62	3	13	zhou	zhou	PROPN
ejpam-62	3	14	guofei2,†	guofei2,†	PROPN
ejpam-62	3	15	1	1	NUM
ejpam-62	3	16	department	department	NOUN
ejpam-62	3	17	of	of	ADP
ejpam-62	3	18	mathematics	mathematic	NOUN
ejpam-62	3	19	,	,	PUNCT
ejpam-62	3	20	university	university	PROPN
ejpam-62	3	21	of	of	ADP
ejpam-62	3	22	kashmir	kashmir	PROPN
ejpam-62	3	23	,	,	PUNCT
ejpam-62	3	24	srinagar	srinagar	NOUN
ejpam-62	3	25	,	,	PUNCT
ejpam-62	3	26	190006	190006	NUM
ejpam-62	3	27	,	,	PUNCT
ejpam-62	3	28	india	india	PROPN
ejpam-62	3	29	2	2	NUM
ejpam-62	3	30	department	department	NOUN
ejpam-62	3	31	of	of	ADP
ejpam-62	3	32	mathematics	mathematics	PROPN
ejpam-62	3	33	,	,	PUNCT
ejpam-62	3	34	nanjing	nanjing	PROPN
ejpam-62	3	35	university	university	PROPN
ejpam-62	3	36	,	,	PUNCT
ejpam-62	3	37	nanjing	nanjing	PROPN
ejpam-62	3	38	,	,	PUNCT
ejpam-62	3	39	210093	210093	NUM
ejpam-62	3	40	,	,	PUNCT
ejpam-62	3	41	p.r	p.r	PROPN
ejpam-62	3	42	.	.	PROPN
ejpam-62	3	43	china	china	PROPN
ejpam-62	3	44	abstract	abstract	PROPN
ejpam-62	3	45	.	.	PUNCT
ejpam-62	4	1	given	give	VERB
ejpam-62	4	2	two	two	NUM
ejpam-62	4	3	non	non	ADJ
ejpam-62	4	4	-	-	ADJ
ejpam-62	4	5	negative	negative	ADJ
ejpam-62	4	6	integers	integer	NOUN
ejpam-62	4	7	n	n	PRON
ejpam-62	4	8	and	and	CCONJ
ejpam-62	4	9	k	k	X
ejpam-62	4	10	with	with	ADP
ejpam-62	4	11	n	n	PRON
ejpam-62	4	12	≥	≥	NOUN
ejpam-62	4	13	k	k	X
ejpam-62	4	14	>	>	X
ejpam-62	4	15	1	1	NUM
ejpam-62	4	16	,	,	PUNCT
ejpam-62	4	17	an	an	DET
ejpam-62	4	18	oriented	oriented	ADJ
ejpam-62	4	19	k	k	NOUN
ejpam-62	4	20	-	-	NOUN
ejpam-62	4	21	hypergraph	hypergraph	VERB
ejpam-62	4	22	on	on	ADP
ejpam-62	4	23	n	n	DET
ejpam-62	4	24	vertices	vertex	NOUN
ejpam-62	4	25	is	be	AUX
ejpam-62	4	26	a	a	DET
ejpam-62	4	27	pair	pair	NOUN
ejpam-62	4	28	(	(	PUNCT
ejpam-62	4	29	v	v	NOUN
ejpam-62	4	30	,	,	PUNCT
ejpam-62	4	31	a	a	PRON
ejpam-62	4	32	)	)	PUNCT
ejpam-62	4	33	,	,	PUNCT
ejpam-62	4	34	where	where	SCONJ
ejpam-62	4	35	v	v	NOUN
ejpam-62	4	36	is	be	AUX
ejpam-62	4	37	a	a	DET
ejpam-62	4	38	set	set	NOUN
ejpam-62	4	39	of	of	ADP
ejpam-62	4	40	vertices	vertex	NOUN
ejpam-62	4	41	with	with	ADP
ejpam-62	4	42	|v	|v	PROPN
ejpam-62	4	43	|	|	NOUN
ejpam-62	4	44	=	=	SYM
ejpam-62	4	45	n	n	PROPN
ejpam-62	4	46	and	and	CCONJ
ejpam-62	4	47	a	a	PRON
ejpam-62	4	48	is	be	AUX
ejpam-62	4	49	a	a	DET
ejpam-62	4	50	set	set	NOUN
ejpam-62	4	51	of	of	ADP
ejpam-62	4	52	k	k	PROPN
ejpam-62	4	53	-	-	PUNCT
ejpam-62	4	54	tuples	tuple	NOUN
ejpam-62	4	55	of	of	ADP
ejpam-62	4	56	vertices	vertex	NOUN
ejpam-62	4	57	,	,	PUNCT
ejpam-62	4	58	called	call	VERB
ejpam-62	4	59	arcs	arc	NOUN
ejpam-62	4	60	,	,	PUNCT
ejpam-62	4	61	such	such	ADJ
ejpam-62	4	62	that	that	PRON
ejpam-62	4	63	for	for	ADP
ejpam-62	4	64	any	any	DET
ejpam-62	4	65	k	k	NOUN
ejpam-62	4	66	-	-	PUNCT
ejpam-62	4	67	subset	subset	NOUN
ejpam-62	4	68	s	s	PROPN
ejpam-62	4	69	of	of	ADP
ejpam-62	4	70	v	v	NOUN
ejpam-62	4	71	,	,	PUNCT
ejpam-62	4	72	a	a	PRON
ejpam-62	4	73	contains	contain	VERB
ejpam-62	4	74	at	at	ADP
ejpam-62	4	75	most	most	ADJ
ejpam-62	4	76	one	one	NUM
ejpam-62	4	77	of	of	ADP
ejpam-62	4	78	the	the	DET
ejpam-62	4	79	k	k	PROPN
ejpam-62	4	80	!	!	PUNCT
ejpam-62	5	1	k	k	X
ejpam-62	5	2	-	-	PUNCT
ejpam-62	5	3	tuples	tuple	NOUN
ejpam-62	5	4	whose	whose	DET
ejpam-62	5	5	entries	entry	NOUN
ejpam-62	5	6	belong	belong	VERB
ejpam-62	5	7	to	to	ADP
ejpam-62	5	8	s.	s.	PROPN
ejpam-62	5	9	in	in	ADP
ejpam-62	5	10	this	this	DET
ejpam-62	5	11	paper	paper	NOUN
ejpam-62	5	12	,	,	PUNCT
ejpam-62	5	13	we	we	PRON
ejpam-62	5	14	define	define	VERB
ejpam-62	5	15	the	the	DET
ejpam-62	5	16	score	score	NOUN
ejpam-62	5	17	of	of	ADP
ejpam-62	5	18	a	a	DET
ejpam-62	5	19	vertex	vertex	NOUN
ejpam-62	5	20	in	in	ADP
ejpam-62	5	21	an	an	DET
ejpam-62	5	22	oriented	oriented	ADJ
ejpam-62	5	23	k	k	NOUN
ejpam-62	5	24	-	-	NOUN
ejpam-62	5	25	hypergraph	hypergraph	NOUN
ejpam-62	5	26	and	and	CCONJ
ejpam-62	5	27	then	then	ADV
ejpam-62	5	28	obtain	obtain	VERB
ejpam-62	5	29	a	a	DET
ejpam-62	5	30	necessary	necessary	ADJ
ejpam-62	5	31	and	and	CCONJ
ejpam-62	5	32	sufficient	sufficient	ADJ
ejpam-62	5	33	condition	condition	NOUN
ejpam-62	5	34	for	for	ADP
ejpam-62	5	35	the	the	DET
ejpam-62	5	36	sequence	sequence	NOUN
ejpam-62	5	37	of	of	ADP
ejpam-62	5	38	non	non	ADJ
ejpam-62	5	39	-	-	ADJ
ejpam-62	5	40	negative	negative	ADJ
ejpam-62	5	41	integers	integer	NOUN
ejpam-62	5	42	[	[	X
ejpam-62	5	43	s1	s1	NOUN
ejpam-62	5	44	,	,	PUNCT
ejpam-62	5	45	s2	s2	PROPN
ejpam-62	5	46	,	,	PUNCT
ejpam-62	5	47	·	·	PUNCT
ejpam-62	5	48	·	·	PUNCT
ejpam-62	5	49	·	·	PUNCT
ejpam-62	5	50	,	,	PUNCT
ejpam-62	5	51	sn	sn	X
ejpam-62	5	52	]	]	PUNCT
ejpam-62	5	53	to	to	PART
ejpam-62	5	54	be	be	AUX
ejpam-62	5	55	a	a	DET
ejpam-62	5	56	score	score	NOUN
ejpam-62	5	57	sequence	sequence	NOUN
ejpam-62	5	58	of	of	ADP
ejpam-62	5	59	some	some	DET
ejpam-62	5	60	oriented	orient	VERB
ejpam-62	5	61	k	k	NOUN
ejpam-62	5	62	-	-	NOUN
ejpam-62	5	63	hypergraph	hypergraph	VERB
ejpam-62	5	64	.	.	PUNCT
ejpam-62	6	1	ams	am	NOUN
ejpam-62	6	2	subject	subject	ADJ
ejpam-62	6	3	classifications	classification	NOUN
ejpam-62	6	4	:	:	PUNCT
ejpam-62	6	5	05c20	05c20	NUM
ejpam-62	6	6	key	key	ADJ
ejpam-62	6	7	words	word	NOUN
ejpam-62	6	8	:	:	PUNCT
ejpam-62	6	9	hypergraphs	hypergraph	NOUN
ejpam-62	6	10	,	,	PUNCT
ejpam-62	6	11	oriented	orient	VERB
ejpam-62	6	12	k	k	NOUN
ejpam-62	6	13	-	-	PUNCT
ejpam-62	6	14	hypergraphs	hypergraph	NOUN
ejpam-62	6	15	,	,	PUNCT
ejpam-62	6	16	score	score	VERB
ejpam-62	6	17	sequences	sequence	NOUN
ejpam-62	6	18	1	1	NUM
ejpam-62	6	19	.	.	PUNCT
ejpam-62	6	20	introduction	introduction	NOUN
ejpam-62	6	21	an	an	DET
ejpam-62	6	22	edge	edge	NOUN
ejpam-62	6	23	of	of	ADP
ejpam-62	6	24	a	a	DET
ejpam-62	6	25	graph	graph	NOUN
ejpam-62	6	26	is	be	AUX
ejpam-62	6	27	a	a	DET
ejpam-62	6	28	pair	pair	NOUN
ejpam-62	6	29	of	of	ADP
ejpam-62	6	30	vertices	vertex	NOUN
ejpam-62	6	31	and	and	CCONJ
ejpam-62	6	32	an	an	DET
ejpam-62	6	33	edge	edge	NOUN
ejpam-62	6	34	of	of	ADP
ejpam-62	6	35	a	a	DET
ejpam-62	6	36	hypergraph	hypergraph	NOUN
ejpam-62	6	37	is	be	AUX
ejpam-62	6	38	a	a	DET
ejpam-62	6	39	subset	subset	NOUN
ejpam-62	6	40	of	of	ADP
ejpam-62	6	41	the	the	DET
ejpam-62	6	42	vertex	vertex	NOUN
ejpam-62	6	43	set	set	NOUN
ejpam-62	6	44	,	,	PUNCT
ejpam-62	6	45	consisting	consist	VERB
ejpam-62	6	46	of	of	ADP
ejpam-62	6	47	at	at	ADV
ejpam-62	6	48	least	least	ADV
ejpam-62	6	49	two	two	NUM
ejpam-62	6	50	vertices	vertex	NOUN
ejpam-62	6	51	.	.	PUNCT
ejpam-62	7	1	an	an	DET
ejpam-62	7	2	edge	edge	NOUN
ejpam-62	7	3	in	in	ADP
ejpam-62	7	4	a	a	DET
ejpam-62	7	5	hypergraph	hypergraph	NOUN
ejpam-62	7	6	consisting	consisting	NOUN
ejpam-62	7	7	of	of	ADP
ejpam-62	7	8	k	k	PROPN
ejpam-62	7	9	vertices	vertex	NOUN
ejpam-62	7	10	is	be	AUX
ejpam-62	7	11	called	call	VERB
ejpam-62	7	12	a	a	DET
ejpam-62	7	13	k	k	NOUN
ejpam-62	7	14	-	-	NOUN
ejpam-62	7	15	edge	edge	NOUN
ejpam-62	7	16	,	,	PUNCT
ejpam-62	7	17	and	and	CCONJ
ejpam-62	7	18	a	a	DET
ejpam-62	7	19	hypergraph	hypergraph	NOUN
ejpam-62	7	20	all	all	PRON
ejpam-62	7	21	of	of	ADP
ejpam-62	7	22	whose	whose	DET
ejpam-62	7	23	edges	edge	NOUN
ejpam-62	7	24	are	be	AUX
ejpam-62	7	25	k	k	NOUN
ejpam-62	7	26	-	-	PUNCT
ejpam-62	7	27	edges	edge	NOUN
ejpam-62	7	28	is	be	AUX
ejpam-62	7	29	called	call	VERB
ejpam-62	7	30	a	a	DET
ejpam-62	7	31	k	k	NOUN
ejpam-62	7	32	-	-	NOUN
ejpam-62	7	33	hypergraph	hypergraph	VERB
ejpam-62	7	34	.	.	PUNCT
ejpam-62	8	1	a	a	DET
ejpam-62	8	2	k	k	NOUN
ejpam-62	8	3	-	-	NOUN
ejpam-62	8	4	hypertournament	hypertournament	NOUN
ejpam-62	8	5	is	be	AUX
ejpam-62	8	6	a	a	DET
ejpam-62	8	7	complete	complete	ADJ
ejpam-62	8	8	k	k	NOUN
ejpam-62	8	9	-	-	NOUN
ejpam-62	8	10	hypergraph	hypergraph	VERB
ejpam-62	8	11	with	with	ADP
ejpam-62	8	12	each	each	DET
ejpam-62	8	13	k	k	NOUN
ejpam-62	8	14	-	-	PUNCT
ejpam-62	8	15	edge	edge	NOUN
ejpam-62	8	16	endowed	endow	VERB
ejpam-62	8	17	with	with	ADP
ejpam-62	8	18	an	an	DET
ejpam-62	8	19	orientation	orientation	NOUN
ejpam-62	8	20	,	,	PUNCT
ejpam-62	8	21	that	that	ADV
ejpam-62	8	22	is	is	ADV
ejpam-62	8	23	,	,	PUNCT
ejpam-62	8	24	a	a	DET
ejpam-62	8	25	linear	linear	ADJ
ejpam-62	8	26	arrangement	arrangement	NOUN
ejpam-62	8	27	of	of	ADP
ejpam-62	8	28	the	the	DET
ejpam-62	8	29	vertices	vertex	NOUN
ejpam-62	8	30	contained	contain	VERB
ejpam-62	8	31	in	in	ADP
ejpam-62	8	32	the	the	DET
ejpam-62	8	33	hyperedge	hyperedge	NOUN
ejpam-62	8	34	.	.	PUNCT
ejpam-62	9	1	in	in	ADP
ejpam-62	9	2	other	other	ADJ
ejpam-62	9	3	words	word	NOUN
ejpam-62	9	4	,	,	PUNCT
ejpam-62	9	5	given	give	VERB
ejpam-62	9	6	two	two	NUM
ejpam-62	9	7	non	non	ADJ
ejpam-62	9	8	-	-	ADJ
ejpam-62	9	9	negative	negative	ADJ
ejpam-62	9	10	integers	integer	NOUN
ejpam-62	9	11	n	n	PRON
ejpam-62	9	12	and	and	CCONJ
ejpam-62	9	13	k	k	X
ejpam-62	9	14	with	with	ADP
ejpam-62	9	15	n	n	PRON
ejpam-62	9	16	≥	≥	NOUN
ejpam-62	9	17	k	k	X
ejpam-62	9	18	>	>	X
ejpam-62	9	19	1	1	NUM
ejpam-62	9	20	,	,	PUNCT
ejpam-62	9	21	a	a	DET
ejpam-62	9	22	k	k	NOUN
ejpam-62	9	23	-	-	NOUN
ejpam-62	9	24	hypertournament	hypertournament	NOUN
ejpam-62	9	25	on	on	ADP
ejpam-62	9	26	n	n	DET
ejpam-62	9	27	vertices	vertex	NOUN
ejpam-62	9	28	is	be	AUX
ejpam-62	9	29	a	a	DET
ejpam-62	9	30	pair	pair	NOUN
ejpam-62	9	31	(	(	PUNCT
ejpam-62	9	32	v	v	NOUN
ejpam-62	9	33	,	,	PUNCT
ejpam-62	9	34	a	a	PRON
ejpam-62	9	35	)	)	PUNCT
ejpam-62	9	36	,	,	PUNCT
ejpam-62	9	37	where	where	SCONJ
ejpam-62	9	38	v	v	NOUN
ejpam-62	9	39	is	be	AUX
ejpam-62	9	40	a	a	DET
ejpam-62	9	41	set	set	NOUN
ejpam-62	9	42	of	of	ADP
ejpam-62	9	43	vertices	vertex	NOUN
ejpam-62	9	44	with	with	ADP
ejpam-62	9	45	|v	|v	PROPN
ejpam-62	9	46	|	|	NOUN
ejpam-62	9	47	=	=	SYM
ejpam-62	9	48	n	n	PROPN
ejpam-62	9	49	and	and	CCONJ
ejpam-62	9	50	a	a	PRON
ejpam-62	9	51	is	be	AUX
ejpam-62	9	52	a	a	DET
ejpam-62	9	53	set	set	NOUN
ejpam-62	9	54	of	of	ADP
ejpam-62	9	55	k	k	PROPN
ejpam-62	9	56	-	-	PUNCT
ejpam-62	9	57	tuples	tuple	NOUN
ejpam-62	9	58	of	of	ADP
ejpam-62	9	59	vertices	vertex	NOUN
ejpam-62	9	60	,	,	PUNCT
ejpam-62	9	61	called	call	VERB
ejpam-62	9	62	arcs	arc	NOUN
ejpam-62	9	63	,	,	PUNCT
ejpam-62	9	64	such	such	ADJ
ejpam-62	9	65	that	that	PRON
ejpam-62	9	66	for	for	ADP
ejpam-62	9	67	any	any	DET
ejpam-62	9	68	k	k	NOUN
ejpam-62	9	69	-	-	PUNCT
ejpam-62	9	70	subset	subset	NOUN
ejpam-62	9	71	s	s	PROPN
ejpam-62	9	72	of	of	ADP
ejpam-62	9	73	v	v	NOUN
ejpam-62	9	74	,	,	PUNCT
ejpam-62	9	75	a	a	PRON
ejpam-62	9	76	contains	contain	VERB
ejpam-62	9	77	exactly	exactly	ADV
ejpam-62	9	78	one	one	NUM
ejpam-62	9	79	of	of	ADP
ejpam-62	9	80	the	the	DET
ejpam-62	9	81	k	k	PROPN
ejpam-62	9	82	!	!	PUNCT
ejpam-62	10	1	k	k	X
ejpam-62	10	2	-	-	PUNCT
ejpam-62	10	3	tuples	tuple	NOUN
ejpam-62	10	4	whose	whose	DET
ejpam-62	10	5	entries	entry	NOUN
ejpam-62	10	6	belong	belong	VERB
ejpam-62	10	7	to	to	ADP
ejpam-62	10	8	s.	s.	PROPN
ejpam-62	10	9	if	if	SCONJ
ejpam-62	10	10	n	n	CCONJ
ejpam-62	10	11	<	<	X
ejpam-62	10	12	k	k	X
ejpam-62	10	13	,	,	PUNCT
ejpam-62	10	14	a=	a=	PROPN
ejpam-62	10	15	φ	φ	PROPN
ejpam-62	10	16	and	and	CCONJ
ejpam-62	10	17	this	this	DET
ejpam-62	10	18	type	type	NOUN
ejpam-62	10	19	of	of	ADP
ejpam-62	10	20	hypertournament	hypertournament	NOUN
ejpam-62	10	21	is	be	AUX
ejpam-62	10	22	called	call	VERB
ejpam-62	10	23	a	a	DET
ejpam-62	10	24	null	null	ADJ
ejpam-62	10	25	-	-	PUNCT
ejpam-62	10	26	hypertournament	hypertournament	NOUN
ejpam-62	10	27	.	.	PUNCT
ejpam-62	11	1	clearly	clearly	ADV
ejpam-62	11	2	,	,	PUNCT
ejpam-62	11	3	a	a	DET
ejpam-62	11	4	2	2	NUM
ejpam-62	11	5	-	-	PUNCT
ejpam-62	11	6	hypertournament	hypertournament	NOUN
ejpam-62	11	7	is	be	AUX
ejpam-62	11	8	simply	simply	ADV
ejpam-62	11	9	a	a	DET
ejpam-62	11	10	tournament	tournament	NOUN
ejpam-62	11	11	.	.	PUNCT
ejpam-62	12	1	instead	instead	ADV
ejpam-62	12	2	of	of	ADP
ejpam-62	12	3	scores	score	NOUN
ejpam-62	12	4	of	of	ADP
ejpam-62	12	5	vertices	vertex	NOUN
ejpam-62	12	6	in	in	ADP
ejpam-62	12	7	a	a	DET
ejpam-62	12	8	tournament	tournament	NOUN
ejpam-62	12	9	,	,	PUNCT
ejpam-62	12	10	zhou	zhou	PROPN
ejpam-62	12	11	et	et	PROPN
ejpam-62	12	12	al	al	PROPN
ejpam-62	12	13	.	.	PUNCT
ejpam-62	13	1	[	[	X
ejpam-62	13	2	8	8	NUM
ejpam-62	13	3	]	]	PUNCT
ejpam-62	13	4	considered	consider	VERB
ejpam-62	13	5	scores	score	NOUN
ejpam-62	13	6	and	and	CCONJ
ejpam-62	13	7	losing	lose	VERB
ejpam-62	13	8	scores	score	NOUN
ejpam-62	13	9	of	of	ADP
ejpam-62	13	10	vertices	vertex	NOUN
ejpam-62	13	11	in	in	ADP
ejpam-62	13	12	a	a	DET
ejpam-62	13	13	k	k	NOUN
ejpam-62	13	14	-	-	NOUN
ejpam-62	13	15	hypertournament	hypertournament	NOUN
ejpam-62	13	16	,	,	PUNCT
ejpam-62	13	17	and	and	CCONJ
ejpam-62	13	18	derived	derive	VERB
ejpam-62	13	19	a	a	DET
ejpam-62	13	20	result	result	NOUN
ejpam-62	13	21	analogous	analogous	ADJ
ejpam-62	13	22	to	to	ADP
ejpam-62	13	23	landau	landau	NOUN
ejpam-62	13	24	’s	’s	PART
ejpam-62	13	25	theorem	theorem	NOUN
ejpam-62	13	26	[	[	X
ejpam-62	13	27	5	5	NUM
ejpam-62	13	28	]	]	PUNCT
ejpam-62	13	29	.	.	PUNCT
ejpam-62	14	1	the	the	DET
ejpam-62	14	2	score	score	NOUN
ejpam-62	14	3	s(vi	s(vi	PROPN
ejpam-62	14	4	)	)	PUNCT
ejpam-62	14	5	or	or	CCONJ
ejpam-62	14	6	si	si	X
ejpam-62	14	7	of	of	ADP
ejpam-62	14	8	a	a	DET
ejpam-62	14	9	vertex	vertex	NOUN
ejpam-62	14	10	vi	vi	PROPN
ejpam-62	14	11	is	be	AUX
ejpam-62	14	12	the	the	DET
ejpam-62	14	13	number	number	NOUN
ejpam-62	14	14	of	of	ADP
ejpam-62	14	15	arcs	arc	NOUN
ejpam-62	14	16	containing	contain	VERB
ejpam-62	14	17	vi	vi	NOUN
ejpam-62	14	18	and	and	CCONJ
ejpam-62	14	19	in	in	ADP
ejpam-62	14	20	which	which	PRON
ejpam-62	14	21	vi	vi	NOUN
ejpam-62	14	22	is	be	AUX
ejpam-62	14	23	not	not	PART
ejpam-62	14	24	the	the	DET
ejpam-62	14	25	last	last	ADJ
ejpam-62	14	26	element	element	NOUN
ejpam-62	14	27	,	,	PUNCT
ejpam-62	14	28	and	and	CCONJ
ejpam-62	14	29	the	the	DET
ejpam-62	14	30	losing	lose	VERB
ejpam-62	14	31	score	score	NOUN
ejpam-62	14	32	r(vi	r(vi	NOUN
ejpam-62	14	33	)	)	PUNCT
ejpam-62	14	34	or	or	CCONJ
ejpam-62	14	35	ri	ri	NOUN
ejpam-62	14	36	of	of	ADP
ejpam-62	14	37	a	a	DET
ejpam-62	14	38	vertex	vertex	NOUN
ejpam-62	14	39	vi	vi	PROPN
ejpam-62	14	40	is	be	AUX
ejpam-62	14	41	the	the	DET
ejpam-62	14	42	number	number	NOUN
ejpam-62	14	43	of	of	ADP
ejpam-62	14	44	arcs	arc	NOUN
ejpam-62	14	45	containing	contain	VERB
ejpam-62	14	46	vi	vi	NOUN
ejpam-62	14	47	and	and	CCONJ
ejpam-62	14	48	in	in	ADP
ejpam-62	14	49	which	which	PRON
ejpam-62	14	50	vi	vi	PROPN
ejpam-62	14	51	is	be	AUX
ejpam-62	14	52	the	the	DET
ejpam-62	14	53	last	last	ADJ
ejpam-62	14	54	element	element	NOUN
ejpam-62	14	55	.	.	PUNCT
ejpam-62	15	1	the	the	DET
ejpam-62	15	2	score	score	NOUN
ejpam-62	15	3	sequence	sequence	NOUN
ejpam-62	15	4	(	(	PUNCT
ejpam-62	15	5	losing	lose	VERB
ejpam-62	15	6	score	score	NOUN
ejpam-62	15	7	sequence	sequence	NOUN
ejpam-62	15	8	)	)	PUNCT
ejpam-62	15	9	is	be	AUX
ejpam-62	15	10	formed	form	VERB
ejpam-62	15	11	by	by	ADP
ejpam-62	15	12	listing	list	VERB
ejpam-62	15	13	the	the	DET
ejpam-62	15	14	scores	score	NOUN
ejpam-62	15	15	(	(	PUNCT
ejpam-62	15	16	losing	lose	VERB
ejpam-62	15	17	scores	score	NOUN
ejpam-62	15	18	)	)	PUNCT
ejpam-62	15	19	in	in	ADP
ejpam-62	15	20	non	non	ADJ
ejpam-62	15	21	-	-	ADJ
ejpam-62	15	22	decreasing	decrease	VERB
ejpam-62	15	23	order	order	NOUN
ejpam-62	15	24	.	.	PUNCT
ejpam-62	16	1	∗corresponding	∗corresponde	VERB
ejpam-62	16	2	author	author	NOUN
ejpam-62	16	3	.	.	PUNCT
ejpam-62	17	1	email	email	NOUN
ejpam-62	17	2	addresses	address	NOUN
ejpam-62	17	3	:	:	PUNCT
ejpam-62	17	4	sdpirzada@yahoo.co.in	sdpirzada@yahoo.co.in	X
ejpam-62	17	5	(	(	PUNCT
ejpam-62	17	6	s.	s.	PROPN
ejpam-62	17	7	pirzada	pirzada	PROPN
ejpam-62	17	8	)	)	PUNCT
ejpam-62	17	9	gfzhou@nju.edu.cn	gfzhou@nju.edu.cn	NOUN
ejpam-62	17	10	(	(	PUNCT
ejpam-62	17	11	z.	z.	PROPN
ejpam-62	17	12	guofei	guofei	PROPN
ejpam-62	17	13	)	)	PUNCT
ejpam-62	17	14	†the	†the	DET
ejpam-62	17	15	work	work	NOUN
ejpam-62	17	16	of	of	ADP
ejpam-62	17	17	the	the	DET
ejpam-62	17	18	second	second	ADJ
ejpam-62	17	19	author	author	NOUN
ejpam-62	17	20	was	be	AUX
ejpam-62	17	21	supported	support	VERB
ejpam-62	17	22	in	in	ADP
ejpam-62	17	23	part	part	NOUN
ejpam-62	17	24	by	by	ADP
ejpam-62	17	25	the	the	DET
ejpam-62	17	26	national	national	ADJ
ejpam-62	17	27	natural	natural	PROPN
ejpam-62	17	28	science	science	PROPN
ejpam-62	17	29	foundation	foundation	PROPN
ejpam-62	17	30	of	of	ADP
ejpam-62	17	31	china	china	PROPN
ejpam-62	17	32	and	and	CCONJ
ejpam-62	17	33	the	the	DET
ejpam-62	17	34	dr	dr	PROPN
ejpam-62	17	35	.	.	PROPN
ejpam-62	17	36	delia	delia	PROPN
ejpam-62	17	37	koo	koo	PROPN
ejpam-62	17	38	grant	grant	PROPN
ejpam-62	17	39	in	in	ADP
ejpam-62	17	40	michigan	michigan	PROPN
ejpam-62	17	41	state	state	PROPN
ejpam-62	17	42	university	university	PROPN
ejpam-62	17	43	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-62	18	1	10	10	NUM
ejpam-62	18	2	c	c	X
ejpam-62	18	3	©	©	NOUN
ejpam-62	18	4	2008	2008	NUM
ejpam-62	18	5	ejpam	ejpam	VERB
ejpam-62	18	6	all	all	DET
ejpam-62	18	7	rights	right	NOUN
ejpam-62	18	8	reserved	reserve	VERB
ejpam-62	18	9	.	.	PUNCT
ejpam-62	19	1	s.	s.	PROPN
ejpam-62	19	2	pirzada	pirzada	PROPN
ejpam-62	19	3	,	,	PUNCT
ejpam-62	19	4	z.	z.	PROPN
ejpam-62	19	5	guofei	guofei	PROPN
ejpam-62	19	6	/	/	SYM
ejpam-62	19	7	eur	eur	PROPN
ejpam-62	19	8	.	.	PUNCT
ejpam-62	20	1	j.	j.	PROPN
ejpam-62	20	2	pure	pure	PROPN
ejpam-62	20	3	appl	appl	PROPN
ejpam-62	20	4	.	.	PROPN
ejpam-62	20	5	math	math	PROPN
ejpam-62	20	6	,	,	PUNCT
ejpam-62	20	7	1	1	NUM
ejpam-62	20	8	(	(	PUNCT
ejpam-62	20	9	2008	2008	NUM
ejpam-62	20	10	)	)	PUNCT
ejpam-62	20	11	,	,	PUNCT
ejpam-62	20	12	(	(	PUNCT
ejpam-62	20	13	10	10	NUM
ejpam-62	20	14	-	-	SYM
ejpam-62	20	15	20	20	NUM
ejpam-62	20	16	)	)	PUNCT
ejpam-62	20	17	11	11	NUM
ejpam-62	20	18	the	the	DET
ejpam-62	20	19	following	follow	VERB
ejpam-62	20	20	characterizations	characterization	NOUN
ejpam-62	20	21	of	of	ADP
ejpam-62	20	22	score	score	NOUN
ejpam-62	20	23	sequences	sequence	NOUN
ejpam-62	20	24	and	and	CCONJ
ejpam-62	20	25	losing	lose	VERB
ejpam-62	20	26	score	score	NOUN
ejpam-62	20	27	sequences	sequence	NOUN
ejpam-62	20	28	in	in	ADP
ejpam-62	20	29	k	k	NOUN
ejpam-62	20	30	-	-	NOUN
ejpam-62	20	31	hypertournaments	hypertournament	NOUN
ejpam-62	20	32	are	be	AUX
ejpam-62	20	33	due	due	ADJ
ejpam-62	20	34	to	to	ADP
ejpam-62	20	35	zhou	zhou	PROPN
ejpam-62	20	36	et	et	PROPN
ejpam-62	20	37	al	al	PROPN
ejpam-62	20	38	.	.	PUNCT
ejpam-62	21	1	[	[	X
ejpam-62	21	2	8	8	NUM
ejpam-62	21	3	]	]	PUNCT
ejpam-62	21	4	.	.	PUNCT
ejpam-62	22	1	theorem	theorem	VERB
ejpam-62	22	2	1.1	1.1	NUM
ejpam-62	22	3	.	.	PUNCT
ejpam-62	23	1	given	give	VERB
ejpam-62	23	2	two	two	NUM
ejpam-62	23	3	non	non	ADJ
ejpam-62	23	4	-	-	ADJ
ejpam-62	23	5	negative	negative	ADJ
ejpam-62	23	6	integers	integer	NOUN
ejpam-62	23	7	n	n	PRON
ejpam-62	23	8	and	and	CCONJ
ejpam-62	23	9	k	k	X
ejpam-62	23	10	with	with	ADP
ejpam-62	23	11	n≥	n≥	PROPN
ejpam-62	23	12	k	k	X
ejpam-62	23	13	>	>	X
ejpam-62	23	14	1	1	NUM
ejpam-62	23	15	,	,	PUNCT
ejpam-62	23	16	a	a	DET
ejpam-62	23	17	non	non	ADJ
ejpam-62	23	18	-	-	ADJ
ejpam-62	23	19	decreasing	decrease	VERB
ejpam-62	23	20	sequence	sequence	NOUN
ejpam-62	23	21	r	r	NOUN
ejpam-62	23	22	=	=	PUNCT
ejpam-62	24	1	[	[	X
ejpam-62	24	2	r1	r1	NOUN
ejpam-62	24	3	,	,	PUNCT
ejpam-62	24	4	r2	r2	PROPN
ejpam-62	24	5	,	,	PUNCT
ejpam-62	24	6	·	·	PUNCT
ejpam-62	24	7	·	·	PUNCT
ejpam-62	24	8	·	·	PUNCT
ejpam-62	24	9	,	,	PUNCT
ejpam-62	24	10	rn	rn	PROPN
ejpam-62	24	11	]	]	PUNCT
ejpam-62	24	12	of	of	ADP
ejpam-62	24	13	non	non	ADJ
ejpam-62	24	14	-	-	ADJ
ejpam-62	24	15	negative	negative	ADJ
ejpam-62	24	16	integers	integer	NOUN
ejpam-62	24	17	is	be	AUX
ejpam-62	24	18	a	a	DET
ejpam-62	24	19	losing	lose	VERB
ejpam-62	24	20	score	score	NOUN
ejpam-62	24	21	sequence	sequence	NOUN
ejpam-62	24	22	of	of	ADP
ejpam-62	24	23	some	some	DET
ejpam-62	24	24	khypertournament	khypertournament	NOUN
ejpam-62	24	25	if	if	SCONJ
ejpam-62	24	26	and	and	CCONJ
ejpam-62	24	27	only	only	ADV
ejpam-62	24	28	if	if	SCONJ
ejpam-62	24	29	for	for	ADP
ejpam-62	24	30	each	each	DET
ejpam-62	24	31	j	j	PROPN
ejpam-62	24	32	,	,	PUNCT
ejpam-62	24	33	j	j	PROPN
ejpam-62	24	34	∑	∑	PROPN
ejpam-62	24	35	i=1	i=1	PROPN
ejpam-62	24	36	ri	ri	PROPN
ejpam-62	24	37	≥	≥	NUM
ejpam-62	24	38	�	�	PROPN
ejpam-62	24	39	j	j	PROPN
ejpam-62	24	40	k	k	PROPN
ejpam-62	24	41	�	�	PROPN
ejpam-62	24	42	,	,	PUNCT
ejpam-62	24	43	with	with	ADP
ejpam-62	24	44	equality	equality	NOUN
ejpam-62	24	45	when	when	SCONJ
ejpam-62	24	46	j	j	PROPN
ejpam-62	24	47	=	=	PROPN
ejpam-62	24	48	n.	n.	PROPN
ejpam-62	24	49	theorem	theorem	VERB
ejpam-62	24	50	1.2	1.2	NUM
ejpam-62	24	51	.	.	PUNCT
ejpam-62	25	1	given	give	VERB
ejpam-62	25	2	non	non	ADJ
ejpam-62	25	3	-	-	ADJ
ejpam-62	25	4	negative	negative	ADJ
ejpam-62	25	5	integers	integer	NOUN
ejpam-62	25	6	n	n	PRON
ejpam-62	25	7	and	and	CCONJ
ejpam-62	25	8	k	k	X
ejpam-62	25	9	with	with	ADP
ejpam-62	25	10	n	n	PRON
ejpam-62	25	11	≥	≥	NOUN
ejpam-62	25	12	k	k	X
ejpam-62	25	13	>	>	X
ejpam-62	25	14	1	1	NUM
ejpam-62	25	15	,	,	PUNCT
ejpam-62	25	16	a	a	DET
ejpam-62	25	17	non	non	ADJ
ejpam-62	25	18	-	-	ADJ
ejpam-62	25	19	decreasing	decrease	VERB
ejpam-62	25	20	sequence	sequence	NOUN
ejpam-62	25	21	s	s	PART
ejpam-62	25	22	=	=	PUNCT
ejpam-62	25	23	[	[	X
ejpam-62	25	24	s1	s1	NOUN
ejpam-62	25	25	,	,	PUNCT
ejpam-62	25	26	s2	s2	PROPN
ejpam-62	25	27	,	,	PUNCT
ejpam-62	25	28	·	·	PUNCT
ejpam-62	25	29	·	·	PUNCT
ejpam-62	25	30	·	·	PUNCT
ejpam-62	25	31	,	,	PUNCT
ejpam-62	25	32	sn	sn	PROPN
ejpam-62	25	33	]	]	PUNCT
ejpam-62	25	34	of	of	ADP
ejpam-62	25	35	non	non	ADJ
ejpam-62	25	36	-	-	ADJ
ejpam-62	25	37	negative	negative	ADJ
ejpam-62	25	38	integers	integer	NOUN
ejpam-62	25	39	is	be	AUX
ejpam-62	25	40	a	a	DET
ejpam-62	25	41	score	score	NOUN
ejpam-62	25	42	sequence	sequence	NOUN
ejpam-62	25	43	of	of	ADP
ejpam-62	25	44	some	some	DET
ejpam-62	25	45	k	k	NOUN
ejpam-62	25	46	-	-	NOUN
ejpam-62	25	47	hypertournament	hypertournament	NOUN
ejpam-62	25	48	if	if	SCONJ
ejpam-62	25	49	and	and	CCONJ
ejpam-62	25	50	only	only	ADV
ejpam-62	25	51	if	if	SCONJ
ejpam-62	25	52	for	for	ADP
ejpam-62	25	53	each	each	DET
ejpam-62	25	54	j	j	PROPN
ejpam-62	25	55	,	,	PUNCT
ejpam-62	25	56	j	j	PROPN
ejpam-62	25	57	∑	∑	PROPN
ejpam-62	25	58	i=1	i=1	PROPN
ejpam-62	25	59	si	si	PROPN
ejpam-62	25	60	≥	≥	PROPN
ejpam-62	25	61	j	j	PROPN
ejpam-62	25	62	�	�	PROPN
ejpam-62	25	63	n−	n−	PROPN
ejpam-62	25	64	1	1	NUM
ejpam-62	25	65	k−	k−	PROPN
ejpam-62	25	66	1	1	NUM
ejpam-62	25	67	�	�	PROPN
ejpam-62	25	68	+	+	CCONJ
ejpam-62	25	69	�	�	PROPN
ejpam-62	26	1	n−	n−	PROPN
ejpam-62	26	2	j	j	PROPN
ejpam-62	26	3	k	k	PROPN
ejpam-62	26	4	�	�	PROPN
ejpam-62	26	5	−	−	PROPN
ejpam-62	26	6	�	�	PROPN
ejpam-62	26	7	n	n	CCONJ
ejpam-62	26	8	k	k	PROPN
ejpam-62	26	9	�	�	PROPN
ejpam-62	26	10	,	,	PUNCT
ejpam-62	26	11	with	with	ADP
ejpam-62	26	12	equality	equality	NOUN
ejpam-62	26	13	when	when	SCONJ
ejpam-62	26	14	j	j	PROPN
ejpam-62	26	15	=	=	PROPN
ejpam-62	26	16	n.	n.	PROPN
ejpam-62	26	17	bang	bang	PROPN
ejpam-62	26	18	and	and	CCONJ
ejpam-62	26	19	sharp	sharp	ADJ
ejpam-62	26	20	[	[	X
ejpam-62	26	21	2	2	NUM
ejpam-62	26	22	]	]	PUNCT
ejpam-62	26	23	proved	prove	VERB
ejpam-62	26	24	landau	landau	NOUN
ejpam-62	26	25	’s	’s	PART
ejpam-62	26	26	theorem	theorem	ADJ
ejpam-62	26	27	using	use	VERB
ejpam-62	26	28	hall	hall	PROPN
ejpam-62	26	29	’s	’s	PART
ejpam-62	26	30	theorem	theorem	NOUN
ejpam-62	26	31	on	on	ADP
ejpam-62	26	32	a	a	DET
ejpam-62	26	33	system	system	NOUN
ejpam-62	26	34	of	of	ADP
ejpam-62	26	35	distinct	distinct	ADJ
ejpam-62	26	36	representatives	representative	NOUN
ejpam-62	26	37	of	of	ADP
ejpam-62	26	38	a	a	DET
ejpam-62	26	39	collection	collection	NOUN
ejpam-62	26	40	of	of	ADP
ejpam-62	26	41	sets	set	NOUN
ejpam-62	26	42	.	.	PUNCT
ejpam-62	27	1	based	base	VERB
ejpam-62	27	2	on	on	ADP
ejpam-62	27	3	bang	bang	PROPN
ejpam-62	27	4	and	and	CCONJ
ejpam-62	27	5	sharp	sharp	PROPN
ejpam-62	27	6	’s	’s	PART
ejpam-62	27	7	ideas	idea	NOUN
ejpam-62	27	8	,	,	PUNCT
ejpam-62	27	9	koh	koh	PROPN
ejpam-62	27	10	and	and	CCONJ
ejpam-62	27	11	ree	ree	PRON
ejpam-62	27	12	[	[	X
ejpam-62	27	13	4	4	NUM
ejpam-62	27	14	]	]	PUNCT
ejpam-62	27	15	have	have	AUX
ejpam-62	27	16	given	give	VERB
ejpam-62	27	17	a	a	DET
ejpam-62	27	18	different	different	ADJ
ejpam-62	27	19	proof	proof	NOUN
ejpam-62	27	20	of	of	ADP
ejpam-62	27	21	theorem	theorem	ADJ
ejpam-62	27	22	1.1	1.1	NUM
ejpam-62	27	23	and	and	CCONJ
ejpam-62	27	24	1.2	1.2	NUM
ejpam-62	27	25	.	.	PUNCT
ejpam-62	28	1	some	some	DET
ejpam-62	28	2	more	more	ADJ
ejpam-62	28	3	results	result	NOUN
ejpam-62	28	4	on	on	ADP
ejpam-62	28	5	scores	score	NOUN
ejpam-62	28	6	of	of	ADP
ejpam-62	28	7	khypertournaments	khypertournament	NOUN
ejpam-62	28	8	can	can	AUX
ejpam-62	28	9	be	be	AUX
ejpam-62	28	10	found	find	VERB
ejpam-62	28	11	in	in	ADP
ejpam-62	28	12	[	[	X
ejpam-62	28	13	3,7	3,7	NUM
ejpam-62	28	14	]	]	PUNCT
ejpam-62	28	15	.	.	PUNCT
ejpam-62	29	1	an	an	DET
ejpam-62	29	2	oriented	orient	VERB
ejpam-62	29	3	graph	graph	NOUN
ejpam-62	29	4	is	be	AUX
ejpam-62	29	5	a	a	DET
ejpam-62	29	6	graph	graph	NOUN
ejpam-62	29	7	with	with	ADP
ejpam-62	29	8	each	each	DET
ejpam-62	29	9	edge	edge	NOUN
ejpam-62	29	10	endowed	endow	VERB
ejpam-62	29	11	with	with	ADP
ejpam-62	29	12	an	an	DET
ejpam-62	29	13	orientation	orientation	NOUN
ejpam-62	29	14	.	.	PUNCT
ejpam-62	30	1	as	as	SCONJ
ejpam-62	30	2	given	give	VERB
ejpam-62	30	3	by	by	ADP
ejpam-62	30	4	avery	avery	NOUN
ejpam-62	30	5	[	[	X
ejpam-62	30	6	1	1	NUM
ejpam-62	30	7	]	]	PUNCT
ejpam-62	30	8	,	,	PUNCT
ejpam-62	30	9	the	the	DET
ejpam-62	30	10	score	score	NOUN
ejpam-62	30	11	s(vi	s(vi	PROPN
ejpam-62	30	12	)	)	PUNCT
ejpam-62	30	13	or	or	CCONJ
ejpam-62	30	14	si	si	X
ejpam-62	30	15	of	of	ADP
ejpam-62	30	16	a	a	DET
ejpam-62	30	17	vertex	vertex	NOUN
ejpam-62	30	18	vi	vi	NOUN
ejpam-62	30	19	in	in	ADP
ejpam-62	30	20	an	an	DET
ejpam-62	30	21	oriented	orient	VERB
ejpam-62	30	22	graph	graph	NOUN
ejpam-62	30	23	with	with	ADP
ejpam-62	30	24	n	n	DET
ejpam-62	30	25	vertices	vertex	NOUN
ejpam-62	30	26	is	be	AUX
ejpam-62	30	27	s(vi	s(vi	NUM
ejpam-62	30	28	)	)	PUNCT
ejpam-62	30	29	=	=	SYM
ejpam-62	30	30	n−1+d+(vi)−d−(vi	n−1+d+(vi)−d−(vi	PROPN
ejpam-62	30	31	)	)	PUNCT
ejpam-62	30	32	,	,	PUNCT
ejpam-62	30	33	where	where	SCONJ
ejpam-62	30	34	d+(vi	d+(vi	NOUN
ejpam-62	30	35	)	)	PUNCT
ejpam-62	30	36	and	and	CCONJ
ejpam-62	30	37	d−(vi	d−(vi	PROPN
ejpam-62	30	38	)	)	PUNCT
ejpam-62	30	39	are	be	AUX
ejpam-62	30	40	respectively	respectively	ADV
ejpam-62	30	41	the	the	DET
ejpam-62	30	42	outdegree	outdegree	NOUN
ejpam-62	30	43	and	and	CCONJ
ejpam-62	30	44	indegree	indegree	NOUN
ejpam-62	30	45	of	of	ADP
ejpam-62	30	46	vi	vi	PROPN
ejpam-62	30	47	.	.	PUNCT
ejpam-62	31	1	the	the	DET
ejpam-62	31	2	score	score	NOUN
ejpam-62	31	3	sequence	sequence	NOUN
ejpam-62	31	4	of	of	ADP
ejpam-62	31	5	an	an	DET
ejpam-62	31	6	oriented	orient	VERB
ejpam-62	31	7	graph	graph	NOUN
ejpam-62	31	8	is	be	AUX
ejpam-62	31	9	formed	form	VERB
ejpam-62	31	10	by	by	ADP
ejpam-62	31	11	listing	list	VERB
ejpam-62	31	12	the	the	DET
ejpam-62	31	13	scores	score	NOUN
ejpam-62	31	14	in	in	ADP
ejpam-62	31	15	non	non	ADJ
ejpam-62	31	16	-	-	ADJ
ejpam-62	31	17	decreasing	decrease	VERB
ejpam-62	31	18	order	order	NOUN
ejpam-62	31	19	.	.	PUNCT
ejpam-62	32	1	the	the	DET
ejpam-62	32	2	following	follow	VERB
ejpam-62	32	3	result	result	NOUN
ejpam-62	32	4	due	due	ADP
ejpam-62	32	5	to	to	ADP
ejpam-62	32	6	avery	avery	NOUN
ejpam-62	32	7	[	[	X
ejpam-62	32	8	1	1	NUM
ejpam-62	32	9	]	]	PUNCT
ejpam-62	32	10	characterizes	characterize	VERB
ejpam-62	32	11	score	score	NOUN
ejpam-62	32	12	sequences	sequence	NOUN
ejpam-62	32	13	in	in	ADP
ejpam-62	32	14	oriented	orient	VERB
ejpam-62	32	15	graphs	graph	NOUN
ejpam-62	32	16	,	,	PUNCT
ejpam-62	32	17	and	and	CCONJ
ejpam-62	32	18	a	a	DET
ejpam-62	32	19	new	new	ADJ
ejpam-62	32	20	proof	proof	NOUN
ejpam-62	32	21	of	of	ADP
ejpam-62	32	22	it	it	PRON
ejpam-62	32	23	is	be	AUX
ejpam-62	32	24	due	due	ADJ
ejpam-62	32	25	to	to	ADP
ejpam-62	32	26	pirzada	pirzada	PROPN
ejpam-62	32	27	et	et	PROPN
ejpam-62	32	28	al	al	PROPN
ejpam-62	32	29	.	.	PUNCT
ejpam-62	33	1	[	[	X
ejpam-62	33	2	6	6	NUM
ejpam-62	33	3	]	]	PUNCT
ejpam-62	33	4	.	.	PUNCT
ejpam-62	34	1	theorem	theorem	VERB
ejpam-62	34	2	1.3	1.3	NUM
ejpam-62	34	3	.	.	PUNCT
ejpam-62	35	1	a	a	DET
ejpam-62	35	2	sequence	sequence	NOUN
ejpam-62	35	3	s	s	PART
ejpam-62	35	4	=	=	PUNCT
ejpam-62	36	1	[	[	X
ejpam-62	36	2	s1	s1	NOUN
ejpam-62	36	3	,	,	PUNCT
ejpam-62	36	4	s2	s2	PROPN
ejpam-62	36	5	,	,	PUNCT
ejpam-62	36	6	·	·	PUNCT
ejpam-62	36	7	·	·	PUNCT
ejpam-62	36	8	·	·	PUNCT
ejpam-62	36	9	,	,	PUNCT
ejpam-62	36	10	sn	sn	PROPN
ejpam-62	36	11	]	]	PUNCT
ejpam-62	36	12	of	of	ADP
ejpam-62	36	13	non	non	ADJ
ejpam-62	36	14	-	-	ADJ
ejpam-62	36	15	negative	negative	ADJ
ejpam-62	36	16	integers	integer	NOUN
ejpam-62	36	17	in	in	ADP
ejpam-62	36	18	non	non	ADJ
ejpam-62	36	19	-	-	ADJ
ejpam-62	36	20	decreasing	decrease	VERB
ejpam-62	36	21	order	order	NOUN
ejpam-62	36	22	is	be	AUX
ejpam-62	36	23	a	a	DET
ejpam-62	36	24	score	score	NOUN
ejpam-62	36	25	sequence	sequence	NOUN
ejpam-62	36	26	of	of	ADP
ejpam-62	36	27	an	an	DET
ejpam-62	36	28	oriented	orient	VERB
ejpam-62	36	29	graph	graph	NOUN
ejpam-62	36	30	if	if	SCONJ
ejpam-62	36	31	and	and	CCONJ
ejpam-62	36	32	only	only	ADV
ejpam-62	36	33	if	if	SCONJ
ejpam-62	36	34	for	for	ADP
ejpam-62	36	35	each	each	DET
ejpam-62	36	36	j	j	PROPN
ejpam-62	36	37	(	(	PUNCT
ejpam-62	36	38	1≤	1≤	NUM
ejpam-62	36	39	j	j	PROPN
ejpam-62	36	40	≤	≤	PROPN
ejpam-62	36	41	n	n	CCONJ
ejpam-62	36	42	)	)	PUNCT
ejpam-62	37	1	j	j	PROPN
ejpam-62	37	2	∑	∑	PUNCT
ejpam-62	37	3	i=1	i=1	PROPN
ejpam-62	37	4	si	si	PROPN
ejpam-62	37	5	≥	≥	PROPN
ejpam-62	37	6	2	2	NUM
ejpam-62	37	7	�	�	PROPN
ejpam-62	37	8	j	j	PROPN
ejpam-62	37	9	2	2	NUM
ejpam-62	37	10	�	�	PROPN
ejpam-62	37	11	,	,	PUNCT
ejpam-62	37	12	with	with	ADP
ejpam-62	37	13	equality	equality	NOUN
ejpam-62	37	14	when	when	SCONJ
ejpam-62	37	15	j	j	PROPN
ejpam-62	37	16	=	=	PROPN
ejpam-62	37	17	n.	n.	PROPN
ejpam-62	38	1	an	an	DET
ejpam-62	38	2	oriented	orient	VERB
ejpam-62	38	3	k	k	NOUN
ejpam-62	38	4	-	-	NOUN
ejpam-62	38	5	hypergraph	hypergraph	NOUN
ejpam-62	38	6	is	be	AUX
ejpam-62	38	7	a	a	DET
ejpam-62	38	8	k	k	NOUN
ejpam-62	38	9	-	-	NOUN
ejpam-62	38	10	hypergraph	hypergraph	VERB
ejpam-62	38	11	with	with	ADP
ejpam-62	38	12	each	each	DET
ejpam-62	38	13	k	k	NOUN
ejpam-62	38	14	-	-	PUNCT
ejpam-62	38	15	edge	edge	NOUN
ejpam-62	38	16	endowed	endow	VERB
ejpam-62	38	17	with	with	ADP
ejpam-62	38	18	an	an	DET
ejpam-62	38	19	orientation	orientation	NOUN
ejpam-62	38	20	,	,	PUNCT
ejpam-62	38	21	that	that	ADV
ejpam-62	38	22	is	is	ADV
ejpam-62	38	23	,	,	PUNCT
ejpam-62	38	24	a	a	DET
ejpam-62	38	25	linear	linear	ADJ
ejpam-62	38	26	arrangement	arrangement	NOUN
ejpam-62	38	27	of	of	ADP
ejpam-62	38	28	the	the	DET
ejpam-62	38	29	vertices	vertex	NOUN
ejpam-62	38	30	contained	contain	VERB
ejpam-62	38	31	in	in	ADP
ejpam-62	38	32	the	the	DET
ejpam-62	38	33	hyperedge	hyperedge	NOUN
ejpam-62	38	34	.	.	PUNCT
ejpam-62	39	1	in	in	ADP
ejpam-62	39	2	other	other	ADJ
ejpam-62	39	3	words	word	NOUN
ejpam-62	39	4	,	,	PUNCT
ejpam-62	39	5	given	give	VERB
ejpam-62	39	6	two	two	NUM
ejpam-62	39	7	non	non	ADJ
ejpam-62	39	8	-	-	ADJ
ejpam-62	39	9	negative	negative	ADJ
ejpam-62	39	10	integers	integer	NOUN
ejpam-62	39	11	n	n	PRON
ejpam-62	39	12	and	and	CCONJ
ejpam-62	39	13	k	k	X
ejpam-62	39	14	with	with	ADP
ejpam-62	39	15	n	n	PRON
ejpam-62	39	16	≥	≥	NOUN
ejpam-62	39	17	k	k	X
ejpam-62	39	18	>	>	X
ejpam-62	39	19	1	1	NUM
ejpam-62	39	20	,	,	PUNCT
ejpam-62	39	21	an	an	DET
ejpam-62	39	22	oriented	oriented	ADJ
ejpam-62	39	23	k	k	NOUN
ejpam-62	39	24	-	-	NOUN
ejpam-62	39	25	hypergraph	hypergraph	VERB
ejpam-62	39	26	on	on	ADP
ejpam-62	39	27	n	n	DET
ejpam-62	39	28	vertices	vertex	NOUN
ejpam-62	39	29	is	be	AUX
ejpam-62	39	30	a	a	DET
ejpam-62	39	31	pair	pair	NOUN
ejpam-62	39	32	(	(	PUNCT
ejpam-62	39	33	v	v	NOUN
ejpam-62	39	34	,	,	PUNCT
ejpam-62	39	35	a	a	PRON
ejpam-62	39	36	)	)	PUNCT
ejpam-62	39	37	,	,	PUNCT
ejpam-62	39	38	where	where	SCONJ
ejpam-62	39	39	v	v	NOUN
ejpam-62	39	40	is	be	AUX
ejpam-62	39	41	a	a	DET
ejpam-62	39	42	set	set	NOUN
ejpam-62	39	43	of	of	ADP
ejpam-62	39	44	vertices	vertex	NOUN
ejpam-62	39	45	with	with	ADP
ejpam-62	39	46	|v	|v	PROPN
ejpam-62	39	47	|	|	NOUN
ejpam-62	39	48	=	=	SYM
ejpam-62	39	49	n	n	PROPN
ejpam-62	39	50	and	and	CCONJ
ejpam-62	39	51	a	a	PRON
ejpam-62	39	52	is	be	AUX
ejpam-62	39	53	a	a	DET
ejpam-62	39	54	set	set	NOUN
ejpam-62	39	55	of	of	ADP
ejpam-62	39	56	k	k	PROPN
ejpam-62	39	57	-	-	PUNCT
ejpam-62	39	58	tuples	tuple	NOUN
ejpam-62	39	59	of	of	ADP
ejpam-62	39	60	vertices	vertex	NOUN
ejpam-62	39	61	,	,	PUNCT
ejpam-62	39	62	called	call	VERB
ejpam-62	39	63	arcs	arc	NOUN
ejpam-62	39	64	,	,	PUNCT
ejpam-62	39	65	such	such	ADJ
ejpam-62	39	66	that	that	PRON
ejpam-62	39	67	for	for	ADP
ejpam-62	39	68	any	any	DET
ejpam-62	39	69	k	k	NOUN
ejpam-62	39	70	-	-	PUNCT
ejpam-62	39	71	subset	subset	NOUN
ejpam-62	39	72	s	s	PROPN
ejpam-62	39	73	of	of	ADP
ejpam-62	39	74	v	v	NOUN
ejpam-62	39	75	,	,	PUNCT
ejpam-62	39	76	a	a	PRON
ejpam-62	39	77	contains	contain	VERB
ejpam-62	39	78	at	at	ADP
ejpam-62	39	79	most	most	ADJ
ejpam-62	39	80	one	one	NUM
ejpam-62	39	81	of	of	ADP
ejpam-62	39	82	the	the	DET
ejpam-62	39	83	k	k	PROPN
ejpam-62	39	84	!	!	PUNCT
ejpam-62	39	85	s.	s.	PROPN
ejpam-62	39	86	pirzada	pirzada	PROPN
ejpam-62	39	87	,	,	PUNCT
ejpam-62	39	88	z.	z.	PROPN
ejpam-62	39	89	guofei	guofei	PROPN
ejpam-62	39	90	/	/	SYM
ejpam-62	39	91	eur	eur	PROPN
ejpam-62	39	92	.	.	PUNCT
ejpam-62	40	1	j.	j.	PROPN
ejpam-62	40	2	pure	pure	PROPN
ejpam-62	40	3	appl	appl	PROPN
ejpam-62	40	4	.	.	PROPN
ejpam-62	40	5	math	math	PROPN
ejpam-62	40	6	,	,	PUNCT
ejpam-62	40	7	1	1	NUM
ejpam-62	40	8	(	(	PUNCT
ejpam-62	40	9	2008	2008	NUM
ejpam-62	40	10	)	)	PUNCT
ejpam-62	40	11	,	,	PUNCT
ejpam-62	40	12	(	(	PUNCT
ejpam-62	40	13	10	10	NUM
ejpam-62	40	14	-	-	SYM
ejpam-62	40	15	20	20	NUM
ejpam-62	40	16	)	)	PUNCT
ejpam-62	40	17	12	12	NUM
ejpam-62	41	1	k	k	NOUN
ejpam-62	41	2	-	-	PUNCT
ejpam-62	41	3	tuples	tuple	NOUN
ejpam-62	41	4	whose	whose	DET
ejpam-62	41	5	entries	entry	NOUN
ejpam-62	41	6	belong	belong	VERB
ejpam-62	41	7	to	to	ADP
ejpam-62	41	8	s.	s.	PROPN
ejpam-62	41	9	clearly	clearly	ADV
ejpam-62	41	10	,	,	PUNCT
ejpam-62	41	11	an	an	DET
ejpam-62	41	12	oriented	orient	VERB
ejpam-62	41	13	2	2	NUM
ejpam-62	41	14	-	-	PUNCT
ejpam-62	41	15	hypergraph	hypergraph	NOUN
ejpam-62	41	16	is	be	AUX
ejpam-62	41	17	simply	simply	ADV
ejpam-62	41	18	an	an	DET
ejpam-62	41	19	oriented	orient	VERB
ejpam-62	41	20	graph	graph	NOUN
ejpam-62	41	21	.	.	PUNCT
ejpam-62	42	1	let	let	VERB
ejpam-62	42	2	d	d	NOUN
ejpam-62	42	3	=	=	SYM
ejpam-62	42	4	(	(	PUNCT
ejpam-62	42	5	v	v	NOUN
ejpam-62	42	6	,	,	PUNCT
ejpam-62	42	7	a	a	PRON
ejpam-62	42	8	)	)	PUNCT
ejpam-62	42	9	denote	denote	NOUN
ejpam-62	42	10	an	an	DET
ejpam-62	42	11	oriented	oriented	ADJ
ejpam-62	42	12	k	k	NOUN
ejpam-62	42	13	-	-	NOUN
ejpam-62	42	14	hypergraph	hypergraph	VERB
ejpam-62	42	15	with	with	ADP
ejpam-62	42	16	n	n	CCONJ
ejpam-62	42	17	vertices	vertex	NOUN
ejpam-62	42	18	and	and	CCONJ
ejpam-62	42	19	let	let	VERB
ejpam-62	42	20	1	1	NUM
ejpam-62	42	21	<	<	X
ejpam-62	42	22	k	k	PROPN
ejpam-62	42	23	≤	≤	PROPN
ejpam-62	42	24	n.	n.	NOUN
ejpam-62	42	25	clearly	clearly	ADV
ejpam-62	42	26	,	,	PUNCT
ejpam-62	42	27	there	there	PRON
ejpam-62	42	28	can	can	AUX
ejpam-62	42	29	or	or	CCONJ
ejpam-62	42	30	can	can	AUX
ejpam-62	42	31	not	not	PART
ejpam-62	42	32	be	be	AUX
ejpam-62	42	33	an	an	DET
ejpam-62	42	34	arc	arc	NOUN
ejpam-62	42	35	among	among	ADP
ejpam-62	42	36	any	any	DET
ejpam-62	42	37	k	k	PROPN
ejpam-62	42	38	distinct	distinct	ADJ
ejpam-62	42	39	vertices	vertex	NOUN
ejpam-62	42	40	v1	v1	NOUN
ejpam-62	42	41	,	,	PUNCT
ejpam-62	42	42	v2	v2	PROPN
ejpam-62	42	43	,	,	PUNCT
ejpam-62	42	44	·	·	PUNCT
ejpam-62	42	45	·	·	PUNCT
ejpam-62	42	46	·	·	PUNCT
ejpam-62	42	47	,	,	PUNCT
ejpam-62	42	48	vk	vk	INTJ
ejpam-62	42	49	of	of	ADP
ejpam-62	42	50	v	v	NOUN
ejpam-62	42	51	.	.	PUNCT
ejpam-62	43	1	if	if	SCONJ
ejpam-62	43	2	there	there	PRON
ejpam-62	43	3	is	be	VERB
ejpam-62	43	4	an	an	DET
ejpam-62	43	5	arc	arc	NOUN
ejpam-62	43	6	among	among	ADP
ejpam-62	43	7	v1	v1	NOUN
ejpam-62	43	8	,	,	PUNCT
ejpam-62	43	9	v2	v2	PROPN
ejpam-62	43	10	,	,	PUNCT
ejpam-62	43	11	·	·	PUNCT
ejpam-62	43	12	·	·	PUNCT
ejpam-62	43	13	·	·	PUNCT
ejpam-62	43	14	,	,	PUNCT
ejpam-62	43	15	vk	vk	INTJ
ejpam-62	43	16	,	,	PUNCT
ejpam-62	43	17	we	we	PRON
ejpam-62	43	18	denote	denote	VERB
ejpam-62	43	19	it	it	PRON
ejpam-62	43	20	by	by	ADP
ejpam-62	43	21	e	e	X
ejpam-62	43	22	=	=	SYM
ejpam-62	43	23	(	(	PUNCT
ejpam-62	43	24	v1	v1	PROPN
ejpam-62	43	25	,	,	PUNCT
ejpam-62	43	26	v2	v2	PROPN
ejpam-62	43	27	,	,	PUNCT
ejpam-62	43	28	·	·	PUNCT
ejpam-62	43	29	·	·	PUNCT
ejpam-62	43	30	·	·	PUNCT
ejpam-62	43	31	,	,	PUNCT
ejpam-62	43	32	vk	vk	PROPN
ejpam-62	43	33	)	)	PUNCT
ejpam-62	43	34	and	and	CCONJ
ejpam-62	43	35	if	if	SCONJ
ejpam-62	43	36	there	there	PRON
ejpam-62	43	37	is	be	VERB
ejpam-62	43	38	not	not	PART
ejpam-62	43	39	an	an	DET
ejpam-62	43	40	arc	arc	NOUN
ejpam-62	43	41	among	among	ADP
ejpam-62	43	42	v1	v1	NOUN
ejpam-62	43	43	,	,	PUNCT
ejpam-62	43	44	v2	v2	PROPN
ejpam-62	43	45	,	,	PUNCT
ejpam-62	43	46	·	·	PUNCT
ejpam-62	43	47	·	·	PUNCT
ejpam-62	43	48	·	·	PUNCT
ejpam-62	43	49	,	,	PUNCT
ejpam-62	43	50	vk	vk	INTJ
ejpam-62	43	51	,	,	PUNCT
ejpam-62	43	52	it	it	PRON
ejpam-62	43	53	is	be	AUX
ejpam-62	43	54	denoted	denote	VERB
ejpam-62	43	55	by	by	ADP
ejpam-62	43	56	v1	v1	NOUN
ejpam-62	43	57	,	,	PUNCT
ejpam-62	43	58	v2	v2	PROPN
ejpam-62	43	59	,	,	PUNCT
ejpam-62	43	60	·	·	PUNCT
ejpam-62	43	61	·	·	PUNCT
ejpam-62	43	62	·	·	PUNCT
ejpam-62	43	63	,	,	PUNCT
ejpam-62	43	64	vk	vk	ADP
ejpam-62	43	65	�	�	PROPN
ejpam-62	43	66	,	,	PUNCT
ejpam-62	43	67	and	and	CCONJ
ejpam-62	43	68	we	we	PRON
ejpam-62	43	69	call	call	VERB
ejpam-62	43	70	it	it	PRON
ejpam-62	43	71	a	a	DET
ejpam-62	43	72	non	non	ADJ
ejpam-62	43	73	arc	arc	NOUN
ejpam-62	43	74	.	.	PUNCT
ejpam-62	44	1	we	we	PRON
ejpam-62	44	2	note	note	VERB
ejpam-62	44	3	that	that	SCONJ
ejpam-62	44	4	d	d	PROPN
ejpam-62	44	5	contains	contain	VERB
ejpam-62	44	6	at	at	ADP
ejpam-62	44	7	most	most	ADJ
ejpam-62	44	8	�	�	PROPN
ejpam-62	44	9	n	n	CCONJ
ejpam-62	44	10	k	k	PROPN
ejpam-62	44	11	�	�	PROPN
ejpam-62	44	12	arcs	arcs	PROPN
ejpam-62	44	13	,	,	PUNCT
ejpam-62	44	14	that	that	PRON
ejpam-62	44	15	is	be	AUX
ejpam-62	44	16	|a|	|a|	PROPN
ejpam-62	44	17	≤	≤	PROPN
ejpam-62	44	18	�	�	PROPN
ejpam-62	44	19	n	n	CCONJ
ejpam-62	44	20	k	k	PROPN
ejpam-62	44	21	�	�	PROPN
ejpam-62	44	22	,	,	PUNCT
ejpam-62	44	23	and	and	CCONJ
ejpam-62	44	24	a	a	DET
ejpam-62	44	25	vertex	vertex	NOUN
ejpam-62	44	26	vi	vi	NOUN
ejpam-62	44	27	in	in	ADP
ejpam-62	44	28	d	d	PROPN
ejpam-62	44	29	can	can	AUX
ejpam-62	44	30	be	be	AUX
ejpam-62	44	31	in	in	ADP
ejpam-62	44	32	at	at	ADP
ejpam-62	44	33	most	most	ADJ
ejpam-62	44	34	�	�	PROPN
ejpam-62	44	35	n−	n−	PROPN
ejpam-62	44	36	1	1	NUM
ejpam-62	44	37	k−	k−	PROPN
ejpam-62	44	38	1	1	NUM
ejpam-62	44	39	�	�	PROPN
ejpam-62	44	40	arcs	arc	NOUN
ejpam-62	44	41	.	.	PUNCT
ejpam-62	45	1	we	we	PRON
ejpam-62	45	2	denote	denote	VERB
ejpam-62	45	3	by	by	ADP
ejpam-62	45	4	d+(vi	d+(vi	PROPN
ejpam-62	45	5	)	)	PUNCT
ejpam-62	45	6	�	�	PROPN
ejpam-62	45	7	d−(vi	d−(vi	PROPN
ejpam-62	45	8	)	)	PUNCT
ejpam-62	45	9	�	�	PROPN
ejpam-62	45	10	,	,	PUNCT
ejpam-62	45	11	the	the	DET
ejpam-62	45	12	number	number	NOUN
ejpam-62	45	13	of	of	ADP
ejpam-62	45	14	arcs	arc	NOUN
ejpam-62	45	15	in	in	ADP
ejpam-62	45	16	which	which	PRON
ejpam-62	45	17	vi	vi	PROPN
ejpam-62	45	18	is	be	AUX
ejpam-62	45	19	not	not	PART
ejpam-62	45	20	the	the	DET
ejpam-62	45	21	last	last	ADJ
ejpam-62	45	22	element	element	NOUN
ejpam-62	45	23	(	(	PUNCT
ejpam-62	45	24	(	(	PUNCT
ejpam-62	45	25	vi	vi	X
ejpam-62	45	26	is	be	AUX
ejpam-62	45	27	the	the	DET
ejpam-62	45	28	last	last	ADJ
ejpam-62	45	29	element	element	NOUN
ejpam-62	45	30	)	)	PUNCT
ejpam-62	45	31	,	,	PUNCT
ejpam-62	45	32	furthermore	furthermore	ADV
ejpam-62	45	33	,	,	PUNCT
ejpam-62	45	34	we	we	PRON
ejpam-62	45	35	denote	denote	VERB
ejpam-62	45	36	by	by	ADP
ejpam-62	45	37	d+i	d+i	PROPN
ejpam-62	45	38	(	(	PUNCT
ejpam-62	45	39	u	u	NOUN
ejpam-62	45	40	)	)	PUNCT
ejpam-62	45	41	(	(	PUNCT
ejpam-62	45	42	d−i	d−i	X
ejpam-62	45	43	(	(	PUNCT
ejpam-62	45	44	u	u	NOUN
ejpam-62	45	45	)	)	PUNCT
ejpam-62	45	46	)	)	PUNCT
ejpam-62	46	1	the	the	DET
ejpam-62	46	2	number	number	NOUN
ejpam-62	46	3	of	of	ADP
ejpam-62	46	4	arcs	arc	NOUN
ejpam-62	46	5	that	that	PRON
ejpam-62	46	6	are	be	AUX
ejpam-62	46	7	contained	contain	VERB
ejpam-62	46	8	in	in	ADP
ejpam-62	46	9	u	u	NOUN
ejpam-62	46	10	and	and	CCONJ
ejpam-62	46	11	in	in	ADP
ejpam-62	46	12	which	which	PRON
ejpam-62	46	13	vi	vi	NOUN
ejpam-62	46	14	is	be	AUX
ejpam-62	46	15	not	not	PART
ejpam-62	46	16	the	the	DET
ejpam-62	46	17	last	last	ADJ
ejpam-62	46	18	element	element	NOUN
ejpam-62	46	19	(	(	PUNCT
ejpam-62	46	20	(	(	PUNCT
ejpam-62	46	21	vi	vi	X
ejpam-62	46	22	is	be	AUX
ejpam-62	46	23	the	the	DET
ejpam-62	46	24	last	last	ADJ
ejpam-62	46	25	element	element	NOUN
ejpam-62	46	26	)	)	PUNCT
ejpam-62	46	27	.	.	PUNCT
ejpam-62	47	1	now	now	ADV
ejpam-62	47	2	,	,	PUNCT
ejpam-62	47	3	let	let	VERB
ejpam-62	47	4	v1	v1	VERB
ejpam-62	47	5	=	=	SYM
ejpam-62	47	6	{	{	PUNCT
ejpam-62	47	7	v1	v1	PROPN
ejpam-62	47	8	,	,	PUNCT
ejpam-62	47	9	v2	v2	PROPN
ejpam-62	47	10	,	,	PUNCT
ejpam-62	47	11	·	·	PUNCT
ejpam-62	47	12	·	·	PUNCT
ejpam-62	47	13	·	·	PUNCT
ejpam-62	47	14	,	,	PUNCT
ejpam-62	47	15	v	v	X
ejpam-62	47	16	j	j	PROPN
ejpam-62	47	17	}	}	PUNCT
ejpam-62	47	18	⊂	⊂	PROPN
ejpam-62	47	19	v	v	NOUN
ejpam-62	47	20	and	and	CCONJ
ejpam-62	47	21	v2	v2	PROPN
ejpam-62	47	22	=	=	SYM
ejpam-62	47	23	v	v	ADJ
ejpam-62	47	24	−	−	PROPN
ejpam-62	47	25	v1	v1	NOUN
ejpam-62	47	26	.	.	PUNCT
ejpam-62	48	1	if	if	SCONJ
ejpam-62	48	2	q	q	NOUN
ejpam-62	48	3	is	be	AUX
ejpam-62	48	4	the	the	DET
ejpam-62	48	5	number	number	NOUN
ejpam-62	48	6	of	of	ADP
ejpam-62	48	7	those	those	DET
ejpam-62	48	8	arcs	arc	NOUN
ejpam-62	48	9	which	which	PRON
ejpam-62	48	10	contain	contain	VERB
ejpam-62	48	11	at	at	ADV
ejpam-62	48	12	least	least	ADV
ejpam-62	48	13	one	one	NUM
ejpam-62	48	14	vertex	vertex	NOUN
ejpam-62	48	15	from	from	ADP
ejpam-62	48	16	v1	v1	NOUN
ejpam-62	48	17	and	and	CCONJ
ejpam-62	48	18	at	at	ADV
ejpam-62	48	19	least	least	ADV
ejpam-62	48	20	one	one	NUM
ejpam-62	48	21	vertex	vertex	NOUN
ejpam-62	48	22	from	from	ADP
ejpam-62	48	23	v2	v2	PROPN
ejpam-62	48	24	,	,	PUNCT
ejpam-62	48	25	then	then	ADV
ejpam-62	48	26	q	q	PROPN
ejpam-62	48	27	≤	≤	PROPN
ejpam-62	48	28	k−1	k−1	PROPN
ejpam-62	48	29	∑	∑	PUNCT
ejpam-62	48	30	i=1	i=1	PROPN
ejpam-62	48	31	�	�	PROPN
ejpam-62	49	1	j	j	PROPN
ejpam-62	49	2	i	i	PROPN
ejpam-62	49	3	�	�	PROPN
ejpam-62	49	4	�	�	PROPN
ejpam-62	49	5	n−	n−	PROPN
ejpam-62	49	6	j	j	PROPN
ejpam-62	49	7	k−	k−	PROPN
ejpam-62	49	8	i	i	PRON
ejpam-62	49	9	�	�	PROPN
ejpam-62	49	10	.	.	PUNCT
ejpam-62	50	1	the	the	DET
ejpam-62	50	2	set	set	NOUN
ejpam-62	50	3	of	of	ADP
ejpam-62	50	4	those	those	DET
ejpam-62	50	5	arcs	arc	NOUN
ejpam-62	50	6	having	have	VERB
ejpam-62	50	7	at	at	ADV
ejpam-62	50	8	least	least	ADV
ejpam-62	50	9	one	one	NUM
ejpam-62	50	10	vertex	vertex	NOUN
ejpam-62	50	11	in	in	ADP
ejpam-62	50	12	v1	v1	NOUN
ejpam-62	50	13	and	and	CCONJ
ejpam-62	50	14	at	at	ADV
ejpam-62	50	15	least	least	ADV
ejpam-62	50	16	one	one	NUM
ejpam-62	50	17	vertex	vertex	NOUN
ejpam-62	50	18	in	in	ADP
ejpam-62	50	19	v2	v2	PROPN
ejpam-62	50	20	is	be	AUX
ejpam-62	50	21	denoted	denote	VERB
ejpam-62	50	22	by	by	ADP
ejpam-62	50	23	v1	v1	NOUN
ejpam-62	50	24	∗	∗	NOUN
ejpam-62	50	25	v2	v2	NOUN
ejpam-62	50	26	.	.	PUNCT
ejpam-62	51	1	let	let	AUX
ejpam-62	51	2	e	e	NOUN
ejpam-62	51	3	=	=	SYM
ejpam-62	51	4	(	(	PUNCT
ejpam-62	51	5	v1	v1	PROPN
ejpam-62	51	6	,	,	PUNCT
ejpam-62	51	7	v2	v2	PROPN
ejpam-62	51	8	,	,	PUNCT
ejpam-62	51	9	·	·	PUNCT
ejpam-62	51	10	·	·	PUNCT
ejpam-62	51	11	·	·	PUNCT
ejpam-62	51	12	,	,	PUNCT
ejpam-62	51	13	vk	vk	AUX
ejpam-62	51	14	)	)	PUNCT
ejpam-62	51	15	be	be	AUX
ejpam-62	51	16	an	an	DET
ejpam-62	51	17	arc	arc	NOUN
ejpam-62	51	18	in	in	ADP
ejpam-62	51	19	d	d	PROPN
ejpam-62	52	1	and	and	CCONJ
ejpam-62	52	2	i	i	PRON
ejpam-62	52	3	<	<	X
ejpam-62	52	4	j	j	PROPN
ejpam-62	52	5	≤	≤	PROPN
ejpam-62	52	6	k.	k.	PROPN
ejpam-62	52	7	we	we	PRON
ejpam-62	52	8	denote	denote	VERB
ejpam-62	52	9	by	by	ADP
ejpam-62	52	10	e(vi	e(vi	PROPN
ejpam-62	52	11	,	,	PUNCT
ejpam-62	52	12	v	v	PROPN
ejpam-62	52	13	j	j	NOUN
ejpam-62	52	14	)	)	PUNCT
ejpam-62	53	1	=	=	SYM
ejpam-62	53	2	(	(	PUNCT
ejpam-62	53	3	v1	v1	PROPN
ejpam-62	53	4	,	,	PUNCT
ejpam-62	53	5	·	·	PUNCT
ejpam-62	53	6	·	·	PUNCT
ejpam-62	53	7	·	·	PUNCT
ejpam-62	53	8	,	,	PUNCT
ejpam-62	53	9	vi−1	vi−1	PROPN
ejpam-62	53	10	,	,	PUNCT
ejpam-62	53	11	v	v	PROPN
ejpam-62	53	12	j	j	PROPN
ejpam-62	53	13	,	,	PUNCT
ejpam-62	53	14	vi+1	vi+1	PROPN
ejpam-62	53	15	,	,	PUNCT
ejpam-62	53	16	·	·	PUNCT
ejpam-62	53	17	·	·	PUNCT
ejpam-62	53	18	·	·	PUNCT
ejpam-62	53	19	,	,	PUNCT
ejpam-62	53	20	v	v	X
ejpam-62	53	21	j−1	j−1	PROPN
ejpam-62	53	22	,	,	PUNCT
ejpam-62	53	23	vi	vi	PROPN
ejpam-62	53	24	,	,	PUNCT
ejpam-62	53	25	v	v	ADP
ejpam-62	53	26	j+1	j+1	NUM
ejpam-62	53	27	,	,	PUNCT
ejpam-62	53	28	·	·	PUNCT
ejpam-62	53	29	·	·	PUNCT
ejpam-62	53	30	·	·	PUNCT
ejpam-62	53	31	,	,	PUNCT
ejpam-62	53	32	vk	vk	PROPN
ejpam-62	53	33	)	)	PUNCT
ejpam-62	53	34	,	,	PUNCT
ejpam-62	53	35	that	that	ADV
ejpam-62	53	36	is	is	ADV
ejpam-62	53	37	,	,	PUNCT
ejpam-62	53	38	the	the	DET
ejpam-62	53	39	new	new	ADJ
ejpam-62	53	40	arc	arc	NOUN
ejpam-62	53	41	obtained	obtain	VERB
ejpam-62	53	42	from	from	ADP
ejpam-62	53	43	e	e	NOUN
ejpam-62	53	44	by	by	ADP
ejpam-62	53	45	interchanging	interchange	VERB
ejpam-62	53	46	vi	vi	PROPN
ejpam-62	53	47	and	and	CCONJ
ejpam-62	53	48	v	v	ADP
ejpam-62	53	49	j	j	PROPN
ejpam-62	53	50	in	in	ADP
ejpam-62	53	51	e.	e.	PROPN
ejpam-62	53	52	similarly	similarly	ADV
ejpam-62	53	53	,	,	PUNCT
ejpam-62	53	54	we	we	PRON
ejpam-62	53	55	denote	denote	VERB
ejpam-62	53	56	by	by	ADP
ejpam-62	53	57	f	f	PROPN
ejpam-62	53	58	¬	¬	PROPN
ejpam-62	53	59	vi	vi	PROPN
ejpam-62	53	60	,	,	PUNCT
ejpam-62	53	61	v	v	PROPN
ejpam-62	53	62	j	j	PROPN
ejpam-62	53	63	¶	¶	PROPN
ejpam-62	53	64	the	the	DET
ejpam-62	53	65	new	new	ADJ
ejpam-62	53	66	non	non	ADJ
ejpam-62	53	67	arc	arc	NOUN
ejpam-62	53	68	obtained	obtain	VERB
ejpam-62	53	69	from	from	ADP
ejpam-62	53	70	the	the	DET
ejpam-62	53	71	non	non	PROPN
ejpam-62	53	72	arc	arc	NOUN
ejpam-62	53	73	f	f	PROPN
ejpam-62	53	74	=	=	PUNCT
ejpam-62	53	75	¬	¬	PROPN
ejpam-62	53	76	v1	v1	PROPN
ejpam-62	53	77	,	,	PUNCT
ejpam-62	53	78	v2	v2	PROPN
ejpam-62	53	79	,	,	PUNCT
ejpam-62	53	80	·	·	PUNCT
ejpam-62	53	81	·	·	PUNCT
ejpam-62	53	82	·	·	PUNCT
ejpam-62	53	83	,	,	PUNCT
ejpam-62	53	84	v	v	X
ejpam-62	53	85	j	j	PROPN
ejpam-62	53	86	¶	¶	ADV
ejpam-62	53	87	by	by	ADP
ejpam-62	53	88	interchanging	interchanging	PROPN
ejpam-62	53	89	vi	vi	PROPN
ejpam-62	53	90	and	and	CCONJ
ejpam-62	53	91	v	v	ADP
ejpam-62	53	92	j	j	PROPN
ejpam-62	53	93	in	in	ADP
ejpam-62	53	94	f	f	PROPN
ejpam-62	53	95	.	.	PUNCT
ejpam-62	54	1	define	define	VERB
ejpam-62	54	2	the	the	DET
ejpam-62	54	3	score	score	NOUN
ejpam-62	54	4	s(vi	s(vi	NOUN
ejpam-62	54	5	)	)	PUNCT
ejpam-62	54	6	or	or	CCONJ
ejpam-62	54	7	si	si	X
ejpam-62	54	8	of	of	ADP
ejpam-62	54	9	a	a	DET
ejpam-62	54	10	vertex	vertex	NOUN
ejpam-62	54	11	vi	vi	NOUN
ejpam-62	54	12	in	in	ADP
ejpam-62	54	13	oriented	orient	VERB
ejpam-62	54	14	k	k	NOUN
ejpam-62	54	15	-	-	ADJ
ejpam-62	54	16	hypergraph	hypergraph	ADJ
ejpam-62	54	17	d	d	NOUN
ejpam-62	54	18	as	as	ADP
ejpam-62	54	19	s(vi	s(vi	NOUN
ejpam-62	54	20	)	)	PUNCT
ejpam-62	54	21	=	=	SYM
ejpam-62	54	22	(	(	PUNCT
ejpam-62	54	23	k−	k−	NOUN
ejpam-62	54	24	1	1	NUM
ejpam-62	54	25	)	)	PUNCT
ejpam-62	54	26	�	�	PROPN
ejpam-62	54	27	n−	n−	NOUN
ejpam-62	54	28	1	1	NUM
ejpam-62	54	29	k−	k−	PROPN
ejpam-62	54	30	1	1	NUM
ejpam-62	54	31	�	�	PROPN
ejpam-62	54	32	+	+	NUM
ejpam-62	54	33	d+(vi)−	d+(vi)−	PROPN
ejpam-62	54	34	(	(	PUNCT
ejpam-62	54	35	k−	k−	NOUN
ejpam-62	54	36	1)d−(vi	1)d−(vi	NUM
ejpam-62	54	37	)	)	PUNCT
ejpam-62	54	38	.	.	PUNCT
ejpam-62	55	1	clearly	clearly	ADV
ejpam-62	55	2	,	,	PUNCT
ejpam-62	55	3	0	0	NUM
ejpam-62	55	4	≤	≤	NUM
ejpam-62	55	5	si	si	NOUN
ejpam-62	55	6	≤	≤	PROPN
ejpam-62	55	7	k	k	PROPN
ejpam-62	55	8	�	�	PROPN
ejpam-62	55	9	n−	n−	PROPN
ejpam-62	55	10	1	1	NUM
ejpam-62	55	11	k−	k−	PROPN
ejpam-62	55	12	1	1	NUM
ejpam-62	55	13	�	�	PROPN
ejpam-62	55	14	.	.	PUNCT
ejpam-62	56	1	the	the	DET
ejpam-62	56	2	score	score	NOUN
ejpam-62	56	3	sequence	sequence	NOUN
ejpam-62	56	4	s	s	PART
ejpam-62	56	5	=	=	PUNCT
ejpam-62	57	1	[	[	X
ejpam-62	57	2	s1	s1	NOUN
ejpam-62	57	3	,	,	PUNCT
ejpam-62	57	4	s2	s2	PROPN
ejpam-62	57	5	,	,	PUNCT
ejpam-62	57	6	·	·	PUNCT
ejpam-62	57	7	·	·	PUNCT
ejpam-62	57	8	·	·	PUNCT
ejpam-62	57	9	,	,	PUNCT
ejpam-62	57	10	sn	sn	PROPN
ejpam-62	57	11	]	]	PUNCT
ejpam-62	57	12	of	of	ADP
ejpam-62	57	13	d	d	PROPN
ejpam-62	57	14	is	be	AUX
ejpam-62	57	15	formed	form	VERB
ejpam-62	57	16	by	by	ADP
ejpam-62	57	17	listing	list	VERB
ejpam-62	57	18	the	the	DET
ejpam-62	57	19	scores	score	NOUN
ejpam-62	57	20	in	in	ADP
ejpam-62	57	21	non	non	ADJ
ejpam-62	57	22	-	-	ADJ
ejpam-62	57	23	decreasing	decrease	VERB
ejpam-62	57	24	order	order	NOUN
ejpam-62	57	25	.	.	PUNCT
ejpam-62	58	1	let	let	VERB
ejpam-62	59	1	r	r	NOUN
ejpam-62	59	2	=	=	PUNCT
ejpam-62	60	1	[	[	X
ejpam-62	60	2	s1	s1	NOUN
ejpam-62	60	3	,	,	PUNCT
ejpam-62	60	4	s2	s2	PROPN
ejpam-62	60	5	,	,	PUNCT
ejpam-62	60	6	·	·	PUNCT
ejpam-62	60	7	·	·	PUNCT
ejpam-62	60	8	·	·	PUNCT
ejpam-62	60	9	,	,	PUNCT
ejpam-62	60	10	sn	sn	PROPN
ejpam-62	60	11	]	]	PUNCT
ejpam-62	60	12	be	be	AUX
ejpam-62	60	13	an	an	DET
ejpam-62	60	14	integer	integer	NOUN
ejpam-62	60	15	sequence	sequence	NOUN
ejpam-62	60	16	.	.	PUNCT
ejpam-62	61	1	for	for	ADP
ejpam-62	61	2	1	1	NUM
ejpam-62	61	3	≤	≤	NUM
ejpam-62	62	1	i	i	PRON
ejpam-62	62	2	<	<	X
ejpam-62	62	3	j	j	PROPN
ejpam-62	62	4	≤	≤	NUM
ejpam-62	62	5	n	n	CCONJ
ejpam-62	62	6	,	,	PUNCT
ejpam-62	62	7	we	we	PRON
ejpam-62	62	8	define	define	VERB
ejpam-62	62	9	s(s+i	s(s+i	PUNCT
ejpam-62	62	10	,	,	PUNCT
ejpam-62	62	11	s−j	s−j	ADJ
ejpam-62	62	12	)	)	PUNCT
ejpam-62	62	13	=	=	PUNCT
ejpam-62	63	1	[	[	X
ejpam-62	63	2	s1	s1	NOUN
ejpam-62	63	3	,	,	PUNCT
ejpam-62	63	4	s2	s2	PROPN
ejpam-62	63	5	,	,	PUNCT
ejpam-62	63	6	·	·	PUNCT
ejpam-62	63	7	·	·	PUNCT
ejpam-62	63	8	·	·	PUNCT
ejpam-62	63	9	,	,	PUNCT
ejpam-62	63	10	si	si	PROPN
ejpam-62	64	1	+	+	CCONJ
ejpam-62	64	2	1	1	NUM
ejpam-62	64	3	,	,	PUNCT
ejpam-62	64	4	·	·	PUNCT
ejpam-62	64	5	·	·	PUNCT
ejpam-62	64	6	·	·	PUNCT
ejpam-62	64	7	,	,	PUNCT
ejpam-62	64	8	s	s	X
ejpam-62	64	9	j	j	PROPN
ejpam-62	64	10	−	−	PROPN
ejpam-62	64	11	1	1	NUM
ejpam-62	64	12	,	,	PUNCT
ejpam-62	64	13	·	·	PUNCT
ejpam-62	64	14	·	·	PUNCT
ejpam-62	64	15	·	·	PUNCT
ejpam-62	64	16	,	,	PUNCT
ejpam-62	64	17	sn	sn	PROPN
ejpam-62	64	18	]	]	PUNCT
ejpam-62	64	19	,	,	PUNCT
ejpam-62	64	20	and	and	CCONJ
ejpam-62	64	21	s+(s+i	s+(s+i	NOUN
ejpam-62	64	22	,	,	PUNCT
ejpam-62	64	23	s−j	s−j	ADJ
ejpam-62	64	24	)	)	PUNCT
ejpam-62	64	25	=	=	PUNCT
ejpam-62	65	1	(	(	PUNCT
ejpam-62	65	2	s	s	NOUN
ejpam-62	65	3	′	′	NUM
ejpam-62	65	4	1	1	NUM
ejpam-62	65	5	,	,	PUNCT
ejpam-62	65	6	s′2	s′2	NOUN
ejpam-62	65	7	,	,	PUNCT
ejpam-62	65	8	·	·	PUNCT
ejpam-62	65	9	·	·	PUNCT
ejpam-62	65	10	·	·	PUNCT
ejpam-62	65	11	,	,	PUNCT
ejpam-62	65	12	s′n	s′n	NUM
ejpam-62	65	13	)	)	PUNCT
ejpam-62	65	14	denotes	denote	VERB
ejpam-62	65	15	an	an	DET
ejpam-62	65	16	arrangement	arrangement	NOUN
ejpam-62	65	17	of	of	ADP
ejpam-62	65	18	s(s+i	s(s+i	PROPN
ejpam-62	65	19	,	,	PUNCT
ejpam-62	65	20	s−j	s−j	PROPN
ejpam-62	65	21	)	)	PUNCT
ejpam-62	65	22	such	such	ADJ
ejpam-62	65	23	that	that	PRON
ejpam-62	65	24	s′1	s′1	VERB
ejpam-62	65	25	≤	≤	ADJ
ejpam-62	65	26	s′2	s′2	NOUN
ejpam-62	65	27	≤	≤	NOUN
ejpam-62	65	28	·	·	PUNCT
ejpam-62	65	29	·	·	PUNCT
ejpam-62	65	30	·	·	PUNCT
ejpam-62	66	1	≤	≤	NUM
ejpam-62	66	2	s′n	s′n	X
ejpam-62	66	3	.	.	PUNCT
ejpam-62	67	1	let	let	VERB
ejpam-62	67	2	s	s	PRON
ejpam-62	67	3	=	=	PUNCT
ejpam-62	68	1	[	[	X
ejpam-62	68	2	s1	s1	NOUN
ejpam-62	68	3	,	,	PUNCT
ejpam-62	68	4	s2	s2	PROPN
ejpam-62	68	5	,	,	PUNCT
ejpam-62	68	6	·	·	PUNCT
ejpam-62	68	7	·	·	PUNCT
ejpam-62	68	8	·	·	PUNCT
ejpam-62	68	9	,	,	PUNCT
ejpam-62	68	10	sn	sn	PROPN
ejpam-62	68	11	]	]	PUNCT
ejpam-62	68	12	be	be	VERB
ejpam-62	68	13	a	a	DET
ejpam-62	68	14	non	non	ADJ
ejpam-62	68	15	-	-	ADJ
ejpam-62	68	16	decreasing	decrease	VERB
ejpam-62	68	17	sequence	sequence	NOUN
ejpam-62	68	18	of	of	ADP
ejpam-62	68	19	non	non	ADJ
ejpam-62	68	20	-	-	ADJ
ejpam-62	68	21	negative	negative	ADJ
ejpam-62	68	22	integers	integer	NOUN
ejpam-62	68	23	with	with	ADP
ejpam-62	68	24	each	each	DET
ejpam-62	68	25	si	si	X
ejpam-62	68	26	having	have	VERB
ejpam-62	68	27	the	the	DET
ejpam-62	68	28	form	form	NOUN
ejpam-62	68	29	si	si	NOUN
ejpam-62	68	30	=	=	NOUN
ejpam-62	68	31	x	x	SYM
ejpam-62	68	32	ik+	ik+	ADJ
ejpam-62	68	33	yi(k−	yi(k−	NOUN
ejpam-62	68	34	1	1	NUM
ejpam-62	68	35	)	)	PUNCT
ejpam-62	68	36	,	,	PUNCT
ejpam-62	68	37	where	where	SCONJ
ejpam-62	68	38	x	x	PUNCT
ejpam-62	68	39	i	i	PRON
ejpam-62	68	40	and	and	CCONJ
ejpam-62	68	41	yi	yi	PROPN
ejpam-62	68	42	are	be	AUX
ejpam-62	68	43	nonnegative	nonnegative	ADJ
ejpam-62	68	44	integers	integer	NOUN
ejpam-62	68	45	and	and	CCONJ
ejpam-62	68	46	satisfy	satisfy	VERB
ejpam-62	68	47	0≤	0≤	NUM
ejpam-62	69	1	x	x	VERB
ejpam-62	69	2	i	i	PRON
ejpam-62	69	3	,	,	PUNCT
ejpam-62	69	4	yi	yi	PROPN
ejpam-62	69	5	≤	≤	PROPN
ejpam-62	69	6	�	�	PROPN
ejpam-62	69	7	n−	n−	PROPN
ejpam-62	69	8	1	1	NUM
ejpam-62	69	9	k−	k−	PROPN
ejpam-62	69	10	1	1	NUM
ejpam-62	69	11	�	�	PROPN
ejpam-62	69	12	,	,	PUNCT
ejpam-62	69	13	s	s	VERB
ejpam-62	69	14	is	be	AUX
ejpam-62	69	15	called	call	VERB
ejpam-62	69	16	to	to	PART
ejpam-62	69	17	be	be	AUX
ejpam-62	69	18	strict	strict	ADJ
ejpam-62	69	19	if	if	SCONJ
ejpam-62	69	20	for	for	ADP
ejpam-62	69	21	all	all	DET
ejpam-62	69	22	si	si	X
ejpam-62	69	23	<	<	X
ejpam-62	69	24	s	s	X
ejpam-62	69	25	j	j	PROPN
ejpam-62	69	26	,	,	PUNCT
ejpam-62	69	27	we	we	PRON
ejpam-62	69	28	have	have	VERB
ejpam-62	69	29	yi	yi	VERB
ejpam-62	69	30	>	>	PUNCT
ejpam-62	69	31	y	y	PROPN
ejpam-62	69	32	j	j	PROPN
ejpam-62	69	33	.	.	PUNCT
ejpam-62	70	1	2	2	X
ejpam-62	70	2	.	.	X
ejpam-62	70	3	main	main	ADJ
ejpam-62	70	4	results	result	NOUN
ejpam-62	70	5	our	our	PRON
ejpam-62	70	6	main	main	ADJ
ejpam-62	70	7	result	result	NOUN
ejpam-62	70	8	is	be	AUX
ejpam-62	70	9	the	the	DET
ejpam-62	70	10	following	follow	VERB
ejpam-62	70	11	theorem	theorem	VERB
ejpam-62	70	12	.	.	PUNCT
ejpam-62	71	1	s.	s.	PROPN
ejpam-62	71	2	pirzada	pirzada	PROPN
ejpam-62	71	3	,	,	PUNCT
ejpam-62	71	4	z.	z.	PROPN
ejpam-62	71	5	guofei	guofei	PROPN
ejpam-62	71	6	/	/	SYM
ejpam-62	71	7	eur	eur	PROPN
ejpam-62	71	8	.	.	PUNCT
ejpam-62	72	1	j.	j.	PROPN
ejpam-62	72	2	pure	pure	PROPN
ejpam-62	72	3	appl	appl	PROPN
ejpam-62	72	4	.	.	PROPN
ejpam-62	72	5	math	math	PROPN
ejpam-62	72	6	,	,	PUNCT
ejpam-62	72	7	1	1	NUM
ejpam-62	72	8	(	(	PUNCT
ejpam-62	72	9	2008	2008	NUM
ejpam-62	72	10	)	)	PUNCT
ejpam-62	72	11	,	,	PUNCT
ejpam-62	72	12	(	(	PUNCT
ejpam-62	72	13	10	10	NUM
ejpam-62	72	14	-	-	SYM
ejpam-62	72	15	20	20	NUM
ejpam-62	72	16	)	)	PUNCT
ejpam-62	72	17	13	13	NUM
ejpam-62	72	18	theorem	theorem	VERB
ejpam-62	72	19	2.1	2.1	NUM
ejpam-62	72	20	.	.	PUNCT
ejpam-62	73	1	given	give	VERB
ejpam-62	73	2	two	two	NUM
ejpam-62	73	3	non	non	ADJ
ejpam-62	73	4	-	-	ADJ
ejpam-62	73	5	negative	negative	ADJ
ejpam-62	73	6	integers	integer	NOUN
ejpam-62	73	7	n	n	PRON
ejpam-62	73	8	and	and	CCONJ
ejpam-62	73	9	k	k	X
ejpam-62	73	10	with	with	ADP
ejpam-62	73	11	n≥	n≥	PROPN
ejpam-62	73	12	k	k	X
ejpam-62	73	13	>	>	X
ejpam-62	73	14	1	1	NUM
ejpam-62	73	15	,	,	PUNCT
ejpam-62	73	16	a	a	DET
ejpam-62	73	17	non	non	ADJ
ejpam-62	73	18	-	-	ADJ
ejpam-62	73	19	decreasing	decrease	VERB
ejpam-62	73	20	strict	strict	ADJ
ejpam-62	73	21	sequence	sequence	NOUN
ejpam-62	73	22	s	s	PART
ejpam-62	73	23	=	=	PUNCT
ejpam-62	74	1	[	[	X
ejpam-62	74	2	s1	s1	NOUN
ejpam-62	74	3	,	,	PUNCT
ejpam-62	74	4	s2	s2	PROPN
ejpam-62	74	5	,	,	PUNCT
ejpam-62	74	6	·	·	PUNCT
ejpam-62	74	7	·	·	PUNCT
ejpam-62	74	8	·	·	PUNCT
ejpam-62	74	9	,	,	PUNCT
ejpam-62	74	10	sn	sn	PROPN
ejpam-62	74	11	]	]	PUNCT
ejpam-62	74	12	of	of	ADP
ejpam-62	74	13	non	non	ADJ
ejpam-62	74	14	-	-	ADJ
ejpam-62	74	15	negative	negative	ADJ
ejpam-62	74	16	integers	integer	NOUN
ejpam-62	74	17	with	with	ADP
ejpam-62	74	18	si	si	NOUN
ejpam-62	74	19	=	=	SYM
ejpam-62	74	20	x	x	X
ejpam-62	74	21	ik	ik	PROPN
ejpam-62	74	22	+	+	CCONJ
ejpam-62	74	23	yi(k	yi(k	NUM
ejpam-62	74	24	−	−	PROPN
ejpam-62	74	25	1	1	NUM
ejpam-62	74	26	)	)	PUNCT
ejpam-62	74	27	,	,	PUNCT
ejpam-62	74	28	where	where	SCONJ
ejpam-62	74	29	x	x	X
ejpam-62	74	30	i	i	PRON
ejpam-62	74	31	,	,	PUNCT
ejpam-62	74	32	yi	yi	PROPN
ejpam-62	74	33	are	be	AUX
ejpam-62	74	34	nonnegative	nonnegative	ADJ
ejpam-62	74	35	integers	integer	NOUN
ejpam-62	74	36	and	and	CCONJ
ejpam-62	74	37	satisfies	satisfie	NOUN
ejpam-62	74	38	0	0	NUM
ejpam-62	74	39	≤	≤	NUM
ejpam-62	75	1	x	x	X
ejpam-62	76	1	i	i	PRON
ejpam-62	76	2	,	,	PUNCT
ejpam-62	76	3	yi	yi	PROPN
ejpam-62	76	4	≤	≤	PROPN
ejpam-62	76	5	�	�	PROPN
ejpam-62	76	6	n−	n−	PROPN
ejpam-62	76	7	1	1	NUM
ejpam-62	76	8	k−	k−	PROPN
ejpam-62	76	9	1	1	NUM
ejpam-62	76	10	�	�	PROPN
ejpam-62	76	11	,	,	PUNCT
ejpam-62	76	12	is	be	AUX
ejpam-62	76	13	a	a	DET
ejpam-62	76	14	score	score	NOUN
ejpam-62	76	15	sequence	sequence	NOUN
ejpam-62	76	16	of	of	ADP
ejpam-62	76	17	some	some	PRON
ejpam-62	76	18	oriented	orient	VERB
ejpam-62	76	19	k	k	NOUN
ejpam-62	76	20	-	-	NOUN
ejpam-62	76	21	hypergraph	hypergraph	VERB
ejpam-62	76	22	if	if	SCONJ
ejpam-62	77	1	and	and	CCONJ
ejpam-62	77	2	only	only	ADV
ejpam-62	77	3	if	if	SCONJ
ejpam-62	77	4	j	j	PROPN
ejpam-62	77	5	∑	∑	PROPN
ejpam-62	77	6	i=1	i=1	PROPN
ejpam-62	77	7	si	si	PROPN
ejpam-62	77	8	≥	≥	X
ejpam-62	77	9	j(k−	j(k−	NOUN
ejpam-62	77	10	1	1	NUM
ejpam-62	77	11	)	)	PUNCT
ejpam-62	77	12	�	�	PROPN
ejpam-62	77	13	n−	n−	NOUN
ejpam-62	77	14	1	1	NUM
ejpam-62	77	15	k−	k−	PROPN
ejpam-62	77	16	1	1	NUM
ejpam-62	77	17	�	�	PROPN
ejpam-62	77	18	+	+	CCONJ
ejpam-62	77	19	k−1	k−1	PROPN
ejpam-62	77	20	∑	∑	PROPN
ejpam-62	77	21	i=1	i=1	PROPN
ejpam-62	77	22	(	(	PUNCT
ejpam-62	77	23	i−	i−	PROPN
ejpam-62	77	24	k	k	PROPN
ejpam-62	77	25	)	)	PUNCT
ejpam-62	77	26	�	�	PROPN
ejpam-62	78	1	j	j	PROPN
ejpam-62	78	2	i	i	PROPN
ejpam-62	78	3	�	�	VERB
ejpam-62	78	4	�	�	PROPN
ejpam-62	78	5	n−	n−	PROPN
ejpam-62	78	6	j	j	PROPN
ejpam-62	78	7	k−	k−	PROPN
ejpam-62	78	8	i	i	PRON
ejpam-62	78	9	�	�	PROPN
ejpam-62	78	10	(	(	PUNCT
ejpam-62	78	11	2.1	2.1	NUM
ejpam-62	78	12	)	)	PUNCT
ejpam-62	78	13	with	with	ADP
ejpam-62	78	14	equality	equality	NOUN
ejpam-62	78	15	for	for	ADP
ejpam-62	78	16	j	j	PROPN
ejpam-62	78	17	=	=	SYM
ejpam-62	78	18	n.	n.	PROPN
ejpam-62	78	19	in	in	ADP
ejpam-62	78	20	order	order	NOUN
ejpam-62	78	21	to	to	PART
ejpam-62	78	22	prove	prove	VERB
ejpam-62	78	23	this	this	DET
ejpam-62	78	24	theorem	theorem	NOUN
ejpam-62	78	25	,	,	PUNCT
ejpam-62	78	26	we	we	PRON
ejpam-62	78	27	need	need	VERB
ejpam-62	78	28	some	some	DET
ejpam-62	78	29	lemmas	lemma	NOUN
ejpam-62	78	30	.	.	PUNCT
ejpam-62	79	1	lemma	lemma	PROPN
ejpam-62	79	2	2.1	2.1	NUM
ejpam-62	79	3	.	.	PUNCT
ejpam-62	80	1	if	if	SCONJ
ejpam-62	80	2	d	d	PROPN
ejpam-62	80	3	is	be	AUX
ejpam-62	80	4	an	an	DET
ejpam-62	80	5	oriented	oriented	ADJ
ejpam-62	80	6	k	k	NOUN
ejpam-62	80	7	-	-	NOUN
ejpam-62	80	8	hypergraph	hypergraph	NOUN
ejpam-62	80	9	of	of	ADP
ejpam-62	80	10	order	order	NOUN
ejpam-62	80	11	n	n	CCONJ
ejpam-62	80	12	,	,	PUNCT
ejpam-62	80	13	then	then	ADV
ejpam-62	80	14	s(vi	s(vi	NUM
ejpam-62	80	15	)	)	PUNCT
ejpam-62	80	16	=	=	SYM
ejpam-62	80	17	xk+	xk+	PROPN
ejpam-62	80	18	y(k−1	y(k−1	PROPN
ejpam-62	80	19	)	)	PUNCT
ejpam-62	80	20	,	,	PUNCT
ejpam-62	80	21	where	where	SCONJ
ejpam-62	80	22	x	x	PRON
ejpam-62	80	23	and	and	CCONJ
ejpam-62	80	24	y	y	PROPN
ejpam-62	80	25	are	be	AUX
ejpam-62	80	26	non	non	ADJ
ejpam-62	80	27	-	-	ADJ
ejpam-62	80	28	negative	negative	ADJ
ejpam-62	80	29	integers	integer	NOUN
ejpam-62	80	30	.	.	PUNCT
ejpam-62	81	1	proof	proof	NOUN
ejpam-62	81	2	.	.	PUNCT
ejpam-62	82	1	let	let	VERB
ejpam-62	82	2	d∗(vi	d∗(vi	PROPN
ejpam-62	82	3	)	)	PUNCT
ejpam-62	82	4	be	be	AUX
ejpam-62	82	5	the	the	DET
ejpam-62	82	6	number	number	NOUN
ejpam-62	82	7	of	of	ADP
ejpam-62	82	8	non	non	ADJ
ejpam-62	82	9	arcs	arc	NOUN
ejpam-62	82	10	in	in	ADP
ejpam-62	82	11	which	which	PRON
ejpam-62	82	12	vertex	vertex	NOUN
ejpam-62	82	13	vi	vi	PROPN
ejpam-62	82	14	is	be	AUX
ejpam-62	82	15	contained	contain	VERB
ejpam-62	82	16	.	.	PUNCT
ejpam-62	83	1	then	then	ADV
ejpam-62	83	2	,	,	PUNCT
ejpam-62	83	3	d+(vi	d+(vi	ADJ
ejpam-62	83	4	)	)	PUNCT
ejpam-62	83	5	+	+	X
ejpam-62	83	6	d−(vi	d−(vi	PROPN
ejpam-62	83	7	)	)	PUNCT
ejpam-62	83	8	+	+	CCONJ
ejpam-62	83	9	d∗(vi	d∗(vi	PROPN
ejpam-62	83	10	)	)	PUNCT
ejpam-62	83	11	=	=	PUNCT
ejpam-62	83	12	�	�	PROPN
ejpam-62	83	13	n−	n−	PROPN
ejpam-62	83	14	1	1	NUM
ejpam-62	83	15	k−	k−	PROPN
ejpam-62	83	16	1	1	NUM
ejpam-62	83	17	�	�	PROPN
ejpam-62	83	18	,	,	PUNCT
ejpam-62	83	19	or	or	CCONJ
ejpam-62	83	20	d−(vi	d−(vi	PROPN
ejpam-62	83	21	)	)	PUNCT
ejpam-62	83	22	=	=	PUNCT
ejpam-62	83	23	�	�	PROPN
ejpam-62	83	24	n−	n−	PROPN
ejpam-62	83	25	1	1	NUM
ejpam-62	83	26	k−	k−	PROPN
ejpam-62	83	27	1	1	NUM
ejpam-62	83	28	�	�	PROPN
ejpam-62	83	29	−	−	PROPN
ejpam-62	83	30	d+(vi)−	d+(vi)−	ADJ
ejpam-62	83	31	d∗(vi	d∗(vi	PROPN
ejpam-62	83	32	)	)	PUNCT
ejpam-62	83	33	.	.	PUNCT
ejpam-62	84	1	therefore	therefore	ADV
ejpam-62	84	2	,	,	PUNCT
ejpam-62	84	3	s(vi	s(vi	PROPN
ejpam-62	84	4	)	)	PUNCT
ejpam-62	84	5	=	=	SYM
ejpam-62	84	6	(	(	PUNCT
ejpam-62	84	7	k−	k−	NOUN
ejpam-62	84	8	1	1	NUM
ejpam-62	84	9	)	)	PUNCT
ejpam-62	84	10	�	�	PROPN
ejpam-62	84	11	n−	n−	NOUN
ejpam-62	84	12	1	1	NUM
ejpam-62	84	13	k−	k−	PROPN
ejpam-62	84	14	1	1	NUM
ejpam-62	84	15	�	�	PROPN
ejpam-62	84	16	+	+	NUM
ejpam-62	84	17	d+(vi)−	d+(vi)−	PROPN
ejpam-62	84	18	(	(	PUNCT
ejpam-62	84	19	k−	k−	NOUN
ejpam-62	84	20	1)d−(vi	1)d−(vi	NUM
ejpam-62	84	21	)	)	PUNCT
ejpam-62	84	22	gives	give	VERB
ejpam-62	84	23	s(vi	s(vi	NOUN
ejpam-62	84	24	)	)	PUNCT
ejpam-62	85	1	=	=	SYM
ejpam-62	85	2	(	(	PUNCT
ejpam-62	85	3	k−	k−	NOUN
ejpam-62	85	4	1	1	NUM
ejpam-62	85	5	)	)	PUNCT
ejpam-62	85	6	�	�	PROPN
ejpam-62	85	7	n−	n−	NOUN
ejpam-62	85	8	1	1	NUM
ejpam-62	85	9	k−	k−	PROPN
ejpam-62	85	10	1	1	NUM
ejpam-62	85	11	�	�	PROPN
ejpam-62	85	12	+	+	NUM
ejpam-62	85	13	d+(vi)−	d+(vi)−	PROPN
ejpam-62	85	14	(	(	PUNCT
ejpam-62	85	15	k−	k−	NOUN
ejpam-62	85	16	1	1	NUM
ejpam-62	85	17	)	)	PUNCT
ejpam-62	85	18	�	�	PROPN
ejpam-62	85	19	�	�	PROPN
ejpam-62	85	20	n−	n−	PROPN
ejpam-62	85	21	1	1	NUM
ejpam-62	85	22	k−	k−	PROPN
ejpam-62	85	23	1	1	NUM
ejpam-62	85	24	�	�	PROPN
ejpam-62	85	25	−	−	PROPN
ejpam-62	85	26	d+(vi)−	d+(vi)−	PROPN
ejpam-62	85	27	d∗(vi	d∗(vi	PROPN
ejpam-62	85	28	)	)	PUNCT
ejpam-62	85	29	�	�	PROPN
ejpam-62	85	30	=	=	SYM
ejpam-62	85	31	kd+(vi	kd+(vi	PROPN
ejpam-62	85	32	)	)	PUNCT
ejpam-62	85	33	+	+	CCONJ
ejpam-62	85	34	(	(	PUNCT
ejpam-62	85	35	k−	k−	PROPN
ejpam-62	85	36	1)d∗(vi	1)d∗(vi	NUM
ejpam-62	85	37	)	)	PUNCT
ejpam-62	85	38	as	as	ADP
ejpam-62	85	39	d+(vi	d+(vi	NOUN
ejpam-62	85	40	)	)	PUNCT
ejpam-62	85	41	and	and	CCONJ
ejpam-62	85	42	d∗(vi	d∗(vi	PROPN
ejpam-62	85	43	)	)	PUNCT
ejpam-62	85	44	are	be	AUX
ejpam-62	85	45	non	non	ADJ
ejpam-62	85	46	-	-	ADJ
ejpam-62	85	47	negative	negative	ADJ
ejpam-62	85	48	integers	integer	NOUN
ejpam-62	85	49	,	,	PUNCT
ejpam-62	85	50	the	the	DET
ejpam-62	85	51	proof	proof	NOUN
ejpam-62	85	52	follows	follow	VERB
ejpam-62	85	53	.	.	PUNCT
ejpam-62	86	1	�	�	PROPN
ejpam-62	86	2	it	it	PRON
ejpam-62	86	3	follows	follow	VERB
ejpam-62	86	4	from	from	ADP
ejpam-62	86	5	lemma	lemma	PROPN
ejpam-62	86	6	2.1	2.1	NUM
ejpam-62	86	7	that	that	SCONJ
ejpam-62	86	8	the	the	DET
ejpam-62	86	9	score	score	NOUN
ejpam-62	86	10	of	of	ADP
ejpam-62	86	11	a	a	DET
ejpam-62	86	12	vertex	vertex	NOUN
ejpam-62	86	13	vi	vi	NOUN
ejpam-62	86	14	besides	besides	SCONJ
ejpam-62	86	15	satisfying	satisfy	VERB
ejpam-62	86	16	0	0	NUM
ejpam-62	86	17	≤	≤	NUM
ejpam-62	86	18	si	si	X
ejpam-62	86	19	≤	≤	PROPN
ejpam-62	86	20	k	k	PROPN
ejpam-62	86	21	�	�	PROPN
ejpam-62	86	22	n−	n−	PROPN
ejpam-62	86	23	1	1	NUM
ejpam-62	86	24	k−	k−	PROPN
ejpam-62	86	25	1	1	NUM
ejpam-62	86	26	�	�	PROPN
ejpam-62	86	27	should	should	AUX
ejpam-62	86	28	also	also	ADV
ejpam-62	86	29	satisfy	satisfy	VERB
ejpam-62	86	30	si	si	X
ejpam-62	86	31	=	=	SYM
ejpam-62	86	32	xk	xk	PROPN
ejpam-62	87	1	+	+	PROPN
ejpam-62	87	2	y(k	y(k	PROPN
ejpam-62	87	3	−	−	PROPN
ejpam-62	87	4	1	1	NUM
ejpam-62	87	5	)	)	PUNCT
ejpam-62	87	6	,	,	PUNCT
ejpam-62	87	7	where	where	SCONJ
ejpam-62	87	8	x	x	PRON
ejpam-62	87	9	and	and	CCONJ
ejpam-62	87	10	y	y	PROPN
ejpam-62	87	11	are	be	AUX
ejpam-62	87	12	non	non	ADJ
ejpam-62	87	13	-	-	ADJ
ejpam-62	87	14	negative	negative	ADJ
ejpam-62	87	15	integers	integer	NOUN
ejpam-62	87	16	.	.	PUNCT
ejpam-62	88	1	a	a	DET
ejpam-62	88	2	vertex	vertex	NOUN
ejpam-62	88	3	vi	vi	NOUN
ejpam-62	88	4	if	if	SCONJ
ejpam-62	88	5	belonging	belong	VERB
ejpam-62	88	6	to	to	ADP
ejpam-62	88	7	an	an	DET
ejpam-62	88	8	arc	arc	NOUN
ejpam-62	88	9	and	and	CCONJ
ejpam-62	88	10	not	not	PART
ejpam-62	88	11	the	the	DET
ejpam-62	88	12	last	last	ADJ
ejpam-62	88	13	element	element	NOUN
ejpam-62	88	14	contributes	contribute	VERB
ejpam-62	88	15	k	k	PROPN
ejpam-62	88	16	to	to	ADP
ejpam-62	88	17	the	the	DET
ejpam-62	88	18	score	score	NOUN
ejpam-62	88	19	of	of	ADP
ejpam-62	88	20	vi	vi	NOUN
ejpam-62	88	21	,	,	PUNCT
ejpam-62	88	22	and	and	CCONJ
ejpam-62	88	23	if	if	SCONJ
ejpam-62	88	24	not	not	PART
ejpam-62	88	25	belonging	belong	VERB
ejpam-62	88	26	to	to	ADP
ejpam-62	88	27	an	an	DET
ejpam-62	88	28	arc	arc	NOUN
ejpam-62	88	29	contributes	contribute	VERB
ejpam-62	88	30	k−	k−	NOUN
ejpam-62	88	31	1	1	NUM
ejpam-62	88	32	to	to	ADP
ejpam-62	88	33	the	the	DET
ejpam-62	88	34	score	score	NOUN
ejpam-62	88	35	of	of	ADP
ejpam-62	88	36	vi	vi	PROPN
ejpam-62	88	37	.	.	PUNCT
ejpam-62	89	1	for	for	ADP
ejpam-62	89	2	k	k	PROPN
ejpam-62	89	3	=	=	SYM
ejpam-62	89	4	2	2	NUM
ejpam-62	89	5	,	,	PUNCT
ejpam-62	89	6	d	d	PRON
ejpam-62	89	7	is	be	AUX
ejpam-62	89	8	simply	simply	ADV
ejpam-62	89	9	an	an	DET
ejpam-62	89	10	oriented	orient	VERB
ejpam-62	89	11	graph	graph	NOUN
ejpam-62	89	12	and	and	CCONJ
ejpam-62	89	13	the	the	DET
ejpam-62	89	14	score	score	NOUN
ejpam-62	89	15	of	of	ADP
ejpam-62	89	16	a	a	DET
ejpam-62	89	17	vertex	vertex	NOUN
ejpam-62	89	18	in	in	ADP
ejpam-62	89	19	that	that	DET
ejpam-62	89	20	case	case	NOUN
ejpam-62	89	21	becomes	become	VERB
ejpam-62	89	22	s(vi	s(vi	NOUN
ejpam-62	89	23	)	)	PUNCT
ejpam-62	89	24	=	=	SYM
ejpam-62	89	25	�	�	PROPN
ejpam-62	89	26	n−	n−	NOUN
ejpam-62	89	27	1	1	NUM
ejpam-62	89	28	2	2	NUM
ejpam-62	89	29	�	�	PROPN
ejpam-62	89	30	+	+	CCONJ
ejpam-62	89	31	d+(vi)−	d+(vi)−	PROPN
ejpam-62	89	32	d−(vi	d−(vi	NOUN
ejpam-62	89	33	)	)	PUNCT
ejpam-62	89	34	,	,	PUNCT
ejpam-62	89	35	which	which	PRON
ejpam-62	89	36	is	be	AUX
ejpam-62	89	37	same	same	ADJ
ejpam-62	89	38	as	as	SCONJ
ejpam-62	89	39	defined	define	VERB
ejpam-62	89	40	by	by	ADP
ejpam-62	89	41	avery	avery	PROPN
ejpam-62	89	42	.	.	PUNCT
ejpam-62	90	1	lemma	lemma	PROPN
ejpam-62	90	2	2.2	2.2	NUM
ejpam-62	90	3	.	.	PUNCT
ejpam-62	91	1	if	if	SCONJ
ejpam-62	91	2	[	[	X
ejpam-62	91	3	s1	s1	NOUN
ejpam-62	91	4	,	,	PUNCT
ejpam-62	91	5	s2	s2	PROPN
ejpam-62	91	6	,	,	PUNCT
ejpam-62	91	7	·	·	PUNCT
ejpam-62	91	8	·	·	PUNCT
ejpam-62	91	9	·	·	PUNCT
ejpam-62	91	10	,	,	PUNCT
ejpam-62	91	11	sn	sn	PROPN
ejpam-62	91	12	]	]	X
ejpam-62	91	13	is	be	AUX
ejpam-62	91	14	a	a	DET
ejpam-62	91	15	score	score	NOUN
ejpam-62	91	16	sequence	sequence	NOUN
ejpam-62	91	17	of	of	ADP
ejpam-62	91	18	an	an	DET
ejpam-62	91	19	oriented	oriented	ADJ
ejpam-62	91	20	k	k	NOUN
ejpam-62	91	21	-	-	NOUN
ejpam-62	91	22	hypergraph	hypergraph	NOUN
ejpam-62	91	23	of	of	ADP
ejpam-62	91	24	order	order	NOUN
ejpam-62	91	25	n	n	CCONJ
ejpam-62	91	26	,	,	PUNCT
ejpam-62	91	27	then	then	ADV
ejpam-62	91	28	n	n	CCONJ
ejpam-62	91	29	∑	∑	ADV
ejpam-62	91	30	i=1	i=1	PROPN
ejpam-62	91	31	si	si	X
ejpam-62	91	32	=	=	SYM
ejpam-62	91	33	n(k−	n(k−	PROPN
ejpam-62	91	34	1	1	NUM
ejpam-62	91	35	)	)	PUNCT
ejpam-62	91	36	�	�	PROPN
ejpam-62	91	37	n−	n−	NOUN
ejpam-62	91	38	1	1	NUM
ejpam-62	91	39	k−	k−	PROPN
ejpam-62	91	40	1	1	NUM
ejpam-62	91	41	�	�	PROPN
ejpam-62	91	42	.	.	PUNCT
ejpam-62	92	1	proof	proof	NOUN
ejpam-62	92	2	.	.	PUNCT
ejpam-62	93	1	in	in	ADP
ejpam-62	93	2	the	the	DET
ejpam-62	93	3	following	following	NOUN
ejpam-62	93	4	,	,	PUNCT
ejpam-62	93	5	d+i	d+i	X
ejpam-62	93	6	and	and	CCONJ
ejpam-62	93	7	d−i	d−i	ADJ
ejpam-62	93	8	denote	denote	NOUN
ejpam-62	93	9	d(vi)+	d(vi)+	PROPN
ejpam-62	93	10	and	and	CCONJ
ejpam-62	93	11	d(vi)−	d(vi)−	NOUN
ejpam-62	93	12	respectively	respectively	ADV
ejpam-62	93	13	.	.	PUNCT
ejpam-62	94	1	let	let	VERB
ejpam-62	94	2	d	d	PRON
ejpam-62	94	3	be	be	AUX
ejpam-62	94	4	an	an	DET
ejpam-62	94	5	oriented	oriented	ADJ
ejpam-62	94	6	k	k	NOUN
ejpam-62	94	7	-	-	NOUN
ejpam-62	94	8	hypergraph	hypergraph	VERB
ejpam-62	94	9	with	with	ADP
ejpam-62	94	10	score	score	NOUN
ejpam-62	94	11	sequence	sequence	NOUN
ejpam-62	94	12	[	[	X
ejpam-62	94	13	s1	s1	NOUN
ejpam-62	94	14	,	,	PUNCT
ejpam-62	94	15	s2	s2	PROPN
ejpam-62	94	16	,	,	PUNCT
ejpam-62	94	17	·	·	PUNCT
ejpam-62	94	18	·	·	PUNCT
ejpam-62	94	19	·	·	PUNCT
ejpam-62	94	20	,	,	PUNCT
ejpam-62	94	21	sn	sn	PROPN
ejpam-62	94	22	]	]	PUNCT
ejpam-62	94	23	.	.	PUNCT
ejpam-62	95	1	we	we	PRON
ejpam-62	95	2	have	have	VERB
ejpam-62	95	3	,	,	PUNCT
ejpam-62	95	4	s.	s.	PROPN
ejpam-62	95	5	pirzada	pirzada	PROPN
ejpam-62	95	6	,	,	PUNCT
ejpam-62	95	7	z.	z.	PROPN
ejpam-62	95	8	guofei	guofei	PROPN
ejpam-62	95	9	/	/	SYM
ejpam-62	95	10	eur	eur	PROPN
ejpam-62	95	11	.	.	PUNCT
ejpam-62	96	1	j.	j.	PROPN
ejpam-62	96	2	pure	pure	PROPN
ejpam-62	96	3	appl	appl	PROPN
ejpam-62	96	4	.	.	PROPN
ejpam-62	96	5	math	math	PROPN
ejpam-62	96	6	,	,	PUNCT
ejpam-62	96	7	1	1	NUM
ejpam-62	96	8	(	(	PUNCT
ejpam-62	96	9	2008	2008	NUM
ejpam-62	96	10	)	)	PUNCT
ejpam-62	96	11	,	,	PUNCT
ejpam-62	96	12	(	(	PUNCT
ejpam-62	96	13	10	10	NUM
ejpam-62	96	14	-	-	SYM
ejpam-62	96	15	20	20	NUM
ejpam-62	96	16	)	)	PUNCT
ejpam-62	96	17	14	14	NUM
ejpam-62	97	1	n	n	NOUN
ejpam-62	97	2	∑	∑	PUNCT
ejpam-62	97	3	i=1	i=1	PROPN
ejpam-62	97	4	si	si	PROPN
ejpam-62	97	5	=	=	SYM
ejpam-62	97	6	n	n	PROPN
ejpam-62	97	7	∑	∑	PROPN
ejpam-62	97	8	i=1	i=1	PROPN
ejpam-62	97	9	�	�	PROPN
ejpam-62	97	10	(	(	PUNCT
ejpam-62	97	11	k−	k−	PROPN
ejpam-62	97	12	1	1	NUM
ejpam-62	97	13	)	)	PUNCT
ejpam-62	97	14	�	�	PROPN
ejpam-62	97	15	n−	n−	NOUN
ejpam-62	97	16	1	1	NUM
ejpam-62	97	17	k−	k−	PROPN
ejpam-62	97	18	1	1	NUM
ejpam-62	97	19	�	�	PROPN
ejpam-62	97	20	+	+	CCONJ
ejpam-62	97	21	d+i	d+i	X
ejpam-62	97	22	−	−	PROPN
ejpam-62	97	23	(	(	PUNCT
ejpam-62	97	24	k−	k−	PROPN
ejpam-62	97	25	1)d−i	1)d−i	PROPN
ejpam-62	97	26	�	�	PROPN
ejpam-62	97	27	=	=	SYM
ejpam-62	97	28	n(k−	n(k−	PROPN
ejpam-62	97	29	1	1	NUM
ejpam-62	97	30	)	)	PUNCT
ejpam-62	97	31	�	�	PROPN
ejpam-62	97	32	n−	n−	NOUN
ejpam-62	97	33	1	1	NUM
ejpam-62	97	34	k−	k−	PROPN
ejpam-62	97	35	1	1	NUM
ejpam-62	97	36	�	�	PROPN
ejpam-62	97	37	+	+	CCONJ
ejpam-62	97	38	n	n	CCONJ
ejpam-62	97	39	∑	∑	ADV
ejpam-62	97	40	i=1	i=1	PROPN
ejpam-62	97	41	d+i	d+i	X
ejpam-62	97	42	−	−	PROPN
ejpam-62	97	43	(	(	PUNCT
ejpam-62	97	44	k−	k−	PROPN
ejpam-62	97	45	1	1	NUM
ejpam-62	97	46	)	)	PUNCT
ejpam-62	97	47	n	n	CCONJ
ejpam-62	97	48	∑	∑	PUNCT
ejpam-62	97	49	i=1	i=1	PROPN
ejpam-62	97	50	d−i	d−i	ADV
ejpam-62	97	51	.	.	PUNCT
ejpam-62	98	1	let	let	VERB
ejpam-62	98	2	d	d	NOUN
ejpam-62	98	3	contains	contain	VERB
ejpam-62	98	4	p	p	PROPN
ejpam-62	98	5	k	k	NOUN
ejpam-62	98	6	-	-	PUNCT
ejpam-62	98	7	arcs	arcs	NOUN
ejpam-62	98	8	.	.	PUNCT
ejpam-62	99	1	then	then	ADV
ejpam-62	99	2	,	,	PUNCT
ejpam-62	99	3	n	n	CCONJ
ejpam-62	99	4	∑	∑	ADP
ejpam-62	99	5	i=1	i=1	X
ejpam-62	99	6	d+i	d+i	X
ejpam-62	99	7	=	=	SYM
ejpam-62	99	8	(	(	PUNCT
ejpam-62	99	9	k−	k−	PROPN
ejpam-62	99	10	1)p	1)p	NUM
ejpam-62	99	11	and	and	CCONJ
ejpam-62	99	12	n	n	CCONJ
ejpam-62	99	13	∑	∑	PROPN
ejpam-62	99	14	i=1	i=1	PROPN
ejpam-62	99	15	d−i	d−i	PROPN
ejpam-62	99	16	=	=	SYM
ejpam-62	99	17	p.	p.	NOUN
ejpam-62	99	18	therefore	therefore	ADV
ejpam-62	99	19	,	,	PUNCT
ejpam-62	99	20	n	n	CCONJ
ejpam-62	99	21	∑	∑	ADV
ejpam-62	99	22	i=1	i=1	PROPN
ejpam-62	99	23	si	si	X
ejpam-62	99	24	=	=	SYM
ejpam-62	99	25	n(k−	n(k−	PROPN
ejpam-62	99	26	1	1	NUM
ejpam-62	99	27	)	)	PUNCT
ejpam-62	99	28	�	�	PROPN
ejpam-62	99	29	n−	n−	NOUN
ejpam-62	99	30	1	1	NUM
ejpam-62	99	31	k−	k−	PROPN
ejpam-62	99	32	1	1	NUM
ejpam-62	99	33	�	�	PROPN
ejpam-62	99	34	+	+	CCONJ
ejpam-62	99	35	(	(	PUNCT
ejpam-62	99	36	k−	k−	PROPN
ejpam-62	99	37	1)p−	1)p−	NUM
ejpam-62	99	38	(	(	PUNCT
ejpam-62	99	39	k−	k−	NOUN
ejpam-62	99	40	1)p	1)p	NUM
ejpam-62	99	41	=	=	SYM
ejpam-62	99	42	n(k−	n(k−	PROPN
ejpam-62	99	43	1	1	NUM
ejpam-62	99	44	)	)	PUNCT
ejpam-62	99	45	�	�	PROPN
ejpam-62	99	46	n−	n−	NOUN
ejpam-62	99	47	1	1	NUM
ejpam-62	99	48	k−	k−	PROPN
ejpam-62	99	49	1	1	NUM
ejpam-62	99	50	�	�	PROPN
ejpam-62	99	51	�	�	PROPN
ejpam-62	99	52	lemma	lemma	PROPN
ejpam-62	99	53	2.3	2.3	NUM
ejpam-62	99	54	.	.	PUNCT
ejpam-62	100	1	if	if	SCONJ
ejpam-62	100	2	s	s	PRON
ejpam-62	100	3	=	=	PUNCT
ejpam-62	101	1	[	[	X
ejpam-62	101	2	s1	s1	NOUN
ejpam-62	101	3	,	,	PUNCT
ejpam-62	101	4	s2	s2	PROPN
ejpam-62	101	5	,	,	PUNCT
ejpam-62	101	6	·	·	PUNCT
ejpam-62	101	7	·	·	PUNCT
ejpam-62	101	8	·	·	PUNCT
ejpam-62	101	9	,	,	PUNCT
ejpam-62	101	10	sn	sn	PROPN
ejpam-62	101	11	]	]	X
ejpam-62	101	12	is	be	AUX
ejpam-62	101	13	a	a	DET
ejpam-62	101	14	score	score	NOUN
ejpam-62	101	15	sequence	sequence	NOUN
ejpam-62	101	16	of	of	ADP
ejpam-62	101	17	an	an	DET
ejpam-62	101	18	oriented	oriented	ADJ
ejpam-62	101	19	k	k	NOUN
ejpam-62	101	20	-	-	ADJ
ejpam-62	101	21	hypergraph	hypergraph	VERB
ejpam-62	101	22	d	d	NOUN
ejpam-62	101	23	with	with	ADP
ejpam-62	101	24	si	si	INTJ
ejpam-62	101	25	<	<	X
ejpam-62	101	26	s	s	PROPN
ejpam-62	101	27	j	j	PROPN
ejpam-62	101	28	and	and	CCONJ
ejpam-62	101	29	si	si	PROPN
ejpam-62	101	30	=	=	PROPN
ejpam-62	101	31	xk	xk	PROPN
ejpam-62	102	1	+	+	PROPN
ejpam-62	102	2	y(k	y(k	PROPN
ejpam-62	102	3	−	−	PROPN
ejpam-62	102	4	1	1	NUM
ejpam-62	102	5	)	)	PUNCT
ejpam-62	102	6	,	,	PUNCT
ejpam-62	102	7	s	s	VERB
ejpam-62	102	8	j	j	NOUN
ejpam-62	102	9	=	=	PUNCT
ejpam-62	102	10	αk	αk	PROPN
ejpam-62	103	1	+	+	ADJ
ejpam-62	103	2	β(k	β(k	X
ejpam-62	103	3	−	−	PROPN
ejpam-62	103	4	1	1	NUM
ejpam-62	103	5	)	)	PUNCT
ejpam-62	103	6	,	,	PUNCT
ejpam-62	103	7	where	where	SCONJ
ejpam-62	103	8	x	x	X
ejpam-62	103	9	,	,	PUNCT
ejpam-62	103	10	y	y	PROPN
ejpam-62	103	11	,	,	PUNCT
ejpam-62	103	12	α	α	PROPN
ejpam-62	103	13	and	and	CCONJ
ejpam-62	103	14	β	β	PROPN
ejpam-62	103	15	are	be	AUX
ejpam-62	103	16	non	non	ADJ
ejpam-62	103	17	-	-	ADJ
ejpam-62	103	18	negative	negative	ADJ
ejpam-62	103	19	integers	integer	NOUN
ejpam-62	103	20	.	.	PUNCT
ejpam-62	104	1	if	if	SCONJ
ejpam-62	104	2	y	y	PROPN
ejpam-62	104	3	>	>	X
ejpam-62	104	4	β	β	X
ejpam-62	104	5	,	,	PUNCT
ejpam-62	104	6	then	then	ADV
ejpam-62	104	7	s+(s+i	s+(s+i	VERB
ejpam-62	104	8	,	,	PUNCT
ejpam-62	104	9	s−j	s−j	PROPN
ejpam-62	104	10	)	)	PUNCT
ejpam-62	104	11	is	be	AUX
ejpam-62	104	12	a	a	DET
ejpam-62	104	13	score	score	NOUN
ejpam-62	104	14	sequence	sequence	NOUN
ejpam-62	104	15	of	of	ADP
ejpam-62	104	16	an	an	DET
ejpam-62	104	17	oriented	oriented	ADJ
ejpam-62	104	18	k	k	NOUN
ejpam-62	104	19	-	-	ADJ
ejpam-62	104	20	hypergraph	hypergraph	ADJ
ejpam-62	104	21	d′.	d′.	NOUN
ejpam-62	104	22	proof	proof	NOUN
ejpam-62	104	23	.	.	PUNCT
ejpam-62	105	1	for	for	ADP
ejpam-62	105	2	simplicity	simplicity	NOUN
ejpam-62	105	3	,	,	PUNCT
ejpam-62	105	4	a(d	a(d	PROPN
ejpam-62	105	5	)	)	PUNCT
ejpam-62	105	6	denotes	denote	VERB
ejpam-62	105	7	the	the	DET
ejpam-62	105	8	set	set	NOUN
ejpam-62	105	9	of	of	ADP
ejpam-62	105	10	arcs	arc	NOUN
ejpam-62	105	11	in	in	ADP
ejpam-62	105	12	d	d	PROPN
ejpam-62	105	13	;	;	PUNCT
ejpam-62	105	14	a∗(d	a∗(d	PROPN
ejpam-62	105	15	)	)	PUNCT
ejpam-62	105	16	denotes	denote	VERB
ejpam-62	105	17	the	the	DET
ejpam-62	105	18	set	set	NOUN
ejpam-62	105	19	of	of	ADP
ejpam-62	105	20	non	non	ADJ
ejpam-62	105	21	arcs	arcs	PROPN
ejpam-62	105	22	in	in	ADP
ejpam-62	105	23	d.	d.	PROPN
ejpam-62	105	24	since	since	SCONJ
ejpam-62	105	25	d(v)∗	d(v)∗	PROPN
ejpam-62	105	26	=	=	SYM
ejpam-62	105	27	y	y	PROPN
ejpam-62	105	28	>	>	X
ejpam-62	105	29	β	β	X
ejpam-62	105	30	≥	≥	NUM
ejpam-62	105	31	0	0	NUM
ejpam-62	105	32	,	,	PUNCT
ejpam-62	105	33	we	we	PRON
ejpam-62	105	34	have	have	VERB
ejpam-62	105	35	a∗(d	a∗(d	PROPN
ejpam-62	105	36	)	)	PUNCT
ejpam-62	105	37	6=	6=	PUNCT
ejpam-62	105	38	;	;	PUNCT
ejpam-62	105	39	.	.	PUNCT
ejpam-62	106	1	case	case	NOUN
ejpam-62	106	2	1	1	X
ejpam-62	106	3	.	.	PUNCT
ejpam-62	107	1	there	there	PRON
ejpam-62	107	2	exists	exist	VERB
ejpam-62	107	3	a	a	DET
ejpam-62	107	4	non	non	ADJ
ejpam-62	107	5	arc	arc	NOUN
ejpam-62	107	6	e∗	e∗	NOUN
ejpam-62	107	7	=	=	SYM
ejpam-62	107	8	〈	〈	PROPN
ejpam-62	107	9	u1	u1	NOUN
ejpam-62	107	10	,	,	PUNCT
ejpam-62	107	11	u2	u2	NOUN
ejpam-62	107	12	,	,	PUNCT
ejpam-62	107	13	·	·	PUNCT
ejpam-62	107	14	·	·	PUNCT
ejpam-62	107	15	·	·	PUNCT
ejpam-62	107	16	,	,	PUNCT
ejpam-62	107	17	uk−1	uk−1	PROPN
ejpam-62	107	18	,	,	PUNCT
ejpam-62	107	19	vi	vi	X
ejpam-62	107	20	〉	〉	NOUN
ejpam-62	107	21	∈	∈	PROPN
ejpam-62	107	22	a∗(d	a∗(d	PROPN
ejpam-62	107	23	)	)	PUNCT
ejpam-62	107	24	which	which	PRON
ejpam-62	107	25	does	do	AUX
ejpam-62	107	26	not	not	PART
ejpam-62	107	27	contain	contain	VERB
ejpam-62	107	28	v	v	ADP
ejpam-62	107	29	j	j	PROPN
ejpam-62	107	30	and	and	CCONJ
ejpam-62	107	31	such	such	ADJ
ejpam-62	108	1	that	that	PRON
ejpam-62	108	2	e	e	NOUN
ejpam-62	108	3	=	=	PUNCT
ejpam-62	108	4	(	(	PUNCT
ejpam-62	108	5	u′1	u′1	NOUN
ejpam-62	108	6	,	,	PUNCT
ejpam-62	108	7	u′2	u′2	ADJ
ejpam-62	108	8	,	,	PUNCT
ejpam-62	108	9	·	·	PUNCT
ejpam-62	108	10	·	·	PUNCT
ejpam-62	108	11	·	·	PUNCT
ejpam-62	108	12	,	,	PUNCT
ejpam-62	108	13	u′k−1	u′k−1	PROPN
ejpam-62	108	14	,	,	PUNCT
ejpam-62	108	15	v	v	PART
ejpam-62	108	16	j	j	NOUN
ejpam-62	108	17	)	)	PUNCT
ejpam-62	108	18	∈	∈	PROPN
ejpam-62	108	19	a(d	a(d	PROPN
ejpam-62	108	20	)	)	PUNCT
ejpam-62	108	21	,	,	PUNCT
ejpam-62	108	22	where	where	SCONJ
ejpam-62	108	23	(	(	PUNCT
ejpam-62	108	24	u′1	u′1	NOUN
ejpam-62	108	25	,	,	PUNCT
ejpam-62	108	26	u′2	u′2	ADJ
ejpam-62	108	27	,	,	PUNCT
ejpam-62	108	28	·	·	PUNCT
ejpam-62	108	29	·	·	PUNCT
ejpam-62	108	30	·	·	PUNCT
ejpam-62	108	31	,	,	PUNCT
ejpam-62	108	32	u′k−1	u′k−1	PROPN
ejpam-62	108	33	)	)	PUNCT
ejpam-62	108	34	is	be	AUX
ejpam-62	108	35	a	a	DET
ejpam-62	108	36	permutation	permutation	NOUN
ejpam-62	108	37	of	of	ADP
ejpam-62	108	38	(	(	PUNCT
ejpam-62	108	39	u1	u1	PROPN
ejpam-62	108	40	,	,	PUNCT
ejpam-62	108	41	u2	u2	NOUN
ejpam-62	108	42	,	,	PUNCT
ejpam-62	108	43	·	·	PUNCT
ejpam-62	108	44	·	·	PUNCT
ejpam-62	108	45	·	·	PUNCT
ejpam-62	108	46	,	,	PUNCT
ejpam-62	108	47	uk−1	uk−1	PROPN
ejpam-62	108	48	)	)	PUNCT
ejpam-62	108	49	.	.	PUNCT
ejpam-62	109	1	if	if	SCONJ
ejpam-62	109	2	there	there	PRON
ejpam-62	109	3	exists	exist	VERB
ejpam-62	109	4	an	an	DET
ejpam-62	109	5	arc	arc	NOUN
ejpam-62	109	6	e1	e1	NOUN
ejpam-62	109	7	that	that	PRON
ejpam-62	109	8	contains	contain	VERB
ejpam-62	109	9	both	both	DET
ejpam-62	109	10	vi	vi	NOUN
ejpam-62	109	11	and	and	CCONJ
ejpam-62	109	12	v	v	NOUN
ejpam-62	109	13	j	j	PROPN
ejpam-62	109	14	and	and	CCONJ
ejpam-62	109	15	that	that	DET
ejpam-62	109	16	vi	vi	PROPN
ejpam-62	109	17	is	be	AUX
ejpam-62	109	18	the	the	DET
ejpam-62	109	19	last	last	ADJ
ejpam-62	109	20	entry	entry	NOUN
ejpam-62	109	21	.	.	PUNCT
ejpam-62	110	1	then	then	ADV
ejpam-62	110	2	by	by	ADP
ejpam-62	110	3	exchanging	exchange	VERB
ejpam-62	110	4	vi	vi	PROPN
ejpam-62	110	5	and	and	CCONJ
ejpam-62	110	6	v	v	ADP
ejpam-62	110	7	j	j	PROPN
ejpam-62	110	8	in	in	ADP
ejpam-62	110	9	e1	e1	PROPN
ejpam-62	110	10	,	,	PUNCT
ejpam-62	110	11	adding	add	VERB
ejpam-62	110	12	the	the	DET
ejpam-62	110	13	arc	arc	NOUN
ejpam-62	110	14	e′	e′	X
ejpam-62	110	15	=	=	SYM
ejpam-62	110	16	(	(	PUNCT
ejpam-62	110	17	u1	u1	PROPN
ejpam-62	110	18	,	,	PUNCT
ejpam-62	110	19	u2	u2	PROPN
ejpam-62	110	20	,	,	PUNCT
ejpam-62	110	21	·	·	PUNCT
ejpam-62	110	22	·	·	PUNCT
ejpam-62	110	23	·	·	PUNCT
ejpam-62	110	24	,	,	PUNCT
ejpam-62	110	25	uk−1	uk−1	PROPN
ejpam-62	110	26	,	,	PUNCT
ejpam-62	110	27	vi	vi	NOUN
ejpam-62	110	28	)	)	PUNCT
ejpam-62	110	29	to	to	ADP
ejpam-62	110	30	d	d	PROPN
ejpam-62	110	31	,	,	PUNCT
ejpam-62	110	32	and	and	CCONJ
ejpam-62	110	33	deleting	delete	VERB
ejpam-62	110	34	e	e	PROPN
ejpam-62	110	35	from	from	ADP
ejpam-62	110	36	d	d	PROPN
ejpam-62	110	37	,	,	PUNCT
ejpam-62	110	38	we	we	PRON
ejpam-62	110	39	get	get	VERB
ejpam-62	110	40	an	an	DET
ejpam-62	110	41	oriented	oriented	ADJ
ejpam-62	110	42	k	k	NOUN
ejpam-62	110	43	-	-	NOUN
ejpam-62	110	44	hypergraph	hypergraph	VERB
ejpam-62	110	45	d′	d′	X
ejpam-62	110	46	with	with	ADP
ejpam-62	110	47	s+(s+i	s+(s+i	NOUN
ejpam-62	110	48	,	,	PUNCT
ejpam-62	110	49	s−j	s−j	PROPN
ejpam-62	110	50	)	)	PUNCT
ejpam-62	110	51	as	as	ADP
ejpam-62	110	52	its	its	PRON
ejpam-62	110	53	score	score	NOUN
ejpam-62	110	54	sequence	sequence	NOUN
ejpam-62	110	55	.	.	PUNCT
ejpam-62	111	1	so	so	ADV
ejpam-62	111	2	in	in	ADP
ejpam-62	111	3	the	the	DET
ejpam-62	111	4	following	following	NOUN
ejpam-62	111	5	,	,	PUNCT
ejpam-62	111	6	we	we	PRON
ejpam-62	111	7	assume	assume	VERB
ejpam-62	111	8	that	that	SCONJ
ejpam-62	111	9	for	for	ADP
ejpam-62	111	10	each	each	DET
ejpam-62	111	11	arc	arc	NOUN
ejpam-62	111	12	containing	contain	VERB
ejpam-62	111	13	both	both	DET
ejpam-62	111	14	vi	vi	NOUN
ejpam-62	111	15	and	and	CCONJ
ejpam-62	111	16	v	v	NOUN
ejpam-62	111	17	j	j	PROPN
ejpam-62	111	18	,	,	PUNCT
ejpam-62	111	19	vi	vi	PROPN
ejpam-62	111	20	is	be	AUX
ejpam-62	111	21	not	not	PART
ejpam-62	111	22	the	the	DET
ejpam-62	111	23	last	last	ADJ
ejpam-62	111	24	entry	entry	NOUN
ejpam-62	111	25	.	.	PUNCT
ejpam-62	112	1	if	if	SCONJ
ejpam-62	112	2	there	there	PRON
ejpam-62	112	3	exists	exist	VERB
ejpam-62	112	4	a	a	DET
ejpam-62	112	5	pair	pair	NOUN
ejpam-62	112	6	of	of	ADP
ejpam-62	112	7	arcs	arc	NOUN
ejpam-62	112	8	f	f	X
ejpam-62	112	9	=	=	PUNCT
ejpam-62	112	10	(	(	PUNCT
ejpam-62	112	11	w1	w1	NOUN
ejpam-62	112	12	,	,	PUNCT
ejpam-62	112	13	w2	w2	NOUN
ejpam-62	112	14	,	,	PUNCT
ejpam-62	112	15	·	·	PUNCT
ejpam-62	112	16	·	·	PUNCT
ejpam-62	112	17	·	·	PUNCT
ejpam-62	112	18	,	,	PUNCT
ejpam-62	112	19	wk−1	wk−1	PROPN
ejpam-62	112	20	,	,	PUNCT
ejpam-62	112	21	vi	vi	NOUN
ejpam-62	112	22	)	)	PUNCT
ejpam-62	112	23	,	,	PUNCT
ejpam-62	112	24	and	and	CCONJ
ejpam-62	112	25	f	f	NOUN
ejpam-62	113	1	′	′	NUM
ejpam-62	113	2	=	=	SYM
ejpam-62	113	3	(	(	PUNCT
ejpam-62	113	4	w′1	w′1	X
ejpam-62	113	5	,	,	PUNCT
ejpam-62	113	6	w′2	w′2	PROPN
ejpam-62	113	7	,	,	PUNCT
ejpam-62	113	8	·	·	PUNCT
ejpam-62	113	9	·	·	PUNCT
ejpam-62	113	10	·	·	PUNCT
ejpam-62	113	11	,	,	PUNCT
ejpam-62	113	12	v	v	X
ejpam-62	113	13	j	j	PROPN
ejpam-62	113	14	,	,	PUNCT
ejpam-62	113	15	·	·	PUNCT
ejpam-62	113	16	·	·	PUNCT
ejpam-62	113	17	·	·	PUNCT
ejpam-62	113	18	,	,	PUNCT
ejpam-62	113	19	w′k−1	w′k−1	PROPN
ejpam-62	113	20	)	)	PUNCT
ejpam-62	113	21	,	,	PUNCT
ejpam-62	113	22	where	where	SCONJ
ejpam-62	113	23	(	(	PUNCT
ejpam-62	113	24	w′1	w′1	ADJ
ejpam-62	113	25	,	,	PUNCT
ejpam-62	113	26	w′2	w′2	PROPN
ejpam-62	113	27	,	,	PUNCT
ejpam-62	113	28	·	·	PUNCT
ejpam-62	113	29	·	·	PUNCT
ejpam-62	113	30	·	·	PUNCT
ejpam-62	113	31	,	,	PUNCT
ejpam-62	113	32	w′k−1	w′k−1	PROPN
ejpam-62	113	33	)	)	PUNCT
ejpam-62	113	34	is	be	AUX
ejpam-62	113	35	a	a	DET
ejpam-62	113	36	permutation	permutation	NOUN
ejpam-62	113	37	of	of	ADP
ejpam-62	113	38	(	(	PUNCT
ejpam-62	113	39	w1	w1	NOUN
ejpam-62	113	40	,	,	PUNCT
ejpam-62	113	41	w2	w2	NOUN
ejpam-62	113	42	,	,	PUNCT
ejpam-62	113	43	·	·	PUNCT
ejpam-62	113	44	·	·	PUNCT
ejpam-62	113	45	·	·	PUNCT
ejpam-62	113	46	,	,	PUNCT
ejpam-62	113	47	wk−1	wk−1	PROPN
ejpam-62	113	48	)	)	PUNCT
ejpam-62	113	49	.	.	PUNCT
ejpam-62	114	1	then	then	ADV
ejpam-62	114	2	by	by	ADP
ejpam-62	114	3	exchanging	exchange	VERB
ejpam-62	114	4	vi	vi	PROPN
ejpam-62	114	5	and	and	CCONJ
ejpam-62	114	6	v	v	ADP
ejpam-62	114	7	j	j	PROPN
ejpam-62	114	8	between	between	ADP
ejpam-62	114	9	f	f	PROPN
ejpam-62	114	10	and	and	CCONJ
ejpam-62	114	11	f	f	PROPN
ejpam-62	114	12	′	′	PROPN
ejpam-62	114	13	,	,	PUNCT
ejpam-62	114	14	adding	add	VERB
ejpam-62	114	15	the	the	DET
ejpam-62	114	16	arc	arc	NOUN
ejpam-62	114	17	e′	e′	X
ejpam-62	114	18	=	=	SYM
ejpam-62	114	19	(	(	PUNCT
ejpam-62	114	20	u1	u1	PROPN
ejpam-62	114	21	,	,	PUNCT
ejpam-62	114	22	u2	u2	PROPN
ejpam-62	114	23	,	,	PUNCT
ejpam-62	114	24	·	·	PUNCT
ejpam-62	114	25	·	·	PUNCT
ejpam-62	114	26	·	·	PUNCT
ejpam-62	114	27	,	,	PUNCT
ejpam-62	114	28	uk−1	uk−1	PROPN
ejpam-62	114	29	,	,	PUNCT
ejpam-62	114	30	vi	vi	NOUN
ejpam-62	114	31	)	)	PUNCT
ejpam-62	114	32	to	to	ADP
ejpam-62	114	33	d	d	PROPN
ejpam-62	114	34	,	,	PUNCT
ejpam-62	114	35	and	and	CCONJ
ejpam-62	114	36	deleting	delete	VERB
ejpam-62	114	37	e	e	PROPN
ejpam-62	114	38	from	from	ADP
ejpam-62	114	39	d	d	PROPN
ejpam-62	114	40	,	,	PUNCT
ejpam-62	114	41	we	we	PRON
ejpam-62	114	42	get	get	VERB
ejpam-62	114	43	an	an	DET
ejpam-62	114	44	oriented	oriented	ADJ
ejpam-62	114	45	k	k	NOUN
ejpam-62	114	46	-	-	NOUN
ejpam-62	114	47	hypergraph	hypergraph	VERB
ejpam-62	114	48	d′	d′	X
ejpam-62	114	49	with	with	ADP
ejpam-62	114	50	s+(s+i	s+(s+i	NOUN
ejpam-62	114	51	,	,	PUNCT
ejpam-62	114	52	s−j	s−j	PROPN
ejpam-62	114	53	)	)	PUNCT
ejpam-62	114	54	as	as	ADP
ejpam-62	114	55	its	its	PRON
ejpam-62	114	56	score	score	NOUN
ejpam-62	114	57	sequence	sequence	NOUN
ejpam-62	114	58	.	.	PUNCT
ejpam-62	115	1	so	so	ADV
ejpam-62	115	2	in	in	ADP
ejpam-62	115	3	the	the	DET
ejpam-62	115	4	following	following	NOUN
ejpam-62	115	5	,	,	PUNCT
ejpam-62	115	6	we	we	PRON
ejpam-62	115	7	assume	assume	VERB
ejpam-62	115	8	that	that	SCONJ
ejpam-62	115	9	no	no	DET
ejpam-62	115	10	such	such	ADJ
ejpam-62	115	11	pair	pair	NOUN
ejpam-62	115	12	of	of	ADP
ejpam-62	115	13	arcs	arc	NOUN
ejpam-62	115	14	exist	exist	VERB
ejpam-62	115	15	.	.	PUNCT
ejpam-62	116	1	furthermore	furthermore	ADV
ejpam-62	116	2	,	,	PUNCT
ejpam-62	116	3	for	for	ADP
ejpam-62	116	4	each	each	DET
ejpam-62	116	5	f	f	NOUN
ejpam-62	116	6	′	′	NUM
ejpam-62	117	1	=	=	SYM
ejpam-62	117	2	(	(	PUNCT
ejpam-62	117	3	w′1	w′1	X
ejpam-62	117	4	,	,	PUNCT
ejpam-62	117	5	w′2	w′2	PROPN
ejpam-62	117	6	,	,	PUNCT
ejpam-62	117	7	·	·	PUNCT
ejpam-62	117	8	·	·	PUNCT
ejpam-62	117	9	·	·	PUNCT
ejpam-62	117	10	,	,	PUNCT
ejpam-62	117	11	v	v	X
ejpam-62	117	12	j	j	PROPN
ejpam-62	117	13	,	,	PUNCT
ejpam-62	117	14	·	·	PUNCT
ejpam-62	117	15	·	·	PUNCT
ejpam-62	117	16	·	·	PUNCT
ejpam-62	117	17	,	,	PUNCT
ejpam-62	117	18	w′k−1	w′k−1	PROPN
ejpam-62	117	19	)	)	PUNCT
ejpam-62	117	20	,	,	PUNCT
ejpam-62	117	21	f	f	X
ejpam-62	117	22	=	=	PUNCT
ejpam-62	117	23	(	(	PUNCT
ejpam-62	117	24	w1	w1	NOUN
ejpam-62	117	25	,	,	PUNCT
ejpam-62	117	26	w2	w2	NOUN
ejpam-62	117	27	,	,	PUNCT
ejpam-62	117	28	·	·	PUNCT
ejpam-62	117	29	·	·	PUNCT
ejpam-62	117	30	·	·	PUNCT
ejpam-62	117	31	,	,	PUNCT
ejpam-62	117	32	vi	vi	X
ejpam-62	117	33	,	,	PUNCT
ejpam-62	117	34	·	·	PUNCT
ejpam-62	117	35	·	·	PUNCT
ejpam-62	117	36	·	·	PUNCT
ejpam-62	117	37	,	,	PUNCT
ejpam-62	117	38	wk−1	wk−1	PROPN
ejpam-62	117	39	)	)	PUNCT
ejpam-62	117	40	must	must	AUX
ejpam-62	117	41	be	be	AUX
ejpam-62	117	42	an	an	DET
ejpam-62	117	43	arc	arc	NOUN
ejpam-62	117	44	,	,	PUNCT
ejpam-62	117	45	where	where	SCONJ
ejpam-62	117	46	(	(	PUNCT
ejpam-62	117	47	w′1	w′1	ADJ
ejpam-62	117	48	,	,	PUNCT
ejpam-62	117	49	w′2	w′2	PROPN
ejpam-62	117	50	,	,	PUNCT
ejpam-62	117	51	·	·	PUNCT
ejpam-62	117	52	·	·	PUNCT
ejpam-62	117	53	·	·	PUNCT
ejpam-62	117	54	,	,	PUNCT
ejpam-62	117	55	w′k−1	w′k−1	PROPN
ejpam-62	117	56	)	)	PUNCT
ejpam-62	117	57	is	be	AUX
ejpam-62	117	58	a	a	DET
ejpam-62	117	59	permutation	permutation	NOUN
ejpam-62	117	60	of	of	ADP
ejpam-62	117	61	(	(	PUNCT
ejpam-62	117	62	w1	w1	NOUN
ejpam-62	117	63	,	,	PUNCT
ejpam-62	117	64	w2	w2	NOUN
ejpam-62	117	65	,	,	PUNCT
ejpam-62	117	66	·	·	PUNCT
ejpam-62	117	67	·	·	PUNCT
ejpam-62	117	68	·	·	PUNCT
ejpam-62	117	69	,	,	PUNCT
ejpam-62	117	70	wk−1	wk−1	PROPN
ejpam-62	117	71	)	)	PUNCT
ejpam-62	117	72	,	,	PUNCT
ejpam-62	117	73	otherwise	otherwise	ADV
ejpam-62	117	74	,	,	PUNCT
ejpam-62	117	75	by	by	ADP
ejpam-62	117	76	adding	add	VERB
ejpam-62	117	77	(	(	PUNCT
ejpam-62	117	78	w1	w1	NOUN
ejpam-62	117	79	,	,	PUNCT
ejpam-62	117	80	w2	w2	NOUN
ejpam-62	117	81	,	,	PUNCT
ejpam-62	117	82	·	·	PUNCT
ejpam-62	117	83	·	·	PUNCT
ejpam-62	117	84	·	·	PUNCT
ejpam-62	117	85	,	,	PUNCT
ejpam-62	117	86	vi	vi	X
ejpam-62	117	87	,	,	PUNCT
ejpam-62	117	88	·	·	PUNCT
ejpam-62	117	89	·	·	PUNCT
ejpam-62	117	90	·	·	PUNCT
ejpam-62	117	91	,	,	PUNCT
ejpam-62	117	92	wk−1	wk−1	PROPN
ejpam-62	117	93	)	)	PUNCT
ejpam-62	117	94	to	to	ADP
ejpam-62	117	95	d	d	PROPN
ejpam-62	117	96	and	and	CCONJ
ejpam-62	117	97	deleting	delete	VERB
ejpam-62	117	98	f	f	PROPN
ejpam-62	117	99	′	′	NUM
ejpam-62	117	100	from	from	ADP
ejpam-62	117	101	d	d	PROPN
ejpam-62	117	102	,	,	PUNCT
ejpam-62	117	103	we	we	PRON
ejpam-62	117	104	get	get	VERB
ejpam-62	117	105	an	an	DET
ejpam-62	117	106	oriented	oriented	ADJ
ejpam-62	117	107	k	k	NOUN
ejpam-62	117	108	-	-	NOUN
ejpam-62	117	109	hypergraph	hypergraph	VERB
ejpam-62	117	110	d′	d′	X
ejpam-62	117	111	with	with	ADP
ejpam-62	117	112	s+(s+i	s+(s+i	NOUN
ejpam-62	117	113	,	,	PUNCT
ejpam-62	117	114	s−j	s−j	PROPN
ejpam-62	117	115	)	)	PUNCT
ejpam-62	117	116	as	as	ADP
ejpam-62	117	117	its	its	PRON
ejpam-62	117	118	score	score	NOUN
ejpam-62	117	119	sequence	sequence	NOUN
ejpam-62	117	120	.	.	PUNCT
ejpam-62	118	1	and	and	CCONJ
ejpam-62	118	2	therefore	therefore	ADV
ejpam-62	118	3	,	,	PUNCT
ejpam-62	118	4	we	we	PRON
ejpam-62	118	5	have	have	VERB
ejpam-62	118	6	d+(v	d+(v	PROPN
ejpam-62	118	7	j	j	NOUN
ejpam-62	118	8	)	)	PUNCT
ejpam-62	118	9	≤	≤	NOUN
ejpam-62	118	10	d+(vi	d+(vi	PROPN
ejpam-62	118	11	)	)	PUNCT
ejpam-62	118	12	.	.	PUNCT
ejpam-62	119	1	meanwhile	meanwhile	ADV
ejpam-62	119	2	,	,	PUNCT
ejpam-62	119	3	since	since	SCONJ
ejpam-62	119	4	y	y	PROPN
ejpam-62	119	5	>	>	X
ejpam-62	119	6	β	β	X
ejpam-62	119	7	,	,	PUNCT
ejpam-62	119	8	si	si	X
ejpam-62	119	9	<	<	X
ejpam-62	119	10	s	s	PROPN
ejpam-62	119	11	j	j	PROPN
ejpam-62	119	12	and	and	CCONJ
ejpam-62	119	13	by	by	ADP
ejpam-62	119	14	the	the	DET
ejpam-62	119	15	proof	proof	NOUN
ejpam-62	119	16	of	of	ADP
ejpam-62	119	17	lemma	lemma	PROPN
ejpam-62	119	18	2.1	2.1	NUM
ejpam-62	119	19	,	,	PUNCT
ejpam-62	119	20	si	si	PROPN
ejpam-62	119	21	=	=	PUNCT
ejpam-62	119	22	kd+(vi	kd+(vi	PROPN
ejpam-62	119	23	)	)	PUNCT
ejpam-62	120	1	+	+	CCONJ
ejpam-62	120	2	(	(	PUNCT
ejpam-62	120	3	k−	k−	PROPN
ejpam-62	120	4	1)d∗(vi	1)d∗(vi	NUM
ejpam-62	120	5	)	)	PUNCT
ejpam-62	121	1	<	<	X
ejpam-62	121	2	s	s	X
ejpam-62	121	3	j	j	PROPN
ejpam-62	121	4	=	=	SYM
ejpam-62	121	5	kd+(v	kd+(v	PROPN
ejpam-62	121	6	j	j	PROPN
ejpam-62	121	7	)	)	PUNCT
ejpam-62	121	8	+	+	CCONJ
ejpam-62	121	9	(	(	PUNCT
ejpam-62	121	10	k−	k−	PROPN
ejpam-62	121	11	1)d∗(v	1)d∗(v	PROPN
ejpam-62	121	12	j	j	PROPN
ejpam-62	121	13	)	)	PUNCT
ejpam-62	121	14	,	,	PUNCT
ejpam-62	121	15	which	which	PRON
ejpam-62	121	16	implies	imply	VERB
ejpam-62	121	17	that	that	DET
ejpam-62	121	18	k(d+(v	k(d+(v	PROPN
ejpam-62	121	19	j)−	j)−	PROPN
ejpam-62	121	20	d+(vi	d+(vi	PROPN
ejpam-62	121	21	)	)	PUNCT
ejpam-62	121	22	)	)	PUNCT
ejpam-62	122	1	>	>	PUNCT
ejpam-62	122	2	(	(	PUNCT
ejpam-62	122	3	k−	k−	PROPN
ejpam-62	122	4	1)(d∗(vi)−	1)(d∗(vi)−	PROPN
ejpam-62	122	5	d∗(v	d∗(v	PROPN
ejpam-62	122	6	j	j	PROPN
ejpam-62	122	7	)	)	PUNCT
ejpam-62	122	8	)	)	PUNCT
ejpam-62	123	1	>	>	X
ejpam-62	123	2	0	0	NUM
ejpam-62	123	3	,	,	PUNCT
ejpam-62	123	4	thus	thus	ADV
ejpam-62	123	5	we	we	PRON
ejpam-62	123	6	have	have	VERB
ejpam-62	123	7	(	(	PUNCT
ejpam-62	123	8	d+(v	d+(v	ADV
ejpam-62	123	9	j)−	j)−	PROPN
ejpam-62	123	10	d+(vi	d+(vi	PROPN
ejpam-62	123	11	)	)	PUNCT
ejpam-62	123	12	>	>	X
ejpam-62	124	1	0	0	NUM
ejpam-62	124	2	,	,	PUNCT
ejpam-62	124	3	which	which	PRON
ejpam-62	124	4	contradicts	contradict	VERB
ejpam-62	124	5	the	the	DET
ejpam-62	124	6	fact	fact	NOUN
ejpam-62	124	7	that	that	SCONJ
ejpam-62	124	8	d+(v	d+(v	ADV
ejpam-62	124	9	j)≤	j)≤	NOUN
ejpam-62	124	10	d+(vi	d+(vi	ADJ
ejpam-62	124	11	)	)	PUNCT
ejpam-62	124	12	.	.	PUNCT
ejpam-62	125	1	s.	s.	PROPN
ejpam-62	125	2	pirzada	pirzada	PROPN
ejpam-62	125	3	,	,	PUNCT
ejpam-62	125	4	z.	z.	PROPN
ejpam-62	125	5	guofei	guofei	PROPN
ejpam-62	125	6	/	/	SYM
ejpam-62	125	7	eur	eur	PROPN
ejpam-62	125	8	.	.	PUNCT
ejpam-62	126	1	j.	j.	PROPN
ejpam-62	126	2	pure	pure	PROPN
ejpam-62	126	3	appl	appl	PROPN
ejpam-62	126	4	.	.	PROPN
ejpam-62	126	5	math	math	PROPN
ejpam-62	126	6	,	,	PUNCT
ejpam-62	126	7	1	1	NUM
ejpam-62	126	8	(	(	PUNCT
ejpam-62	126	9	2008	2008	NUM
ejpam-62	126	10	)	)	PUNCT
ejpam-62	126	11	,	,	PUNCT
ejpam-62	126	12	(	(	PUNCT
ejpam-62	126	13	10	10	NUM
ejpam-62	126	14	-	-	SYM
ejpam-62	126	15	20	20	NUM
ejpam-62	126	16	)	)	PUNCT
ejpam-62	126	17	15	15	NUM
ejpam-62	126	18	case	case	NOUN
ejpam-62	126	19	2	2	NUM
ejpam-62	126	20	.	.	X
ejpam-62	127	1	for	for	ADP
ejpam-62	127	2	each	each	DET
ejpam-62	127	3	non	non	ADJ
ejpam-62	127	4	arc	arc	NOUN
ejpam-62	127	5	e∗	e∗	PROPN
ejpam-62	127	6	=	=	SYM
ejpam-62	127	7	〈	〈	PROPN
ejpam-62	127	8	u1	u1	NOUN
ejpam-62	127	9	,	,	PUNCT
ejpam-62	127	10	u2	u2	NOUN
ejpam-62	127	11	,	,	PUNCT
ejpam-62	127	12	·	·	PUNCT
ejpam-62	127	13	·	·	PUNCT
ejpam-62	127	14	·	·	PUNCT
ejpam-62	127	15	,	,	PUNCT
ejpam-62	127	16	uk−1	uk−1	PROPN
ejpam-62	127	17	,	,	PUNCT
ejpam-62	127	18	vi	vi	NOUN
ejpam-62	127	19	〉	〉	NOUN
ejpam-62	127	20	,	,	PUNCT
ejpam-62	127	21	either	either	CCONJ
ejpam-62	127	22	f	f	PROPN
ejpam-62	127	23	∗	∗	NOUN
ejpam-62	127	24	=	=	PUNCT
ejpam-62	127	25	〈	〈	NOUN
ejpam-62	127	26	u1	u1	NOUN
ejpam-62	127	27	,	,	PUNCT
ejpam-62	127	28	u2	u2	NOUN
ejpam-62	127	29	,	,	PUNCT
ejpam-62	127	30	·	·	PUNCT
ejpam-62	127	31	·	·	PUNCT
ejpam-62	127	32	·	·	PUNCT
ejpam-62	127	33	,	,	PUNCT
ejpam-62	127	34	uk−1	uk−1	PROPN
ejpam-62	127	35	,	,	PUNCT
ejpam-62	127	36	v	v	ADP
ejpam-62	127	37	j	j	PROPN
ejpam-62	127	38	〉	〉	NOUN
ejpam-62	127	39	is	be	AUX
ejpam-62	127	40	a	a	DET
ejpam-62	127	41	non	non	ADJ
ejpam-62	127	42	arc	arc	NOUN
ejpam-62	127	43	,	,	PUNCT
ejpam-62	127	44	or	or	CCONJ
ejpam-62	127	45	{	{	PUNCT
ejpam-62	127	46	u1	u1	NOUN
ejpam-62	127	47	,	,	PUNCT
ejpam-62	127	48	u2	u2	NOUN
ejpam-62	127	49	,	,	PUNCT
ejpam-62	127	50	·	·	PUNCT
ejpam-62	127	51	·	·	PUNCT
ejpam-62	127	52	·	·	PUNCT
ejpam-62	127	53	,	,	PUNCT
ejpam-62	127	54	uk−1	uk−1	PROPN
ejpam-62	127	55	,	,	PUNCT
ejpam-62	127	56	v	v	PROPN
ejpam-62	127	57	j	j	NOUN
ejpam-62	127	58	}	}	PUNCT
ejpam-62	127	59	forms	form	VERB
ejpam-62	127	60	an	an	DET
ejpam-62	127	61	arc	arc	NOUN
ejpam-62	127	62	,	,	PUNCT
ejpam-62	127	63	but	but	CCONJ
ejpam-62	127	64	v	v	X
ejpam-62	127	65	j	j	PROPN
ejpam-62	127	66	is	be	AUX
ejpam-62	127	67	not	not	PART
ejpam-62	127	68	the	the	DET
ejpam-62	127	69	last	last	ADJ
ejpam-62	127	70	entry	entry	NOUN
ejpam-62	127	71	.	.	PUNCT
ejpam-62	128	1	note	note	VERB
ejpam-62	128	2	that	that	SCONJ
ejpam-62	128	3	the	the	DET
ejpam-62	128	4	later	later	ADJ
ejpam-62	128	5	case	case	NOUN
ejpam-62	128	6	will	will	AUX
ejpam-62	128	7	deduce	deduce	VERB
ejpam-62	128	8	that	that	DET
ejpam-62	128	9	result	result	NOUN
ejpam-62	128	10	is	be	AUX
ejpam-62	128	11	valid	valid	ADJ
ejpam-62	128	12	,	,	PUNCT
ejpam-62	128	13	so	so	ADV
ejpam-62	128	14	we	we	PRON
ejpam-62	128	15	assume	assume	VERB
ejpam-62	128	16	that	that	SCONJ
ejpam-62	128	17	for	for	ADP
ejpam-62	128	18	each	each	DET
ejpam-62	128	19	non	non	ADJ
ejpam-62	128	20	arc	arc	NOUN
ejpam-62	128	21	e∗	e∗	PROPN
ejpam-62	128	22	=	=	SYM
ejpam-62	128	23	〈	〈	PROPN
ejpam-62	128	24	u1	u1	NOUN
ejpam-62	128	25	,	,	PUNCT
ejpam-62	128	26	u2	u2	NOUN
ejpam-62	128	27	,	,	PUNCT
ejpam-62	128	28	·	·	PUNCT
ejpam-62	128	29	·	·	PUNCT
ejpam-62	129	1	·	·	PUNCT
ejpam-62	129	2	,	,	PUNCT
ejpam-62	129	3	uk−1	uk−1	PROPN
ejpam-62	129	4	,	,	PUNCT
ejpam-62	129	5	vi	vi	NOUN
ejpam-62	129	6	〉	〉	NOUN
ejpam-62	129	7	,	,	PUNCT
ejpam-62	129	8	f	f	PROPN
ejpam-62	129	9	∗	∗	NOUN
ejpam-62	129	10	=	=	PUNCT
ejpam-62	129	11	〈	〈	NOUN
ejpam-62	129	12	u1	u1	NOUN
ejpam-62	129	13	,	,	PUNCT
ejpam-62	129	14	u2	u2	NOUN
ejpam-62	129	15	,	,	PUNCT
ejpam-62	129	16	·	·	PUNCT
ejpam-62	129	17	·	·	PUNCT
ejpam-62	129	18	·	·	PUNCT
ejpam-62	129	19	,	,	PUNCT
ejpam-62	129	20	uk−1	uk−1	PROPN
ejpam-62	129	21	,	,	PUNCT
ejpam-62	129	22	v	v	ADP
ejpam-62	129	23	j	j	NOUN
ejpam-62	129	24	〉	〉	NOUN
ejpam-62	129	25	is	be	AUX
ejpam-62	129	26	also	also	ADV
ejpam-62	129	27	a	a	DET
ejpam-62	129	28	non	non	ADJ
ejpam-62	129	29	arc	arc	NOUN
ejpam-62	129	30	.	.	PUNCT
ejpam-62	130	1	this	this	PRON
ejpam-62	130	2	implies	imply	VERB
ejpam-62	130	3	that	that	SCONJ
ejpam-62	130	4	d∗(vi	d∗(vi	PROPN
ejpam-62	130	5	)	)	PUNCT
ejpam-62	130	6	≤	≤	NUM
ejpam-62	130	7	d∗(v	d∗(v	PROPN
ejpam-62	130	8	j	j	PROPN
ejpam-62	130	9	)	)	PUNCT
ejpam-62	130	10	,	,	PUNCT
ejpam-62	130	11	which	which	PRON
ejpam-62	130	12	contradicts	contradict	VERB
ejpam-62	130	13	that	that	SCONJ
ejpam-62	130	14	y	y	PROPN
ejpam-62	130	15	>	>	X
ejpam-62	130	16	β	β	X
ejpam-62	130	17	.	.	PUNCT
ejpam-62	131	1	�	�	PROPN
ejpam-62	131	2	we	we	PRON
ejpam-62	131	3	note	note	VERB
ejpam-62	131	4	when	when	SCONJ
ejpam-62	131	5	y	y	PROPN
ejpam-62	131	6	≤	≤	PROPN
ejpam-62	131	7	β	β	X
ejpam-62	131	8	,	,	PUNCT
ejpam-62	131	9	lemma	lemma	PROPN
ejpam-62	131	10	2.3	2.3	NUM
ejpam-62	131	11	need	need	AUX
ejpam-62	131	12	not	not	PART
ejpam-62	131	13	be	be	AUX
ejpam-62	131	14	true	true	ADJ
ejpam-62	131	15	.	.	PUNCT
ejpam-62	132	1	to	to	PART
ejpam-62	132	2	see	see	VERB
ejpam-62	132	3	this	this	PRON
ejpam-62	132	4	consider	consider	VERB
ejpam-62	132	5	a	a	DET
ejpam-62	132	6	3	3	NUM
ejpam-62	132	7	-	-	NOUN
ejpam-62	132	8	hypergraph	hypergraph	NOUN
ejpam-62	132	9	d	d	NOUN
ejpam-62	132	10	=	=	SYM
ejpam-62	132	11	(	(	PUNCT
ejpam-62	132	12	v	v	NOUN
ejpam-62	132	13	,	,	PUNCT
ejpam-62	132	14	a	a	PRON
ejpam-62	132	15	)	)	PUNCT
ejpam-62	132	16	with	with	ADP
ejpam-62	132	17	v	v	NOUN
ejpam-62	132	18	=	=	SYM
ejpam-62	132	19	{	{	PUNCT
ejpam-62	132	20	1	1	NUM
ejpam-62	132	21	,	,	PUNCT
ejpam-62	132	22	2	2	NUM
ejpam-62	132	23	,	,	PUNCT
ejpam-62	132	24	3,4	3,4	NUM
ejpam-62	132	25	}	}	PUNCT
ejpam-62	132	26	and	and	CCONJ
ejpam-62	132	27	a=	a=	VERB
ejpam-62	132	28	{	{	PUNCT
ejpam-62	132	29	(	(	PUNCT
ejpam-62	132	30	1,2	1,2	NUM
ejpam-62	132	31	,	,	PUNCT
ejpam-62	132	32	3	3	NUM
ejpam-62	132	33	)	)	PUNCT
ejpam-62	132	34	,	,	PUNCT
ejpam-62	132	35	(	(	PUNCT
ejpam-62	132	36	3,4	3,4	NUM
ejpam-62	132	37	,	,	PUNCT
ejpam-62	132	38	1	1	NUM
ejpam-62	132	39	)	)	PUNCT
ejpam-62	132	40	}	}	PUNCT
ejpam-62	132	41	it	it	PRON
ejpam-62	132	42	is	be	AUX
ejpam-62	132	43	easy	easy	ADJ
ejpam-62	132	44	to	to	PART
ejpam-62	132	45	check	check	VERB
ejpam-62	132	46	that	that	SCONJ
ejpam-62	132	47	[	[	X
ejpam-62	132	48	5,5,7,7	5,5,7,7	NUM
ejpam-62	132	49	]	]	X
ejpam-62	132	50	is	be	AUX
ejpam-62	132	51	the	the	DET
ejpam-62	132	52	score	score	NOUN
ejpam-62	132	53	sequence	sequence	NOUN
ejpam-62	132	54	of	of	ADP
ejpam-62	132	55	d.	d.	PROPN
ejpam-62	132	56	but	but	CCONJ
ejpam-62	132	57	the	the	DET
ejpam-62	132	58	sequence	sequence	NOUN
ejpam-62	132	59	[	[	X
ejpam-62	132	60	5,6,6,7	5,6,6,7	NUM
ejpam-62	132	61	]	]	X
ejpam-62	132	62	,	,	PUNCT
ejpam-62	132	63	which	which	PRON
ejpam-62	132	64	is	be	AUX
ejpam-62	132	65	just	just	ADV
ejpam-62	132	66	s+(s+i	s+(s+i	NOUN
ejpam-62	132	67	,	,	PUNCT
ejpam-62	132	68	s−j	s−j	PROPN
ejpam-62	132	69	)	)	PUNCT
ejpam-62	132	70	,	,	PUNCT
ejpam-62	132	71	where	where	SCONJ
ejpam-62	132	72	si	si	NOUN
ejpam-62	132	73	=	=	SYM
ejpam-62	132	74	5	5	NUM
ejpam-62	132	75	and	and	CCONJ
ejpam-62	132	76	s	s	X
ejpam-62	132	77	j	j	NOUN
ejpam-62	132	78	=	=	SYM
ejpam-62	132	79	7	7	NUM
ejpam-62	132	80	,	,	PUNCT
ejpam-62	132	81	is	be	AUX
ejpam-62	132	82	not	not	PART
ejpam-62	132	83	a	a	DET
ejpam-62	132	84	score	score	NOUN
ejpam-62	132	85	sequence	sequence	NOUN
ejpam-62	132	86	of	of	ADP
ejpam-62	132	87	any	any	DET
ejpam-62	132	88	3	3	NUM
ejpam-62	132	89	-	-	PUNCT
ejpam-62	132	90	hypergraph	hypergraph	NOUN
ejpam-62	132	91	.	.	PUNCT
ejpam-62	133	1	lemma	lemma	PROPN
ejpam-62	133	2	2.4	2.4	NUM
ejpam-62	133	3	.	.	PUNCT
ejpam-62	134	1	if	if	SCONJ
ejpam-62	134	2	s	s	PRON
ejpam-62	134	3	=	=	PUNCT
ejpam-62	135	1	[	[	X
ejpam-62	135	2	s1	s1	NOUN
ejpam-62	135	3	,	,	PUNCT
ejpam-62	135	4	s2	s2	PROPN
ejpam-62	135	5	,	,	PUNCT
ejpam-62	135	6	·	·	PUNCT
ejpam-62	135	7	·	·	PUNCT
ejpam-62	135	8	·	·	PUNCT
ejpam-62	135	9	,	,	PUNCT
ejpam-62	135	10	sn	sn	X
ejpam-62	135	11	]	]	PUNCT
ejpam-62	135	12	with	with	ADP
ejpam-62	135	13	s1	s1	PROPN
ejpam-62	135	14	≤	≤	NUM
ejpam-62	135	15	s2	s2	VERB
ejpam-62	135	16	≤	≤	NOUN
ejpam-62	135	17	·	·	PUNCT
ejpam-62	135	18	·	·	PUNCT
ejpam-62	135	19	·	·	PUNCT
ejpam-62	135	20	≤	≤	NUM
ejpam-62	135	21	sn	sn	PROPN
ejpam-62	135	22	is	be	AUX
ejpam-62	135	23	a	a	DET
ejpam-62	135	24	non	non	ADJ
ejpam-62	135	25	-	-	ADJ
ejpam-62	135	26	negative	negative	ADJ
ejpam-62	135	27	integer	integer	NOUN
ejpam-62	135	28	sequence	sequence	NOUN
ejpam-62	135	29	satisfying	satisfy	VERB
ejpam-62	135	30	(	(	PUNCT
ejpam-62	135	31	1	1	NUM
ejpam-62	135	32	)	)	PUNCT
ejpam-62	135	33	,	,	PUNCT
ejpam-62	135	34	and	and	CCONJ
ejpam-62	135	35	if	if	SCONJ
ejpam-62	135	36	sn	sn	PROPN
ejpam-62	135	37	<	<	X
ejpam-62	135	38	k	k	X
ejpam-62	135	39	�	�	PROPN
ejpam-62	135	40	n−	n−	PROPN
ejpam-62	135	41	1	1	NUM
ejpam-62	135	42	k−	k−	PROPN
ejpam-62	135	43	1	1	NUM
ejpam-62	135	44	�	�	PROPN
ejpam-62	135	45	,	,	PUNCT
ejpam-62	135	46	then	then	ADV
ejpam-62	135	47	there	there	PRON
ejpam-62	135	48	exists	exist	VERB
ejpam-62	135	49	p	p	X
ejpam-62	135	50	(	(	PUNCT
ejpam-62	135	51	1≤	1≤	NUM
ejpam-62	135	52	p	p	X
ejpam-62	135	53	≤	≤	PROPN
ejpam-62	135	54	n−1	n−1	PROPN
ejpam-62	135	55	)	)	PUNCT
ejpam-62	135	56	such	such	ADJ
ejpam-62	135	57	that	that	SCONJ
ejpam-62	135	58	s(s+n	s(s+n	PROPN
ejpam-62	135	59	,	,	PUNCT
ejpam-62	135	60	s−p	s−p	PROPN
ejpam-62	135	61	)	)	PUNCT
ejpam-62	135	62	is	be	AUX
ejpam-62	135	63	non	non	ADJ
ejpam-62	135	64	-	-	ADJ
ejpam-62	135	65	decreasing	decrease	VERB
ejpam-62	135	66	and	and	CCONJ
ejpam-62	135	67	satisfies	satisfie	NOUN
ejpam-62	135	68	(	(	PUNCT
ejpam-62	135	69	2.1	2.1	NUM
ejpam-62	135	70	)	)	PUNCT
ejpam-62	135	71	.	.	PUNCT
ejpam-62	136	1	proof	proof	NOUN
ejpam-62	136	2	.	.	PUNCT
ejpam-62	137	1	let	let	VERB
ejpam-62	137	2	p	p	PRON
ejpam-62	137	3	be	be	AUX
ejpam-62	137	4	the	the	DET
ejpam-62	137	5	maximum	maximum	ADJ
ejpam-62	137	6	integer	integer	NOUN
ejpam-62	137	7	such	such	DET
ejpam-62	137	8	that	that	DET
ejpam-62	137	9	sp−1	sp−1	PROPN
ejpam-62	137	10	<	<	X
ejpam-62	137	11	sp	sp	NOUN
ejpam-62	137	12	=	=	SYM
ejpam-62	137	13	sp+1	sp+1	NOUN
ejpam-62	137	14	=	=	SYM
ejpam-62	137	15	·	·	PUNCT
ejpam-62	137	16	·	·	PUNCT
ejpam-62	137	17	·	·	PUNCT
ejpam-62	138	1	=	=	SYM
ejpam-62	138	2	sn−1	sn−1	ADJ
ejpam-62	138	3	with	with	ADP
ejpam-62	138	4	s0	s0	PROPN
ejpam-62	138	5	=	=	PUNCT
ejpam-62	138	6	0	0	PUNCT
ejpam-62	139	1	if	if	SCONJ
ejpam-62	139	2	p	p	NOUN
ejpam-62	139	3	=	=	NOUN
ejpam-62	139	4	1	1	X
ejpam-62	139	5	.	.	PUNCT
ejpam-62	139	6	to	to	PART
ejpam-62	139	7	see	see	VERB
ejpam-62	139	8	s(s+n	s(s+n	PROPN
ejpam-62	139	9	,	,	PUNCT
ejpam-62	139	10	s−p	s−p	NOUN
ejpam-62	139	11	)	)	PUNCT
ejpam-62	139	12	satisfies	satisfie	NOUN
ejpam-62	139	13	(	(	PUNCT
ejpam-62	139	14	2.1	2.1	NUM
ejpam-62	139	15	)	)	PUNCT
ejpam-62	139	16	,	,	PUNCT
ejpam-62	139	17	we	we	PRON
ejpam-62	139	18	only	only	ADV
ejpam-62	139	19	need	need	VERB
ejpam-62	139	20	to	to	PART
ejpam-62	139	21	show	show	VERB
ejpam-62	139	22	for	for	ADP
ejpam-62	139	23	each	each	DET
ejpam-62	139	24	j	j	NOUN
ejpam-62	139	25	(	(	PUNCT
ejpam-62	139	26	p	p	NOUN
ejpam-62	139	27	≤	≤	PROPN
ejpam-62	139	28	j	j	PROPN
ejpam-62	139	29	≤	≤	ADJ
ejpam-62	139	30	n−	n−	PROPN
ejpam-62	139	31	1	1	NUM
ejpam-62	139	32	)	)	PUNCT
ejpam-62	139	33	,	,	PUNCT
ejpam-62	139	34	j	j	PROPN
ejpam-62	139	35	∑	∑	PUNCT
ejpam-62	139	36	i=1	i=1	PROPN
ejpam-62	140	1	si	si	X
ejpam-62	140	2	>	>	X
ejpam-62	140	3	j(k−	j(k−	PROPN
ejpam-62	140	4	1	1	NUM
ejpam-62	140	5	)	)	PUNCT
ejpam-62	140	6	�	�	PROPN
ejpam-62	140	7	n−	n−	NOUN
ejpam-62	140	8	1	1	NUM
ejpam-62	140	9	k−	k−	PROPN
ejpam-62	140	10	1	1	NUM
ejpam-62	140	11	�	�	PROPN
ejpam-62	140	12	+	+	CCONJ
ejpam-62	140	13	k−1	k−1	PROPN
ejpam-62	140	14	∑	∑	PROPN
ejpam-62	140	15	i=1	i=1	PROPN
ejpam-62	140	16	(	(	PUNCT
ejpam-62	140	17	i−	i−	PROPN
ejpam-62	140	18	k	k	PROPN
ejpam-62	140	19	)	)	PUNCT
ejpam-62	140	20	�	�	PROPN
ejpam-62	141	1	j	j	PROPN
ejpam-62	141	2	i	i	PROPN
ejpam-62	141	3	�	�	VERB
ejpam-62	141	4	�	�	PROPN
ejpam-62	141	5	n−	n−	PROPN
ejpam-62	141	6	j	j	PROPN
ejpam-62	141	7	k−	k−	PROPN
ejpam-62	141	8	i	i	PRON
ejpam-62	141	9	�	�	PROPN
ejpam-62	141	10	.	.	PUNCT
ejpam-62	142	1	(	(	PUNCT
ejpam-62	142	2	2.2	2.2	NUM
ejpam-62	142	3	)	)	PUNCT
ejpam-62	142	4	since	since	SCONJ
ejpam-62	142	5	sn	sn	PROPN
ejpam-62	142	6	<	<	X
ejpam-62	142	7	k	k	PROPN
ejpam-62	142	8	�	�	PROPN
ejpam-62	142	9	n−	n−	PROPN
ejpam-62	142	10	1	1	NUM
ejpam-62	142	11	k−	k−	PROPN
ejpam-62	142	12	1	1	NUM
ejpam-62	142	13	�	�	PROPN
ejpam-62	142	14	,	,	PUNCT
ejpam-62	142	15	therefore	therefore	ADV
ejpam-62	142	16	n−1	n−1	PROPN
ejpam-62	142	17	∑	∑	PUNCT
ejpam-62	142	18	i=1	i=1	PROPN
ejpam-62	142	19	si	si	PROPN
ejpam-62	142	20	=	=	SYM
ejpam-62	142	21	n	n	PROPN
ejpam-62	142	22	∑	∑	PROPN
ejpam-62	142	23	i=1	i=1	PROPN
ejpam-62	142	24	si	si	PROPN
ejpam-62	142	25	−	−	PROPN
ejpam-62	142	26	sn	sn	NOUN
ejpam-62	142	27	=	=	SYM
ejpam-62	142	28	n(k−	n(k−	PROPN
ejpam-62	142	29	1	1	NUM
ejpam-62	142	30	)	)	PUNCT
ejpam-62	142	31	�	�	PROPN
ejpam-62	142	32	n−	n−	NOUN
ejpam-62	142	33	1	1	NUM
ejpam-62	142	34	k−	k−	PROPN
ejpam-62	142	35	1	1	NUM
ejpam-62	142	36	�	�	PROPN
ejpam-62	142	37	−	−	PROPN
ejpam-62	142	38	sn	sn	PROPN
ejpam-62	142	39	>	>	X
ejpam-62	142	40	n(k−	n(k−	PROPN
ejpam-62	142	41	1	1	NUM
ejpam-62	142	42	)	)	PUNCT
ejpam-62	142	43	�	�	PROPN
ejpam-62	142	44	n−	n−	NOUN
ejpam-62	142	45	1	1	NUM
ejpam-62	142	46	k−	k−	PROPN
ejpam-62	142	47	1	1	NUM
ejpam-62	142	48	�	�	PROPN
ejpam-62	142	49	−	−	PROPN
ejpam-62	142	50	k	k	PROPN
ejpam-62	142	51	�	�	PROPN
ejpam-62	142	52	n−	n−	PROPN
ejpam-62	142	53	1	1	NUM
ejpam-62	142	54	k−	k−	PROPN
ejpam-62	142	55	1	1	NUM
ejpam-62	142	56	�	�	NOUN
ejpam-62	142	57	=	=	PUNCT
ejpam-62	142	58	(	(	PUNCT
ejpam-62	142	59	n−	n−	NOUN
ejpam-62	142	60	1)(k−	1)(k−	NUM
ejpam-62	142	61	1	1	NUM
ejpam-62	142	62	)	)	PUNCT
ejpam-62	142	63	�	�	PROPN
ejpam-62	142	64	n−	n−	NOUN
ejpam-62	142	65	1	1	NUM
ejpam-62	142	66	k−	k−	PROPN
ejpam-62	142	67	1	1	NUM
ejpam-62	142	68	�	�	PROPN
ejpam-62	142	69	−	−	PROPN
ejpam-62	142	70	�	�	PROPN
ejpam-62	142	71	n−	n−	PROPN
ejpam-62	142	72	1	1	NUM
ejpam-62	142	73	k−	k−	PROPN
ejpam-62	142	74	1	1	NUM
ejpam-62	142	75	�	�	PROPN
ejpam-62	142	76	.	.	PUNCT
ejpam-62	143	1	as	as	SCONJ
ejpam-62	143	2	�	�	PROPN
ejpam-62	143	3	n−	n−	PROPN
ejpam-62	143	4	1	1	NUM
ejpam-62	143	5	k−	k−	PROPN
ejpam-62	143	6	1	1	NUM
ejpam-62	143	7	�	�	PROPN
ejpam-62	143	8	≤	≤	NOUN
ejpam-62	143	9	k−1	k−1	PROPN
ejpam-62	143	10	∑	∑	PROPN
ejpam-62	143	11	i=1	i=1	PROPN
ejpam-62	143	12	(	(	PUNCT
ejpam-62	143	13	k−	k−	PROPN
ejpam-62	143	14	i	i	NOUN
ejpam-62	143	15	)	)	PUNCT
ejpam-62	143	16	�	�	PROPN
ejpam-62	143	17	n−	n−	NOUN
ejpam-62	143	18	1	1	NUM
ejpam-62	143	19	i	i	PRON
ejpam-62	143	20	�	�	VERB
ejpam-62	143	21	�	�	PROPN
ejpam-62	143	22	n−	n−	PROPN
ejpam-62	143	23	(	(	PUNCT
ejpam-62	143	24	n−	n−	NOUN
ejpam-62	143	25	1	1	NUM
ejpam-62	143	26	)	)	PUNCT
ejpam-62	143	27	k−	k−	NOUN
ejpam-62	143	28	i	i	PRON
ejpam-62	143	29	�	�	PROPN
ejpam-62	143	30	,	,	PUNCT
ejpam-62	143	31	so	so	ADV
ejpam-62	143	32	−	−	PROPN
ejpam-62	143	33	�	�	PROPN
ejpam-62	143	34	n−	n−	PROPN
ejpam-62	143	35	1	1	NUM
ejpam-62	143	36	k−	k−	PROPN
ejpam-62	143	37	1	1	NUM
ejpam-62	143	38	�	�	PROPN
ejpam-62	143	39	≥−	≥−	PROPN
ejpam-62	143	40	k−1	k−1	PROPN
ejpam-62	143	41	∑	∑	PROPN
ejpam-62	143	42	i=1	i=1	PROPN
ejpam-62	143	43	(	(	PUNCT
ejpam-62	143	44	k−	k−	PROPN
ejpam-62	143	45	i	i	NOUN
ejpam-62	143	46	)	)	PUNCT
ejpam-62	143	47	�	�	PROPN
ejpam-62	143	48	n−	n−	NOUN
ejpam-62	143	49	1	1	NUM
ejpam-62	143	50	i	i	PRON
ejpam-62	143	51	�	�	VERB
ejpam-62	143	52	�	�	PROPN
ejpam-62	143	53	1	1	NUM
ejpam-62	143	54	k−	k−	PROPN
ejpam-62	143	55	i	i	PRON
ejpam-62	143	56	�	�	PROPN
ejpam-62	144	1	=	=	SYM
ejpam-62	144	2	k−1	k−1	PROPN
ejpam-62	144	3	∑	∑	PROPN
ejpam-62	144	4	i=1	i=1	PROPN
ejpam-62	144	5	(	(	PUNCT
ejpam-62	144	6	i−	i−	PROPN
ejpam-62	144	7	k	k	PROPN
ejpam-62	144	8	)	)	PUNCT
ejpam-62	144	9	�	�	PROPN
ejpam-62	144	10	n−	n−	NOUN
ejpam-62	144	11	1	1	NUM
ejpam-62	144	12	i	i	PRON
ejpam-62	144	13	�	�	VERB
ejpam-62	144	14	�	�	PROPN
ejpam-62	144	15	1	1	NUM
ejpam-62	144	16	k−	k−	PROPN
ejpam-62	144	17	i	i	PRON
ejpam-62	144	18	�	�	PROPN
ejpam-62	144	19	.	.	PUNCT
ejpam-62	145	1	s.	s.	PROPN
ejpam-62	145	2	pirzada	pirzada	PROPN
ejpam-62	145	3	,	,	PUNCT
ejpam-62	145	4	z.	z.	PROPN
ejpam-62	145	5	guofei	guofei	PROPN
ejpam-62	145	6	/	/	SYM
ejpam-62	145	7	eur	eur	PROPN
ejpam-62	145	8	.	.	PUNCT
ejpam-62	146	1	j.	j.	PROPN
ejpam-62	146	2	pure	pure	PROPN
ejpam-62	146	3	appl	appl	PROPN
ejpam-62	146	4	.	.	PROPN
ejpam-62	146	5	math	math	PROPN
ejpam-62	146	6	,	,	PUNCT
ejpam-62	146	7	1	1	NUM
ejpam-62	146	8	(	(	PUNCT
ejpam-62	146	9	2008	2008	NUM
ejpam-62	146	10	)	)	PUNCT
ejpam-62	146	11	,	,	PUNCT
ejpam-62	146	12	(	(	PUNCT
ejpam-62	146	13	10	10	NUM
ejpam-62	146	14	-	-	SYM
ejpam-62	146	15	20	20	NUM
ejpam-62	146	16	)	)	PUNCT
ejpam-62	146	17	16	16	NUM
ejpam-62	146	18	therefore	therefore	ADV
ejpam-62	146	19	,	,	PUNCT
ejpam-62	146	20	n−1	n−1	PROPN
ejpam-62	146	21	∑	∑	PUNCT
ejpam-62	146	22	i=1	i=1	PROPN
ejpam-62	146	23	si	si	X
ejpam-62	146	24	>	>	X
ejpam-62	146	25	(	(	PUNCT
ejpam-62	146	26	n−	n−	NOUN
ejpam-62	146	27	1)(k−	1)(k−	NUM
ejpam-62	146	28	1	1	NUM
ejpam-62	146	29	)	)	PUNCT
ejpam-62	146	30	�	�	PROPN
ejpam-62	146	31	n−	n−	NOUN
ejpam-62	146	32	1	1	NUM
ejpam-62	146	33	k−	k−	PROPN
ejpam-62	146	34	1	1	NUM
ejpam-62	146	35	�	�	PROPN
ejpam-62	146	36	+	+	CCONJ
ejpam-62	146	37	k−1	k−1	PROPN
ejpam-62	146	38	∑	∑	PROPN
ejpam-62	146	39	i=1	i=1	PROPN
ejpam-62	146	40	(	(	PUNCT
ejpam-62	146	41	i−	i−	PROPN
ejpam-62	146	42	k	k	PROPN
ejpam-62	146	43	)	)	PUNCT
ejpam-62	146	44	�	�	PROPN
ejpam-62	147	1	n−	n−	NOUN
ejpam-62	147	2	1	1	NUM
ejpam-62	147	3	i	i	PRON
ejpam-62	147	4	�	�	VERB
ejpam-62	147	5	�	�	PROPN
ejpam-62	147	6	1	1	NUM
ejpam-62	147	7	k−	k−	PROPN
ejpam-62	147	8	i	i	PRON
ejpam-62	147	9	�	�	PROPN
ejpam-62	147	10	.	.	PUNCT
ejpam-62	148	1	thus	thus	ADV
ejpam-62	148	2	for	for	ADP
ejpam-62	148	3	p	p	NOUN
ejpam-62	148	4	=	=	SYM
ejpam-62	148	5	1	1	NUM
ejpam-62	148	6	,	,	PUNCT
ejpam-62	148	7	(	(	PUNCT
ejpam-62	148	8	2.2	2.2	NUM
ejpam-62	148	9	)	)	PUNCT
ejpam-62	148	10	holds	hold	VERB
ejpam-62	148	11	.	.	PUNCT
ejpam-62	149	1	now	now	ADV
ejpam-62	149	2	,	,	PUNCT
ejpam-62	149	3	we	we	PRON
ejpam-62	149	4	assume	assume	VERB
ejpam-62	149	5	p	p	NOUN
ejpam-62	149	6	≤	≤	ADJ
ejpam-62	149	7	n−	n−	NOUN
ejpam-62	149	8	2	2	NUM
ejpam-62	149	9	.	.	PUNCT
ejpam-62	150	1	clearly	clearly	ADV
ejpam-62	150	2	,	,	PUNCT
ejpam-62	150	3	(	(	PUNCT
ejpam-62	150	4	2.2	2.2	NUM
ejpam-62	150	5	)	)	PUNCT
ejpam-62	150	6	holds	hold	VERB
ejpam-62	150	7	for	for	ADP
ejpam-62	150	8	j	j	NOUN
ejpam-62	150	9	=	=	SYM
ejpam-62	150	10	n−	n−	NOUN
ejpam-62	150	11	1	1	NUM
ejpam-62	150	12	.	.	PUNCT
ejpam-62	151	1	if	if	SCONJ
ejpam-62	151	2	there	there	PRON
ejpam-62	151	3	exists	exist	VERB
ejpam-62	151	4	j0	j0	PROPN
ejpam-62	151	5	(	(	PUNCT
ejpam-62	151	6	p	p	PROPN
ejpam-62	151	7	≤	≤	PROPN
ejpam-62	151	8	j0	j0	PROPN
ejpam-62	151	9	≤	≤	PROPN
ejpam-62	151	10	n−	n−	NOUN
ejpam-62	151	11	2	2	NUM
ejpam-62	151	12	)	)	PUNCT
ejpam-62	151	13	such	such	ADJ
ejpam-62	151	14	that	that	SCONJ
ejpam-62	151	15	j0	j0	PROPN
ejpam-62	151	16	∑	∑	PROPN
ejpam-62	151	17	i=1	i=1	PROPN
ejpam-62	151	18	si	si	X
ejpam-62	152	1	=	=	SYM
ejpam-62	152	2	j0(k−	j0(k−	ADJ
ejpam-62	152	3	1	1	NUM
ejpam-62	152	4	)	)	PUNCT
ejpam-62	152	5	�	�	PROPN
ejpam-62	152	6	n−1	n−1	PROPN
ejpam-62	152	7	k−1	k−1	PROPN
ejpam-62	152	8	�	�	PROPN
ejpam-62	152	9	+	+	CCONJ
ejpam-62	153	1	k−1	k−1	PROPN
ejpam-62	153	2	∑	∑	PROPN
ejpam-62	153	3	i=1	i=1	PROPN
ejpam-62	153	4	(	(	PUNCT
ejpam-62	153	5	i−	i−	PROPN
ejpam-62	153	6	k	k	PROPN
ejpam-62	153	7	)	)	PUNCT
ejpam-62	153	8	�	�	PROPN
ejpam-62	153	9	j0	j0	PROPN
ejpam-62	153	10	i	i	PROPN
ejpam-62	153	11	�	�	PROPN
ejpam-62	153	12	�	�	PROPN
ejpam-62	153	13	n−	n−	PROPN
ejpam-62	153	14	j0	j0	PROPN
ejpam-62	153	15	k−i	k−i	NOUN
ejpam-62	153	16	�	�	PROPN
ejpam-62	153	17	,	,	PUNCT
ejpam-62	153	18	choose	choose	VERB
ejpam-62	153	19	j0	j0	PROPN
ejpam-62	153	20	as	as	ADV
ejpam-62	153	21	large	large	ADJ
ejpam-62	153	22	as	as	ADP
ejpam-62	153	23	possible	possible	ADJ
ejpam-62	153	24	.	.	PUNCT
ejpam-62	154	1	since	since	SCONJ
ejpam-62	154	2	j0	j0	PROPN
ejpam-62	154	3	+	+	PROPN
ejpam-62	154	4	1	1	NUM
ejpam-62	154	5	∑	∑	ADV
ejpam-62	154	6	i=1	i=1	PROPN
ejpam-62	154	7	si	si	X
ejpam-62	154	8	>	>	X
ejpam-62	154	9	(	(	PUNCT
ejpam-62	154	10	j0	j0	PROPN
ejpam-62	154	11	+	+	PROPN
ejpam-62	154	12	1)(k−	1)(k−	NUM
ejpam-62	154	13	1	1	NUM
ejpam-62	154	14	)	)	PUNCT
ejpam-62	154	15	�	�	PROPN
ejpam-62	154	16	n−	n−	NOUN
ejpam-62	154	17	1	1	NUM
ejpam-62	154	18	k−	k−	PROPN
ejpam-62	154	19	1	1	NUM
ejpam-62	154	20	�	�	PROPN
ejpam-62	154	21	+	+	CCONJ
ejpam-62	154	22	k−1	k−1	PROPN
ejpam-62	154	23	∑	∑	PROPN
ejpam-62	154	24	i=1	i=1	PROPN
ejpam-62	154	25	(	(	PUNCT
ejpam-62	154	26	i−	i−	PROPN
ejpam-62	154	27	k	k	PROPN
ejpam-62	154	28	)	)	PUNCT
ejpam-62	154	29	�	�	PROPN
ejpam-62	154	30	j0	j0	PROPN
ejpam-62	154	31	+	+	PROPN
ejpam-62	154	32	1	1	NUM
ejpam-62	154	33	i	i	NOUN
ejpam-62	154	34	�	�	VERB
ejpam-62	154	35	�	�	PROPN
ejpam-62	154	36	n−	n−	PROPN
ejpam-62	154	37	(	(	PUNCT
ejpam-62	154	38	j0	j0	PROPN
ejpam-62	154	39	+	+	NOUN
ejpam-62	154	40	1	1	NUM
ejpam-62	154	41	)	)	PUNCT
ejpam-62	154	42	k−	k−	NOUN
ejpam-62	154	43	i	i	PRON
ejpam-62	154	44	�	�	PROPN
ejpam-62	154	45	,	,	PUNCT
ejpam-62	154	46	therefore	therefore	ADV
ejpam-62	154	47	s	s	PROPN
ejpam-62	154	48	j0	j0	PROPN
ejpam-62	154	49	=	=	SYM
ejpam-62	154	50	s	s	PART
ejpam-62	154	51	j0	j0	NUM
ejpam-62	154	52	+	+	PROPN
ejpam-62	154	53	1	1	NUM
ejpam-62	154	54	=	=	SYM
ejpam-62	154	55	j0	j0	NUM
ejpam-62	154	56	+	+	PROPN
ejpam-62	154	57	1	1	NUM
ejpam-62	154	58	∑	∑	ADV
ejpam-62	154	59	i=1	i=1	PROPN
ejpam-62	154	60	si	si	PROPN
ejpam-62	154	61	−	−	PROPN
ejpam-62	154	62	j0	j0	PROPN
ejpam-62	154	63	∑	∑	PROPN
ejpam-62	154	64	i=1	i=1	PROPN
ejpam-62	154	65	si	si	X
ejpam-62	154	66	>	>	X
ejpam-62	154	67	(	(	PUNCT
ejpam-62	154	68	j0	j0	PROPN
ejpam-62	154	69	+	+	PROPN
ejpam-62	154	70	1)(k−	1)(k−	NUM
ejpam-62	154	71	1	1	NUM
ejpam-62	154	72	)	)	PUNCT
ejpam-62	154	73	�	�	PROPN
ejpam-62	154	74	n−	n−	NOUN
ejpam-62	154	75	1	1	NUM
ejpam-62	154	76	k−	k−	PROPN
ejpam-62	154	77	1	1	NUM
ejpam-62	154	78	�	�	PROPN
ejpam-62	154	79	+	+	CCONJ
ejpam-62	154	80	k−1	k−1	PROPN
ejpam-62	154	81	∑	∑	PROPN
ejpam-62	154	82	i=1	i=1	PROPN
ejpam-62	154	83	(	(	PUNCT
ejpam-62	154	84	i−	i−	PROPN
ejpam-62	154	85	k	k	PROPN
ejpam-62	154	86	)	)	PUNCT
ejpam-62	154	87	�	�	PROPN
ejpam-62	154	88	j0	j0	PROPN
ejpam-62	154	89	+	+	PROPN
ejpam-62	154	90	1	1	NUM
ejpam-62	154	91	i	i	NOUN
ejpam-62	154	92	�	�	VERB
ejpam-62	154	93	�	�	PROPN
ejpam-62	154	94	n−	n−	PROPN
ejpam-62	154	95	j0−	j0−	NOUN
ejpam-62	154	96	1	1	NUM
ejpam-62	154	97	k−	k−	NOUN
ejpam-62	154	98	i	i	PRON
ejpam-62	154	99	�	�	PROPN
ejpam-62	154	100	−	−	NOUN
ejpam-62	154	101	j0(k−	j0(k−	NOUN
ejpam-62	154	102	1	1	NUM
ejpam-62	154	103	)	)	PUNCT
ejpam-62	154	104	�	�	PROPN
ejpam-62	154	105	n−	n−	NOUN
ejpam-62	154	106	1	1	NUM
ejpam-62	154	107	k−	k−	PROPN
ejpam-62	154	108	1	1	NUM
ejpam-62	154	109	�	�	PROPN
ejpam-62	154	110	=	=	SYM
ejpam-62	154	111	(	(	PUNCT
ejpam-62	154	112	k−	k−	NOUN
ejpam-62	154	113	1	1	NUM
ejpam-62	154	114	)	)	PUNCT
ejpam-62	154	115	�	�	PROPN
ejpam-62	154	116	n−	n−	NOUN
ejpam-62	154	117	1	1	NUM
ejpam-62	154	118	k−	k−	PROPN
ejpam-62	154	119	1	1	NUM
ejpam-62	154	120	�	�	PROPN
ejpam-62	154	121	+	+	CCONJ
ejpam-62	154	122	k−1	k−1	PROPN
ejpam-62	154	123	∑	∑	PROPN
ejpam-62	154	124	i=1	i=1	PROPN
ejpam-62	154	125	(	(	PUNCT
ejpam-62	154	126	i−	i−	PROPN
ejpam-62	154	127	k	k	PROPN
ejpam-62	154	128	)	)	PUNCT
ejpam-62	154	129	�	�	PROPN
ejpam-62	154	130	j0	j0	PROPN
ejpam-62	154	131	+	+	PROPN
ejpam-62	154	132	1	1	NUM
ejpam-62	154	133	i	i	NOUN
ejpam-62	154	134	�	�	VERB
ejpam-62	154	135	�	�	PROPN
ejpam-62	154	136	n−	n−	PROPN
ejpam-62	154	137	j0−	j0−	NOUN
ejpam-62	154	138	1	1	NUM
ejpam-62	154	139	k−	k−	NOUN
ejpam-62	154	140	i	i	PRON
ejpam-62	154	141	�	�	PROPN
ejpam-62	154	142	thus	thus	ADV
ejpam-62	154	143	,	,	PUNCT
ejpam-62	154	144	j0−1	j0−1	PROPN
ejpam-62	154	145	∑	∑	PROPN
ejpam-62	154	146	i=1	i=1	PROPN
ejpam-62	154	147	si	si	PROPN
ejpam-62	154	148	=	=	SYM
ejpam-62	154	149	j0	j0	PROPN
ejpam-62	154	150	∑	∑	PROPN
ejpam-62	154	151	i=1	i=1	PROPN
ejpam-62	154	152	si	si	PROPN
ejpam-62	155	1	−	−	PROPN
ejpam-62	155	2	s	s	PROPN
ejpam-62	155	3	j0	j0	PROPN
ejpam-62	155	4	<	<	X
ejpam-62	155	5	j0(k−	j0(k−	X
ejpam-62	155	6	1	1	NUM
ejpam-62	155	7	)	)	PUNCT
ejpam-62	155	8	�	�	PROPN
ejpam-62	155	9	n−	n−	NOUN
ejpam-62	155	10	1	1	NUM
ejpam-62	155	11	k−	k−	PROPN
ejpam-62	155	12	1	1	NUM
ejpam-62	155	13	�	�	PROPN
ejpam-62	155	14	−	−	PROPN
ejpam-62	155	15			NOUN
ejpam-62	155	16	(k−	(k−	NUM
ejpam-62	155	17	1	1	NUM
ejpam-62	155	18	)	)	PUNCT
ejpam-62	155	19	�	�	PROPN
ejpam-62	155	20	n−	n−	NOUN
ejpam-62	155	21	1	1	NUM
ejpam-62	155	22	k−	k−	PROPN
ejpam-62	155	23	1	1	NUM
ejpam-62	155	24	�	�	PROPN
ejpam-62	155	25	+	+	CCONJ
ejpam-62	155	26	k−1	k−1	PROPN
ejpam-62	155	27	∑	∑	PROPN
ejpam-62	155	28	i=1	i=1	PROPN
ejpam-62	155	29	(	(	PUNCT
ejpam-62	155	30	i−	i−	PROPN
ejpam-62	155	31	k	k	PROPN
ejpam-62	155	32	)	)	PUNCT
ejpam-62	155	33	�	�	PROPN
ejpam-62	155	34	j0	j0	PROPN
ejpam-62	155	35	+	+	PROPN
ejpam-62	155	36	1	1	NUM
ejpam-62	155	37	i	i	NOUN
ejpam-62	155	38	�	�	VERB
ejpam-62	155	39	�	�	PROPN
ejpam-62	155	40	n−	n−	PROPN
ejpam-62	155	41	j0−	j0−	NOUN
ejpam-62	155	42	1	1	NUM
ejpam-62	155	43	k−	k−	NOUN
ejpam-62	155	44	i	i	PRON
ejpam-62	155	45	�	�	PROPN
ejpam-62	155	46			PROPN
ejpam-62	155	47			PROPN
ejpam-62	155	48	=	=	PUNCT
ejpam-62	155	49	(	(	PUNCT
ejpam-62	155	50	j0−	j0−	NOUN
ejpam-62	155	51	1)(k−	1)(k−	NUM
ejpam-62	155	52	1	1	NUM
ejpam-62	155	53	)	)	PUNCT
ejpam-62	155	54	�	�	PROPN
ejpam-62	155	55	n−	n−	NOUN
ejpam-62	155	56	1	1	NUM
ejpam-62	155	57	k−	k−	PROPN
ejpam-62	155	58	1	1	NUM
ejpam-62	155	59	�	�	PROPN
ejpam-62	155	60	−	−	PROPN
ejpam-62	155	61	k−1	k−1	PROPN
ejpam-62	155	62	∑	∑	PROPN
ejpam-62	155	63	i=1	i=1	PROPN
ejpam-62	155	64	(	(	PUNCT
ejpam-62	155	65	i−	i−	PROPN
ejpam-62	155	66	k	k	PROPN
ejpam-62	155	67	)	)	PUNCT
ejpam-62	155	68	�	�	PROPN
ejpam-62	155	69	j0	j0	PROPN
ejpam-62	155	70	+	+	PROPN
ejpam-62	155	71	1	1	NUM
ejpam-62	155	72	i	i	NOUN
ejpam-62	155	73	�	�	VERB
ejpam-62	155	74	�	�	PROPN
ejpam-62	155	75	n−	n−	PROPN
ejpam-62	155	76	j0−	j0−	NOUN
ejpam-62	155	77	1	1	NUM
ejpam-62	155	78	k−	k−	NOUN
ejpam-62	155	79	i	i	PRON
ejpam-62	155	80	�	�	PROPN
ejpam-62	155	81	now	now	ADV
ejpam-62	155	82	,	,	PUNCT
ejpam-62	155	83	�	�	PROPN
ejpam-62	155	84	j0	j0	PROPN
ejpam-62	155	85	+	+	PROPN
ejpam-62	155	86	1	1	NUM
ejpam-62	155	87	i	i	PROPN
ejpam-62	155	88	�	�	PROPN
ejpam-62	155	89	=	=	SYM
ejpam-62	155	90	j0	j0	PROPN
ejpam-62	155	91	(	(	PUNCT
ejpam-62	155	92	j0	j0	PROPN
ejpam-62	155	93	+	+	PROPN
ejpam-62	155	94	1	1	NUM
ejpam-62	155	95	)	)	PUNCT
ejpam-62	155	96	(	(	PUNCT
ejpam-62	155	97	j0−i+1	j0−i+1	NOUN
ejpam-62	155	98	)	)	PUNCT
ejpam-62	155	99	(	(	PUNCT
ejpam-62	155	100	j0−i	j0−i	PROPN
ejpam-62	155	101	)	)	PUNCT
ejpam-62	155	102	�	�	PROPN
ejpam-62	156	1	j0−	j0−	PROPN
ejpam-62	156	2	1	1	NUM
ejpam-62	156	3	i	i	PRON
ejpam-62	156	4	�	�	PROPN
ejpam-62	156	5	and	and	CCONJ
ejpam-62	156	6	�	�	PROPN
ejpam-62	156	7	n−	n−	NOUN
ejpam-62	156	8	j0−	j0−	NOUN
ejpam-62	156	9	1	1	NUM
ejpam-62	156	10	k−	k−	NOUN
ejpam-62	156	11	i	i	PRON
ejpam-62	156	12	�	�	PROPN
ejpam-62	156	13	=	=	PUNCT
ejpam-62	156	14	(	(	PUNCT
ejpam-62	156	15	n−	n−	NOUN
ejpam-62	156	16	j0−k+i+1)(n−	j0−k+i+1)(n−	NOUN
ejpam-62	156	17	j0−k+i	j0−k+i	NOUN
ejpam-62	156	18	)	)	PUNCT
ejpam-62	156	19	(	(	PUNCT
ejpam-62	156	20	n−	n−	NOUN
ejpam-62	156	21	j0	j0	PROPN
ejpam-62	156	22	+	+	PROPN
ejpam-62	156	23	1)(n−	1)(n−	PROPN
ejpam-62	156	24	j0	j0	PROPN
ejpam-62	156	25	)	)	PUNCT
ejpam-62	156	26	�	�	PROPN
ejpam-62	156	27	n−	n−	PROPN
ejpam-62	156	28	(	(	PUNCT
ejpam-62	156	29	j0−	j0−	NOUN
ejpam-62	156	30	1	1	NUM
ejpam-62	156	31	)	)	PUNCT
ejpam-62	156	32	k−	k−	NOUN
ejpam-62	157	1	i	i	PRON
ejpam-62	157	2	�	�	PROPN
ejpam-62	157	3	.	.	PUNCT
ejpam-62	158	1	so	so	ADV
ejpam-62	158	2	,	,	PUNCT
ejpam-62	158	3	j0−1	j0−1	PROPN
ejpam-62	158	4	∑	∑	PROPN
ejpam-62	158	5	i=1	i=1	PROPN
ejpam-62	158	6	si	si	X
ejpam-62	159	1	<	<	X
ejpam-62	159	2	(	(	PUNCT
ejpam-62	159	3	j0−	j0−	NOUN
ejpam-62	159	4	1)(k−	1)(k−	NUM
ejpam-62	159	5	1	1	NUM
ejpam-62	159	6	)	)	PUNCT
ejpam-62	159	7	�	�	PROPN
ejpam-62	159	8	n−	n−	NOUN
ejpam-62	159	9	1	1	NUM
ejpam-62	159	10	k−	k−	PROPN
ejpam-62	159	11	1	1	NUM
ejpam-62	159	12	�	�	PROPN
ejpam-62	159	13	−	−	PROPN
ejpam-62	159	14	k−1	k−1	PROPN
ejpam-62	159	15	∑	∑	PROPN
ejpam-62	159	16	i=1	i=1	PROPN
ejpam-62	159	17	(	(	PUNCT
ejpam-62	159	18	i−k	i−k	NOUN
ejpam-62	159	19	)	)	PUNCT
ejpam-62	159	20	j0	j0	PROPN
ejpam-62	159	21	(	(	PUNCT
ejpam-62	159	22	j0	j0	PROPN
ejpam-62	159	23	+	+	PROPN
ejpam-62	159	24	1)(n−	1)(n−	PROPN
ejpam-62	159	25	j0−k+i+1)(n−	j0−k+i+1)(n−	ADP
ejpam-62	159	26	j0−k+i	j0−k+i	NOUN
ejpam-62	159	27	)	)	PUNCT
ejpam-62	159	28	(	(	PUNCT
ejpam-62	159	29	j0−i+1	j0−i+1	NOUN
ejpam-62	159	30	)	)	PUNCT
ejpam-62	159	31	(	(	PUNCT
ejpam-62	159	32	j0−i)(n−	j0−i)(n−	PROPN
ejpam-62	159	33	j0	j0	PROPN
ejpam-62	159	34	+	+	PROPN
ejpam-62	159	35	1)(n−	1)(n−	PROPN
ejpam-62	159	36	j0	j0	PROPN
ejpam-62	159	37	)	)	PUNCT
ejpam-62	159	38	�	�	PROPN
ejpam-62	159	39	j0−	j0−	PROPN
ejpam-62	159	40	1	1	NUM
ejpam-62	159	41	i	i	PRON
ejpam-62	159	42	�	�	VERB
ejpam-62	159	43	�	�	PROPN
ejpam-62	159	44	n−	n−	PROPN
ejpam-62	159	45	(	(	PUNCT
ejpam-62	159	46	j0−	j0−	NOUN
ejpam-62	159	47	1	1	NUM
ejpam-62	159	48	)	)	PUNCT
ejpam-62	159	49	k−	k−	NOUN
ejpam-62	159	50	i	i	PRON
ejpam-62	159	51	�	�	PROPN
ejpam-62	159	52	,	,	PUNCT
ejpam-62	159	53	or	or	CCONJ
ejpam-62	159	54	j0−1	j0−1	PROPN
ejpam-62	159	55	∑	∑	PROPN
ejpam-62	159	56	i=1	i=1	PROPN
ejpam-62	159	57	si	si	X
ejpam-62	159	58	<	<	X
ejpam-62	159	59	(	(	PUNCT
ejpam-62	159	60	j0−	j0−	NOUN
ejpam-62	159	61	1)(k−	1)(k−	NUM
ejpam-62	159	62	1	1	NUM
ejpam-62	159	63	)	)	PUNCT
ejpam-62	159	64	�	�	PROPN
ejpam-62	159	65	n−	n−	NOUN
ejpam-62	159	66	1	1	NUM
ejpam-62	159	67	k−	k−	PROPN
ejpam-62	159	68	1	1	NUM
ejpam-62	159	69	�	�	PROPN
ejpam-62	159	70	+	+	CCONJ
ejpam-62	159	71	k−1	k−1	PROPN
ejpam-62	159	72	∑	∑	PROPN
ejpam-62	159	73	i=1	i=1	PROPN
ejpam-62	159	74	(	(	PUNCT
ejpam-62	159	75	i−	i−	PROPN
ejpam-62	159	76	k	k	PROPN
ejpam-62	159	77	)	)	PUNCT
ejpam-62	159	78	�	�	PROPN
ejpam-62	159	79	j0−	j0−	PROPN
ejpam-62	159	80	1	1	NUM
ejpam-62	159	81	i	i	PRON
ejpam-62	159	82	�	�	VERB
ejpam-62	159	83	�	�	PROPN
ejpam-62	159	84	n−	n−	PROPN
ejpam-62	159	85	(	(	PUNCT
ejpam-62	159	86	j0−	j0−	NOUN
ejpam-62	159	87	1	1	NUM
ejpam-62	159	88	)	)	PUNCT
ejpam-62	159	89	k−	k−	NOUN
ejpam-62	159	90	i	i	PRON
ejpam-62	159	91	�	�	PROPN
ejpam-62	159	92	,	,	PUNCT
ejpam-62	159	93	s.	s.	PROPN
ejpam-62	159	94	pirzada	pirzada	PROPN
ejpam-62	159	95	,	,	PUNCT
ejpam-62	159	96	z.	z.	PROPN
ejpam-62	159	97	guofei	guofei	PROPN
ejpam-62	159	98	/	/	SYM
ejpam-62	159	99	eur	eur	PROPN
ejpam-62	159	100	.	.	PUNCT
ejpam-62	160	1	j.	j.	PROPN
ejpam-62	160	2	pure	pure	PROPN
ejpam-62	160	3	appl	appl	PROPN
ejpam-62	160	4	.	.	PROPN
ejpam-62	160	5	math	math	PROPN
ejpam-62	160	6	,	,	PUNCT
ejpam-62	160	7	1	1	NUM
ejpam-62	160	8	(	(	PUNCT
ejpam-62	160	9	2008	2008	NUM
ejpam-62	160	10	)	)	PUNCT
ejpam-62	160	11	,	,	PUNCT
ejpam-62	160	12	(	(	PUNCT
ejpam-62	160	13	10	10	NUM
ejpam-62	160	14	-	-	SYM
ejpam-62	160	15	20	20	NUM
ejpam-62	160	16	)	)	PUNCT
ejpam-62	160	17	17	17	NUM
ejpam-62	160	18	a	a	DET
ejpam-62	160	19	contradiction	contradiction	NOUN
ejpam-62	160	20	to	to	ADP
ejpam-62	160	21	the	the	DET
ejpam-62	160	22	hypothesis	hypothesis	NOUN
ejpam-62	160	23	on	on	ADP
ejpam-62	160	24	s.	s.	PROPN
ejpam-62	160	25	hence	hence	PROPN
ejpam-62	160	26	,	,	PUNCT
ejpam-62	160	27	(	(	PUNCT
ejpam-62	160	28	2.2	2.2	NUM
ejpam-62	160	29	)	)	PUNCT
ejpam-62	160	30	holds	hold	VERB
ejpam-62	160	31	.	.	PUNCT
ejpam-62	161	1	�	�	PROPN
ejpam-62	161	2	proof	proof	NOUN
ejpam-62	161	3	of	of	ADP
ejpam-62	161	4	theorem	theorem	ADJ
ejpam-62	161	5	2.1	2.1	NUM
ejpam-62	161	6	.	.	PUNCT
ejpam-62	162	1	necessity	necessity	NOUN
ejpam-62	162	2	.	.	PUNCT
ejpam-62	163	1	let	let	VERB
ejpam-62	163	2	s	s	PRON
ejpam-62	163	3	=	=	PUNCT
ejpam-62	164	1	[	[	X
ejpam-62	164	2	s1	s1	NOUN
ejpam-62	164	3	,	,	PUNCT
ejpam-62	164	4	s2	s2	PROPN
ejpam-62	164	5	,	,	PUNCT
ejpam-62	164	6	·	·	PUNCT
ejpam-62	164	7	·	·	PUNCT
ejpam-62	164	8	·	·	PUNCT
ejpam-62	164	9	,	,	PUNCT
ejpam-62	164	10	sn	sn	PROPN
ejpam-62	164	11	]	]	PUNCT
ejpam-62	164	12	be	be	AUX
ejpam-62	164	13	the	the	DET
ejpam-62	164	14	score	score	NOUN
ejpam-62	164	15	sequence	sequence	NOUN
ejpam-62	164	16	of	of	ADP
ejpam-62	164	17	an	an	DET
ejpam-62	164	18	oriented	oriented	ADJ
ejpam-62	164	19	k	k	NOUN
ejpam-62	164	20	-	-	ADJ
ejpam-62	164	21	hypergraph	hypergraph	VERB
ejpam-62	164	22	d.	d.	NOUN
ejpam-62	164	23	further	far	ADV
ejpam-62	164	24	,	,	PUNCT
ejpam-62	164	25	let	let	VERB
ejpam-62	164	26	v1	v1	VERB
ejpam-62	164	27	=	=	PUNCT
ejpam-62	165	1	[	[	X
ejpam-62	165	2	v1	v1	NOUN
ejpam-62	165	3	,	,	PUNCT
ejpam-62	165	4	v2	v2	PROPN
ejpam-62	165	5	,	,	PUNCT
ejpam-62	165	6	·	·	PUNCT
ejpam-62	165	7	·	·	PUNCT
ejpam-62	165	8	·	·	PUNCT
ejpam-62	165	9	,	,	PUNCT
ejpam-62	165	10	v	v	X
ejpam-62	165	11	j	j	X
ejpam-62	165	12	]	]	PUNCT
ejpam-62	165	13	and	and	CCONJ
ejpam-62	165	14	v2	v2	PROPN
ejpam-62	165	15	=	=	SYM
ejpam-62	165	16	v	v	ADJ
ejpam-62	165	17	−	−	PROPN
ejpam-62	165	18	v1	v1	NOUN
ejpam-62	165	19	.	.	PUNCT
ejpam-62	166	1	clearly	clearly	ADV
ejpam-62	166	2	,	,	PUNCT
ejpam-62	166	3	�	�	PROPN
ejpam-62	166	4	�	�	PROPN
ejpam-62	166	5	v1	v1	PROPN
ejpam-62	166	6	�	�	PROPN
ejpam-62	166	7	�	�	PROPN
ejpam-62	166	8	=	=	SYM
ejpam-62	166	9	j	j	PROPN
ejpam-62	166	10	,	,	PUNCT
ejpam-62	166	11	�	�	PROPN
ejpam-62	166	12	�	�	PROPN
ejpam-62	166	13	v2	v2	PROPN
ejpam-62	166	14	�	�	PROPN
ejpam-62	166	15	�	�	PROPN
ejpam-62	166	16	=	=	SYM
ejpam-62	166	17	n−	n−	PROPN
ejpam-62	166	18	j	j	PROPN
ejpam-62	166	19	.	.	PUNCT
ejpam-62	167	1	now	now	ADV
ejpam-62	167	2	,	,	PUNCT
ejpam-62	167	3	j	j	PROPN
ejpam-62	167	4	∑	∑	PROPN
ejpam-62	167	5	i=1	i=1	PROPN
ejpam-62	167	6	si	si	PROPN
ejpam-62	167	7	=	=	SYM
ejpam-62	167	8	j	j	PROPN
ejpam-62	167	9	∑	∑	PROPN
ejpam-62	167	10	i=1	i=1	PROPN
ejpam-62	167	11	(	(	PUNCT
ejpam-62	167	12	k−	k−	NOUN
ejpam-62	167	13	1	1	NUM
ejpam-62	167	14	)	)	PUNCT
ejpam-62	167	15	�	�	PROPN
ejpam-62	167	16	n−	n−	NOUN
ejpam-62	167	17	1	1	NUM
ejpam-62	167	18	k−	k−	PROPN
ejpam-62	167	19	1	1	NUM
ejpam-62	167	20	�	�	PROPN
ejpam-62	167	21	+	+	CCONJ
ejpam-62	167	22	d+i	d+i	X
ejpam-62	167	23	(	(	PUNCT
ejpam-62	167	24	d)−	d)−	PROPN
ejpam-62	167	25	(	(	PUNCT
ejpam-62	167	26	k−	k−	PROPN
ejpam-62	167	27	1)d−i	1)d−i	PROPN
ejpam-62	167	28	(	(	PUNCT
ejpam-62	167	29	d	d	NOUN
ejpam-62	167	30	)	)	PUNCT
ejpam-62	168	1	=	=	SYM
ejpam-62	168	2	j(k−	j(k−	DET
ejpam-62	168	3	1	1	NUM
ejpam-62	168	4	)	)	PUNCT
ejpam-62	168	5	�	�	PROPN
ejpam-62	168	6	n−	n−	NOUN
ejpam-62	168	7	1	1	NUM
ejpam-62	168	8	k−	k−	PROPN
ejpam-62	168	9	1	1	NUM
ejpam-62	168	10	�	�	PROPN
ejpam-62	168	11	+	+	CCONJ
ejpam-62	168	12	j	j	PROPN
ejpam-62	168	13	∑	∑	PUNCT
ejpam-62	168	14	i=1	i=1	X
ejpam-62	168	15	d+i	d+i	X
ejpam-62	168	16	(	(	PUNCT
ejpam-62	168	17	d)−	d)−	PROPN
ejpam-62	168	18	(	(	PUNCT
ejpam-62	168	19	k−	k−	PROPN
ejpam-62	168	20	1	1	NUM
ejpam-62	168	21	)	)	PUNCT
ejpam-62	168	22	j	j	PROPN
ejpam-62	168	23	∑	∑	PUNCT
ejpam-62	168	24	i=1	i=1	PROPN
ejpam-62	168	25	d−i	d−i	ADV
ejpam-62	168	26	(	(	PUNCT
ejpam-62	168	27	d	d	NOUN
ejpam-62	168	28	)	)	PUNCT
ejpam-62	168	29	=	=	SYM
ejpam-62	169	1	j(k−	j(k−	DET
ejpam-62	169	2	1	1	NUM
ejpam-62	169	3	)	)	PUNCT
ejpam-62	169	4	�	�	PROPN
ejpam-62	169	5	n−	n−	NOUN
ejpam-62	169	6	1	1	NUM
ejpam-62	169	7	k−	k−	PROPN
ejpam-62	169	8	1	1	NUM
ejpam-62	169	9	�	�	PROPN
ejpam-62	169	10	+	+	CCONJ
ejpam-62	169	11	j	j	PROPN
ejpam-62	169	12	∑	∑	PUNCT
ejpam-62	169	13	i=1	i=1	PROPN
ejpam-62	169	14	�	�	PROPN
ejpam-62	169	15	d+i	d+i	X
ejpam-62	169	16	(	(	PUNCT
ejpam-62	169	17	v1	v1	NOUN
ejpam-62	169	18	)	)	PUNCT
ejpam-62	169	19	+	+	CCONJ
ejpam-62	169	20	d+i	d+i	X
ejpam-62	169	21	(	(	PUNCT
ejpam-62	169	22	v1	v1	NOUN
ejpam-62	169	23	∗	∗	NOUN
ejpam-62	169	24	v2	v2	NOUN
ejpam-62	169	25	)	)	PUNCT
ejpam-62	169	26	�	�	PROPN
ejpam-62	169	27	−	−	PROPN
ejpam-62	169	28	(	(	PUNCT
ejpam-62	169	29	k−	k−	PROPN
ejpam-62	169	30	1	1	NUM
ejpam-62	169	31	)	)	PUNCT
ejpam-62	169	32	j	j	NOUN
ejpam-62	169	33	∑	∑	PUNCT
ejpam-62	169	34	i=1	i=1	PROPN
ejpam-62	169	35	�	�	PROPN
ejpam-62	169	36	d−i	d−i	PUNCT
ejpam-62	169	37	(	(	PUNCT
ejpam-62	169	38	v1	v1	NOUN
ejpam-62	169	39	)	)	PUNCT
ejpam-62	169	40	+	+	CCONJ
ejpam-62	169	41	d−i	d−i	PUNCT
ejpam-62	169	42	(	(	PUNCT
ejpam-62	169	43	v1	v1	NOUN
ejpam-62	169	44	∗	∗	NOUN
ejpam-62	169	45	v2	v2	NOUN
ejpam-62	169	46	)	)	PUNCT
ejpam-62	169	47	�	�	PROPN
ejpam-62	169	48	if	if	SCONJ
ejpam-62	169	49	there	there	PRON
ejpam-62	169	50	are	be	VERB
ejpam-62	169	51	α	α	PRON
ejpam-62	169	52	arcs	arc	NOUN
ejpam-62	169	53	in	in	ADP
ejpam-62	169	54	v	v	NOUN
ejpam-62	169	55	,	,	PUNCT
ejpam-62	169	56	then	then	ADV
ejpam-62	169	57	j	j	PROPN
ejpam-62	169	58	∑	∑	PROPN
ejpam-62	169	59	i=1	i=1	PROPN
ejpam-62	169	60	d+i	d+i	X
ejpam-62	169	61	(	(	PUNCT
ejpam-62	169	62	v1	v1	NOUN
ejpam-62	169	63	)	)	PUNCT
ejpam-62	169	64	=	=	SYM
ejpam-62	169	65	(	(	PUNCT
ejpam-62	169	66	k−	k−	PROPN
ejpam-62	169	67	1)α	1)α	NUM
ejpam-62	169	68	and	and	CCONJ
ejpam-62	169	69	j	j	PROPN
ejpam-62	169	70	∑	∑	PROPN
ejpam-62	169	71	i=1	i=1	PROPN
ejpam-62	169	72	d−i	d−i	PROPN
ejpam-62	169	73	(	(	PUNCT
ejpam-62	169	74	v1	v1	NOUN
ejpam-62	169	75	)	)	PUNCT
ejpam-62	169	76	=	=	SYM
ejpam-62	169	77	α	α	PROPN
ejpam-62	169	78	,	,	PUNCT
ejpam-62	169	79	so	so	SCONJ
ejpam-62	169	80	that	that	SCONJ
ejpam-62	169	81	j	j	PROPN
ejpam-62	169	82	∑	∑	PUNCT
ejpam-62	169	83	i=1	i=1	PROPN
ejpam-62	169	84	d+i	d+i	X
ejpam-62	169	85	(	(	PUNCT
ejpam-62	169	86	v1)−	v1)−	PROPN
ejpam-62	169	87	(	(	PUNCT
ejpam-62	169	88	k−	k−	PROPN
ejpam-62	169	89	1	1	NUM
ejpam-62	169	90	)	)	PUNCT
ejpam-62	169	91	j	j	PROPN
ejpam-62	169	92	∑	∑	PUNCT
ejpam-62	169	93	i=1	i=1	PROPN
ejpam-62	169	94	d−i	d−i	PROPN
ejpam-62	169	95	(	(	PUNCT
ejpam-62	169	96	v1	v1	NOUN
ejpam-62	169	97	)	)	PUNCT
ejpam-62	169	98	=	=	SYM
ejpam-62	169	99	(	(	PUNCT
ejpam-62	169	100	k−	k−	PROPN
ejpam-62	169	101	1)α−	1)α−	PROPN
ejpam-62	169	102	(	(	PUNCT
ejpam-62	169	103	k−	k−	PROPN
ejpam-62	169	104	1)α=	1)α=	NOUN
ejpam-62	169	105	0	0	NUM
ejpam-62	169	106	.	.	PUNCT
ejpam-62	170	1	also	also	ADV
ejpam-62	170	2	,	,	PUNCT
ejpam-62	170	3	j	j	PROPN
ejpam-62	170	4	∑	∑	PUNCT
ejpam-62	170	5	i=1	i=1	PROPN
ejpam-62	171	1	d−i	d−i	PROPN
ejpam-62	171	2	(	(	PUNCT
ejpam-62	171	3	v1	v1	NOUN
ejpam-62	171	4	∗	∗	NOUN
ejpam-62	171	5	v2)≤	v2)≤	PROPN
ejpam-62	171	6	k−1	k−1	PROPN
ejpam-62	171	7	∑	∑	PUNCT
ejpam-62	171	8	i=1	i=1	PROPN
ejpam-62	171	9	�	�	PROPN
ejpam-62	171	10	j	j	PROPN
ejpam-62	172	1	i	i	PROPN
ejpam-62	172	2	�	�	PROPN
ejpam-62	172	3	�	�	PROPN
ejpam-62	172	4	n−	n−	PROPN
ejpam-62	172	5	j	j	PROPN
ejpam-62	172	6	k−	k−	PROPN
ejpam-62	172	7	i	i	PRON
ejpam-62	172	8	�	�	PROPN
ejpam-62	172	9	,	,	PUNCT
ejpam-62	172	10	and	and	CCONJ
ejpam-62	172	11	j	j	PROPN
ejpam-62	172	12	∑	∑	PUNCT
ejpam-62	172	13	i=1	i=1	PROPN
ejpam-62	172	14	d+i	d+i	X
ejpam-62	172	15	(	(	PUNCT
ejpam-62	172	16	v1	v1	NOUN
ejpam-62	172	17	∗	∗	NOUN
ejpam-62	172	18	v2)≥	v2)≥	X
ejpam-62	172	19	k−1	k−1	PROPN
ejpam-62	172	20	∑	∑	PROPN
ejpam-62	172	21	i=1	i=1	PROPN
ejpam-62	172	22	(	(	PUNCT
ejpam-62	172	23	i−	i−	PROPN
ejpam-62	172	24	1	1	NUM
ejpam-62	172	25	)	)	PUNCT
ejpam-62	172	26	�	�	PROPN
ejpam-62	172	27	j	j	PROPN
ejpam-62	172	28	i	i	PROPN
ejpam-62	172	29	�	�	VERB
ejpam-62	172	30	�	�	PROPN
ejpam-62	172	31	n−	n−	PROPN
ejpam-62	172	32	j	j	PROPN
ejpam-62	172	33	k−	k−	PROPN
ejpam-62	172	34	i	i	PRON
ejpam-62	172	35	�	�	PROPN
ejpam-62	172	36	.	.	PUNCT
ejpam-62	173	1	therefore	therefore	ADV
ejpam-62	173	2	,	,	PUNCT
ejpam-62	173	3	j	j	PROPN
ejpam-62	173	4	∑	∑	PROPN
ejpam-62	173	5	i=1	i=1	PROPN
ejpam-62	173	6	si	si	PROPN
ejpam-62	173	7	≥	≥	X
ejpam-62	173	8	j(k−	j(k−	NOUN
ejpam-62	173	9	1	1	NUM
ejpam-62	173	10	)	)	PUNCT
ejpam-62	173	11	�	�	PROPN
ejpam-62	173	12	n−	n−	NOUN
ejpam-62	173	13	1	1	NUM
ejpam-62	173	14	k−	k−	PROPN
ejpam-62	173	15	1	1	NUM
ejpam-62	173	16	�	�	PROPN
ejpam-62	173	17	+	+	CCONJ
ejpam-62	173	18	k−1	k−1	PROPN
ejpam-62	173	19	∑	∑	PROPN
ejpam-62	173	20	i=1	i=1	PROPN
ejpam-62	173	21	(	(	PUNCT
ejpam-62	173	22	i−	i−	PROPN
ejpam-62	173	23	1	1	NUM
ejpam-62	173	24	)	)	PUNCT
ejpam-62	173	25	�	�	PROPN
ejpam-62	173	26	j	j	PROPN
ejpam-62	173	27	i	i	PROPN
ejpam-62	173	28	�	�	VERB
ejpam-62	173	29	�	�	PROPN
ejpam-62	173	30	n−	n−	PROPN
ejpam-62	173	31	j	j	PROPN
ejpam-62	173	32	k−	k−	PROPN
ejpam-62	173	33	i	i	PRON
ejpam-62	173	34	�	�	PROPN
ejpam-62	173	35	−	−	PROPN
ejpam-62	173	36	(	(	PUNCT
ejpam-62	173	37	k−	k−	PROPN
ejpam-62	173	38	1	1	NUM
ejpam-62	173	39	)	)	PUNCT
ejpam-62	173	40	k−1	k−1	PROPN
ejpam-62	173	41	∑	∑	PUNCT
ejpam-62	173	42	i=1	i=1	PROPN
ejpam-62	173	43	�	�	PROPN
ejpam-62	173	44	j	j	PROPN
ejpam-62	173	45	i	i	PROPN
ejpam-62	173	46	�	�	PROPN
ejpam-62	173	47	�	�	PROPN
ejpam-62	173	48	n−	n−	PROPN
ejpam-62	173	49	j	j	PROPN
ejpam-62	173	50	k−	k−	PROPN
ejpam-62	173	51	i	i	PRON
ejpam-62	173	52	�	�	PROPN
ejpam-62	173	53	=	=	PUNCT
ejpam-62	173	54	j(k−	j(k−	PRON
ejpam-62	173	55	1	1	NUM
ejpam-62	173	56	)	)	PUNCT
ejpam-62	173	57	�	�	PROPN
ejpam-62	173	58	n−	n−	NOUN
ejpam-62	173	59	1	1	NUM
ejpam-62	173	60	k−	k−	PROPN
ejpam-62	173	61	1	1	NUM
ejpam-62	173	62	�	�	PROPN
ejpam-62	173	63	+	+	CCONJ
ejpam-62	173	64	k−1	k−1	PROPN
ejpam-62	173	65	∑	∑	PROPN
ejpam-62	173	66	i=1	i=1	PROPN
ejpam-62	173	67	(	(	PUNCT
ejpam-62	173	68	i−	i−	PROPN
ejpam-62	173	69	k	k	PROPN
ejpam-62	173	70	)	)	PUNCT
ejpam-62	173	71	�	�	PROPN
ejpam-62	173	72	j	j	PROPN
ejpam-62	173	73	i	i	PROPN
ejpam-62	173	74	�	�	VERB
ejpam-62	173	75	�	�	PROPN
ejpam-62	173	76	n−	n−	PROPN
ejpam-62	173	77	j	j	PROPN
ejpam-62	173	78	k−	k−	PROPN
ejpam-62	173	79	i	i	PRON
ejpam-62	173	80	�	�	PROPN
ejpam-62	173	81	sufficiency	sufficiency	PROPN
ejpam-62	173	82	.	.	PUNCT
ejpam-62	174	1	induct	induct	PROPN
ejpam-62	174	2	on	on	ADP
ejpam-62	174	3	n.	n.	PROPN
ejpam-62	174	4	if	if	SCONJ
ejpam-62	174	5	n=	n=	ADJ
ejpam-62	174	6	k	k	PROPN
ejpam-62	174	7	,	,	PUNCT
ejpam-62	174	8	there	there	PRON
ejpam-62	174	9	is	be	VERB
ejpam-62	174	10	only	only	ADV
ejpam-62	174	11	one	one	NUM
ejpam-62	174	12	arc	arc	NOUN
ejpam-62	174	13	(	(	PUNCT
ejpam-62	174	14	or	or	CCONJ
ejpam-62	174	15	one	one	NUM
ejpam-62	174	16	non	non	ADJ
ejpam-62	174	17	arc	arc	NOUN
ejpam-62	174	18	)	)	PUNCT
ejpam-62	174	19	in	in	ADP
ejpam-62	174	20	which	which	DET
ejpam-62	174	21	case	case	NOUN
ejpam-62	174	22	the	the	DET
ejpam-62	174	23	scores	score	NOUN
ejpam-62	174	24	are	be	AUX
ejpam-62	174	25	n	n	CCONJ
ejpam-62	174	26	,	,	PUNCT
ejpam-62	174	27	n	n	CCONJ
ejpam-62	174	28	,	,	PUNCT
ejpam-62	174	29	·	·	PUNCT
ejpam-62	174	30	·	·	PUNCT
ejpam-62	174	31	·	·	PUNCT
ejpam-62	174	32	,	,	PUNCT
ejpam-62	174	33	n	n	CCONJ
ejpam-62	174	34	,	,	PUNCT
ejpam-62	174	35	0(n−	0(n−	NUM
ejpam-62	174	36	1	1	NUM
ejpam-62	174	37	,	,	PUNCT
ejpam-62	174	38	n−	n−	NOUN
ejpam-62	174	39	1	1	NUM
ejpam-62	174	40	,	,	PUNCT
ejpam-62	174	41	·	·	PUNCT
ejpam-62	174	42	·	·	PUNCT
ejpam-62	174	43	·	·	PUNCT
ejpam-62	174	44	,	,	PUNCT
ejpam-62	174	45	n−	n−	NOUN
ejpam-62	174	46	1	1	NUM
ejpam-62	174	47	)	)	PUNCT
ejpam-62	174	48	,	,	PUNCT
ejpam-62	174	49	and	and	CCONJ
ejpam-62	174	50	the	the	DET
ejpam-62	174	51	result	result	NOUN
ejpam-62	174	52	is	be	AUX
ejpam-62	174	53	true	true	ADJ
ejpam-62	174	54	.	.	PUNCT
ejpam-62	175	1	assume	assume	VERB
ejpam-62	175	2	n	n	PRON
ejpam-62	175	3	>	>	X
ejpam-62	175	4	k.	k.	PROPN
ejpam-62	176	1	now	now	ADV
ejpam-62	176	2	,	,	PUNCT
ejpam-62	176	3	sn	sn	PROPN
ejpam-62	176	4	=	=	SYM
ejpam-62	176	5	n	n	CCONJ
ejpam-62	176	6	∑	∑	ADV
ejpam-62	176	7	i=1	i=1	PROPN
ejpam-62	176	8	si	si	PROPN
ejpam-62	177	1	−	−	PROPN
ejpam-62	177	2	n−1	n−1	PROPN
ejpam-62	177	3	∑	∑	PUNCT
ejpam-62	177	4	i=1	i=1	PROPN
ejpam-62	177	5	si	si	PROPN
ejpam-62	177	6	≤	≤	NUM
ejpam-62	177	7	n(k−	n(k−	PROPN
ejpam-62	177	8	1	1	NUM
ejpam-62	177	9	)	)	PUNCT
ejpam-62	177	10	�	�	PROPN
ejpam-62	177	11	n−	n−	NOUN
ejpam-62	177	12	1	1	NUM
ejpam-62	177	13	k−	k−	PROPN
ejpam-62	177	14	1	1	NUM
ejpam-62	177	15	�	�	PROPN
ejpam-62	177	16	−	−	PROPN
ejpam-62	178	1	(	(	PUNCT
ejpam-62	178	2	n−	n−	NOUN
ejpam-62	178	3	1)(k−	1)(k−	NUM
ejpam-62	178	4	1	1	NUM
ejpam-62	178	5	)	)	PUNCT
ejpam-62	178	6	�	�	PROPN
ejpam-62	178	7	n−	n−	NOUN
ejpam-62	178	8	1	1	NUM
ejpam-62	178	9	k−	k−	PROPN
ejpam-62	178	10	1	1	NUM
ejpam-62	178	11	�	�	PROPN
ejpam-62	178	12	−	−	PROPN
ejpam-62	178	13	k−1	k−1	PROPN
ejpam-62	178	14	∑	∑	PROPN
ejpam-62	178	15	i=1	i=1	PROPN
ejpam-62	178	16	(	(	PUNCT
ejpam-62	178	17	i−	i−	PROPN
ejpam-62	178	18	k	k	PROPN
ejpam-62	178	19	)	)	PUNCT
ejpam-62	178	20	�	�	PROPN
ejpam-62	178	21	n−	n−	NOUN
ejpam-62	178	22	1	1	NUM
ejpam-62	178	23	i	i	PRON
ejpam-62	178	24	�	�	VERB
ejpam-62	178	25	�	�	PROPN
ejpam-62	178	26	1	1	NUM
ejpam-62	178	27	k−	k−	PROPN
ejpam-62	178	28	i	i	PRON
ejpam-62	178	29	�	�	PROPN
ejpam-62	179	1	=	=	SYM
ejpam-62	179	2	k	k	PROPN
ejpam-62	179	3	�	�	PROPN
ejpam-62	179	4	n−	n−	PROPN
ejpam-62	179	5	1	1	NUM
ejpam-62	179	6	k−	k−	PROPN
ejpam-62	179	7	1	1	NUM
ejpam-62	179	8	�	�	PROPN
ejpam-62	179	9	.	.	PUNCT
ejpam-62	180	1	s.	s.	PROPN
ejpam-62	180	2	pirzada	pirzada	PROPN
ejpam-62	180	3	,	,	PUNCT
ejpam-62	180	4	z.	z.	PROPN
ejpam-62	180	5	guofei	guofei	PROPN
ejpam-62	180	6	/	/	SYM
ejpam-62	180	7	eur	eur	PROPN
ejpam-62	180	8	.	.	PUNCT
ejpam-62	181	1	j.	j.	PROPN
ejpam-62	181	2	pure	pure	PROPN
ejpam-62	181	3	appl	appl	PROPN
ejpam-62	181	4	.	.	PROPN
ejpam-62	181	5	math	math	PROPN
ejpam-62	181	6	,	,	PUNCT
ejpam-62	181	7	1	1	NUM
ejpam-62	181	8	(	(	PUNCT
ejpam-62	181	9	2008	2008	NUM
ejpam-62	181	10	)	)	PUNCT
ejpam-62	181	11	,	,	PUNCT
ejpam-62	181	12	(	(	PUNCT
ejpam-62	181	13	10	10	NUM
ejpam-62	181	14	-	-	SYM
ejpam-62	181	15	20	20	NUM
ejpam-62	181	16	)	)	PUNCT
ejpam-62	181	17	18	18	NUM
ejpam-62	181	18	case	case	NOUN
ejpam-62	181	19	1	1	NUM
ejpam-62	181	20	.	.	PUNCT
ejpam-62	182	1	if	if	SCONJ
ejpam-62	182	2	sn	sn	PROPN
ejpam-62	182	3	=	=	SYM
ejpam-62	182	4	k	k	PROPN
ejpam-62	182	5	�	�	PROPN
ejpam-62	182	6	n−	n−	PROPN
ejpam-62	182	7	1	1	NUM
ejpam-62	182	8	k−	k−	PROPN
ejpam-62	182	9	1	1	NUM
ejpam-62	182	10	�	�	PROPN
ejpam-62	182	11	.	.	PUNCT
ejpam-62	183	1	let	let	VERB
ejpam-62	183	2	s′i	s′i	NOUN
ejpam-62	183	3	=	=	PUNCT
ejpam-62	183	4	si	si	PROPN
ejpam-62	183	5	−	−	PROPN
ejpam-62	183	6	k(k−2	k(k−2	PROPN
ejpam-62	183	7	)	)	PUNCT
ejpam-62	183	8	n−1	n−1	PROPN
ejpam-62	183	9	�	�	PROPN
ejpam-62	183	10	n−	n−	PROPN
ejpam-62	183	11	1	1	NUM
ejpam-62	183	12	k−	k−	PROPN
ejpam-62	183	13	1	1	NUM
ejpam-62	183	14	�	�	PROPN
ejpam-62	183	15	,	,	PUNCT
ejpam-62	183	16	1≤	1≤	NUM
ejpam-62	183	17	i	i	PRON
ejpam-62	183	18	≤	≤	VERB
ejpam-62	183	19	n−	n−	PROPN
ejpam-62	183	20	1	1	NUM
ejpam-62	183	21	.	.	PUNCT
ejpam-62	184	1	clearly	clearly	ADV
ejpam-62	184	2	,	,	PUNCT
ejpam-62	184	3	s′i	s′i	NOUN
ejpam-62	184	4	is	be	AUX
ejpam-62	184	5	of	of	ADP
ejpam-62	184	6	the	the	DET
ejpam-62	184	7	form	form	NOUN
ejpam-62	184	8	xk+	xk+	VERB
ejpam-62	184	9	y(k−	y(k−	PROPN
ejpam-62	184	10	1	1	NUM
ejpam-62	184	11	)	)	PUNCT
ejpam-62	184	12	.	.	PUNCT
ejpam-62	185	1	then	then	ADV
ejpam-62	185	2	,	,	PUNCT
ejpam-62	185	3	n−1	n−1	PROPN
ejpam-62	185	4	∑	∑	PUNCT
ejpam-62	185	5	i=1	i=1	PROPN
ejpam-62	185	6	s	s	PROPN
ejpam-62	185	7	/	/	SYM
ejpam-62	185	8	i	i	NOUN
ejpam-62	185	9	=	=	SYM
ejpam-62	185	10	n−1	n−1	PROPN
ejpam-62	185	11	∑	∑	PUNCT
ejpam-62	185	12	i=1	i=1	PROPN
ejpam-62	185	13	�	�	PROPN
ejpam-62	185	14	si	si	PROPN
ejpam-62	185	15	−	−	PROPN
ejpam-62	185	16	k(k−	k(k−	PROPN
ejpam-62	185	17	2	2	NUM
ejpam-62	185	18	)	)	PUNCT
ejpam-62	185	19	n−	n−	NOUN
ejpam-62	185	20	1	1	NUM
ejpam-62	185	21	�	�	PROPN
ejpam-62	185	22	n−	n−	PROPN
ejpam-62	185	23	1	1	NUM
ejpam-62	185	24	k−	k−	PROPN
ejpam-62	185	25	1	1	NUM
ejpam-62	185	26	�	�	PROPN
ejpam-62	185	27	�	�	PROPN
ejpam-62	185	28	=	=	SYM
ejpam-62	185	29	(	(	PUNCT
ejpam-62	185	30	n(k−	n(k−	PROPN
ejpam-62	185	31	1)−	1)−	PROPN
ejpam-62	185	32	k	k	NOUN
ejpam-62	185	33	)	)	PUNCT
ejpam-62	185	34	�	�	PROPN
ejpam-62	185	35	n−	n−	NOUN
ejpam-62	185	36	1	1	NUM
ejpam-62	185	37	k−	k−	PROPN
ejpam-62	185	38	1	1	NUM
ejpam-62	185	39	�	�	PROPN
ejpam-62	185	40	−	−	ADP
ejpam-62	185	41	k(k−	k(k−	PROPN
ejpam-62	185	42	2	2	NUM
ejpam-62	185	43	)	)	PUNCT
ejpam-62	185	44	�	�	PROPN
ejpam-62	185	45	n−	n−	NOUN
ejpam-62	185	46	1	1	NUM
ejpam-62	185	47	k−	k−	PROPN
ejpam-62	185	48	1	1	NUM
ejpam-62	185	49	�	�	PROPN
ejpam-62	185	50	,	,	PUNCT
ejpam-62	185	51	since	since	SCONJ
ejpam-62	185	52	n−1	n−1	PROPN
ejpam-62	185	53	∑	∑	PROPN
ejpam-62	185	54	i=1	i=1	PROPN
ejpam-62	185	55	si	si	PROPN
ejpam-62	185	56	=	=	SYM
ejpam-62	185	57	n	n	PROPN
ejpam-62	185	58	∑	∑	PROPN
ejpam-62	185	59	i=1	i=1	PROPN
ejpam-62	185	60	si	si	PROPN
ejpam-62	185	61	−	−	PROPN
ejpam-62	185	62	sn	sn	NOUN
ejpam-62	186	1	=	=	SYM
ejpam-62	186	2	n(k−	n(k−	PROPN
ejpam-62	186	3	1	1	NUM
ejpam-62	186	4	)	)	PUNCT
ejpam-62	186	5	�	�	PROPN
ejpam-62	186	6	n−	n−	NOUN
ejpam-62	186	7	1	1	NUM
ejpam-62	186	8	k−	k−	PROPN
ejpam-62	186	9	1	1	NUM
ejpam-62	186	10	�	�	PROPN
ejpam-62	186	11	−	−	PROPN
ejpam-62	186	12	k	k	PROPN
ejpam-62	186	13	�	�	PROPN
ejpam-62	186	14	n−	n−	PROPN
ejpam-62	186	15	1	1	NUM
ejpam-62	186	16	k−	k−	PROPN
ejpam-62	186	17	1	1	NUM
ejpam-62	186	18	�	�	NOUN
ejpam-62	186	19	=	=	SYM
ejpam-62	186	20	(	(	PUNCT
ejpam-62	186	21	n(k−	n(k−	PROPN
ejpam-62	186	22	1)−	1)−	PROPN
ejpam-62	186	23	k	k	NOUN
ejpam-62	186	24	)	)	PUNCT
ejpam-62	186	25	�	�	PROPN
ejpam-62	186	26	n−	n−	NOUN
ejpam-62	186	27	1	1	NUM
ejpam-62	186	28	k−	k−	PROPN
ejpam-62	186	29	1	1	NUM
ejpam-62	186	30	�	�	PROPN
ejpam-62	186	31	.	.	PUNCT
ejpam-62	187	1	so	so	ADV
ejpam-62	187	2	,	,	PUNCT
ejpam-62	187	3	n−1	n−1	PROPN
ejpam-62	187	4	∑	∑	PUNCT
ejpam-62	187	5	i=1	i=1	PROPN
ejpam-62	187	6	s	s	PROPN
ejpam-62	187	7	/	/	SYM
ejpam-62	187	8	i	i	NOUN
ejpam-62	187	9	=	=	PUNCT
ejpam-62	187	10	(	(	PUNCT
ejpam-62	187	11	n(k−	n(k−	PROPN
ejpam-62	187	12	1)−	1)−	PROPN
ejpam-62	187	13	k(k−	k(k−	NOUN
ejpam-62	187	14	2	2	NUM
ejpam-62	187	15	)	)	PUNCT
ejpam-62	187	16	)	)	PUNCT
ejpam-62	188	1	�	�	PROPN
ejpam-62	188	2	n−	n−	NOUN
ejpam-62	188	3	1	1	NUM
ejpam-62	188	4	k−	k−	PROPN
ejpam-62	188	5	1	1	NUM
ejpam-62	188	6	�	�	NOUN
ejpam-62	188	7	=	=	SYM
ejpam-62	188	8	(	(	PUNCT
ejpam-62	188	9	n(k−	n(k−	PROPN
ejpam-62	188	10	1)−	1)−	PROPN
ejpam-62	188	11	k(k−	k(k−	NOUN
ejpam-62	188	12	2	2	NUM
ejpam-62	188	13	)	)	PUNCT
ejpam-62	188	14	)	)	PUNCT
ejpam-62	188	15	�	�	PROPN
ejpam-62	188	16	n−	n−	NOUN
ejpam-62	188	17	1	1	NUM
ejpam-62	188	18	n−	n−	NOUN
ejpam-62	188	19	k	k	PROPN
ejpam-62	188	20	�	�	PROPN
ejpam-62	188	21	�	�	PROPN
ejpam-62	188	22	n−	n−	PROPN
ejpam-62	188	23	2	2	NUM
ejpam-62	188	24	k−	k−	PROPN
ejpam-62	188	25	1	1	NUM
ejpam-62	188	26	�	�	NOUN
ejpam-62	188	27	=	=	PUNCT
ejpam-62	188	28	(	(	PUNCT
ejpam-62	188	29	n−	n−	NOUN
ejpam-62	188	30	1)(k−	1)(k−	NUM
ejpam-62	188	31	1	1	NUM
ejpam-62	188	32	)	)	PUNCT
ejpam-62	188	33	�	�	PROPN
ejpam-62	188	34	n−	n−	NOUN
ejpam-62	188	35	2	2	NUM
ejpam-62	188	36	k−	k−	PROPN
ejpam-62	188	37	1	1	NUM
ejpam-62	188	38	�	�	PROPN
ejpam-62	188	39	.	.	PUNCT
ejpam-62	189	1	also	also	ADV
ejpam-62	189	2	,	,	PUNCT
ejpam-62	189	3	for	for	ADP
ejpam-62	189	4	1≤	1≤	NUM
ejpam-62	189	5	j	j	PROPN
ejpam-62	189	6	<	<	X
ejpam-62	189	7	n−	n−	PROPN
ejpam-62	189	8	1	1	NUM
ejpam-62	189	9	,	,	PUNCT
ejpam-62	189	10	s.	s.	PROPN
ejpam-62	189	11	pirzada	pirzada	PROPN
ejpam-62	189	12	,	,	PUNCT
ejpam-62	189	13	z.	z.	PROPN
ejpam-62	189	14	guofei	guofei	PROPN
ejpam-62	189	15	/	/	SYM
ejpam-62	189	16	eur	eur	PROPN
ejpam-62	189	17	.	.	PUNCT
ejpam-62	190	1	j.	j.	PROPN
ejpam-62	190	2	pure	pure	PROPN
ejpam-62	190	3	appl	appl	PROPN
ejpam-62	190	4	.	.	PROPN
ejpam-62	190	5	math	math	PROPN
ejpam-62	190	6	,	,	PUNCT
ejpam-62	190	7	1	1	NUM
ejpam-62	190	8	(	(	PUNCT
ejpam-62	190	9	2008	2008	NUM
ejpam-62	190	10	)	)	PUNCT
ejpam-62	190	11	,	,	PUNCT
ejpam-62	190	12	(	(	PUNCT
ejpam-62	190	13	10	10	NUM
ejpam-62	190	14	-	-	SYM
ejpam-62	190	15	20	20	NUM
ejpam-62	190	16	)	)	PUNCT
ejpam-62	190	17	19	19	NUM
ejpam-62	190	18	j	j	NOUN
ejpam-62	190	19	∑	∑	PUNCT
ejpam-62	190	20	i=1	i=1	PROPN
ejpam-62	190	21	s	s	PROPN
ejpam-62	190	22	/	/	SYM
ejpam-62	190	23	i	i	PROPN
ejpam-62	190	24	=	=	SYM
ejpam-62	190	25	j	j	PROPN
ejpam-62	190	26	∑	∑	PUNCT
ejpam-62	190	27	i=1	i=1	PROPN
ejpam-62	190	28	�	�	PROPN
ejpam-62	190	29	si	si	PROPN
ejpam-62	190	30	−	−	PROPN
ejpam-62	190	31	k(k−	k(k−	PROPN
ejpam-62	190	32	2	2	NUM
ejpam-62	190	33	)	)	PUNCT
ejpam-62	190	34	n−	n−	NOUN
ejpam-62	190	35	1	1	NUM
ejpam-62	190	36	�	�	PROPN
ejpam-62	190	37	n−	n−	PROPN
ejpam-62	190	38	1	1	NUM
ejpam-62	190	39	k−	k−	PROPN
ejpam-62	190	40	1	1	NUM
ejpam-62	190	41	�	�	PROPN
ejpam-62	190	42	�	�	PROPN
ejpam-62	190	43	≥	≥	NOUN
ejpam-62	190	44	j(k−	j(k−	NOUN
ejpam-62	190	45	1	1	NUM
ejpam-62	190	46	)	)	PUNCT
ejpam-62	190	47	�	�	PROPN
ejpam-62	190	48	n−	n−	NOUN
ejpam-62	190	49	1	1	NUM
ejpam-62	190	50	k−	k−	PROPN
ejpam-62	190	51	1	1	NUM
ejpam-62	190	52	�	�	PROPN
ejpam-62	190	53	+	+	CCONJ
ejpam-62	190	54	k−1	k−1	PROPN
ejpam-62	190	55	∑	∑	PROPN
ejpam-62	190	56	i=1	i=1	PROPN
ejpam-62	190	57	(	(	PUNCT
ejpam-62	190	58	i−	i−	PROPN
ejpam-62	190	59	k	k	PROPN
ejpam-62	190	60	)	)	PUNCT
ejpam-62	190	61	�	�	PROPN
ejpam-62	191	1	j	j	PROPN
ejpam-62	191	2	i	i	PROPN
ejpam-62	191	3	�	�	VERB
ejpam-62	191	4	�	�	PROPN
ejpam-62	191	5	n−	n−	PROPN
ejpam-62	191	6	j	j	PROPN
ejpam-62	191	7	k−	k−	PROPN
ejpam-62	191	8	i	i	PRON
ejpam-62	191	9	�	�	PROPN
ejpam-62	191	10	−	−	PROPN
ejpam-62	191	11	jk(k−	jk(k−	PROPN
ejpam-62	191	12	2	2	NUM
ejpam-62	191	13	)	)	PUNCT
ejpam-62	191	14	n−	n−	NOUN
ejpam-62	191	15	1	1	NUM
ejpam-62	191	16	�	�	PROPN
ejpam-62	191	17	n−	n−	PROPN
ejpam-62	191	18	1	1	NUM
ejpam-62	191	19	k−	k−	PROPN
ejpam-62	191	20	1	1	NUM
ejpam-62	191	21	�	�	PROPN
ejpam-62	191	22	=	=	SYM
ejpam-62	191	23	�	�	PROPN
ejpam-62	191	24	j(k−	j(k−	PROPN
ejpam-62	191	25	1)−	1)−	PROPN
ejpam-62	191	26	jk(k−	jk(k−	PROPN
ejpam-62	191	27	2	2	NUM
ejpam-62	191	28	)	)	PUNCT
ejpam-62	191	29	n−	n−	NOUN
ejpam-62	191	30	1	1	NUM
ejpam-62	191	31	�	�	PROPN
ejpam-62	191	32	�	�	PROPN
ejpam-62	191	33	n−	n−	PROPN
ejpam-62	191	34	1	1	NUM
ejpam-62	191	35	n−	n−	NOUN
ejpam-62	191	36	k	k	PROPN
ejpam-62	191	37	�	�	PROPN
ejpam-62	191	38	�	�	PROPN
ejpam-62	191	39	n−	n−	PROPN
ejpam-62	191	40	2	2	NUM
ejpam-62	191	41	k−	k−	PROPN
ejpam-62	191	42	1	1	NUM
ejpam-62	191	43	�	�	PROPN
ejpam-62	191	44	+	+	CCONJ
ejpam-62	191	45	k−1	k−1	PROPN
ejpam-62	191	46	∑	∑	PROPN
ejpam-62	191	47	i=1	i=1	PROPN
ejpam-62	191	48	(	(	PUNCT
ejpam-62	191	49	i−	i−	PROPN
ejpam-62	191	50	k	k	PROPN
ejpam-62	191	51	)	)	PUNCT
ejpam-62	191	52	�	�	PROPN
ejpam-62	191	53	j	j	PROPN
ejpam-62	191	54	i	i	PROPN
ejpam-62	191	55	�	�	PROPN
ejpam-62	191	56	�	�	PROPN
ejpam-62	191	57	n−	n−	NOUN
ejpam-62	191	58	j−	j−	VERB
ejpam-62	191	59	1	1	NUM
ejpam-62	191	60	k−	k−	PROPN
ejpam-62	192	1	i	i	PRON
ejpam-62	192	2	�	�	PROPN
ejpam-62	192	3	≥	≥	PROPN
ejpam-62	192	4	j(n−	j(n−	PROPN
ejpam-62	192	5	1)(k−	1)(k−	PROPN
ejpam-62	192	6	1)−	1)−	PROPN
ejpam-62	192	7	jk(k−	jk(k−	PROPN
ejpam-62	192	8	2	2	NUM
ejpam-62	192	9	)	)	PUNCT
ejpam-62	192	10	n−	n−	NOUN
ejpam-62	192	11	k	k	X
ejpam-62	192	12	�	�	PROPN
ejpam-62	192	13	n−	n−	PROPN
ejpam-62	192	14	2	2	NUM
ejpam-62	192	15	k−	k−	PROPN
ejpam-62	192	16	1	1	NUM
ejpam-62	192	17	�	�	PROPN
ejpam-62	192	18	+	+	CCONJ
ejpam-62	192	19	k−1	k−1	PROPN
ejpam-62	192	20	∑	∑	PROPN
ejpam-62	192	21	i=1	i=1	PROPN
ejpam-62	192	22	(	(	PUNCT
ejpam-62	192	23	i−	i−	PROPN
ejpam-62	192	24	k	k	PROPN
ejpam-62	192	25	)	)	PUNCT
ejpam-62	192	26	�	�	PROPN
ejpam-62	193	1	j	j	PROPN
ejpam-62	193	2	i	i	PROPN
ejpam-62	193	3	�	�	PROPN
ejpam-62	193	4	�	�	PROPN
ejpam-62	193	5	n−	n−	PROPN
ejpam-62	193	6	1−	1−	NUM
ejpam-62	193	7	j	j	PROPN
ejpam-62	193	8	k−	k−	PROPN
ejpam-62	193	9	i	i	PRON
ejpam-62	193	10	�	�	PROPN
ejpam-62	193	11	=	=	SYM
ejpam-62	193	12	j	j	PROPN
ejpam-62	194	1	[	[	X
ejpam-62	194	2	(	(	PUNCT
ejpam-62	194	3	k−	k−	PROPN
ejpam-62	194	4	1)(n−	1)(n−	NUM
ejpam-62	194	5	k	k	NOUN
ejpam-62	194	6	)	)	PUNCT
ejpam-62	195	1	+	+	CCONJ
ejpam-62	195	2	1	1	X
ejpam-62	195	3	]	]	SYM
ejpam-62	195	4	n−	n−	NOUN
ejpam-62	195	5	k	k	X
ejpam-62	195	6	�	�	PROPN
ejpam-62	195	7	n−	n−	PROPN
ejpam-62	195	8	2	2	NUM
ejpam-62	195	9	k−	k−	PROPN
ejpam-62	195	10	1	1	NUM
ejpam-62	195	11	�	�	PROPN
ejpam-62	195	12	+	+	CCONJ
ejpam-62	195	13	k−1	k−1	PROPN
ejpam-62	195	14	∑	∑	PROPN
ejpam-62	195	15	i=1	i=1	PROPN
ejpam-62	195	16	(	(	PUNCT
ejpam-62	195	17	i−	i−	PROPN
ejpam-62	195	18	k	k	PROPN
ejpam-62	195	19	)	)	PUNCT
ejpam-62	195	20	�	�	PROPN
ejpam-62	196	1	j	j	PROPN
ejpam-62	196	2	i	i	PROPN
ejpam-62	196	3	�	�	PROPN
ejpam-62	196	4	�	�	PROPN
ejpam-62	196	5	n−	n−	PROPN
ejpam-62	196	6	1−	1−	NUM
ejpam-62	196	7	j	j	PROPN
ejpam-62	196	8	k−	k−	PROPN
ejpam-62	196	9	i	i	PRON
ejpam-62	196	10	�	�	PROPN
ejpam-62	196	11	≥	≥	NUM
ejpam-62	197	1	j(k−	j(k−	NOUN
ejpam-62	197	2	1)(n−	1)(n−	PROPN
ejpam-62	197	3	k	k	NOUN
ejpam-62	197	4	)	)	PUNCT
ejpam-62	197	5	n−	n−	NOUN
ejpam-62	197	6	k	k	PROPN
ejpam-62	197	7	�	�	PROPN
ejpam-62	197	8	n−	n−	PROPN
ejpam-62	197	9	2	2	NUM
ejpam-62	197	10	k−	k−	PROPN
ejpam-62	197	11	1	1	NUM
ejpam-62	197	12	�	�	PROPN
ejpam-62	197	13	+	+	CCONJ
ejpam-62	197	14	k−1	k−1	PROPN
ejpam-62	197	15	∑	∑	PROPN
ejpam-62	197	16	i=1	i=1	PROPN
ejpam-62	197	17	(	(	PUNCT
ejpam-62	197	18	i−	i−	PROPN
ejpam-62	197	19	k	k	PROPN
ejpam-62	197	20	)	)	PUNCT
ejpam-62	197	21	�	�	PROPN
ejpam-62	198	1	j	j	PROPN
ejpam-62	198	2	i	i	PROPN
ejpam-62	198	3	�	�	PROPN
ejpam-62	198	4	�	�	PROPN
ejpam-62	198	5	n−	n−	PROPN
ejpam-62	198	6	1−	1−	NUM
ejpam-62	198	7	j	j	PROPN
ejpam-62	198	8	k−	k−	PROPN
ejpam-62	198	9	i	i	PRON
ejpam-62	198	10	�	�	PROPN
ejpam-62	198	11	.	.	PUNCT
ejpam-62	199	1	thus	thus	ADV
ejpam-62	199	2	,	,	PUNCT
ejpam-62	199	3	the	the	DET
ejpam-62	199	4	sequence	sequence	NOUN
ejpam-62	199	5	[	[	X
ejpam-62	199	6	s′1	s′1	X
ejpam-62	199	7	,	,	PUNCT
ejpam-62	199	8	s′2	s′2	NOUN
ejpam-62	199	9	,	,	PUNCT
ejpam-62	199	10	·	·	PUNCT
ejpam-62	199	11	·	·	PUNCT
ejpam-62	199	12	·	·	PUNCT
ejpam-62	199	13	,	,	PUNCT
ejpam-62	199	14	s′n−1	s′n−1	PROPN
ejpam-62	199	15	]	]	PUNCT
ejpam-62	199	16	satisfies	satisfie	NOUN
ejpam-62	199	17	(	(	PUNCT
ejpam-62	199	18	2.1	2.1	NUM
ejpam-62	199	19	)	)	PUNCT
ejpam-62	199	20	and	and	CCONJ
ejpam-62	199	21	by	by	ADP
ejpam-62	199	22	induction	induction	NOUN
ejpam-62	199	23	hypothesis	hypothesis	NOUN
ejpam-62	199	24	is	be	AUX
ejpam-62	199	25	a	a	DET
ejpam-62	199	26	score	score	NOUN
ejpam-62	199	27	sequence	sequence	NOUN
ejpam-62	199	28	of	of	ADP
ejpam-62	199	29	some	some	DET
ejpam-62	199	30	oriented	orient	VERB
ejpam-62	199	31	k	k	NOUN
ejpam-62	199	32	-	-	ADJ
ejpam-62	199	33	hypergraph	hypergraph	NOUN
ejpam-62	199	34	d′.	d′.	NOUN
ejpam-62	199	35	now	now	ADV
ejpam-62	199	36	,	,	PUNCT
ejpam-62	199	37	construct	construct	VERB
ejpam-62	199	38	the	the	DET
ejpam-62	199	39	oriented	orient	VERB
ejpam-62	199	40	k	k	NOUN
ejpam-62	199	41	-	-	ADJ
ejpam-62	199	42	hypergraph	hypergraph	ADJ
ejpam-62	199	43	d	d	NOUN
ejpam-62	199	44	as	as	SCONJ
ejpam-62	199	45	follows	follow	VERB
ejpam-62	199	46	.	.	PUNCT
ejpam-62	200	1	let	let	VERB
ejpam-62	200	2	v	v	X
ejpam-62	200	3	(	(	PUNCT
ejpam-62	200	4	d′	d′	X
ejpam-62	200	5	)	)	PUNCT
ejpam-62	201	1	=	=	PRON
ejpam-62	201	2	{	{	PUNCT
ejpam-62	201	3	v1	v1	PROPN
ejpam-62	201	4	,	,	PUNCT
ejpam-62	201	5	v2	v2	PROPN
ejpam-62	201	6	,	,	PUNCT
ejpam-62	201	7	·	·	PUNCT
ejpam-62	201	8	·	·	PUNCT
ejpam-62	201	9	·	·	PUNCT
ejpam-62	201	10	,	,	PUNCT
ejpam-62	201	11	vn−1	vn−1	PROPN
ejpam-62	201	12	}	}	PUNCT
ejpam-62	201	13	with	with	ADP
ejpam-62	201	14	s(vi	s(vi	NOUN
ejpam-62	201	15	)	)	PUNCT
ejpam-62	201	16	=	=	SYM
ejpam-62	201	17	s′i	s′i	NOUN
ejpam-62	201	18	.	.	PUNCT
ejpam-62	202	1	adding	add	VERB
ejpam-62	202	2	a	a	DET
ejpam-62	202	3	new	new	ADJ
ejpam-62	202	4	vertex	vertex	NOUN
ejpam-62	202	5	vn	vn	NOUN
ejpam-62	202	6	,	,	PUNCT
ejpam-62	202	7	and	and	CCONJ
ejpam-62	202	8	taking	take	VERB
ejpam-62	202	9	all	all	DET
ejpam-62	202	10	�	�	PROPN
ejpam-62	202	11	n−	n−	PROPN
ejpam-62	202	12	1	1	NUM
ejpam-62	202	13	k−	k−	PROPN
ejpam-62	202	14	1	1	NUM
ejpam-62	202	15	�	�	PROPN
ejpam-62	202	16	�	�	PROPN
ejpam-62	202	17	1	1	NUM
ejpam-62	202	18	1	1	NUM
ejpam-62	202	19	�	�	PROPN
ejpam-62	202	20	arcs	arc	NOUN
ejpam-62	202	21	with	with	ADP
ejpam-62	202	22	vn	vn	X
ejpam-62	202	23	not	not	PART
ejpam-62	202	24	in	in	ADP
ejpam-62	202	25	the	the	DET
ejpam-62	202	26	last	last	ADJ
ejpam-62	202	27	entry	entry	NOUN
ejpam-62	202	28	in	in	ADP
ejpam-62	202	29	any	any	PRON
ejpam-62	202	30	of	of	ADP
ejpam-62	202	31	these	these	DET
ejpam-62	202	32	arcs	arc	NOUN
ejpam-62	202	33	,	,	PUNCT
ejpam-62	202	34	we	we	PRON
ejpam-62	202	35	get	get	VERB
ejpam-62	202	36	an	an	DET
ejpam-62	202	37	oriented	oriented	ADJ
ejpam-62	202	38	k	k	NOUN
ejpam-62	202	39	-	-	ADJ
ejpam-62	202	40	hypergraph	hypergraph	ADJ
ejpam-62	202	41	d	d	NOUN
ejpam-62	202	42	of	of	ADP
ejpam-62	202	43	order	order	NOUN
ejpam-62	202	44	n	n	NOUN
ejpam-62	202	45	with	with	ADP
ejpam-62	202	46	score	score	NOUN
ejpam-62	202	47	sequence	sequence	NOUN
ejpam-62	202	48	�	�	PROPN
ejpam-62	202	49	s/1	s/1	PROPN
ejpam-62	202	50	+	+	PROPN
ejpam-62	202	51	k(k−2	k(k−2	PROPN
ejpam-62	202	52	)	)	PUNCT
ejpam-62	202	53	n−1	n−1	PROPN
ejpam-62	202	54	�	�	PROPN
ejpam-62	202	55	n−	n−	PROPN
ejpam-62	202	56	1	1	NUM
ejpam-62	202	57	k−	k−	PROPN
ejpam-62	202	58	1	1	NUM
ejpam-62	202	59	�	�	PROPN
ejpam-62	202	60	,	,	PUNCT
ejpam-62	202	61	·	·	PUNCT
ejpam-62	202	62	·	·	PUNCT
ejpam-62	202	63	·	·	PUNCT
ejpam-62	202	64	,	,	PUNCT
ejpam-62	202	65	k(k−2	k(k−2	PROPN
ejpam-62	202	66	)	)	PUNCT
ejpam-62	202	67	n−1	n−1	PROPN
ejpam-62	202	68	�	�	PROPN
ejpam-62	202	69	n−	n−	PROPN
ejpam-62	202	70	1	1	NUM
ejpam-62	202	71	k−	k−	PROPN
ejpam-62	202	72	1	1	NUM
ejpam-62	202	73	�	�	PROPN
ejpam-62	202	74	,	,	PUNCT
ejpam-62	202	75	k	k	PROPN
ejpam-62	202	76	�	�	PROPN
ejpam-62	202	77	n−	n−	PROPN
ejpam-62	202	78	1	1	NUM
ejpam-62	202	79	k−	k−	PROPN
ejpam-62	202	80	1	1	NUM
ejpam-62	202	81	�	�	PROPN
ejpam-62	202	82	�	�	NOUN
ejpam-62	202	83	=	=	PUNCT
ejpam-62	203	1	[	[	X
ejpam-62	203	2	s1	s1	NOUN
ejpam-62	203	3	,	,	PUNCT
ejpam-62	203	4	s2	s2	PROPN
ejpam-62	203	5	,	,	PUNCT
ejpam-62	203	6	·	·	PUNCT
ejpam-62	203	7	·	·	PUNCT
ejpam-62	203	8	·	·	PUNCT
ejpam-62	203	9	,	,	PUNCT
ejpam-62	203	10	sn	sn	PROPN
ejpam-62	203	11	]	]	PUNCT
ejpam-62	203	12	.	.	PUNCT
ejpam-62	204	1	case	case	NOUN
ejpam-62	204	2	2	2	X
ejpam-62	204	3	.	.	PUNCT
ejpam-62	205	1	if	if	SCONJ
ejpam-62	205	2	sn	sn	PROPN
ejpam-62	205	3	<	<	X
ejpam-62	205	4	k	k	X
ejpam-62	205	5	�	�	PROPN
ejpam-62	205	6	n−	n−	PROPN
ejpam-62	205	7	1	1	NUM
ejpam-62	205	8	k−	k−	PROPN
ejpam-62	205	9	1	1	NUM
ejpam-62	205	10	�	�	PROPN
ejpam-62	205	11	.	.	PUNCT
ejpam-62	206	1	by	by	ADP
ejpam-62	206	2	(	(	PUNCT
ejpam-62	206	3	2.1	2.1	NUM
ejpam-62	206	4	)	)	PUNCT
ejpam-62	206	5	,	,	PUNCT
ejpam-62	206	6	we	we	PRON
ejpam-62	206	7	get	get	VERB
ejpam-62	206	8	that	that	PRON
ejpam-62	206	9	sn	sn	PROPN
ejpam-62	206	10	≥	≥	X
ejpam-62	206	11	(	(	PUNCT
ejpam-62	206	12	k	k	NOUN
ejpam-62	206	13	−	−	PROPN
ejpam-62	206	14	1	1	X
ejpam-62	206	15	)	)	PUNCT
ejpam-62	206	16	�	�	PROPN
ejpam-62	206	17	n−	n−	NOUN
ejpam-62	206	18	1	1	NUM
ejpam-62	206	19	k−	k−	PROPN
ejpam-62	206	20	1	1	NUM
ejpam-62	206	21	�	�	PROPN
ejpam-62	206	22	.	.	PUNCT
ejpam-62	207	1	let	let	VERB
ejpam-62	207	2	xn	xn	PUNCT
ejpam-62	208	1	=	=	SYM
ejpam-62	208	2	sn−	sn−	PROPN
ejpam-62	208	3	(	(	PUNCT
ejpam-62	208	4	k−1	k−1	PROPN
ejpam-62	208	5	)	)	PUNCT
ejpam-62	208	6	�	�	PROPN
ejpam-62	208	7	n−	n−	NOUN
ejpam-62	208	8	1	1	NUM
ejpam-62	208	9	k−	k−	PROPN
ejpam-62	208	10	1	1	NUM
ejpam-62	208	11	�	�	PROPN
ejpam-62	208	12	,	,	PUNCT
ejpam-62	208	13	and	and	CCONJ
ejpam-62	208	14	yn	yn	PRON
ejpam-62	208	15	=	=	SYM
ejpam-62	208	16	k	k	PROPN
ejpam-62	208	17	�	�	PROPN
ejpam-62	208	18	n−	n−	PROPN
ejpam-62	208	19	1	1	NUM
ejpam-62	208	20	k−	k−	PROPN
ejpam-62	208	21	1	1	NUM
ejpam-62	208	22	�	�	PROPN
ejpam-62	208	23	−	−	PROPN
ejpam-62	208	24	sn	sn	PROPN
ejpam-62	208	25	,	,	PUNCT
ejpam-62	208	26	then	then	ADV
ejpam-62	208	27	sn	sn	PROPN
ejpam-62	208	28	=	=	SYM
ejpam-62	208	29	kxn+(k−1)yn	kxn+(k−1)yn	PROPN
ejpam-62	208	30	.	.	PUNCT
ejpam-62	209	1	now	now	ADV
ejpam-62	209	2	applying	apply	VERB
ejpam-62	209	3	lemma	lemma	PROPN
ejpam-62	209	4	2.4	2.4	NUM
ejpam-62	209	5	repeatedly	repeatedly	ADV
ejpam-62	209	6	until	until	SCONJ
ejpam-62	209	7	we	we	PRON
ejpam-62	209	8	obtain	obtain	VERB
ejpam-62	209	9	a	a	DET
ejpam-62	209	10	new	new	ADJ
ejpam-62	209	11	non	non	ADJ
ejpam-62	209	12	-	-	ADJ
ejpam-62	209	13	decreasing	decrease	VERB
ejpam-62	209	14	sequence	sequence	NOUN
ejpam-62	209	15	s′	s′	PUNCT
ejpam-62	209	16	=	=	PUNCT
ejpam-62	210	1	[	[	X
ejpam-62	210	2	s′1	s′1	X
ejpam-62	210	3	,	,	PUNCT
ejpam-62	210	4	s′2	s′2	NOUN
ejpam-62	210	5	,	,	PUNCT
ejpam-62	210	6	·	·	PUNCT
ejpam-62	210	7	·	·	PUNCT
ejpam-62	210	8	·	·	PUNCT
ejpam-62	210	9	,	,	PUNCT
ejpam-62	210	10	s′n	s′n	ADP
ejpam-62	210	11	]	]	X
ejpam-62	210	12	such	such	ADJ
ejpam-62	210	13	that	that	SCONJ
ejpam-62	210	14	s′n	s′n	NUM
ejpam-62	210	15	=	=	SYM
ejpam-62	210	16	k	k	PROPN
ejpam-62	210	17	�	�	PROPN
ejpam-62	210	18	n−	n−	PROPN
ejpam-62	210	19	1	1	NUM
ejpam-62	210	20	k−	k−	PROPN
ejpam-62	210	21	1	1	NUM
ejpam-62	210	22	�	�	PROPN
ejpam-62	210	23	.	.	PUNCT
ejpam-62	211	1	it	it	PRON
ejpam-62	211	2	is	be	AUX
ejpam-62	211	3	obvious	obvious	ADJ
ejpam-62	211	4	that	that	SCONJ
ejpam-62	211	5	lemma	lemma	PROPN
ejpam-62	211	6	2.4	2.4	NUM
ejpam-62	211	7	is	be	AUX
ejpam-62	211	8	applied	apply	VERB
ejpam-62	211	9	yn	yn	PROPN
ejpam-62	211	10	times	time	NOUN
ejpam-62	211	11	.	.	PUNCT
ejpam-62	212	1	we	we	PRON
ejpam-62	212	2	denote	denote	VERB
ejpam-62	212	3	by	by	ADP
ejpam-62	212	4	p1	p1	PROPN
ejpam-62	212	5	the	the	DET
ejpam-62	212	6	operation	operation	NOUN
ejpam-62	212	7	that	that	PRON
ejpam-62	212	8	makes	make	VERB
ejpam-62	212	9	s	s	PRON
ejpam-62	212	10	become	become	VERB
ejpam-62	212	11	some	some	DET
ejpam-62	212	12	s1	s1	NOUN
ejpam-62	212	13	=	=	SYM
ejpam-62	212	14	s(s+n	s(s+n	PROPN
ejpam-62	212	15	,	,	PUNCT
ejpam-62	212	16	s−p1	s−p1	ADV
ejpam-62	212	17	)	)	PUNCT
ejpam-62	212	18	and	and	CCONJ
ejpam-62	212	19	p2	p2	VERB
ejpam-62	212	20	the	the	DET
ejpam-62	212	21	operation	operation	NOUN
ejpam-62	212	22	that	that	PRON
ejpam-62	212	23	makes	make	VERB
ejpam-62	212	24	s1	s1	NOUN
ejpam-62	212	25	become	become	VERB
ejpam-62	212	26	some	some	DET
ejpam-62	212	27	s2	s2	NOUN
ejpam-62	212	28	=	=	PUNCT
ejpam-62	212	29	s1(s+n	s1(s+n	NOUN
ejpam-62	212	30	,	,	PUNCT
ejpam-62	212	31	s−p2	s−p2	NOUN
ejpam-62	212	32	)	)	PUNCT
ejpam-62	212	33	,	,	PUNCT
ejpam-62	212	34	and	and	CCONJ
ejpam-62	212	35	so	so	ADV
ejpam-62	212	36	on	on	ADV
ejpam-62	212	37	.	.	PUNCT
ejpam-62	213	1	furthermore	furthermore	ADV
ejpam-62	213	2	will	will	AUX
ejpam-62	213	3	denote	denote	VERB
ejpam-62	213	4	by	by	ADP
ejpam-62	213	5	p−1	p−1	PROPN
ejpam-62	213	6	i	i	PRON
ejpam-62	213	7	the	the	DET
ejpam-62	213	8	corresponding	corresponding	ADJ
ejpam-62	213	9	reversal	reversal	NOUN
ejpam-62	213	10	operation	operation	NOUN
ejpam-62	213	11	.	.	PUNCT
ejpam-62	214	1	note	note	VERB
ejpam-62	214	2	that	that	SCONJ
ejpam-62	214	3	since	since	SCONJ
ejpam-62	214	4	si	si	PROPN
ejpam-62	214	5	−	−	PROPN
ejpam-62	214	6	1	1	NUM
ejpam-62	214	7	=	=	SYM
ejpam-62	214	8	(	(	PUNCT
ejpam-62	214	9	x	x	INTJ
ejpam-62	214	10	i	i	PRON
ejpam-62	214	11	−	−	PROPN
ejpam-62	214	12	1)k	1)k	NUM
ejpam-62	215	1	+	+	CCONJ
ejpam-62	215	2	(	(	PUNCT
ejpam-62	215	3	yi	yi	NOUN
ejpam-62	215	4	+	+	NOUN
ejpam-62	215	5	1)(k	1)(k	NUM
ejpam-62	215	6	−	−	PROPN
ejpam-62	215	7	1	1	NUM
ejpam-62	215	8	)	)	PUNCT
ejpam-62	215	9	and	and	CCONJ
ejpam-62	215	10	sn+	sn+	ADJ
ejpam-62	215	11	1=	1=	X
ejpam-62	215	12	(	(	PUNCT
ejpam-62	215	13	xn+	xn+	PROPN
ejpam-62	215	14	1)k+	1)k+	NUM
ejpam-62	215	15	(	(	PUNCT
ejpam-62	215	16	yn−	yn−	NOUN
ejpam-62	215	17	1)(k−	1)(k−	NUM
ejpam-62	215	18	1	1	NUM
ejpam-62	215	19	)	)	PUNCT
ejpam-62	215	20	,	,	PUNCT
ejpam-62	215	21	the	the	DET
ejpam-62	215	22	resulting	result	VERB
ejpam-62	215	23	sequence	sequence	NOUN
ejpam-62	215	24	syn	syn	NOUN
ejpam-62	215	25	=	=	PROPN
ejpam-62	215	26	s′	s′	PROPN
ejpam-62	215	27	is	be	AUX
ejpam-62	215	28	still	still	ADV
ejpam-62	215	29	strict	strict	ADJ
ejpam-62	215	30	.	.	PUNCT
ejpam-62	216	1	so	so	ADV
ejpam-62	216	2	by	by	ADP
ejpam-62	216	3	case	case	NOUN
ejpam-62	216	4	1	1	NUM
ejpam-62	216	5	,	,	PUNCT
ejpam-62	216	6	s′	s′	ADJ
ejpam-62	216	7	is	be	AUX
ejpam-62	216	8	a	a	DET
ejpam-62	216	9	score	score	NOUN
ejpam-62	216	10	sequence	sequence	NOUN
ejpam-62	216	11	of	of	ADP
ejpam-62	216	12	some	some	DET
ejpam-62	216	13	oriented	orient	VERB
ejpam-62	216	14	k	k	NOUN
ejpam-62	216	15	-	-	NOUN
ejpam-62	216	16	hypergraph	hypergraph	NOUN
ejpam-62	216	17	.	.	PUNCT
ejpam-62	217	1	now	now	ADV
ejpam-62	217	2	,	,	PUNCT
ejpam-62	217	3	we	we	PRON
ejpam-62	217	4	make	make	VERB
ejpam-62	217	5	the	the	DET
ejpam-62	217	6	operations	operation	NOUN
ejpam-62	217	7	p−1	p−1	PROPN
ejpam-62	217	8	yn	yn	PROPN
ejpam-62	217	9	,	,	PUNCT
ejpam-62	217	10	·	·	PUNCT
ejpam-62	217	11	·	·	PUNCT
ejpam-62	217	12	·	·	PUNCT
ejpam-62	217	13	,	,	PUNCT
ejpam-62	217	14	p−1	p−1	PROPN
ejpam-62	217	15	2	2	NUM
ejpam-62	217	16	,	,	PUNCT
ejpam-62	217	17	p−1	p−1	PROPN
ejpam-62	217	18	1	1	NUM
ejpam-62	217	19	,	,	PUNCT
ejpam-62	217	20	applying	apply	VERB
ejpam-62	217	21	lemma	lemma	PROPN
ejpam-62	217	22	2.3	2.3	NUM
ejpam-62	217	23	on	on	ADP
ejpam-62	217	24	each	each	DET
ejpam-62	217	25	operation	operation	NOUN
ejpam-62	217	26	,	,	PUNCT
ejpam-62	217	27	we	we	PRON
ejpam-62	217	28	finally	finally	ADV
ejpam-62	217	29	get	get	VERB
ejpam-62	217	30	the	the	DET
ejpam-62	217	31	original	original	ADJ
ejpam-62	217	32	non	non	ADJ
ejpam-62	217	33	-	-	ADJ
ejpam-62	217	34	decreasing	decrease	VERB
ejpam-62	217	35	sequence	sequence	NOUN
ejpam-62	217	36	s	s	PART
ejpam-62	217	37	=	=	PUNCT
ejpam-62	218	1	[	[	X
ejpam-62	218	2	s1	s1	NOUN
ejpam-62	218	3	,	,	PUNCT
ejpam-62	218	4	s2	s2	PROPN
ejpam-62	218	5	,	,	PUNCT
ejpam-62	218	6	·	·	PUNCT
ejpam-62	218	7	·	·	PUNCT
ejpam-62	218	8	·	·	PUNCT
ejpam-62	218	9	,	,	PUNCT
ejpam-62	218	10	sn	sn	PROPN
ejpam-62	218	11	]	]	PUNCT
ejpam-62	218	12	.	.	PUNCT
ejpam-62	219	1	note	note	VERB
ejpam-62	219	2	that	that	SCONJ
ejpam-62	219	3	after	after	ADP
ejpam-62	219	4	each	each	DET
ejpam-62	219	5	operation	operation	NOUN
ejpam-62	219	6	p−1	p−1	PROPN
ejpam-62	219	7	i	i	PRON
ejpam-62	219	8	,	,	PUNCT
ejpam-62	219	9	the	the	DET
ejpam-62	219	10	references	reference	NOUN
ejpam-62	219	11	20	20	NUM
ejpam-62	219	12	corresponding	correspond	VERB
ejpam-62	219	13	integer	integer	NOUN
ejpam-62	219	14	sequence	sequence	NOUN
ejpam-62	219	15	remains	remain	VERB
ejpam-62	219	16	strict	strict	ADJ
ejpam-62	219	17	,	,	PUNCT
ejpam-62	219	18	so	so	ADV
ejpam-62	219	19	by	by	ADP
ejpam-62	219	20	lemma	lemma	PROPN
ejpam-62	219	21	2.3	2.3	NUM
ejpam-62	219	22	,	,	PUNCT
ejpam-62	219	23	s	s	VERB
ejpam-62	219	24	is	be	AUX
ejpam-62	219	25	a	a	DET
ejpam-62	219	26	score	score	NOUN
ejpam-62	219	27	sequence	sequence	NOUN
ejpam-62	219	28	of	of	ADP
ejpam-62	219	29	an	an	DET
ejpam-62	219	30	oriented	oriented	ADJ
ejpam-62	219	31	k	k	NOUN
ejpam-62	219	32	-	-	NOUN
ejpam-62	219	33	hypergraph	hypergraph	VERB
ejpam-62	219	34	.	.	PUNCT
ejpam-62	220	1	remark	remark	NOUN
ejpam-62	220	2	.	.	PUNCT
ejpam-62	221	1	if	if	SCONJ
ejpam-62	221	2	k	k	PROPN
ejpam-62	221	3	=	=	SYM
ejpam-62	221	4	2	2	NUM
ejpam-62	221	5	in	in	ADP
ejpam-62	221	6	theorem	theorem	NOUN
ejpam-62	221	7	2.1	2.1	NUM
ejpam-62	221	8	,	,	PUNCT
ejpam-62	221	9	then	then	ADV
ejpam-62	221	10	the	the	DET
ejpam-62	221	11	necessary	necessary	ADJ
ejpam-62	221	12	and	and	CCONJ
ejpam-62	221	13	sufficient	sufficient	ADJ
ejpam-62	221	14	condition	condition	NOUN
ejpam-62	221	15	for	for	ADP
ejpam-62	221	16	the	the	DET
ejpam-62	221	17	sequence	sequence	NOUN
ejpam-62	221	18	of	of	ADP
ejpam-62	221	19	non	non	ADJ
ejpam-62	221	20	-	-	ADJ
ejpam-62	221	21	negative	negative	ADJ
ejpam-62	221	22	integers	integer	NOUN
ejpam-62	221	23	[	[	X
ejpam-62	221	24	s1	s1	NOUN
ejpam-62	221	25	,	,	PUNCT
ejpam-62	221	26	s2	s2	PROPN
ejpam-62	221	27	,	,	PUNCT
ejpam-62	221	28	·	·	PUNCT
ejpam-62	221	29	·	·	PUNCT
ejpam-62	221	30	·	·	PUNCT
ejpam-62	221	31	,	,	PUNCT
ejpam-62	221	32	sn	sn	X
ejpam-62	221	33	]	]	PUNCT
ejpam-62	221	34	in	in	ADP
ejpam-62	221	35	non	non	ADJ
ejpam-62	221	36	-	-	ADJ
ejpam-62	221	37	decreasing	decrease	VERB
ejpam-62	221	38	order	order	NOUN
ejpam-62	221	39	becomes	become	VERB
ejpam-62	221	40	j	j	PROPN
ejpam-62	221	41	∑	∑	PROPN
ejpam-62	221	42	i=1	i=1	PROPN
ejpam-62	221	43	si	si	PROPN
ejpam-62	221	44	≥	≥	PROPN
ejpam-62	221	45	j	j	PROPN
ejpam-62	221	46	�	�	PROPN
ejpam-62	221	47	n−	n−	NOUN
ejpam-62	221	48	1	1	NUM
ejpam-62	221	49	1	1	NUM
ejpam-62	221	50	�	�	NOUN
ejpam-62	221	51	+	+	CCONJ
ejpam-62	221	52	1	1	NUM
ejpam-62	221	53	∑	∑	PROPN
ejpam-62	221	54	i=1	i=1	PROPN
ejpam-62	221	55	(	(	PUNCT
ejpam-62	221	56	i−	i−	PROPN
ejpam-62	221	57	2	2	NUM
ejpam-62	221	58	)	)	PUNCT
ejpam-62	221	59	�	�	PROPN
ejpam-62	222	1	j	j	PROPN
ejpam-62	223	1	i	i	PROPN
ejpam-62	223	2	�	�	VERB
ejpam-62	223	3	�	�	PROPN
ejpam-62	223	4	n−	n−	PROPN
ejpam-62	223	5	j	j	PROPN
ejpam-62	223	6	2−	2−	NUM
ejpam-62	223	7	i	i	PROPN
ejpam-62	223	8	�	�	PROPN
ejpam-62	223	9	=	=	SYM
ejpam-62	223	10	j	j	PROPN
ejpam-62	223	11	�	�	PROPN
ejpam-62	223	12	n−	n−	NOUN
ejpam-62	223	13	1	1	NUM
ejpam-62	223	14	1	1	NUM
ejpam-62	223	15	�	�	PROPN
ejpam-62	223	16	−	−	PROPN
ejpam-62	223	17	�	�	PROPN
ejpam-62	223	18	j	j	PROPN
ejpam-62	223	19	1	1	NUM
ejpam-62	223	20	�	�	PROPN
ejpam-62	223	21	�	�	PROPN
ejpam-62	223	22	n−	n−	PROPN
ejpam-62	223	23	j	j	PROPN
ejpam-62	223	24	1	1	NUM
ejpam-62	223	25	�	�	PROPN
ejpam-62	223	26	=	=	SYM
ejpam-62	223	27	j(n−	j(n−	PROPN
ejpam-62	223	28	1)−	1)−	PROPN
ejpam-62	223	29	j(n−	j(n−	PROPN
ejpam-62	223	30	j	j	PROPN
ejpam-62	223	31	)	)	PUNCT
ejpam-62	223	32	=	=	PUNCT
ejpam-62	224	1	j2−	j2−	PRON
ejpam-62	224	2	j	j	PROPN
ejpam-62	224	3	=	=	SYM
ejpam-62	224	4	j	j	PROPN
ejpam-62	224	5	(	(	PUNCT
ejpam-62	224	6	j−	j−	PROPN
ejpam-62	224	7	1	1	NUM
ejpam-62	224	8	)	)	PUNCT
ejpam-62	224	9	with	with	ADP
ejpam-62	224	10	n	n	PROPN
ejpam-62	224	11	∑	∑	ADV
ejpam-62	224	12	i=1	i=1	PROPN
ejpam-62	224	13	si	si	PROPN
ejpam-62	224	14	=	=	PUNCT
ejpam-62	224	15	n(2−	n(2−	PROPN
ejpam-62	224	16	1	1	NUM
ejpam-62	224	17	)	)	PUNCT
ejpam-62	224	18	�	�	PROPN
ejpam-62	224	19	n−	n−	NOUN
ejpam-62	224	20	1	1	NUM
ejpam-62	224	21	1	1	NUM
ejpam-62	224	22	�	�	NOUN
ejpam-62	224	23	=	=	NOUN
ejpam-62	224	24	n(n−	n(n−	ADJ
ejpam-62	224	25	1	1	NUM
ejpam-62	224	26	)	)	PUNCT
ejpam-62	224	27	,	,	PUNCT
ejpam-62	224	28	which	which	PRON
ejpam-62	224	29	is	be	AUX
ejpam-62	224	30	avery	avery	PROPN
ejpam-62	224	31	’s	’s	PART
ejpam-62	224	32	theorem	theorem	NOUN
ejpam-62	224	33	for	for	ADP
ejpam-62	224	34	oriented	orient	VERB
ejpam-62	224	35	graphs	graph	NOUN
ejpam-62	224	36	.	.	PUNCT
ejpam-62	225	1	references	reference	NOUN
ejpam-62	225	2	[	[	X
ejpam-62	225	3	1	1	NUM
ejpam-62	225	4	]	]	X
ejpam-62	225	5	p.	p.	NOUN
ejpam-62	225	6	avery	avery	PROPN
ejpam-62	225	7	,	,	PUNCT
ejpam-62	225	8	score	score	VERB
ejpam-62	225	9	sequences	sequence	NOUN
ejpam-62	225	10	of	of	ADP
ejpam-62	225	11	oriented	orient	VERB
ejpam-62	225	12	graphs	graph	NOUN
ejpam-62	225	13	,	,	PUNCT
ejpam-62	225	14	j.	j.	PROPN
ejpam-62	225	15	graph	graph	PROPN
ejpam-62	225	16	theory	theory	NOUN
ejpam-62	225	17	,	,	PUNCT
ejpam-62	225	18	vol	vol	NOUN
ejpam-62	225	19	.	.	PROPN
ejpam-62	225	20	15	15	NUM
ejpam-62	225	21	,	,	PUNCT
ejpam-62	225	22	no	no	INTJ
ejpam-62	225	23	.	.	NOUN
ejpam-62	226	1	3(1991	3(1991	NUM
ejpam-62	226	2	)	)	PUNCT
ejpam-62	226	3	251	251	NUM
ejpam-62	226	4	-	-	SYM
ejpam-62	226	5	257	257	NUM
ejpam-62	226	6	.	.	PUNCT
ejpam-62	227	1	[	[	X
ejpam-62	227	2	2	2	NUM
ejpam-62	227	3	]	]	PUNCT
ejpam-62	227	4	c.	c.	PROPN
ejpam-62	227	5	m.	m.	PROPN
ejpam-62	227	6	bang	bang	PROPN
ejpam-62	227	7	and	and	CCONJ
ejpam-62	227	8	h.	h.	PROPN
ejpam-62	227	9	sharp	sharp	PROPN
ejpam-62	227	10	jr	jr	PROPN
ejpam-62	227	11	.	.	PROPN
ejpam-62	227	12	,	,	PUNCT
ejpam-62	227	13	score	score	NOUN
ejpam-62	227	14	vectors	vector	NOUN
ejpam-62	227	15	of	of	ADP
ejpam-62	227	16	tournaments	tournament	NOUN
ejpam-62	227	17	,	,	PUNCT
ejpam-62	227	18	j.	j.	PROPN
ejpam-62	227	19	combin.theory	combin.theory	PROPN
ejpam-62	227	20	ser	ser	PROPN
ejpam-62	227	21	.	.	PUNCT
ejpam-62	228	1	b	b	NOUN
ejpam-62	228	2	26	26	NUM
ejpam-62	228	3	(	(	PUNCT
ejpam-62	228	4	1	1	NUM
ejpam-62	228	5	)	)	PUNCT
ejpam-62	228	6	(	(	PUNCT
ejpam-62	228	7	1979	1979	NUM
ejpam-62	228	8	)	)	PUNCT
ejpam-62	228	9	81	81	NUM
ejpam-62	228	10	-	-	SYM
ejpam-62	228	11	84	84	NUM
ejpam-62	228	12	.	.	PUNCT
ejpam-62	229	1	[	[	X
ejpam-62	229	2	3	3	X
ejpam-62	229	3	]	]	X
ejpam-62	229	4	y.	y.	PROPN
ejpam-62	229	5	koh	koh	PROPN
ejpam-62	229	6	and	and	CCONJ
ejpam-62	229	7	s.	s.	PROPN
ejpam-62	229	8	ree	ree	PROPN
ejpam-62	229	9	,	,	PUNCT
ejpam-62	229	10	score	score	VERB
ejpam-62	229	11	sequences	sequence	NOUN
ejpam-62	229	12	of	of	ADP
ejpam-62	229	13	hypertournament	hypertournament	NOUN
ejpam-62	229	14	matrices	matrix	NOUN
ejpam-62	229	15	,	,	PUNCT
ejpam-62	229	16	j.	j.	PROPN
ejpam-62	229	17	korea	korea	PROPN
ejpam-62	229	18	soc	soc	PROPN
ejpam-62	229	19	.	.	PUNCT
ejpam-62	230	1	math	math	PROPN
ejpam-62	230	2	.	.	PUNCT
ejpam-62	231	1	educ	educ	PROPN
ejpam-62	231	2	.	.	PUNCT
ejpam-62	232	1	ser	ser	PROPN
ejpam-62	232	2	.	.	PUNCT
ejpam-62	233	1	b	b	X
ejpam-62	233	2	:	:	PUNCT
ejpam-62	233	3	pure	pure	ADJ
ejpam-62	233	4	and	and	CCONJ
ejpam-62	233	5	appl	appl	PROPN
ejpam-62	233	6	.	.	PROPN
ejpam-62	233	7	math	math	NOUN
ejpam-62	233	8	.	.	PUNCT
ejpam-62	234	1	8	8	NUM
ejpam-62	234	2	(	(	PUNCT
ejpam-62	234	3	2	2	NUM
ejpam-62	234	4	)	)	PUNCT
ejpam-62	234	5	(	(	PUNCT
ejpam-62	234	6	2001	2001	NUM
ejpam-62	234	7	)	)	PUNCT
ejpam-62	234	8	185	185	NUM
ejpam-62	234	9	-	-	SYM
ejpam-62	234	10	191	191	NUM
ejpam-62	234	11	.	.	PUNCT
ejpam-62	235	1	[	[	X
ejpam-62	235	2	4	4	X
ejpam-62	235	3	]	]	X
ejpam-62	235	4	y.	y.	PROPN
ejpam-62	235	5	koh	koh	PROPN
ejpam-62	235	6	and	and	CCONJ
ejpam-62	235	7	s.	s.	PROPN
ejpam-62	235	8	ree	ree	PROPN
ejpam-62	235	9	,	,	PUNCT
ejpam-62	235	10	on	on	ADP
ejpam-62	235	11	k	k	ADJ
ejpam-62	235	12	-	-	ADJ
ejpam-62	235	13	hypertournament	hypertournament	NOUN
ejpam-62	235	14	matrices	matrix	NOUN
ejpam-62	235	15	,	,	PUNCT
ejpam-62	235	16	linear	linear	ADJ
ejpam-62	235	17	algebra	algebra	NOUN
ejpam-62	235	18	and	and	CCONJ
ejpam-62	235	19	its	its	PRON
ejpam-62	235	20	applications	application	NOUN
ejpam-62	235	21	373	373	NUM
ejpam-62	235	22	(	(	PUNCT
ejpam-62	235	23	2003	2003	NUM
ejpam-62	235	24	)	)	PUNCT
ejpam-62	235	25	183	183	NUM
ejpam-62	235	26	-	-	SYM
ejpam-62	235	27	195	195	NUM
ejpam-62	235	28	.	.	PUNCT
ejpam-62	236	1	[	[	X
ejpam-62	236	2	5	5	X
ejpam-62	236	3	]	]	PUNCT
ejpam-62	236	4	h.	h.	PROPN
ejpam-62	236	5	g.	g.	PROPN
ejpam-62	236	6	landau	landau	NOUN
ejpam-62	236	7	,	,	PUNCT
ejpam-62	236	8	on	on	ADP
ejpam-62	236	9	dominance	dominance	NOUN
ejpam-62	236	10	relations	relation	NOUN
ejpam-62	236	11	and	and	CCONJ
ejpam-62	236	12	the	the	DET
ejpam-62	236	13	structure	structure	NOUN
ejpam-62	236	14	of	of	ADP
ejpam-62	236	15	animal	animal	NOUN
ejpam-62	236	16	societies	society	NOUN
ejpam-62	236	17	.	.	PUNCT
ejpam-62	237	1	iii	iii	X
ejpam-62	237	2	.	.	PUNCT
ejpam-62	238	1	the	the	DET
ejpam-62	238	2	condition	condition	NOUN
ejpam-62	238	3	for	for	ADP
ejpam-62	238	4	a	a	DET
ejpam-62	238	5	score	score	NOUN
ejpam-62	238	6	structure	structure	NOUN
ejpam-62	238	7	,	,	PUNCT
ejpam-62	238	8	bull	bull	NOUN
ejpam-62	238	9	.	.	PUNCT
ejpam-62	238	10	math	math	NOUN
ejpam-62	238	11	.	.	PUNCT
ejpam-62	239	1	biophys	biophy	NOUN
ejpam-62	239	2	.	.	PUNCT
ejpam-62	240	1	15	15	NUM
ejpam-62	240	2	(	(	PUNCT
ejpam-62	240	3	1953	1953	NUM
ejpam-62	240	4	)	)	PUNCT
ejpam-62	240	5	143	143	NUM
ejpam-62	240	6	-	-	SYM
ejpam-62	240	7	148	148	NUM
ejpam-62	240	8	.	.	PUNCT
ejpam-62	241	1	[	[	X
ejpam-62	241	2	6	6	NUM
ejpam-62	241	3	]	]	X
ejpam-62	241	4	s.	s.	PROPN
ejpam-62	241	5	pirzada	pirzada	PROPN
ejpam-62	241	6	,	,	PUNCT
ejpam-62	241	7	t.	t.	PROPN
ejpam-62	241	8	a.	a.	NOUN
ejpam-62	241	9	naikoo	naikoo	PROPN
ejpam-62	241	10	and	and	CCONJ
ejpam-62	241	11	n.	n.	PROPN
ejpam-62	241	12	a.	a.	NOUN
ejpam-62	241	13	shah	shah	PROPN
ejpam-62	241	14	,	,	PUNCT
ejpam-62	241	15	score	score	VERB
ejpam-62	241	16	sequences	sequence	NOUN
ejpam-62	241	17	in	in	ADP
ejpam-62	241	18	oriented	orient	VERB
ejpam-62	241	19	graphs	graph	NOUN
ejpam-62	241	20	,	,	PUNCT
ejpam-62	241	21	j.	j.	PROPN
ejpam-62	241	22	applied	apply	VERB
ejpam-62	241	23	mathematics	mathematic	NOUN
ejpam-62	241	24	and	and	CCONJ
ejpam-62	241	25	computing	computing	NOUN
ejpam-62	241	26	(	(	PUNCT
ejpam-62	241	27	2006	2006	NUM
ejpam-62	241	28	)	)	PUNCT
ejpam-62	241	29	,	,	PUNCT
ejpam-62	241	30	22(1	22(1	NUM
ejpam-62	241	31	-	-	SYM
ejpam-62	241	32	2	2	NUM
ejpam-62	241	33	)	)	PUNCT
ejpam-62	241	34	(	(	PUNCT
ejpam-62	241	35	2007	2007	NUM
ejpam-62	241	36	)	)	PUNCT
ejpam-62	241	37	257	257	NUM
ejpam-62	241	38	-	-	SYM
ejpam-62	241	39	268	268	NUM
ejpam-62	241	40	.	.	PUNCT
ejpam-62	242	1	[	[	X
ejpam-62	242	2	7	7	X
ejpam-62	242	3	]	]	X
ejpam-62	242	4	c.	c.	PROPN
ejpam-62	242	5	wang	wang	PROPN
ejpam-62	242	6	and	and	CCONJ
ejpam-62	242	7	g.	g.	PROPN
ejpam-62	242	8	zhou	zhou	PROPN
ejpam-62	242	9	,	,	PUNCT
ejpam-62	242	10	note	note	VERB
ejpam-62	242	11	on	on	ADP
ejpam-62	242	12	the	the	DET
ejpam-62	242	13	degree	degree	NOUN
ejpam-62	242	14	sequences	sequence	NOUN
ejpam-62	242	15	of	of	ADP
ejpam-62	242	16	k	k	NOUN
ejpam-62	242	17	-	-	PUNCT
ejpam-62	242	18	hypertournaments	hypertournament	NOUN
ejpam-62	242	19	,	,	PUNCT
ejpam-62	242	20	discrete	discrete	ADJ
ejpam-62	242	21	mathematics	mathematic	NOUN
ejpam-62	242	22	,	,	PUNCT
ejpam-62	242	23	to	to	PART
ejpam-62	242	24	appear	appear	VERB
ejpam-62	242	25	.	.	PUNCT
ejpam-62	243	1	[	[	X
ejpam-62	243	2	8	8	NUM
ejpam-62	243	3	]	]	X
ejpam-62	243	4	g.	g.	PROPN
ejpam-62	243	5	zhou	zhou	PROPN
ejpam-62	243	6	,	,	PUNCT
ejpam-62	243	7	t.	t.	PROPN
ejpam-62	243	8	yao	yao	PROPN
ejpam-62	243	9	and	and	CCONJ
ejpam-62	243	10	k.	k.	PROPN
ejpam-62	243	11	zhang	zhang	PROPN
ejpam-62	243	12	,	,	PUNCT
ejpam-62	243	13	on	on	ADP
ejpam-62	243	14	score	score	NOUN
ejpam-62	243	15	sequences	sequence	NOUN
ejpam-62	243	16	of	of	ADP
ejpam-62	243	17	k	k	NOUN
ejpam-62	243	18	-	-	PUNCT
ejpam-62	243	19	hypertournaments	hypertournament	NOUN
ejpam-62	243	20	,	,	PUNCT
ejpam-62	243	21	european	european	PROPN
ejpam-62	243	22	j.	j.	PROPN
ejpam-62	243	23	combin	combin	PROPN
ejpam-62	243	24	.	.	PROPN
ejpam-62	243	25	21	21	NUM
ejpam-62	243	26	(	(	PUNCT
ejpam-62	243	27	8)	8)	NUM
ejpam-62	243	28	(	(	PUNCT
ejpam-62	243	29	2000	2000	NUM
ejpam-62	243	30	)	)	PUNCT
ejpam-62	243	31	993	993	NUM
ejpam-62	243	32	-	-	SYM
ejpam-62	243	33	1000	1000	NUM
ejpam-62	243	34	.	.	PUNCT