id	sid	tid	token	lemma	pos
ejpam-3405	1	1	european	european	PROPN
ejpam-3405	1	2	journal	journal	PROPN
ejpam-3405	1	3	of	of	ADP
ejpam-3405	1	4	pure	pure	ADJ
ejpam-3405	1	5	and	and	CCONJ
ejpam-3405	1	6	applied	apply	VERB
ejpam-3405	1	7	mathematics	mathematic	NOUN
ejpam-3405	1	8	vol	vol	NOUN
ejpam-3405	1	9	.	.	PROPN
ejpam-3405	2	1	12	12	NUM
ejpam-3405	2	2	,	,	PUNCT
ejpam-3405	2	3	no	no	INTJ
ejpam-3405	2	4	.	.	NOUN
ejpam-3405	2	5	2	2	NUM
ejpam-3405	2	6	,	,	PUNCT
ejpam-3405	2	7	2019	2019	NUM
ejpam-3405	2	8	,	,	PUNCT
ejpam-3405	2	9	590	590	NUM
ejpam-3405	2	10	-	-	SYM
ejpam-3405	2	11	604	604	NUM
ejpam-3405	2	12	issn	issn	PROPN
ejpam-3405	2	13	1307	1307	NUM
ejpam-3405	2	14	-	-	SYM
ejpam-3405	2	15	5543	5543	NUM
ejpam-3405	2	16	–	–	PUNCT
ejpam-3405	3	1	www.ejpam.com	www.ejpam.com	X
ejpam-3405	3	2	published	publish	VERB
ejpam-3405	3	3	by	by	ADP
ejpam-3405	3	4	new	new	PROPN
ejpam-3405	3	5	york	york	PROPN
ejpam-3405	3	6	business	business	PROPN
ejpam-3405	3	7	global	global	PROPN
ejpam-3405	3	8	on	on	ADP
ejpam-3405	3	9	a	a	DET
ejpam-3405	3	10	nonsingular	nonsingular	ADJ
ejpam-3405	3	11	equation	equation	NOUN
ejpam-3405	3	12	of	of	ADP
ejpam-3405	3	13	length	length	NOUN
ejpam-3405	3	14	9	9	NUM
ejpam-3405	3	15	over	over	ADP
ejpam-3405	3	16	torsion	torsion	NOUN
ejpam-3405	3	17	free	free	ADJ
ejpam-3405	3	18	groups	group	NOUN
ejpam-3405	3	19	m.	m.	NOUN
ejpam-3405	3	20	fazeel	fazeel	PROPN
ejpam-3405	3	21	anwar1,∗	anwar1,∗	NOUN
ejpam-3405	3	22	,	,	PUNCT
ejpam-3405	3	23	mairaj	mairaj	PROPN
ejpam-3405	3	24	bibi2	bibi2	PROPN
ejpam-3405	3	25	,	,	PUNCT
ejpam-3405	3	26	m.	m.	PROPN
ejpam-3405	3	27	saeed	saeed	PROPN
ejpam-3405	3	28	akram3	akram3	PROPN
ejpam-3405	3	29	1	1	NUM
ejpam-3405	3	30	department	department	NOUN
ejpam-3405	3	31	of	of	ADP
ejpam-3405	3	32	mathematics	mathematic	NOUN
ejpam-3405	3	33	,	,	PUNCT
ejpam-3405	3	34	sukkur	sukkur	PROPN
ejpam-3405	3	35	iba	iba	PROPN
ejpam-3405	3	36	university	university	PROPN
ejpam-3405	3	37	,	,	PUNCT
ejpam-3405	3	38	sukkur	sukkur	PROPN
ejpam-3405	3	39	.	.	PUNCT
ejpam-3405	4	1	2	2	NUM
ejpam-3405	4	2	department	department	NOUN
ejpam-3405	4	3	of	of	ADP
ejpam-3405	4	4	mathematics	mathematic	NOUN
ejpam-3405	4	5	,	,	PUNCT
ejpam-3405	4	6	comsats	comsats	PROPN
ejpam-3405	4	7	institute	institute	PROPN
ejpam-3405	4	8	of	of	ADP
ejpam-3405	4	9	information	information	NOUN
ejpam-3405	4	10	technology	technology	PROPN
ejpam-3405	4	11	,	,	PUNCT
ejpam-3405	4	12	islamabad	islamabad	PROPN
ejpam-3405	4	13	.	.	PUNCT
ejpam-3405	5	1	3	3	NUM
ejpam-3405	5	2	department	department	NOUN
ejpam-3405	5	3	of	of	ADP
ejpam-3405	5	4	mathematics	mathematics	PROPN
ejpam-3405	5	5	,	,	PUNCT
ejpam-3405	5	6	khwaja	khwaja	PROPN
ejpam-3405	5	7	fareed	fareed	PROPN
ejpam-3405	5	8	university	university	PROPN
ejpam-3405	5	9	of	of	ADP
ejpam-3405	5	10	engineering	engineering	PROPN
ejpam-3405	5	11	&	&	CCONJ
ejpam-3405	5	12	information	information	PROPN
ejpam-3405	5	13	technology	technology	PROPN
ejpam-3405	5	14	,	,	PUNCT
ejpam-3405	5	15	rahim	rahim	PROPN
ejpam-3405	5	16	yar	yar	PROPN
ejpam-3405	5	17	khan	khan	PROPN
ejpam-3405	5	18	.	.	PUNCT
ejpam-3405	6	1	abstract	abstract	ADJ
ejpam-3405	6	2	.	.	PUNCT
ejpam-3405	7	1	in	in	ADP
ejpam-3405	7	2	[	[	X
ejpam-3405	7	3	11	11	NUM
ejpam-3405	7	4	]	]	PUNCT
ejpam-3405	7	5	,	,	PUNCT
ejpam-3405	7	6	levin	levin	PROPN
ejpam-3405	7	7	conjectured	conjecture	VERB
ejpam-3405	7	8	that	that	SCONJ
ejpam-3405	7	9	every	every	DET
ejpam-3405	7	10	equation	equation	NOUN
ejpam-3405	7	11	is	be	AUX
ejpam-3405	7	12	solvable	solvable	ADJ
ejpam-3405	7	13	over	over	ADP
ejpam-3405	7	14	a	a	DET
ejpam-3405	7	15	torsion	torsion	NOUN
ejpam-3405	7	16	free	free	ADJ
ejpam-3405	7	17	group	group	NOUN
ejpam-3405	7	18	.	.	PUNCT
ejpam-3405	8	1	in	in	ADP
ejpam-3405	8	2	this	this	DET
ejpam-3405	8	3	paper	paper	NOUN
ejpam-3405	8	4	we	we	PRON
ejpam-3405	8	5	consider	consider	VERB
ejpam-3405	8	6	a	a	DET
ejpam-3405	8	7	nonsingular	nonsingular	ADJ
ejpam-3405	8	8	equation	equation	NOUN
ejpam-3405	8	9	g1tg2tg3tg4tg5tg6	g1tg2tg3tg4tg5tg6	NOUN
ejpam-3405	8	10	t	t	PROPN
ejpam-3405	8	11	−1g7tg8tg9	−1g7tg8tg9	NOUN
ejpam-3405	8	12	t	t	NOUN
ejpam-3405	8	13	−1	−1	NOUN
ejpam-3405	8	14	=	=	SYM
ejpam-3405	8	15	1	1	NUM
ejpam-3405	8	16	of	of	ADP
ejpam-3405	8	17	length	length	NOUN
ejpam-3405	8	18	9	9	NUM
ejpam-3405	8	19	and	and	CCONJ
ejpam-3405	8	20	show	show	VERB
ejpam-3405	8	21	that	that	SCONJ
ejpam-3405	8	22	it	it	PRON
ejpam-3405	8	23	is	be	AUX
ejpam-3405	8	24	solvable	solvable	ADJ
ejpam-3405	8	25	over	over	ADP
ejpam-3405	8	26	torsion	torsion	NOUN
ejpam-3405	8	27	free	free	ADJ
ejpam-3405	8	28	groups	group	NOUN
ejpam-3405	8	29	modulo	modulo	VERB
ejpam-3405	8	30	some	some	DET
ejpam-3405	8	31	exceptional	exceptional	ADJ
ejpam-3405	8	32	cases	case	NOUN
ejpam-3405	8	33	.	.	PUNCT
ejpam-3405	9	1	2010	2010	NUM
ejpam-3405	9	2	mathematics	mathematic	NOUN
ejpam-3405	9	3	subject	subject	NOUN
ejpam-3405	9	4	classifications	classification	NOUN
ejpam-3405	9	5	:	:	PUNCT
ejpam-3405	9	6	20f05	20f05	NUM
ejpam-3405	9	7	,	,	PUNCT
ejpam-3405	9	8	57m05	57m05	NUM
ejpam-3405	9	9	key	key	ADJ
ejpam-3405	9	10	words	word	NOUN
ejpam-3405	9	11	and	and	CCONJ
ejpam-3405	9	12	phrases	phrase	NOUN
ejpam-3405	9	13	:	:	PUNCT
ejpam-3405	9	14	asphericity	asphericity	NOUN
ejpam-3405	9	15	;	;	PUNCT
ejpam-3405	9	16	relative	relative	ADJ
ejpam-3405	9	17	group	group	NOUN
ejpam-3405	9	18	presentations	presentation	NOUN
ejpam-3405	9	19	;	;	PUNCT
ejpam-3405	9	20	torsion	torsion	NOUN
ejpam-3405	9	21	-	-	PUNCT
ejpam-3405	9	22	free	free	ADJ
ejpam-3405	9	23	groups	group	NOUN
ejpam-3405	9	24	;	;	PUNCT
ejpam-3405	9	25	group	group	NOUN
ejpam-3405	9	26	equations	equation	NOUN
ejpam-3405	9	27	.	.	PUNCT
ejpam-3405	10	1	1	1	X
ejpam-3405	10	2	.	.	X
ejpam-3405	10	3	introduction	introduction	NOUN
ejpam-3405	10	4	let	let	VERB
ejpam-3405	10	5	g	g	PRON
ejpam-3405	10	6	be	be	AUX
ejpam-3405	10	7	a	a	DET
ejpam-3405	10	8	non	non	ADJ
ejpam-3405	10	9	-	-	ADJ
ejpam-3405	10	10	trivial	trivial	ADJ
ejpam-3405	10	11	group	group	NOUN
ejpam-3405	10	12	,	,	PUNCT
ejpam-3405	10	13	t	t	PROPN
ejpam-3405	10	14	be	be	AUX
ejpam-3405	10	15	an	an	DET
ejpam-3405	10	16	unknown	unknown	ADJ
ejpam-3405	10	17	and	and	CCONJ
ejpam-3405	10	18	let	let	VERB
ejpam-3405	10	19	f	f	PRON
ejpam-3405	10	20	be	be	AUX
ejpam-3405	10	21	a	a	DET
ejpam-3405	10	22	free	free	ADJ
ejpam-3405	10	23	group	group	NOUN
ejpam-3405	10	24	generated	generate	VERB
ejpam-3405	10	25	by	by	ADP
ejpam-3405	10	26	t.	t.	PROPN
ejpam-3405	10	27	an	an	DET
ejpam-3405	10	28	equation	equation	NOUN
ejpam-3405	10	29	in	in	ADP
ejpam-3405	10	30	t	t	PROPN
ejpam-3405	10	31	over	over	ADP
ejpam-3405	10	32	g	g	PROPN
ejpam-3405	10	33	is	be	AUX
ejpam-3405	10	34	an	an	DET
ejpam-3405	10	35	expression	expression	NOUN
ejpam-3405	10	36	of	of	ADP
ejpam-3405	10	37	the	the	DET
ejpam-3405	10	38	form	form	NOUN
ejpam-3405	10	39	s(t	s(t	PROPN
ejpam-3405	10	40	)	)	PUNCT
ejpam-3405	10	41	=	=	PUNCT
ejpam-3405	10	42	g1	g1	PROPN
ejpam-3405	10	43	t	t	PROPN
ejpam-3405	10	44	ε1g2	ε1g2	PROPN
ejpam-3405	10	45	t	t	PROPN
ejpam-3405	10	46	ε2	ε2	PROPN
ejpam-3405	10	47	·	·	PUNCT
ejpam-3405	10	48	·	·	PUNCT
ejpam-3405	10	49	·	·	PUNCT
ejpam-3405	11	1	gntεn	gntεn	NOUN
ejpam-3405	11	2	=	=	SYM
ejpam-3405	11	3	1	1	NUM
ejpam-3405	11	4	(	(	PUNCT
ejpam-3405	11	5	gi	gi	VERB
ejpam-3405	11	6	∈	∈	PROPN
ejpam-3405	11	7	g	g	NOUN
ejpam-3405	11	8	,	,	PUNCT
ejpam-3405	11	9	εi	εi	VERB
ejpam-3405	11	10	=	=	SYM
ejpam-3405	11	11	±1	±1	VERB
ejpam-3405	11	12	)	)	PUNCT
ejpam-3405	11	13	in	in	ADP
ejpam-3405	11	14	which	which	PRON
ejpam-3405	11	15	it	it	PRON
ejpam-3405	11	16	is	be	AUX
ejpam-3405	11	17	assumed	assume	VERB
ejpam-3405	11	18	that	that	SCONJ
ejpam-3405	11	19	εi	εi	VERB
ejpam-3405	11	20	+	+	NOUN
ejpam-3405	11	21	εi+1	εi+1	ADP
ejpam-3405	11	22	=	=	SYM
ejpam-3405	11	23	0	0	NUM
ejpam-3405	11	24	implies	imply	VERB
ejpam-3405	11	25	gi+1	gi+1	NOUN
ejpam-3405	11	26	6=	6=	ADP
ejpam-3405	11	27	1	1	NUM
ejpam-3405	11	28	in	in	ADP
ejpam-3405	11	29	g.	g.	PROPN
ejpam-3405	11	30	we	we	PRON
ejpam-3405	11	31	call	call	VERB
ejpam-3405	11	32	the	the	DET
ejpam-3405	11	33	integer	integer	NOUN
ejpam-3405	11	34	n	n	CCONJ
ejpam-3405	11	35	the	the	DET
ejpam-3405	11	36	length	length	NOUN
ejpam-3405	11	37	of	of	ADP
ejpam-3405	11	38	the	the	DET
ejpam-3405	11	39	equation	equation	NOUN
ejpam-3405	11	40	.	.	PUNCT
ejpam-3405	12	1	a	a	DET
ejpam-3405	12	2	solution	solution	NOUN
ejpam-3405	12	3	of	of	ADP
ejpam-3405	12	4	s(t	s(t	PROPN
ejpam-3405	12	5	)	)	PUNCT
ejpam-3405	12	6	=	=	SYM
ejpam-3405	13	1	1	1	NUM
ejpam-3405	13	2	over	over	ADP
ejpam-3405	13	3	g	g	PROPN
ejpam-3405	13	4	is	be	AUX
ejpam-3405	13	5	an	an	DET
ejpam-3405	13	6	embedding	embed	VERB
ejpam-3405	13	7	φ	φ	NOUN
ejpam-3405	13	8	of	of	ADP
ejpam-3405	13	9	g	g	NOUN
ejpam-3405	13	10	into	into	ADP
ejpam-3405	13	11	a	a	DET
ejpam-3405	13	12	group	group	NOUN
ejpam-3405	13	13	h	h	NOUN
ejpam-3405	13	14	and	and	CCONJ
ejpam-3405	13	15	an	an	DET
ejpam-3405	13	16	element	element	NOUN
ejpam-3405	13	17	h	h	NOUN
ejpam-3405	13	18	∈	∈	PROPN
ejpam-3405	13	19	h	h	NOUN
ejpam-3405	13	20	such	such	ADJ
ejpam-3405	13	21	that	that	SCONJ
ejpam-3405	13	22	φ(g1)hε1φ(g2)hε2	φ(g1)hε1φ(g2)hε2	PROPN
ejpam-3405	13	23	·	·	PUNCT
ejpam-3405	13	24	·	·	PUNCT
ejpam-3405	13	25	·	·	PUNCT
ejpam-3405	13	26	φ(gn)hε1	φ(gn)hε1	X
ejpam-3405	13	27	=	=	SYM
ejpam-3405	13	28	1	1	NUM
ejpam-3405	13	29	in	in	ADP
ejpam-3405	13	30	h.	h.	PROPN
ejpam-3405	13	31	equivalently	equivalently	ADV
ejpam-3405	13	32	s(t	s(t	PROPN
ejpam-3405	13	33	)	)	PUNCT
ejpam-3405	13	34	=	=	PUNCT
ejpam-3405	13	35	1	1	NUM
ejpam-3405	13	36	is	be	AUX
ejpam-3405	13	37	solvable	solvable	ADJ
ejpam-3405	13	38	over	over	ADP
ejpam-3405	13	39	g	g	PROPN
ejpam-3405	13	40	if	if	SCONJ
ejpam-3405	14	1	and	and	CCONJ
ejpam-3405	14	2	only	only	ADV
ejpam-3405	14	3	if	if	SCONJ
ejpam-3405	14	4	the	the	DET
ejpam-3405	14	5	natural	natural	ADJ
ejpam-3405	14	6	map	map	NOUN
ejpam-3405	14	7	from	from	ADP
ejpam-3405	14	8	g	g	NOUN
ejpam-3405	14	9	to	to	ADP
ejpam-3405	14	10	〈	〈	PROPN
ejpam-3405	14	11	g∗f	g∗f	PROPN
ejpam-3405	14	12	|s(t	|s(t	PROPN
ejpam-3405	14	13	)	)	PUNCT
ejpam-3405	14	14	〉	〉	PROPN
ejpam-3405	14	15	is	be	AUX
ejpam-3405	14	16	injective	injective	ADJ
ejpam-3405	14	17	,	,	PUNCT
ejpam-3405	14	18	where	where	SCONJ
ejpam-3405	14	19	g	g	PROPN
ejpam-3405	14	20	∗	∗	X
ejpam-3405	14	21	f	f	PROPN
ejpam-3405	14	22	is	be	AUX
ejpam-3405	14	23	the	the	DET
ejpam-3405	14	24	free	free	ADJ
ejpam-3405	14	25	product	product	NOUN
ejpam-3405	14	26	of	of	ADP
ejpam-3405	14	27	g	g	PROPN
ejpam-3405	14	28	and	and	CCONJ
ejpam-3405	14	29	f	f	PROPN
ejpam-3405	14	30	.	.	PUNCT
ejpam-3405	15	1	if	if	SCONJ
ejpam-3405	15	2	g	g	PROPN
ejpam-3405	15	3	is	be	AUX
ejpam-3405	15	4	a	a	DET
ejpam-3405	15	5	torsion	torsion	NOUN
ejpam-3405	15	6	free	free	ADJ
ejpam-3405	15	7	group	group	NOUN
ejpam-3405	15	8	then	then	ADV
ejpam-3405	15	9	by	by	ADP
ejpam-3405	15	10	levin	levin	PROPN
ejpam-3405	15	11	’s	’s	PART
ejpam-3405	15	12	conjecture	conjecture	NOUN
ejpam-3405	15	13	every	every	DET
ejpam-3405	15	14	equation	equation	NOUN
ejpam-3405	15	15	is	be	AUX
ejpam-3405	15	16	solvable	solvable	ADJ
ejpam-3405	15	17	[	[	X
ejpam-3405	15	18	11	11	NUM
ejpam-3405	15	19	]	]	PUNCT
ejpam-3405	15	20	.	.	PUNCT
ejpam-3405	16	1	the	the	DET
ejpam-3405	16	2	conjecture	conjecture	NOUN
ejpam-3405	16	3	is	be	AUX
ejpam-3405	16	4	known	know	VERB
ejpam-3405	16	5	to	to	PART
ejpam-3405	16	6	be	be	AUX
ejpam-3405	16	7	true	true	ADJ
ejpam-3405	16	8	for	for	ADP
ejpam-3405	16	9	n	n	PRON
ejpam-3405	16	10	≤	≤	NUM
ejpam-3405	16	11	7	7	NUM
ejpam-3405	17	1	[	[	SYM
ejpam-3405	17	2	5	5	NUM
ejpam-3405	17	3	,	,	PUNCT
ejpam-3405	17	4	7	7	NUM
ejpam-3405	17	5	,	,	PUNCT
ejpam-3405	17	6	9	9	NUM
ejpam-3405	17	7	,	,	PUNCT
ejpam-3405	17	8	12	12	NUM
ejpam-3405	17	9	]	]	PUNCT
ejpam-3405	17	10	.	.	PUNCT
ejpam-3405	18	1	the	the	DET
ejpam-3405	18	2	authors	author	NOUN
ejpam-3405	18	3	have	have	AUX
ejpam-3405	18	4	done	do	VERB
ejpam-3405	18	5	significant	significant	ADJ
ejpam-3405	18	6	work	work	NOUN
ejpam-3405	18	7	in	in	ADP
ejpam-3405	18	8	[	[	X
ejpam-3405	18	9	1	1	NUM
ejpam-3405	18	10	,	,	PUNCT
ejpam-3405	18	11	2	2	NUM
ejpam-3405	18	12	,	,	PUNCT
ejpam-3405	18	13	4	4	NUM
ejpam-3405	18	14	]	]	PUNCT
ejpam-3405	18	15	to	to	PART
ejpam-3405	18	16	establish	establish	VERB
ejpam-3405	18	17	the	the	DET
ejpam-3405	18	18	conjecture	conjecture	NOUN
ejpam-3405	18	19	for	for	ADP
ejpam-3405	18	20	n	n	NOUN
ejpam-3405	18	21	=	=	SYM
ejpam-3405	18	22	8	8	NUM
ejpam-3405	18	23	.	.	PUNCT
ejpam-3405	19	1	the	the	DET
ejpam-3405	19	2	equation	equation	NOUN
ejpam-3405	19	3	of	of	ADP
ejpam-3405	19	4	length	length	NOUN
ejpam-3405	19	5	9	9	NUM
ejpam-3405	19	6	have	have	AUX
ejpam-3405	19	7	been	be	AUX
ejpam-3405	19	8	consider	consider	VERB
ejpam-3405	19	9	in	in	ADP
ejpam-3405	19	10	[	[	X
ejpam-3405	19	11	3	3	NUM
ejpam-3405	19	12	]	]	PUNCT
ejpam-3405	19	13	.	.	PUNCT
ejpam-3405	20	1	it	it	PRON
ejpam-3405	20	2	has	have	AUX
ejpam-3405	20	3	been	be	AUX
ejpam-3405	20	4	proved	prove	VERB
ejpam-3405	20	5	that	that	SCONJ
ejpam-3405	20	6	there	there	PRON
ejpam-3405	20	7	are	be	VERB
ejpam-3405	20	8	only	only	ADV
ejpam-3405	20	9	three	three	NUM
ejpam-3405	20	10	equations	equation	NOUN
ejpam-3405	20	11	of	of	ADP
ejpam-3405	20	12	length	length	NOUN
ejpam-3405	20	13	9	9	NUM
ejpam-3405	20	14	which	which	PRON
ejpam-3405	20	15	are	be	AUX
ejpam-3405	20	16	still	still	ADV
ejpam-3405	20	17	open	open	ADJ
ejpam-3405	20	18	.	.	PUNCT
ejpam-3405	21	1	in	in	ADP
ejpam-3405	21	2	this	this	DET
ejpam-3405	21	3	paper	paper	NOUN
ejpam-3405	21	4	we	we	PRON
ejpam-3405	21	5	consider	consider	VERB
ejpam-3405	21	6	a	a	DET
ejpam-3405	21	7	nonsingular	nonsingular	ADJ
ejpam-3405	21	8	equation	equation	NOUN
ejpam-3405	21	9	of	of	ADP
ejpam-3405	21	10	length	length	NOUN
ejpam-3405	21	11	9	9	NUM
ejpam-3405	21	12	(	(	PUNCT
ejpam-3405	21	13	one	one	NUM
ejpam-3405	21	14	of	of	ADP
ejpam-3405	21	15	three	three	NUM
ejpam-3405	21	16	)	)	PUNCT
ejpam-3405	21	17	and	and	CCONJ
ejpam-3405	21	18	show	show	VERB
ejpam-3405	21	19	that	that	SCONJ
ejpam-3405	21	20	the	the	DET
ejpam-3405	21	21	equation	equation	NOUN
ejpam-3405	21	22	has	have	VERB
ejpam-3405	21	23	a	a	DET
ejpam-3405	21	24	solution	solution	NOUN
ejpam-3405	21	25	∗corresponding	∗corresponde	VERB
ejpam-3405	21	26	author	author	NOUN
ejpam-3405	21	27	.	.	PUNCT
ejpam-3405	22	1	doi	doi	NOUN
ejpam-3405	22	2	:	:	PUNCT
ejpam-3405	22	3	https://doi.org/10.29020/nybg.ejpam.v12i2.3405	https://doi.org/10.29020/nybg.ejpam.v12i2.3405	PROPN
ejpam-3405	22	4	email	email	NOUN
ejpam-3405	22	5	addresses	address	NOUN
ejpam-3405	22	6	:	:	PUNCT
ejpam-3405	22	7	fazeel.anwar@iba-suk.edu.pk	fazeel.anwar@iba-suk.edu.pk	NOUN
ejpam-3405	22	8	(	(	PUNCT
ejpam-3405	22	9	m.	m.	NOUN
ejpam-3405	22	10	fazeel	fazeel	PROPN
ejpam-3405	22	11	anwar	anwar	PROPN
ejpam-3405	22	12	)	)	PUNCT
ejpam-3405	22	13	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3405	23	1	590	590	NUM
ejpam-3405	23	2	c	c	NOUN
ejpam-3405	23	3	©	©	PROPN
ejpam-3405	23	4	2019	2019	NUM
ejpam-3405	23	5	ejpam	ejpam	NOUN
ejpam-3405	23	6	all	all	DET
ejpam-3405	23	7	rights	right	NOUN
ejpam-3405	23	8	reserved	reserve	VERB
ejpam-3405	23	9	.	.	PUNCT
ejpam-3405	24	1	m.	m.	NOUN
ejpam-3405	24	2	fazeel	fazeel	PROPN
ejpam-3405	24	3	anwar	anwar	PROPN
ejpam-3405	24	4	,	,	PUNCT
ejpam-3405	24	5	mairaj	mairaj	ADJ
ejpam-3405	24	6	bibi	bibi	NOUN
ejpam-3405	24	7	,	,	PUNCT
ejpam-3405	24	8	m.	m.	PROPN
ejpam-3405	24	9	saeed	saeed	PROPN
ejpam-3405	24	10	akram	akram	PROPN
ejpam-3405	24	11	/	/	PUNCT
ejpam-3405	24	12	eur	eur	PROPN
ejpam-3405	24	13	.	.	PUNCT
ejpam-3405	25	1	j.	j.	PROPN
ejpam-3405	25	2	pure	pure	PROPN
ejpam-3405	25	3	appl	appl	PROPN
ejpam-3405	25	4	.	.	PROPN
ejpam-3405	25	5	math	math	PROPN
ejpam-3405	25	6	,	,	PUNCT
ejpam-3405	25	7	12	12	NUM
ejpam-3405	25	8	(	(	PUNCT
ejpam-3405	25	9	2	2	NUM
ejpam-3405	25	10	)	)	PUNCT
ejpam-3405	25	11	(	(	PUNCT
ejpam-3405	25	12	2019	2019	NUM
ejpam-3405	25	13	)	)	PUNCT
ejpam-3405	25	14	,	,	PUNCT
ejpam-3405	25	15	590	590	NUM
ejpam-3405	25	16	-	-	SYM
ejpam-3405	25	17	604	604	NUM
ejpam-3405	25	18	591	591	NUM
ejpam-3405	25	19	over	over	ADP
ejpam-3405	25	20	g	g	PROPN
ejpam-3405	25	21	modulo	modulo	VERB
ejpam-3405	25	22	some	some	DET
ejpam-3405	25	23	exceptional	exceptional	ADJ
ejpam-3405	25	24	cases	case	NOUN
ejpam-3405	25	25	.	.	PUNCT
ejpam-3405	26	1	this	this	DET
ejpam-3405	26	2	paper	paper	NOUN
ejpam-3405	26	3	is	be	AUX
ejpam-3405	26	4	the	the	DET
ejpam-3405	26	5	first	first	ADJ
ejpam-3405	26	6	step	step	NOUN
ejpam-3405	26	7	in	in	ADP
ejpam-3405	26	8	proving	prove	VERB
ejpam-3405	26	9	levin	levin	PROPN
ejpam-3405	26	10	’s	’s	PART
ejpam-3405	26	11	conjecture	conjecture	NOUN
ejpam-3405	26	12	for	for	ADP
ejpam-3405	26	13	equations	equation	NOUN
ejpam-3405	26	14	of	of	ADP
ejpam-3405	26	15	length	length	NOUN
ejpam-3405	26	16	9	9	NUM
ejpam-3405	26	17	.	.	PUNCT
ejpam-3405	27	1	we	we	PRON
ejpam-3405	27	2	first	first	ADV
ejpam-3405	27	3	give	give	VERB
ejpam-3405	27	4	some	some	DET
ejpam-3405	27	5	basic	basic	ADJ
ejpam-3405	27	6	definitions	definition	NOUN
ejpam-3405	27	7	.	.	PUNCT
ejpam-3405	28	1	a	a	DET
ejpam-3405	28	2	relative	relative	ADJ
ejpam-3405	28	3	group	group	NOUN
ejpam-3405	28	4	presentation	presentation	NOUN
ejpam-3405	28	5	is	be	AUX
ejpam-3405	28	6	a	a	DET
ejpam-3405	28	7	presentation	presentation	NOUN
ejpam-3405	28	8	of	of	ADP
ejpam-3405	28	9	the	the	DET
ejpam-3405	28	10	form	form	NOUN
ejpam-3405	28	11	p	p	X
ejpam-3405	28	12	=	=	PUNCT
ejpam-3405	28	13	〈	〈	PROPN
ejpam-3405	28	14	g	g	NOUN
ejpam-3405	28	15	,	,	PUNCT
ejpam-3405	28	16	x	x	PROPN
ejpam-3405	29	1	|	|	ADV
ejpam-3405	29	2	r	r	NOUN
ejpam-3405	29	3	〉	〉	NUM
ejpam-3405	29	4	where	where	SCONJ
ejpam-3405	29	5	r	r	NOUN
ejpam-3405	29	6	is	be	AUX
ejpam-3405	29	7	a	a	DET
ejpam-3405	29	8	set	set	NOUN
ejpam-3405	29	9	of	of	ADP
ejpam-3405	29	10	cyclically	cyclically	ADV
ejpam-3405	29	11	reduced	reduce	VERB
ejpam-3405	29	12	words	word	NOUN
ejpam-3405	29	13	in	in	ADP
ejpam-3405	29	14	g∗〈x	g∗〈x	NOUN
ejpam-3405	29	15	〉	〉	PROPN
ejpam-3405	29	16	.	.	PUNCT
ejpam-3405	30	1	if	if	SCONJ
ejpam-3405	30	2	the	the	DET
ejpam-3405	30	3	relative	relative	ADJ
ejpam-3405	30	4	presentation	presentation	NOUN
ejpam-3405	30	5	is	be	AUX
ejpam-3405	30	6	orientable	orientable	ADJ
ejpam-3405	30	7	and	and	CCONJ
ejpam-3405	30	8	aspherical	aspherical	ADJ
ejpam-3405	30	9	then	then	ADV
ejpam-3405	30	10	the	the	DET
ejpam-3405	30	11	natural	natural	ADJ
ejpam-3405	30	12	map	map	NOUN
ejpam-3405	30	13	from	from	ADP
ejpam-3405	30	14	g	g	NOUN
ejpam-3405	30	15	to	to	ADP
ejpam-3405	30	16	〈	〈	PROPN
ejpam-3405	30	17	g	g	PROPN
ejpam-3405	30	18	,	,	PUNCT
ejpam-3405	30	19	x	x	PUNCT
ejpam-3405	30	20	|	|	ADV
ejpam-3405	30	21	r	r	NOUN
ejpam-3405	30	22	〉	〉	PROPN
ejpam-3405	30	23	is	be	AUX
ejpam-3405	30	24	injective	injective	ADJ
ejpam-3405	30	25	.	.	PUNCT
ejpam-3405	31	1	in	in	ADP
ejpam-3405	31	2	our	our	PRON
ejpam-3405	31	3	case	case	NOUN
ejpam-3405	31	4	x	x	PUNCT
ejpam-3405	31	5	and	and	CCONJ
ejpam-3405	31	6	r	r	NOUN
ejpam-3405	31	7	consist	consist	NOUN
ejpam-3405	31	8	of	of	ADP
ejpam-3405	31	9	the	the	DET
ejpam-3405	31	10	single	single	ADJ
ejpam-3405	31	11	element	element	NOUN
ejpam-3405	31	12	t	t	PROPN
ejpam-3405	31	13	and	and	CCONJ
ejpam-3405	31	14	s(t	s(t	NUM
ejpam-3405	31	15	)	)	PUNCT
ejpam-3405	31	16	respectively	respectively	ADV
ejpam-3405	31	17	,	,	PUNCT
ejpam-3405	31	18	therefore	therefore	ADV
ejpam-3405	31	19	p	p	NOUN
ejpam-3405	31	20	is	be	AUX
ejpam-3405	31	21	orientable	orientable	ADJ
ejpam-3405	31	22	and	and	CCONJ
ejpam-3405	31	23	so	so	ADV
ejpam-3405	31	24	asphericity	asphericity	NOUN
ejpam-3405	31	25	implies	imply	VERB
ejpam-3405	31	26	s(t	s(t	PROPN
ejpam-3405	31	27	)	)	PUNCT
ejpam-3405	31	28	=	=	PUNCT
ejpam-3405	32	1	1	1	NUM
ejpam-3405	32	2	is	be	AUX
ejpam-3405	32	3	solvable	solvable	ADJ
ejpam-3405	32	4	.	.	PUNCT
ejpam-3405	33	1	in	in	ADP
ejpam-3405	33	2	this	this	DET
ejpam-3405	33	3	paper	paper	NOUN
ejpam-3405	33	4	we	we	PRON
ejpam-3405	33	5	use	use	VERB
ejpam-3405	33	6	the	the	DET
ejpam-3405	33	7	weight	weight	NOUN
ejpam-3405	33	8	test	test	NOUN
ejpam-3405	33	9	and	and	CCONJ
ejpam-3405	33	10	the	the	DET
ejpam-3405	33	11	curvature	curvature	NOUN
ejpam-3405	33	12	distribution	distribution	NOUN
ejpam-3405	33	13	method	method	NOUN
ejpam-3405	33	14	to	to	PART
ejpam-3405	33	15	show	show	VERB
ejpam-3405	33	16	that	that	SCONJ
ejpam-3405	33	17	p	p	NOUN
ejpam-3405	33	18	is	be	AUX
ejpam-3405	33	19	aspherical	aspherical	ADJ
ejpam-3405	33	20	[	[	X
ejpam-3405	33	21	6	6	NUM
ejpam-3405	33	22	]	]	PUNCT
ejpam-3405	33	23	.	.	PUNCT
ejpam-3405	34	1	the	the	DET
ejpam-3405	34	2	star	star	NOUN
ejpam-3405	34	3	graph	graph	NOUN
ejpam-3405	34	4	γ	γ	NOUN
ejpam-3405	34	5	of	of	ADP
ejpam-3405	34	6	p	p	PROPN
ejpam-3405	34	7	has	have	VERB
ejpam-3405	34	8	vertex	vertex	NOUN
ejpam-3405	34	9	set	set	VERB
ejpam-3405	34	10	x∪x−1	x∪x−1	PROPN
ejpam-3405	34	11	and	and	CCONJ
ejpam-3405	34	12	edge	edge	VERB
ejpam-3405	34	13	set	set	VERB
ejpam-3405	34	14	r∗	r∗	PROPN
ejpam-3405	34	15	,	,	PUNCT
ejpam-3405	34	16	where	where	SCONJ
ejpam-3405	34	17	r∗	r∗	PROPN
ejpam-3405	34	18	is	be	AUX
ejpam-3405	34	19	the	the	DET
ejpam-3405	34	20	set	set	NOUN
ejpam-3405	34	21	of	of	ADP
ejpam-3405	34	22	all	all	DET
ejpam-3405	34	23	cyclic	cyclic	ADJ
ejpam-3405	34	24	permutations	permutation	NOUN
ejpam-3405	34	25	of	of	ADP
ejpam-3405	34	26	the	the	DET
ejpam-3405	34	27	elements	element	NOUN
ejpam-3405	34	28	of	of	ADP
ejpam-3405	34	29	r∪r−1	r∪r−1	PROPN
ejpam-3405	34	30	which	which	PRON
ejpam-3405	34	31	begin	begin	VERB
ejpam-3405	34	32	with	with	ADP
ejpam-3405	34	33	an	an	DET
ejpam-3405	34	34	element	element	NOUN
ejpam-3405	34	35	of	of	ADP
ejpam-3405	34	36	x∪x−1	x∪x−1	PROPN
ejpam-3405	34	37	.	.	PUNCT
ejpam-3405	35	1	for	for	ADP
ejpam-3405	35	2	r	r	NOUN
ejpam-3405	35	3	∈	∈	PROPN
ejpam-3405	35	4	r∗	r∗	NOUN
ejpam-3405	35	5	write	write	VERB
ejpam-3405	35	6	r	r	NOUN
ejpam-3405	35	7	=	=	PUNCT
ejpam-3405	35	8	sg	sg	NOUN
ejpam-3405	35	9	where	where	SCONJ
ejpam-3405	35	10	g	g	PROPN
ejpam-3405	35	11	∈	∈	PROPN
ejpam-3405	35	12	g	g	PROPN
ejpam-3405	35	13	and	and	CCONJ
ejpam-3405	35	14	s	s	NOUN
ejpam-3405	35	15	begins	begin	VERB
ejpam-3405	35	16	and	and	CCONJ
ejpam-3405	35	17	ends	end	VERB
ejpam-3405	35	18	with	with	ADP
ejpam-3405	35	19	x	x	PROPN
ejpam-3405	35	20	symbols	symbol	NOUN
ejpam-3405	35	21	.	.	PUNCT
ejpam-3405	36	1	then	then	ADV
ejpam-3405	36	2	i(r	i(r	PROPN
ejpam-3405	36	3	)	)	PUNCT
ejpam-3405	36	4	is	be	AUX
ejpam-3405	36	5	the	the	DET
ejpam-3405	36	6	inverse	inverse	NOUN
ejpam-3405	36	7	of	of	ADP
ejpam-3405	36	8	the	the	DET
ejpam-3405	36	9	last	last	ADJ
ejpam-3405	36	10	symbol	symbol	NOUN
ejpam-3405	36	11	of	of	ADP
ejpam-3405	36	12	s	s	PROPN
ejpam-3405	36	13	,	,	PUNCT
ejpam-3405	36	14	τ(r	τ(r	PROPN
ejpam-3405	36	15	)	)	PUNCT
ejpam-3405	36	16	the	the	DET
ejpam-3405	36	17	first	first	ADJ
ejpam-3405	36	18	symbol	symbol	NOUN
ejpam-3405	36	19	of	of	ADP
ejpam-3405	36	20	s	s	PRON
ejpam-3405	36	21	and	and	CCONJ
ejpam-3405	36	22	λ(r	λ(r	X
ejpam-3405	36	23	)	)	PUNCT
ejpam-3405	36	24	=	=	PUNCT
ejpam-3405	37	1	g.	g.	PROPN
ejpam-3405	37	2	a	a	DET
ejpam-3405	37	3	weight	weight	NOUN
ejpam-3405	37	4	function	function	NOUN
ejpam-3405	37	5	θ	θ	PROPN
ejpam-3405	37	6	on	on	ADP
ejpam-3405	37	7	γ	γ	X
ejpam-3405	37	8	is	be	AUX
ejpam-3405	37	9	a	a	DET
ejpam-3405	37	10	real	real	ADV
ejpam-3405	37	11	valued	value	VERB
ejpam-3405	37	12	function	function	NOUN
ejpam-3405	37	13	on	on	ADP
ejpam-3405	37	14	the	the	DET
ejpam-3405	37	15	set	set	NOUN
ejpam-3405	37	16	of	of	ADP
ejpam-3405	37	17	edges	edge	NOUN
ejpam-3405	37	18	of	of	ADP
ejpam-3405	37	19	γ	γ	NOUN
ejpam-3405	37	20	which	which	PRON
ejpam-3405	37	21	satisfies	satisfy	VERB
ejpam-3405	37	22	θ(sh	θ(sh	NOUN
ejpam-3405	37	23	)	)	PUNCT
ejpam-3405	37	24	=	=	PUNCT
ejpam-3405	37	25	θ(s−1h−1	θ(s−1h−1	PROPN
ejpam-3405	37	26	)	)	PUNCT
ejpam-3405	37	27	.	.	PUNCT
ejpam-3405	38	1	a	a	DET
ejpam-3405	38	2	weight	weight	NOUN
ejpam-3405	38	3	function	function	NOUN
ejpam-3405	38	4	θ	θ	PROPN
ejpam-3405	38	5	is	be	AUX
ejpam-3405	38	6	called	call	VERB
ejpam-3405	38	7	aspherical	aspherical	ADJ
ejpam-3405	38	8	if	if	SCONJ
ejpam-3405	38	9	the	the	DET
ejpam-3405	38	10	following	follow	VERB
ejpam-3405	38	11	three	three	NUM
ejpam-3405	38	12	conditions	condition	NOUN
ejpam-3405	38	13	are	be	AUX
ejpam-3405	38	14	satisfied	satisfied	ADJ
ejpam-3405	38	15	(	(	PUNCT
ejpam-3405	38	16	w1	w1	NOUN
ejpam-3405	38	17	)	)	PUNCT
ejpam-3405	38	18	let	let	VERB
ejpam-3405	38	19	r	r	NOUN
ejpam-3405	38	20	∈	∈	PROPN
ejpam-3405	38	21	r∗	r∗	VERB
ejpam-3405	38	22	with	with	ADP
ejpam-3405	38	23	r	r	NOUN
ejpam-3405	38	24	=	=	SYM
ejpam-3405	38	25	xε11	xε11	PROPN
ejpam-3405	38	26	g1	g1	PROPN
ejpam-3405	38	27	·	·	PUNCT
ejpam-3405	38	28	·	·	PUNCT
ejpam-3405	39	1	·	·	PUNCT
ejpam-3405	39	2	xεnn	xεnn	PROPN
ejpam-3405	39	3	gn	gn	PROPN
ejpam-3405	39	4	.	.	PUNCT
ejpam-3405	40	1	then	then	ADV
ejpam-3405	40	2	n∑	n∑	PROPN
ejpam-3405	40	3	i=1	i=1	PROPN
ejpam-3405	41	1	(	(	PUNCT
ejpam-3405	41	2	1−	1−	NUM
ejpam-3405	41	3	θ(xεii	θ(xεii	NOUN
ejpam-3405	41	4	gi	gi	NOUN
ejpam-3405	41	5	·	·	PUNCT
ejpam-3405	41	6	·	·	PUNCT
ejpam-3405	41	7	·	·	PUNCT
ejpam-3405	42	1	x	x	X
ejpam-3405	42	2	εn	εn	ADP
ejpam-3405	42	3	n	n	PRON
ejpam-3405	42	4	gnx	gnx	PROPN
ejpam-3405	42	5	ε1	ε1	PROPN
ejpam-3405	42	6	1	1	NUM
ejpam-3405	42	7	g1	g1	NOUN
ejpam-3405	42	8	·	·	PUNCT
ejpam-3405	42	9	·	·	PUNCT
ejpam-3405	42	10	·	·	PUNCT
ejpam-3405	42	11	xεi−1	xεi−1	PROPN
ejpam-3405	42	12	i−1	i−1	PROPN
ejpam-3405	42	13	gi−1	gi−1	PROPN
ejpam-3405	42	14	)	)	PUNCT
ejpam-3405	42	15	)	)	PUNCT
ejpam-3405	42	16	≥	≥	NOUN
ejpam-3405	42	17	2	2	NUM
ejpam-3405	42	18	.	.	PUNCT
ejpam-3405	42	19	(	(	PUNCT
ejpam-3405	42	20	w2	w2	NOUN
ejpam-3405	42	21	)	)	PUNCT
ejpam-3405	42	22	each	each	DET
ejpam-3405	42	23	admissible	admissible	ADJ
ejpam-3405	42	24	cycle	cycle	NOUN
ejpam-3405	42	25	in	in	ADP
ejpam-3405	42	26	γ	γ	PROPN
ejpam-3405	42	27	has	have	VERB
ejpam-3405	42	28	weight	weight	NOUN
ejpam-3405	42	29	at	at	ADV
ejpam-3405	42	30	least	least	ADJ
ejpam-3405	42	31	2	2	NUM
ejpam-3405	42	32	(	(	PUNCT
ejpam-3405	42	33	where	where	SCONJ
ejpam-3405	42	34	admissible	admissible	ADJ
ejpam-3405	42	35	means	mean	VERB
ejpam-3405	42	36	having	have	VERB
ejpam-3405	42	37	a	a	DET
ejpam-3405	42	38	label	label	NOUN
ejpam-3405	42	39	trivial	trivial	ADJ
ejpam-3405	42	40	in	in	ADP
ejpam-3405	42	41	g	g	NOUN
ejpam-3405	42	42	)	)	PUNCT
ejpam-3405	42	43	.	.	PUNCT
ejpam-3405	43	1	(	(	PUNCT
ejpam-3405	43	2	w3	w3	PROPN
ejpam-3405	43	3	)	)	PUNCT
ejpam-3405	43	4	each	each	DET
ejpam-3405	43	5	edge	edge	NOUN
ejpam-3405	43	6	of	of	ADP
ejpam-3405	43	7	γ	γ	PROPN
ejpam-3405	43	8	has	have	VERB
ejpam-3405	43	9	a	a	DET
ejpam-3405	43	10	non	non	ADJ
ejpam-3405	43	11	-	-	ADJ
ejpam-3405	43	12	negative	negative	ADJ
ejpam-3405	43	13	weight	weight	NOUN
ejpam-3405	43	14	.	.	PUNCT
ejpam-3405	44	1	if	if	SCONJ
ejpam-3405	44	2	γ	γ	PROPN
ejpam-3405	44	3	admits	admit	VERB
ejpam-3405	44	4	an	an	DET
ejpam-3405	44	5	aspherical	aspherical	ADJ
ejpam-3405	44	6	weight	weight	NOUN
ejpam-3405	44	7	function	function	NOUN
ejpam-3405	44	8	then	then	ADV
ejpam-3405	44	9	p	p	NOUN
ejpam-3405	44	10	is	be	AUX
ejpam-3405	44	11	aspherical	aspherical	ADJ
ejpam-3405	44	12	[	[	X
ejpam-3405	44	13	6	6	NUM
ejpam-3405	44	14	]	]	PUNCT
ejpam-3405	44	15	.	.	PUNCT
ejpam-3405	45	1	the	the	DET
ejpam-3405	45	2	following	follow	VERB
ejpam-3405	45	3	lemma	lemma	PROPN
ejpam-3405	45	4	[	[	X
ejpam-3405	45	5	10	10	NUM
ejpam-3405	45	6	]	]	PUNCT
ejpam-3405	45	7	tells	tell	VERB
ejpam-3405	45	8	us	we	PRON
ejpam-3405	45	9	that	that	SCONJ
ejpam-3405	45	10	we	we	PRON
ejpam-3405	45	11	can	can	AUX
ejpam-3405	45	12	apply	apply	VERB
ejpam-3405	45	13	asphericity	asphericity	NOUN
ejpam-3405	45	14	test	test	NOUN
ejpam-3405	45	15	in	in	ADP
ejpam-3405	45	16	k−steps	k−steps	PROPN
ejpam-3405	45	17	.	.	PUNCT
ejpam-3405	46	1	lemma	lemma	PROPN
ejpam-3405	46	2	1	1	X
ejpam-3405	46	3	.	.	PUNCT
ejpam-3405	47	1	let	let	VERB
ejpam-3405	47	2	the	the	DET
ejpam-3405	47	3	relative	relative	ADJ
ejpam-3405	47	4	presentation	presentation	NOUN
ejpam-3405	47	5	p	p	X
ejpam-3405	47	6	=	=	PUNCT
ejpam-3405	47	7	〈	〈	PROPN
ejpam-3405	47	8	h	h	NOUN
ejpam-3405	47	9	,	,	PUNCT
ejpam-3405	47	10	x	x	INTJ
ejpam-3405	47	11	:	:	PUNCT
ejpam-3405	47	12	r	r	AUX
ejpam-3405	47	13	〉	〉	NOUN
ejpam-3405	47	14	define	define	VERB
ejpam-3405	47	15	a	a	DET
ejpam-3405	47	16	group	group	NOUN
ejpam-3405	47	17	g	g	NOUN
ejpam-3405	47	18	and	and	CCONJ
ejpam-3405	47	19	let	let	VERB
ejpam-3405	47	20	q	q	NOUN
ejpam-3405	47	21	=	=	VERB
ejpam-3405	47	22	〈	〈	PROPN
ejpam-3405	47	23	g	g	NOUN
ejpam-3405	47	24	,	,	PUNCT
ejpam-3405	47	25	t	t	X
ejpam-3405	47	26	:	:	PUNCT
ejpam-3405	47	27	s	s	X
ejpam-3405	47	28	〉	〉	NOUN
ejpam-3405	47	29	be	be	AUX
ejpam-3405	47	30	another	another	DET
ejpam-3405	47	31	relative	relative	ADJ
ejpam-3405	47	32	presentation	presentation	NOUN
ejpam-3405	47	33	.	.	PUNCT
ejpam-3405	48	1	if	if	SCONJ
ejpam-3405	48	2	q	q	PROPN
ejpam-3405	48	3	and	and	CCONJ
ejpam-3405	48	4	p	p	NOUN
ejpam-3405	48	5	are	be	AUX
ejpam-3405	48	6	both	both	CCONJ
ejpam-3405	48	7	aspherical	aspherical	ADJ
ejpam-3405	48	8	,	,	PUNCT
ejpam-3405	48	9	then	then	ADV
ejpam-3405	48	10	the	the	DET
ejpam-3405	48	11	relative	relative	ADJ
ejpam-3405	48	12	presentation	presentation	NOUN
ejpam-3405	48	13	r	r	NOUN
ejpam-3405	48	14	=	=	PUNCT
ejpam-3405	48	15	〈	〈	PROPN
ejpam-3405	48	16	h	h	NOUN
ejpam-3405	48	17	,	,	PUNCT
ejpam-3405	48	18	x	x	SYM
ejpam-3405	48	19	∪	∪	PROPN
ejpam-3405	48	20	t	t	NOUN
ejpam-3405	48	21	:	:	PUNCT
ejpam-3405	48	22	r	r	NOUN
ejpam-3405	48	23	∪	∪	ADP
ejpam-3405	48	24	s̃	s̃	PROPN
ejpam-3405	48	25	〉	〉	PROPN
ejpam-3405	48	26	is	be	AUX
ejpam-3405	48	27	aspherical	aspherical	ADJ
ejpam-3405	48	28	,	,	PUNCT
ejpam-3405	48	29	where	where	SCONJ
ejpam-3405	48	30	s̃	s̃	PROPN
ejpam-3405	48	31	is	be	AUX
ejpam-3405	48	32	an	an	DET
ejpam-3405	48	33	element	element	NOUN
ejpam-3405	48	34	of	of	ADP
ejpam-3405	48	35	h	h	PROPN
ejpam-3405	48	36	∗	∗	NOUN
ejpam-3405	48	37	f	f	PROPN
ejpam-3405	48	38	(	(	PUNCT
ejpam-3405	48	39	x	x	NOUN
ejpam-3405	48	40	)	)	PUNCT
ejpam-3405	48	41	∗	∗	NOUN
ejpam-3405	48	42	f	f	PROPN
ejpam-3405	48	43	(	(	PUNCT
ejpam-3405	48	44	t	t	PROPN
ejpam-3405	48	45	)	)	PUNCT
ejpam-3405	48	46	obtained	obtain	VERB
ejpam-3405	48	47	from	from	ADP
ejpam-3405	48	48	s	s	PRON
ejpam-3405	48	49	by	by	ADP
ejpam-3405	48	50	lifting	lift	VERB
ejpam-3405	48	51	.	.	PUNCT
ejpam-3405	49	1	for	for	ADP
ejpam-3405	49	2	a	a	DET
ejpam-3405	49	3	detailed	detailed	ADJ
ejpam-3405	49	4	account	account	NOUN
ejpam-3405	49	5	on	on	ADP
ejpam-3405	49	6	the	the	DET
ejpam-3405	49	7	curvature	curvature	NOUN
ejpam-3405	49	8	distribution	distribution	NOUN
ejpam-3405	49	9	method	method	NOUN
ejpam-3405	49	10	see	see	VERB
ejpam-3405	49	11	[	[	X
ejpam-3405	49	12	3	3	NUM
ejpam-3405	49	13	]	]	PUNCT
ejpam-3405	49	14	.	.	PUNCT
ejpam-3405	50	1	it	it	PRON
ejpam-3405	50	2	is	be	AUX
ejpam-3405	50	3	clear	clear	ADJ
ejpam-3405	50	4	from	from	ADP
ejpam-3405	50	5	our	our	PRON
ejpam-3405	50	6	definition	definition	NOUN
ejpam-3405	50	7	of	of	ADP
ejpam-3405	50	8	a	a	DET
ejpam-3405	50	9	group	group	NOUN
ejpam-3405	50	10	equation	equation	NOUN
ejpam-3405	50	11	that	that	SCONJ
ejpam-3405	50	12	if	if	SCONJ
ejpam-3405	50	13	gi	gi	NOUN
ejpam-3405	50	14	is	be	AUX
ejpam-3405	50	15	a	a	DET
ejpam-3405	50	16	coefficient	coefficient	NOUN
ejpam-3405	50	17	between	between	ADP
ejpam-3405	50	18	a	a	DET
ejpam-3405	50	19	negative	negative	ADJ
ejpam-3405	50	20	and	and	CCONJ
ejpam-3405	50	21	a	a	DET
ejpam-3405	50	22	positive	positive	ADJ
ejpam-3405	50	23	power	power	NOUN
ejpam-3405	50	24	of	of	ADP
ejpam-3405	50	25	t	t	PROPN
ejpam-3405	50	26	than	than	SCONJ
ejpam-3405	50	27	gi	gi	PROPN
ejpam-3405	50	28	is	be	AUX
ejpam-3405	50	29	not	not	PART
ejpam-3405	50	30	trivial	trivial	ADJ
ejpam-3405	50	31	in	in	ADP
ejpam-3405	50	32	g.	g.	PROPN
ejpam-3405	50	33	this	this	DET
ejpam-3405	50	34	fact	fact	NOUN
ejpam-3405	50	35	will	will	AUX
ejpam-3405	50	36	be	be	AUX
ejpam-3405	50	37	used	use	VERB
ejpam-3405	50	38	in	in	ADP
ejpam-3405	50	39	all	all	DET
ejpam-3405	50	40	subsequent	subsequent	ADJ
ejpam-3405	50	41	proofs	proof	NOUN
ejpam-3405	50	42	without	without	ADP
ejpam-3405	50	43	reference	reference	NOUN
ejpam-3405	50	44	.	.	PUNCT
ejpam-3405	51	1	2	2	X
ejpam-3405	51	2	.	.	X
ejpam-3405	51	3	main	main	ADJ
ejpam-3405	51	4	results	result	NOUN
ejpam-3405	51	5	we	we	PRON
ejpam-3405	51	6	now	now	ADV
ejpam-3405	51	7	turn	turn	VERB
ejpam-3405	51	8	our	our	PRON
ejpam-3405	51	9	attention	attention	NOUN
ejpam-3405	51	10	to	to	ADP
ejpam-3405	51	11	length	length	NOUN
ejpam-3405	51	12	9	9	NUM
ejpam-3405	51	13	equations	equation	NOUN
ejpam-3405	51	14	.	.	PUNCT
ejpam-3405	52	1	a	a	DET
ejpam-3405	52	2	list	list	NOUN
ejpam-3405	52	3	of	of	ADP
ejpam-3405	52	4	these	these	DET
ejpam-3405	52	5	equations	equation	NOUN
ejpam-3405	52	6	is	be	AUX
ejpam-3405	52	7	given	give	VERB
ejpam-3405	52	8	in	in	ADP
ejpam-3405	52	9	[	[	X
ejpam-3405	52	10	3	3	NUM
ejpam-3405	52	11	]	]	PUNCT
ejpam-3405	52	12	.	.	PUNCT
ejpam-3405	53	1	consider	consider	VERB
ejpam-3405	53	2	the	the	DET
ejpam-3405	53	3	nonsingular	nonsingular	ADJ
ejpam-3405	53	4	equation	equation	NOUN
ejpam-3405	53	5	of	of	ADP
ejpam-3405	53	6	length	length	NOUN
ejpam-3405	53	7	9	9	NUM
ejpam-3405	53	8	given	give	VERB
ejpam-3405	53	9	by	by	ADP
ejpam-3405	53	10	atbtctdtetft−1gthtit−1	atbtctdtetft−1gthtit−1	PROPN
ejpam-3405	54	1	=	=	PUNCT
ejpam-3405	54	2	1	1	X
ejpam-3405	54	3	.	.	PUNCT
ejpam-3405	55	1	we	we	PRON
ejpam-3405	55	2	write	write	VERB
ejpam-3405	55	3	this	this	PRON
ejpam-3405	55	4	as	as	ADP
ejpam-3405	55	5	p	p	NOUN
ejpam-3405	55	6	=	=	PUNCT
ejpam-3405	55	7	〈	〈	PROPN
ejpam-3405	55	8	g	g	NOUN
ejpam-3405	55	9	,	,	PUNCT
ejpam-3405	55	10	t|s(t	t|s(t	PROPN
ejpam-3405	55	11	)	)	PUNCT
ejpam-3405	55	12	〉	〉	PROPN
ejpam-3405	55	13	,	,	PUNCT
ejpam-3405	55	14	where	where	SCONJ
ejpam-3405	55	15	s(t	s(t	NOUN
ejpam-3405	55	16	)	)	PUNCT
ejpam-3405	55	17	=	=	SYM
ejpam-3405	55	18	atbtctdtetft−1gthtit−1	atbtctdtetft−1gthtit−1	PROPN
ejpam-3405	55	19	.	.	PUNCT
ejpam-3405	56	1	here	here	ADV
ejpam-3405	56	2	b	b	NUM
ejpam-3405	56	3	,	,	PUNCT
ejpam-3405	56	4	c	c	NOUN
ejpam-3405	56	5	,	,	PUNCT
ejpam-3405	56	6	d	d	NOUN
ejpam-3405	56	7	,	,	PUNCT
ejpam-3405	56	8	e	e	NOUN
ejpam-3405	56	9	,	,	PUNCT
ejpam-3405	56	10	h	h	NOUN
ejpam-3405	56	11	∈	∈	PROPN
ejpam-3405	56	12	g	g	PROPN
ejpam-3405	56	13	and	and	CCONJ
ejpam-3405	56	14	a	a	DET
ejpam-3405	56	15	,	,	PUNCT
ejpam-3405	56	16	f	f	X
ejpam-3405	56	17	,	,	PUNCT
ejpam-3405	56	18	g	g	PROPN
ejpam-3405	56	19	,	,	PUNCT
ejpam-3405	56	20	i	i	PROPN
ejpam-3405	56	21	∈	∈	PROPN
ejpam-3405	56	22	g\{1	g\{1	PROPN
ejpam-3405	56	23	}	}	PUNCT
ejpam-3405	56	24	.	.	PUNCT
ejpam-3405	57	1	the	the	DET
ejpam-3405	57	2	star	star	NOUN
ejpam-3405	57	3	graph	graph	NOUN
ejpam-3405	57	4	γ	γ	PROPN
ejpam-3405	57	5	for	for	ADP
ejpam-3405	57	6	p	p	PROPN
ejpam-3405	57	7	is	be	AUX
ejpam-3405	57	8	given	give	VERB
ejpam-3405	57	9	in	in	ADP
ejpam-3405	57	10	figure	figure	NOUN
ejpam-3405	57	11	2	2	NUM
ejpam-3405	57	12	.	.	PUNCT
ejpam-3405	58	1	we	we	PRON
ejpam-3405	58	2	apply	apply	VERB
ejpam-3405	58	3	the	the	DET
ejpam-3405	58	4	transformation	transformation	NOUN
ejpam-3405	58	5	x	x	PUNCT
ejpam-3405	58	6	=	=	NOUN
ejpam-3405	58	7	tb	tb	NOUN
ejpam-3405	58	8	to	to	PART
ejpam-3405	58	9	get	get	VERB
ejpam-3405	58	10	that	that	DET
ejpam-3405	58	11	b	b	NOUN
ejpam-3405	58	12	=	=	SYM
ejpam-3405	58	13	1	1	NUM
ejpam-3405	58	14	in	in	ADP
ejpam-3405	58	15	g.	g.	NOUN
ejpam-3405	58	16	by	by	ADP
ejpam-3405	58	17	using	use	VERB
ejpam-3405	58	18	the	the	DET
ejpam-3405	58	19	methods	method	NOUN
ejpam-3405	58	20	m.	m.	PROPN
ejpam-3405	58	21	fazeel	fazeel	PROPN
ejpam-3405	58	22	anwar	anwar	PROPN
ejpam-3405	58	23	,	,	PUNCT
ejpam-3405	58	24	mairaj	mairaj	ADJ
ejpam-3405	58	25	bibi	bibi	NOUN
ejpam-3405	58	26	,	,	PUNCT
ejpam-3405	58	27	m.	m.	PROPN
ejpam-3405	58	28	saeed	saeed	PROPN
ejpam-3405	58	29	akram	akram	PROPN
ejpam-3405	58	30	/	/	PUNCT
ejpam-3405	58	31	eur	eur	PROPN
ejpam-3405	58	32	.	.	PUNCT
ejpam-3405	59	1	j.	j.	PROPN
ejpam-3405	59	2	pure	pure	PROPN
ejpam-3405	59	3	appl	appl	PROPN
ejpam-3405	59	4	.	.	PROPN
ejpam-3405	59	5	math	math	PROPN
ejpam-3405	59	6	,	,	PUNCT
ejpam-3405	59	7	12	12	NUM
ejpam-3405	59	8	(	(	PUNCT
ejpam-3405	59	9	2	2	NUM
ejpam-3405	59	10	)	)	PUNCT
ejpam-3405	59	11	(	(	PUNCT
ejpam-3405	59	12	2019	2019	NUM
ejpam-3405	59	13	)	)	PUNCT
ejpam-3405	59	14	,	,	PUNCT
ejpam-3405	59	15	590	590	NUM
ejpam-3405	59	16	-	-	SYM
ejpam-3405	59	17	604	604	NUM
ejpam-3405	59	18	592	592	NUM
ejpam-3405	59	19	x	x	SYM
ejpam-3405	59	20	t	t	NOUN
ejpam-3405	59	21	t̄	t̄	NOUN
ejpam-3405	59	22	β3	β3	PROPN
ejpam-3405	59	23	x̄	x̄	PRON
ejpam-3405	59	24	α4	α4	VERB
ejpam-3405	59	25	β1	β1	PROPN
ejpam-3405	59	26	α3	α3	PROPN
ejpam-3405	59	27	α5	α5	PROPN
ejpam-3405	59	28	α2	α2	ADJ
ejpam-3405	59	29	β2	β2	PROPN
ejpam-3405	59	30	α1	α1	PROPN
ejpam-3405	59	31	x	x	SYM
ejpam-3405	59	32	t	t	PROPN
ejpam-3405	59	33	t̄	t̄	PROPN
ejpam-3405	59	34	α4	α4	PROPN
ejpam-3405	59	35	x̄	x̄	PROPN
ejpam-3405	59	36	α2	α2	PROPN
ejpam-3405	59	37	α3	α3	PROPN
ejpam-3405	59	38	β1	β1	PROPN
ejpam-3405	59	39	β3	β3	PROPN
ejpam-3405	59	40	α5	α5	NOUN
ejpam-3405	59	41	α1	α1	PROPN
ejpam-3405	59	42	β2	β2	NOUN
ejpam-3405	59	43	x	x	PROPN
ejpam-3405	59	44	t	t	PROPN
ejpam-3405	60	1	t̄	t̄	PROPN
ejpam-3405	60	2	β3	β3	PROPN
ejpam-3405	60	3	x̄	x̄	PRON
ejpam-3405	60	4	α4	α4	VERB
ejpam-3405	60	5	α2	α2	PROPN
ejpam-3405	60	6	β1	β1	PROPN
ejpam-3405	60	7	α3	α3	PROPN
ejpam-3405	60	8	α7	α7	NOUN
ejpam-3405	60	9	α5	α5	PROPN
ejpam-3405	60	10	α1	α1	PROPN
ejpam-3405	60	11	β2	β2	NOUN
ejpam-3405	60	12	(	(	PUNCT
ejpam-3405	60	13	a	a	NOUN
ejpam-3405	60	14	)	)	PUNCT
ejpam-3405	60	15	(	(	PUNCT
ejpam-3405	60	16	c)(b	c)(b	PROPN
ejpam-3405	60	17	)	)	PUNCT
ejpam-3405	60	18	α6	α6	PROPN
ejpam-3405	60	19	β4	β4	PROPN
ejpam-3405	60	20	β4	β4	PROPN
ejpam-3405	60	21	figure	figure	NOUN
ejpam-3405	60	22	1	1	NUM
ejpam-3405	60	23	:	:	PUNCT
ejpam-3405	60	24	star	star	NOUN
ejpam-3405	60	25	graph	graph	NOUN
ejpam-3405	60	26	γ	γ	PROPN
ejpam-3405	60	27	given	give	VERB
ejpam-3405	60	28	in	in	ADP
ejpam-3405	60	29	[	[	X
ejpam-3405	60	30	5	5	NUM
ejpam-3405	60	31	,	,	PUNCT
ejpam-3405	60	32	8	8	NUM
ejpam-3405	60	33	]	]	PUNCT
ejpam-3405	60	34	we	we	PRON
ejpam-3405	60	35	conclude	conclude	VERB
ejpam-3405	60	36	that	that	SCONJ
ejpam-3405	60	37	possible	possible	ADJ
ejpam-3405	60	38	vertices	vertex	NOUN
ejpam-3405	60	39	of	of	ADP
ejpam-3405	60	40	degree	degree	NOUN
ejpam-3405	60	41	2	2	NUM
ejpam-3405	60	42	(	(	PUNCT
ejpam-3405	60	43	in	in	ADP
ejpam-3405	60	44	the	the	DET
ejpam-3405	60	45	diagram	diagram	NOUN
ejpam-3405	60	46	associated	associate	VERB
ejpam-3405	60	47	to	to	ADP
ejpam-3405	60	48	p	p	PRON
ejpam-3405	60	49	)	)	PUNCT
ejpam-3405	60	50	are	be	AUX
ejpam-3405	60	51	(	(	PUNCT
ejpam-3405	60	52	upto	upto	ADJ
ejpam-3405	60	53	cyclic	cyclic	ADJ
ejpam-3405	60	54	permutation	permutation	NOUN
ejpam-3405	60	55	and	and	CCONJ
ejpam-3405	60	56	inversion	inversion	NOUN
ejpam-3405	60	57	)	)	PUNCT
ejpam-3405	60	58	s	s	PART
ejpam-3405	61	1	=	=	SYM
ejpam-3405	61	2	{	{	PUNCT
ejpam-3405	61	3	ag	ag	PROPN
ejpam-3405	61	4	,	,	PUNCT
ejpam-3405	61	5	ag−1	ag−1	NOUN
ejpam-3405	61	6	,	,	PUNCT
ejpam-3405	61	7	fi	fi	NOUN
ejpam-3405	61	8	,	,	PUNCT
ejpam-3405	61	9	fi−1	fi−1	PROPN
ejpam-3405	61	10	,	,	PUNCT
ejpam-3405	61	11	bc−1	bc−1	PROPN
ejpam-3405	61	12	,	,	PUNCT
ejpam-3405	61	13	bd−1	bd−1	PROPN
ejpam-3405	61	14	be−1	be−1	PROPN
ejpam-3405	61	15	,	,	PUNCT
ejpam-3405	61	16	bh−1	bh−1	PROPN
ejpam-3405	61	17	,	,	PUNCT
ejpam-3405	61	18	cd−1	cd−1	PROPN
ejpam-3405	61	19	,	,	PUNCT
ejpam-3405	61	20	ce−1	ce−1	PROPN
ejpam-3405	61	21	,	,	PUNCT
ejpam-3405	61	22	ch−1	ch−1	PROPN
ejpam-3405	61	23	,	,	PUNCT
ejpam-3405	61	24	de−1	de−1	PROPN
ejpam-3405	61	25	,	,	PUNCT
ejpam-3405	61	26	dh−1	dh−1	PROPN
ejpam-3405	61	27	,	,	PUNCT
ejpam-3405	61	28	eh−1	eh−1	PROPN
ejpam-3405	61	29	}	}	PUNCT
ejpam-3405	61	30	.	.	PUNCT
ejpam-3405	62	1	since	since	SCONJ
ejpam-3405	62	2	g	g	PROPN
ejpam-3405	62	3	is	be	AUX
ejpam-3405	62	4	torsion	torsion	NOUN
ejpam-3405	62	5	free	free	ADJ
ejpam-3405	62	6	therefore	therefore	ADV
ejpam-3405	62	7	it	it	PRON
ejpam-3405	62	8	is	be	AUX
ejpam-3405	62	9	clear	clear	ADJ
ejpam-3405	62	10	that	that	SCONJ
ejpam-3405	62	11	ag	ag	PROPN
ejpam-3405	62	12	and	and	CCONJ
ejpam-3405	62	13	ag−1	ag−1	PROPN
ejpam-3405	62	14	can	can	AUX
ejpam-3405	62	15	not	not	PART
ejpam-3405	62	16	both	both	PRON
ejpam-3405	62	17	hold	hold	VERB
ejpam-3405	62	18	at	at	ADP
ejpam-3405	62	19	the	the	DET
ejpam-3405	62	20	same	same	ADJ
ejpam-3405	62	21	time	time	NOUN
ejpam-3405	62	22	.	.	PUNCT
ejpam-3405	63	1	similarly	similarly	ADV
ejpam-3405	63	2	fi	fi	NOUN
ejpam-3405	63	3	and	and	CCONJ
ejpam-3405	63	4	fi−1	fi−1	PROPN
ejpam-3405	63	5	can	can	AUX
ejpam-3405	63	6	not	not	PART
ejpam-3405	63	7	both	both	PRON
ejpam-3405	63	8	hold	hold	VERB
ejpam-3405	63	9	at	at	ADP
ejpam-3405	63	10	the	the	DET
ejpam-3405	63	11	same	same	ADJ
ejpam-3405	63	12	time	time	NOUN
ejpam-3405	63	13	.	.	PUNCT
ejpam-3405	64	1	the	the	DET
ejpam-3405	64	2	following	follow	VERB
ejpam-3405	64	3	lemma	lemma	PROPN
ejpam-3405	64	4	gives	give	VERB
ejpam-3405	64	5	some	some	DET
ejpam-3405	64	6	general	general	ADJ
ejpam-3405	64	7	results	result	NOUN
ejpam-3405	64	8	that	that	PRON
ejpam-3405	64	9	will	will	AUX
ejpam-3405	64	10	greatly	greatly	ADV
ejpam-3405	64	11	simplify	simplify	VERB
ejpam-3405	64	12	the	the	DET
ejpam-3405	64	13	proofs	proof	NOUN
ejpam-3405	64	14	.	.	PUNCT
ejpam-3405	65	1	this	this	PRON
ejpam-3405	65	2	is	be	AUX
ejpam-3405	65	3	an	an	DET
ejpam-3405	65	4	application	application	NOUN
ejpam-3405	65	5	of	of	ADP
ejpam-3405	65	6	the	the	DET
ejpam-3405	65	7	results	result	NOUN
ejpam-3405	65	8	given	give	VERB
ejpam-3405	65	9	in	in	ADP
ejpam-3405	65	10	[	[	X
ejpam-3405	65	11	1	1	NUM
ejpam-3405	65	12	,	,	PUNCT
ejpam-3405	65	13	2	2	NUM
ejpam-3405	65	14	]	]	PUNCT
ejpam-3405	65	15	.	.	PUNCT
ejpam-3405	66	1	t	t	PROPN
ejpam-3405	66	2	t̄	t̄	PROPN
ejpam-3405	66	3	e	e	PROPN
ejpam-3405	66	4	b	b	PROPN
ejpam-3405	66	5	a	a	DET
ejpam-3405	66	6	h	h	NOUN
ejpam-3405	67	1	i	i	PRON
ejpam-3405	67	2	c	c	VERB
ejpam-3405	68	1	g	g	NOUN
ejpam-3405	68	2	f	f	PROPN
ejpam-3405	68	3	d	d	NOUN
ejpam-3405	68	4	figure	figure	NOUN
ejpam-3405	68	5	2	2	NUM
ejpam-3405	68	6	:	:	PUNCT
ejpam-3405	68	7	star	star	NOUN
ejpam-3405	68	8	graph	graph	NOUN
ejpam-3405	68	9	γ	γ	PROPN
ejpam-3405	68	10	lemma	lemma	PROPN
ejpam-3405	68	11	2	2	NUM
ejpam-3405	68	12	.	.	PUNCT
ejpam-3405	69	1	the	the	DET
ejpam-3405	69	2	presentation	presentation	NOUN
ejpam-3405	69	3	p	p	X
ejpam-3405	69	4	=	=	PUNCT
ejpam-3405	69	5	〈	〈	PROPN
ejpam-3405	69	6	g	g	NOUN
ejpam-3405	69	7	,	,	PUNCT
ejpam-3405	69	8	t|s(t	t|s(t	PROPN
ejpam-3405	69	9	)	)	PUNCT
ejpam-3405	69	10	〉	〉	PROPN
ejpam-3405	69	11	,	,	PUNCT
ejpam-3405	69	12	where	where	SCONJ
ejpam-3405	69	13	s(t	s(t	NOUN
ejpam-3405	69	14	)	)	PUNCT
ejpam-3405	69	15	=	=	PUNCT
ejpam-3405	70	1	atbtctdtetft−1gthtit−1	atbtctdtetft−1gthtit−1	PROPN
ejpam-3405	70	2	is	be	AUX
ejpam-3405	70	3	aspherical	aspherical	ADJ
ejpam-3405	70	4	if	if	SCONJ
ejpam-3405	70	5	any	any	DET
ejpam-3405	70	6	one	one	NUM
ejpam-3405	70	7	of	of	ADP
ejpam-3405	70	8	the	the	DET
ejpam-3405	70	9	following	follow	VERB
ejpam-3405	70	10	holds	hold	VERB
ejpam-3405	70	11	:	:	PUNCT
ejpam-3405	70	12	(	(	PUNCT
ejpam-3405	70	13	i	i	NOUN
ejpam-3405	70	14	)	)	PUNCT
ejpam-3405	70	15	a	a	DET
ejpam-3405	70	16	=	=	X
ejpam-3405	70	17	g−1	g−1	PROPN
ejpam-3405	70	18	(	(	PUNCT
ejpam-3405	70	19	ii	ii	NOUN
ejpam-3405	70	20	)	)	PUNCT
ejpam-3405	70	21	a	a	DET
ejpam-3405	70	22	=	=	SYM
ejpam-3405	70	23	g	g	NOUN
ejpam-3405	70	24	,	,	PUNCT
ejpam-3405	70	25	f	f	PROPN
ejpam-3405	71	1	=	=	SYM
ejpam-3405	71	2	i	i	PRON
ejpam-3405	71	3	m.	m.	VERB
ejpam-3405	71	4	fazeel	fazeel	PROPN
ejpam-3405	71	5	anwar	anwar	PROPN
ejpam-3405	71	6	,	,	PUNCT
ejpam-3405	71	7	mairaj	mairaj	ADJ
ejpam-3405	71	8	bibi	bibi	NOUN
ejpam-3405	71	9	,	,	PUNCT
ejpam-3405	71	10	m.	m.	PROPN
ejpam-3405	71	11	saeed	saeed	PROPN
ejpam-3405	71	12	akram	akram	PROPN
ejpam-3405	71	13	/	/	PUNCT
ejpam-3405	71	14	eur	eur	PROPN
ejpam-3405	71	15	.	.	PUNCT
ejpam-3405	72	1	j.	j.	PROPN
ejpam-3405	72	2	pure	pure	PROPN
ejpam-3405	72	3	appl	appl	PROPN
ejpam-3405	72	4	.	.	PROPN
ejpam-3405	72	5	math	math	PROPN
ejpam-3405	72	6	,	,	PUNCT
ejpam-3405	72	7	12	12	NUM
ejpam-3405	72	8	(	(	PUNCT
ejpam-3405	72	9	2	2	NUM
ejpam-3405	72	10	)	)	PUNCT
ejpam-3405	72	11	(	(	PUNCT
ejpam-3405	72	12	2019	2019	NUM
ejpam-3405	72	13	)	)	PUNCT
ejpam-3405	72	14	,	,	PUNCT
ejpam-3405	72	15	590	590	NUM
ejpam-3405	72	16	-	-	SYM
ejpam-3405	72	17	604	604	NUM
ejpam-3405	72	18	593	593	NUM
ejpam-3405	72	19	(	(	PUNCT
ejpam-3405	72	20	iii	iii	NOUN
ejpam-3405	72	21	)	)	PUNCT
ejpam-3405	72	22	a	a	DET
ejpam-3405	72	23	=	=	SYM
ejpam-3405	72	24	g	g	PROPN
ejpam-3405	72	25	,	,	PUNCT
ejpam-3405	72	26	b	b	NOUN
ejpam-3405	72	27	=	=	SYM
ejpam-3405	72	28	h	h	NOUN
ejpam-3405	72	29	proof	proof	NOUN
ejpam-3405	72	30	.	.	PUNCT
ejpam-3405	73	1	a	a	DET
ejpam-3405	73	2	new	new	ADJ
ejpam-3405	73	3	generator	generator	NOUN
ejpam-3405	73	4	x	x	X
ejpam-3405	73	5	will	will	AUX
ejpam-3405	73	6	be	be	AUX
ejpam-3405	73	7	introduced	introduce	VERB
ejpam-3405	73	8	to	to	PART
ejpam-3405	73	9	obtain	obtain	VERB
ejpam-3405	73	10	the	the	DET
ejpam-3405	73	11	presentationq	presentationq	NOUN
ejpam-3405	73	12	=	=	PUNCT
ejpam-3405	74	1	〈	〈	PROPN
ejpam-3405	74	2	g	g	PROPN
ejpam-3405	74	3	,	,	PUNCT
ejpam-3405	74	4	t	t	PROPN
ejpam-3405	74	5	,	,	PUNCT
ejpam-3405	74	6	x|r1	x|r1	PROPN
ejpam-3405	74	7	,	,	PUNCT
ejpam-3405	74	8	r2	r2	PROPN
ejpam-3405	74	9	〉	〉	PROPN
ejpam-3405	74	10	.	.	PUNCT
ejpam-3405	75	1	(	(	PUNCT
ejpam-3405	75	2	i	i	NOUN
ejpam-3405	75	3	)	)	PUNCT
ejpam-3405	75	4	let	let	VERB
ejpam-3405	75	5	a	a	DET
ejpam-3405	75	6	=	=	SYM
ejpam-3405	75	7	g−1	g−1	PROPN
ejpam-3405	75	8	.	.	PUNCT
ejpam-3405	76	1	the	the	DET
ejpam-3405	76	2	relator	relator	NOUN
ejpam-3405	76	3	s(t	s(t	PROPN
ejpam-3405	76	4	)	)	PUNCT
ejpam-3405	76	5	is	be	AUX
ejpam-3405	76	6	given	give	VERB
ejpam-3405	76	7	by	by	ADP
ejpam-3405	76	8	s(t	s(t	PROPN
ejpam-3405	76	9	)	)	PUNCT
ejpam-3405	76	10	=	=	SYM
ejpam-3405	76	11	atbtctdtetft−1a−1thtit−1	atbtctdtetft−1a−1thtit−1	NOUN
ejpam-3405	76	12	.	.	PUNCT
ejpam-3405	77	1	we	we	PRON
ejpam-3405	77	2	substitute	substitute	VERB
ejpam-3405	77	3	x	x	PUNCT
ejpam-3405	77	4	=	=	SYM
ejpam-3405	77	5	t−1a−1	t−1a−1	PROPN
ejpam-3405	77	6	t	t	NOUN
ejpam-3405	77	7	to	to	PART
ejpam-3405	77	8	get	get	VERB
ejpam-3405	77	9	r1	r1	PROPN
ejpam-3405	77	10	=	=	PUNCT
ejpam-3405	77	11	x−1btctdtetfxhti	x−1btctdtetfxhti	PROPN
ejpam-3405	77	12	and	and	CCONJ
ejpam-3405	77	13	r2	r2	PROPN
ejpam-3405	77	14	=	=	PUNCT
ejpam-3405	77	15	t−1a−1tx−1	t−1a−1tx−1	NOUN
ejpam-3405	77	16	.	.	PUNCT
ejpam-3405	78	1	the	the	DET
ejpam-3405	78	2	star	star	NOUN
ejpam-3405	78	3	graph	graph	NOUN
ejpam-3405	78	4	γ	γ	PROPN
ejpam-3405	78	5	for	for	ADP
ejpam-3405	78	6	q	q	PROPN
ejpam-3405	78	7	is	be	AUX
ejpam-3405	78	8	given	give	VERB
ejpam-3405	78	9	by	by	ADP
ejpam-3405	78	10	figure	figure	NOUN
ejpam-3405	78	11	1	1	NUM
ejpam-3405	78	12	(	(	PUNCT
ejpam-3405	78	13	a	a	NOUN
ejpam-3405	78	14	)	)	PUNCT
ejpam-3405	78	15	in	in	ADP
ejpam-3405	78	16	which	which	PRON
ejpam-3405	78	17	(	(	PUNCT
ejpam-3405	78	18	using	use	VERB
ejpam-3405	78	19	r1	r1	NOUN
ejpam-3405	78	20	)	)	PUNCT
ejpam-3405	78	21	α1	α1	PROPN
ejpam-3405	78	22	=	=	SYM
ejpam-3405	78	23	e	e	NOUN
ejpam-3405	78	24	,	,	PUNCT
ejpam-3405	78	25	α2	α2	NOUN
ejpam-3405	78	26	=	=	SYM
ejpam-3405	79	1	d	d	NOUN
ejpam-3405	79	2	,	,	PUNCT
ejpam-3405	79	3	α3	α3	NOUN
ejpam-3405	79	4	=	=	SYM
ejpam-3405	79	5	c	c	NOUN
ejpam-3405	79	6	,	,	PUNCT
ejpam-3405	79	7	α4	α4	NOUN
ejpam-3405	79	8	=	=	SYM
ejpam-3405	79	9	b	b	PROPN
ejpam-3405	79	10	,	,	PUNCT
ejpam-3405	79	11	α5	α5	NOUN
ejpam-3405	79	12	=	=	SYM
ejpam-3405	79	13	f	f	PROPN
ejpam-3405	79	14	,	,	PUNCT
ejpam-3405	79	15	α6	α6	NOUN
ejpam-3405	79	16	=	=	SYM
ejpam-3405	79	17	i	i	PROPN
ejpam-3405	79	18	,	,	PUNCT
ejpam-3405	79	19	α7	α7	NOUN
ejpam-3405	79	20	=	=	SYM
ejpam-3405	79	21	h	h	NOUN
ejpam-3405	79	22	;	;	PUNCT
ejpam-3405	79	23	and	and	CCONJ
ejpam-3405	79	24	(	(	PUNCT
ejpam-3405	79	25	using	use	VERB
ejpam-3405	79	26	r2	r2	NOUN
ejpam-3405	79	27	)	)	PUNCT
ejpam-3405	79	28	β1	β1	PROPN
ejpam-3405	79	29	=	=	SYM
ejpam-3405	79	30	a−1	a−1	PROPN
ejpam-3405	79	31	,	,	PUNCT
ejpam-3405	79	32	β2	β2	NOUN
ejpam-3405	79	33	=	=	NOUN
ejpam-3405	79	34	1	1	NUM
ejpam-3405	79	35	,	,	PUNCT
ejpam-3405	79	36	β3	β3	VERB
ejpam-3405	79	37	=	=	SYM
ejpam-3405	79	38	1	1	X
ejpam-3405	79	39	.	.	X
ejpam-3405	80	1	we	we	PRON
ejpam-3405	80	2	assign	assign	VERB
ejpam-3405	80	3	a	a	DET
ejpam-3405	80	4	weight	weight	NOUN
ejpam-3405	80	5	function	function	NOUN
ejpam-3405	80	6	θ	θ	NOUN
ejpam-3405	80	7	such	such	ADJ
ejpam-3405	80	8	that	that	PRON
ejpam-3405	80	9	θ(α4	θ(α4	NOUN
ejpam-3405	80	10	)	)	PUNCT
ejpam-3405	80	11	=	=	SYM
ejpam-3405	80	12	θ(α6	θ(α6	NOUN
ejpam-3405	80	13	)	)	PUNCT
ejpam-3405	80	14	=	=	SYM
ejpam-3405	80	15	θ(β1	θ(β1	NOUN
ejpam-3405	80	16	)	)	PUNCT
ejpam-3405	80	17	=	=	SYM
ejpam-3405	80	18	θ(β2	θ(β2	ADJ
ejpam-3405	80	19	)	)	PUNCT
ejpam-3405	81	1	=	=	SYM
ejpam-3405	81	2	0	0	X
ejpam-3405	81	3	.	.	PUNCT
ejpam-3405	82	1	all	all	DET
ejpam-3405	82	2	other	other	ADJ
ejpam-3405	82	3	edges	edge	NOUN
ejpam-3405	82	4	are	be	AUX
ejpam-3405	82	5	assigned	assign	VERB
ejpam-3405	82	6	a	a	DET
ejpam-3405	82	7	weight	weight	NOUN
ejpam-3405	82	8	1	1	NUM
ejpam-3405	82	9	.	.	PUNCT
ejpam-3405	83	1	then	then	ADV
ejpam-3405	83	2	σ(1	σ(1	PROPN
ejpam-3405	83	3	−	−	PROPN
ejpam-3405	83	4	θ(αi	θ(αi	NOUN
ejpam-3405	83	5	)	)	PUNCT
ejpam-3405	83	6	)	)	PUNCT
ejpam-3405	84	1	=	=	PUNCT
ejpam-3405	84	2	σ(1	σ(1	PROPN
ejpam-3405	84	3	−	−	PROPN
ejpam-3405	84	4	θ(βj	θ(βj	NUM
ejpam-3405	84	5	)	)	PUNCT
ejpam-3405	84	6	)	)	PUNCT
ejpam-3405	85	1	=	=	SYM
ejpam-3405	85	2	2	2	NUM
ejpam-3405	85	3	shows	show	VERB
ejpam-3405	85	4	that	that	SCONJ
ejpam-3405	85	5	(	(	PUNCT
ejpam-3405	85	6	w1	w1	NOUN
ejpam-3405	85	7	)	)	PUNCT
ejpam-3405	85	8	is	be	AUX
ejpam-3405	85	9	satisfied	satisfied	ADJ
ejpam-3405	85	10	.	.	PUNCT
ejpam-3405	86	1	also	also	ADV
ejpam-3405	86	2	each	each	DET
ejpam-3405	86	3	cycle	cycle	NOUN
ejpam-3405	86	4	in	in	ADP
ejpam-3405	86	5	γ	γ	NOUN
ejpam-3405	86	6	of	of	ADP
ejpam-3405	86	7	weight	weight	NOUN
ejpam-3405	86	8	less	less	ADJ
ejpam-3405	86	9	than	than	ADP
ejpam-3405	86	10	2	2	NUM
ejpam-3405	86	11	has	have	VERB
ejpam-3405	86	12	label	label	NOUN
ejpam-3405	86	13	am	am	NOUN
ejpam-3405	86	14	or	or	CCONJ
ejpam-3405	86	15	i	i	PRON
ejpam-3405	86	16	m	m	PROPN
ejpam-3405	86	17	,	,	PUNCT
ejpam-3405	86	18	(	(	PUNCT
ejpam-3405	86	19	m	m	PROPN
ejpam-3405	86	20	6=	6=	NUM
ejpam-3405	86	21	0	0	NUM
ejpam-3405	86	22	)	)	PUNCT
ejpam-3405	86	23	and	and	CCONJ
ejpam-3405	86	24	(	(	PUNCT
ejpam-3405	86	25	a	a	X
ejpam-3405	86	26	,	,	PUNCT
ejpam-3405	86	27	i	i	PROPN
ejpam-3405	86	28	6=	6=	PROPN
ejpam-3405	86	29	1	1	NUM
ejpam-3405	86	30	)	)	PUNCT
ejpam-3405	86	31	and	and	CCONJ
ejpam-3405	86	32	since	since	SCONJ
ejpam-3405	86	33	g	g	PROPN
ejpam-3405	86	34	is	be	AUX
ejpam-3405	86	35	torsion	torsion	NOUN
ejpam-3405	86	36	free	free	ADJ
ejpam-3405	86	37	(	(	PUNCT
ejpam-3405	86	38	w2	w2	NOUN
ejpam-3405	86	39	)	)	PUNCT
ejpam-3405	86	40	is	be	AUX
ejpam-3405	86	41	satisfied	satisfied	ADJ
ejpam-3405	86	42	.	.	PUNCT
ejpam-3405	87	1	moreover	moreover	ADV
ejpam-3405	87	2	(	(	PUNCT
ejpam-3405	87	3	w3	w3	PROPN
ejpam-3405	87	4	)	)	PUNCT
ejpam-3405	87	5	clearly	clearly	ADV
ejpam-3405	87	6	holds	hold	VERB
ejpam-3405	87	7	.	.	PUNCT
ejpam-3405	88	1	(	(	PUNCT
ejpam-3405	88	2	ii	ii	X
ejpam-3405	88	3	)	)	PUNCT
ejpam-3405	88	4	we	we	PRON
ejpam-3405	88	5	have	have	AUX
ejpam-3405	88	6	s(t	s(t	VERB
ejpam-3405	88	7	)	)	PUNCT
ejpam-3405	89	1	=	=	SYM
ejpam-3405	89	2	atbtctdtetit−1athtit−1	atbtctdtetit−1athtit−1	PROPN
ejpam-3405	89	3	,	,	PUNCT
ejpam-3405	89	4	r1	r1	NOUN
ejpam-3405	89	5	=	=	SYM
ejpam-3405	89	6	xbtctdtexh	xbtctdtexh	NOUN
ejpam-3405	89	7	,	,	PUNCT
ejpam-3405	89	8	r2	r2	PROPN
ejpam-3405	89	9	=	=	SYM
ejpam-3405	89	10	tit−1atx−1	tit−1atx−1	NOUN
ejpam-3405	89	11	.	.	PUNCT
ejpam-3405	90	1	the	the	DET
ejpam-3405	90	2	star	star	NOUN
ejpam-3405	90	3	graph	graph	NOUN
ejpam-3405	90	4	γ	γ	PROPN
ejpam-3405	90	5	is	be	AUX
ejpam-3405	90	6	given	give	VERB
ejpam-3405	90	7	by	by	ADP
ejpam-3405	90	8	figure	figure	NOUN
ejpam-3405	90	9	1	1	NUM
ejpam-3405	90	10	(	(	PUNCT
ejpam-3405	90	11	b	b	NOUN
ejpam-3405	90	12	)	)	PUNCT
ejpam-3405	90	13	in	in	ADP
ejpam-3405	90	14	which	which	PRON
ejpam-3405	90	15	α1	α1	PROPN
ejpam-3405	90	16	=	=	SYM
ejpam-3405	90	17	c	c	NOUN
ejpam-3405	90	18	,	,	PUNCT
ejpam-3405	90	19	α2	α2	PROPN
ejpam-3405	90	20	=	=	SYM
ejpam-3405	90	21	d	d	NOUN
ejpam-3405	90	22	,	,	PUNCT
ejpam-3405	90	23	α3	α3	NOUN
ejpam-3405	90	24	=	=	SYM
ejpam-3405	90	25	e	e	NOUN
ejpam-3405	90	26	,	,	PUNCT
ejpam-3405	90	27	α4	α4	NOUN
ejpam-3405	90	28	=	=	SYM
ejpam-3405	90	29	h	h	NOUN
ejpam-3405	90	30	,	,	PUNCT
ejpam-3405	90	31	α5	α5	NOUN
ejpam-3405	90	32	=	=	SYM
ejpam-3405	90	33	b	b	PROPN
ejpam-3405	90	34	;	;	PUNCT
ejpam-3405	90	35	and	and	CCONJ
ejpam-3405	90	36	β1	β1	PROPN
ejpam-3405	90	37	=	=	PUNCT
ejpam-3405	90	38	a	a	PROPN
ejpam-3405	90	39	,	,	PUNCT
ejpam-3405	90	40	β2	β2	NOUN
ejpam-3405	90	41	=	=	PROPN
ejpam-3405	90	42	i	i	PROPN
ejpam-3405	90	43	,	,	PUNCT
ejpam-3405	90	44	β3	β3	VERB
ejpam-3405	90	45	=	=	SYM
ejpam-3405	90	46	1	1	NUM
ejpam-3405	90	47	,	,	PUNCT
ejpam-3405	90	48	β4	β4	PROPN
ejpam-3405	90	49	=	=	SYM
ejpam-3405	90	50	1	1	X
ejpam-3405	90	51	.	.	X
ejpam-3405	91	1	we	we	PRON
ejpam-3405	91	2	assign	assign	VERB
ejpam-3405	91	3	a	a	DET
ejpam-3405	91	4	weight	weight	NOUN
ejpam-3405	91	5	function	function	NOUN
ejpam-3405	91	6	θ	θ	NOUN
ejpam-3405	91	7	such	such	ADJ
ejpam-3405	91	8	that	that	SCONJ
ejpam-3405	91	9	θ(α3	θ(α3	NOUN
ejpam-3405	91	10	)	)	PUNCT
ejpam-3405	91	11	=	=	PUNCT
ejpam-3405	91	12	θ(α5	θ(α5	ADV
ejpam-3405	91	13	)	)	PUNCT
ejpam-3405	91	14	=	=	SYM
ejpam-3405	91	15	θ(β1	θ(β1	NOUN
ejpam-3405	91	16	)	)	PUNCT
ejpam-3405	91	17	=	=	SYM
ejpam-3405	91	18	θ(β2	θ(β2	ADJ
ejpam-3405	91	19	)	)	PUNCT
ejpam-3405	92	1	=	=	SYM
ejpam-3405	92	2	0	0	X
ejpam-3405	92	3	.	.	PUNCT
ejpam-3405	93	1	all	all	DET
ejpam-3405	93	2	other	other	ADJ
ejpam-3405	93	3	edges	edge	NOUN
ejpam-3405	93	4	are	be	AUX
ejpam-3405	93	5	assigned	assign	VERB
ejpam-3405	93	6	a	a	DET
ejpam-3405	93	7	weight	weight	NOUN
ejpam-3405	93	8	1	1	NUM
ejpam-3405	93	9	.	.	PUNCT
ejpam-3405	94	1	then	then	ADV
ejpam-3405	94	2	σ(1−	σ(1−	PROPN
ejpam-3405	94	3	θ(αi	θ(αi	NOUN
ejpam-3405	94	4	)	)	PUNCT
ejpam-3405	94	5	)	)	PUNCT
ejpam-3405	95	1	=	=	SYM
ejpam-3405	95	2	σ(1−	σ(1−	PROPN
ejpam-3405	95	3	θ(βj	θ(βj	PROPN
ejpam-3405	95	4	)	)	PUNCT
ejpam-3405	95	5	)	)	PUNCT
ejpam-3405	95	6	=	=	SYM
ejpam-3405	95	7	2	2	NUM
ejpam-3405	95	8	shows	show	VERB
ejpam-3405	95	9	that	that	SCONJ
ejpam-3405	95	10	(	(	PUNCT
ejpam-3405	95	11	w1	w1	NOUN
ejpam-3405	95	12	)	)	PUNCT
ejpam-3405	95	13	is	be	AUX
ejpam-3405	95	14	satisfied	satisfied	ADJ
ejpam-3405	95	15	.	.	PUNCT
ejpam-3405	96	1	also	also	ADV
ejpam-3405	96	2	each	each	DET
ejpam-3405	96	3	cycle	cycle	NOUN
ejpam-3405	96	4	in	in	ADP
ejpam-3405	96	5	γ	γ	NOUN
ejpam-3405	96	6	of	of	ADP
ejpam-3405	96	7	weight	weight	NOUN
ejpam-3405	96	8	less	less	ADJ
ejpam-3405	96	9	than	than	ADP
ejpam-3405	96	10	2	2	NUM
ejpam-3405	96	11	has	have	VERB
ejpam-3405	96	12	label	label	NOUN
ejpam-3405	96	13	am	am	NOUN
ejpam-3405	96	14	or	or	CCONJ
ejpam-3405	96	15	i	i	PRON
ejpam-3405	96	16	m	m	PROPN
ejpam-3405	96	17	,	,	PUNCT
ejpam-3405	96	18	(	(	PUNCT
ejpam-3405	96	19	m	m	PROPN
ejpam-3405	96	20	6=	6=	NUM
ejpam-3405	96	21	0	0	NUM
ejpam-3405	96	22	)	)	PUNCT
ejpam-3405	96	23	and	and	CCONJ
ejpam-3405	96	24	(	(	PUNCT
ejpam-3405	96	25	a	a	X
ejpam-3405	96	26	,	,	PUNCT
ejpam-3405	96	27	i	i	PROPN
ejpam-3405	96	28	6=	6=	PROPN
ejpam-3405	96	29	1	1	NUM
ejpam-3405	96	30	)	)	PUNCT
ejpam-3405	96	31	and	and	CCONJ
ejpam-3405	96	32	since	since	SCONJ
ejpam-3405	96	33	g	g	PROPN
ejpam-3405	96	34	is	be	AUX
ejpam-3405	96	35	torsion	torsion	NOUN
ejpam-3405	96	36	free	free	ADJ
ejpam-3405	96	37	(	(	PUNCT
ejpam-3405	96	38	w2	w2	NOUN
ejpam-3405	96	39	)	)	PUNCT
ejpam-3405	96	40	is	be	AUX
ejpam-3405	96	41	satisfied	satisfied	ADJ
ejpam-3405	96	42	.	.	PUNCT
ejpam-3405	97	1	moreover	moreover	ADV
ejpam-3405	97	2	(	(	PUNCT
ejpam-3405	97	3	w3	w3	PROPN
ejpam-3405	97	4	)	)	PUNCT
ejpam-3405	97	5	clearly	clearly	ADV
ejpam-3405	97	6	holds	hold	VERB
ejpam-3405	97	7	.	.	PUNCT
ejpam-3405	98	1	(	(	PUNCT
ejpam-3405	98	2	iii	iii	X
ejpam-3405	98	3	)	)	PUNCT
ejpam-3405	98	4	we	we	PRON
ejpam-3405	98	5	have	have	AUX
ejpam-3405	98	6	s(t	s(t	VERB
ejpam-3405	98	7	)	)	PUNCT
ejpam-3405	99	1	=	=	SYM
ejpam-3405	99	2	atbtctdtetft−1atbtit−1	atbtctdtetft−1atbtit−1	PROPN
ejpam-3405	99	3	,	,	PUNCT
ejpam-3405	99	4	r1	r1	NOUN
ejpam-3405	99	5	=	=	SYM
ejpam-3405	99	6	xctdtetfxi	xctdtetfxi	PROPN
ejpam-3405	99	7	,	,	PUNCT
ejpam-3405	99	8	r2	r2	PROPN
ejpam-3405	99	9	=	=	SYM
ejpam-3405	99	10	t−1atbtx−1	t−1atbtx−1	PROPN
ejpam-3405	99	11	.	.	PUNCT
ejpam-3405	100	1	the	the	DET
ejpam-3405	100	2	star	star	NOUN
ejpam-3405	100	3	graph	graph	NOUN
ejpam-3405	100	4	γ	γ	PROPN
ejpam-3405	100	5	is	be	AUX
ejpam-3405	100	6	given	give	VERB
ejpam-3405	100	7	by	by	ADP
ejpam-3405	100	8	figure	figure	NOUN
ejpam-3405	100	9	1	1	NUM
ejpam-3405	100	10	(	(	PUNCT
ejpam-3405	100	11	c	c	NOUN
ejpam-3405	100	12	)	)	PUNCT
ejpam-3405	100	13	in	in	ADP
ejpam-3405	100	14	which	which	PRON
ejpam-3405	100	15	α1	α1	PROPN
ejpam-3405	100	16	=	=	SYM
ejpam-3405	100	17	e	e	NOUN
ejpam-3405	100	18	,	,	PUNCT
ejpam-3405	100	19	α2	α2	NOUN
ejpam-3405	100	20	=	=	SYM
ejpam-3405	100	21	d	d	NOUN
ejpam-3405	100	22	,	,	PUNCT
ejpam-3405	100	23	α3	α3	NOUN
ejpam-3405	100	24	=	=	SYM
ejpam-3405	100	25	f	f	PROPN
ejpam-3405	100	26	,	,	PUNCT
ejpam-3405	100	27	α4	α4	NOUN
ejpam-3405	100	28	=	=	SYM
ejpam-3405	100	29	i	i	PROPN
ejpam-3405	100	30	,	,	PUNCT
ejpam-3405	100	31	α5	α5	NOUN
ejpam-3405	100	32	=	=	SYM
ejpam-3405	100	33	c	c	X
ejpam-3405	100	34	;	;	PUNCT
ejpam-3405	100	35	and	and	CCONJ
ejpam-3405	100	36	β1	β1	PROPN
ejpam-3405	100	37	=	=	PUNCT
ejpam-3405	100	38	a	a	PROPN
ejpam-3405	100	39	,	,	PUNCT
ejpam-3405	100	40	β2	β2	NOUN
ejpam-3405	100	41	=	=	SYM
ejpam-3405	100	42	b	b	PROPN
ejpam-3405	100	43	,	,	PUNCT
ejpam-3405	100	44	β3	β3	ADJ
ejpam-3405	100	45	=	=	SYM
ejpam-3405	100	46	1	1	NUM
ejpam-3405	100	47	,	,	PUNCT
ejpam-3405	100	48	β4	β4	PROPN
ejpam-3405	100	49	=	=	SYM
ejpam-3405	100	50	1	1	X
ejpam-3405	100	51	.	.	X
ejpam-3405	101	1	we	we	PRON
ejpam-3405	101	2	assign	assign	VERB
ejpam-3405	101	3	a	a	DET
ejpam-3405	101	4	weight	weight	NOUN
ejpam-3405	101	5	function	function	NOUN
ejpam-3405	101	6	θ	θ	NOUN
ejpam-3405	101	7	such	such	ADJ
ejpam-3405	101	8	that	that	SCONJ
ejpam-3405	101	9	θ(α3	θ(α3	NOUN
ejpam-3405	101	10	)	)	PUNCT
ejpam-3405	101	11	=	=	PUNCT
ejpam-3405	101	12	θ(α5	θ(α5	ADV
ejpam-3405	101	13	)	)	PUNCT
ejpam-3405	101	14	=	=	SYM
ejpam-3405	101	15	θ(β1	θ(β1	NOUN
ejpam-3405	101	16	)	)	PUNCT
ejpam-3405	101	17	=	=	SYM
ejpam-3405	101	18	θ(β3	θ(β3	NOUN
ejpam-3405	101	19	)	)	PUNCT
ejpam-3405	101	20	.	.	PUNCT
ejpam-3405	102	1	all	all	DET
ejpam-3405	102	2	other	other	ADJ
ejpam-3405	102	3	edges	edge	NOUN
ejpam-3405	102	4	are	be	AUX
ejpam-3405	102	5	assigned	assign	VERB
ejpam-3405	102	6	a	a	DET
ejpam-3405	102	7	weight	weight	NOUN
ejpam-3405	102	8	1	1	NUM
ejpam-3405	102	9	.	.	PUNCT
ejpam-3405	103	1	we	we	PRON
ejpam-3405	103	2	have	have	VERB
ejpam-3405	103	3	the	the	DET
ejpam-3405	103	4	desired	desire	VERB
ejpam-3405	103	5	result	result	NOUN
ejpam-3405	103	6	.	.	PUNCT
ejpam-3405	104	1	corollary	corollary	ADJ
ejpam-3405	104	2	1	1	NUM
ejpam-3405	104	3	.	.	PUNCT
ejpam-3405	105	1	the	the	DET
ejpam-3405	105	2	presentation	presentation	NOUN
ejpam-3405	105	3	p	p	X
ejpam-3405	105	4	=	=	PUNCT
ejpam-3405	105	5	〈	〈	PROPN
ejpam-3405	105	6	g	g	NOUN
ejpam-3405	105	7	,	,	PUNCT
ejpam-3405	105	8	t|s(t	t|s(t	PROPN
ejpam-3405	105	9	)	)	PUNCT
ejpam-3405	105	10	〉	〉	PROPN
ejpam-3405	105	11	,	,	PUNCT
ejpam-3405	105	12	is	be	AUX
ejpam-3405	105	13	aspherical	aspherical	ADJ
ejpam-3405	105	14	if	if	SCONJ
ejpam-3405	105	15	any	any	DET
ejpam-3405	105	16	one	one	NUM
ejpam-3405	105	17	of	of	ADP
ejpam-3405	105	18	the	the	DET
ejpam-3405	105	19	following	follow	VERB
ejpam-3405	105	20	holds	hold	VERB
ejpam-3405	105	21	:	:	PUNCT
ejpam-3405	105	22	(	(	PUNCT
ejpam-3405	105	23	i	i	NOUN
ejpam-3405	105	24	)	)	PUNCT
ejpam-3405	106	1	a	a	PRON
ejpam-3405	106	2	=	=	X
ejpam-3405	106	3	g−1	g−1	PROPN
ejpam-3405	106	4	and	and	CCONJ
ejpam-3405	106	5	r	r	NOUN
ejpam-3405	106	6	∈	∈	PROPN
ejpam-3405	106	7	{	{	PUNCT
ejpam-3405	106	8	fi	fi	NOUN
ejpam-3405	106	9	,	,	PUNCT
ejpam-3405	106	10	fi−1	fi−1	PROPN
ejpam-3405	106	11	,	,	PUNCT
ejpam-3405	106	12	bc−1	bc−1	PROPN
ejpam-3405	106	13	,	,	PUNCT
ejpam-3405	106	14	bd−1	bd−1	PROPN
ejpam-3405	106	15	be−1	be−1	PROPN
ejpam-3405	106	16	,	,	PUNCT
ejpam-3405	106	17	bh−1	bh−1	PROPN
ejpam-3405	106	18	,	,	PUNCT
ejpam-3405	106	19	cd−1	cd−1	PROPN
ejpam-3405	106	20	,	,	PUNCT
ejpam-3405	106	21	ce−1	ce−1	PROPN
ejpam-3405	106	22	,	,	PUNCT
ejpam-3405	106	23	ch−1	ch−1	PROPN
ejpam-3405	106	24	,	,	PUNCT
ejpam-3405	106	25	de−1	de−1	PROPN
ejpam-3405	106	26	,	,	PUNCT
ejpam-3405	106	27	dh−1	dh−1	PROPN
ejpam-3405	106	28	,	,	PUNCT
ejpam-3405	106	29	eh−1	eh−1	PROPN
ejpam-3405	106	30	}	}	PUNCT
ejpam-3405	106	31	(	(	PUNCT
ejpam-3405	106	32	ii	ii	NOUN
ejpam-3405	106	33	)	)	PUNCT
ejpam-3405	106	34	a	a	DET
ejpam-3405	106	35	=	=	SYM
ejpam-3405	106	36	g	g	NOUN
ejpam-3405	106	37	,	,	PUNCT
ejpam-3405	106	38	f	f	PROPN
ejpam-3405	107	1	=	=	PUNCT
ejpam-3405	107	2	i	i	PROPN
ejpam-3405	107	3	and	and	CCONJ
ejpam-3405	107	4	r	r	NOUN
ejpam-3405	107	5	∈	∈	PROPN
ejpam-3405	107	6	{	{	PUNCT
ejpam-3405	107	7	bc−1	bc−1	PROPN
ejpam-3405	107	8	,	,	PUNCT
ejpam-3405	107	9	bd−1	bd−1	PROPN
ejpam-3405	107	10	be−1	be−1	PROPN
ejpam-3405	107	11	,	,	PUNCT
ejpam-3405	107	12	bh−1	bh−1	PROPN
ejpam-3405	107	13	,	,	PUNCT
ejpam-3405	107	14	cd−1	cd−1	PROPN
ejpam-3405	107	15	,	,	PUNCT
ejpam-3405	107	16	ce−1	ce−1	PROPN
ejpam-3405	107	17	,	,	PUNCT
ejpam-3405	107	18	ch−1	ch−1	PROPN
ejpam-3405	107	19	,	,	PUNCT
ejpam-3405	107	20	de−1	de−1	PROPN
ejpam-3405	107	21	,	,	PUNCT
ejpam-3405	107	22	dh−1	dh−1	PROPN
ejpam-3405	107	23	,	,	PUNCT
ejpam-3405	107	24	eh−1	eh−1	PROPN
ejpam-3405	107	25	}	}	PUNCT
ejpam-3405	107	26	(	(	PUNCT
ejpam-3405	107	27	iii	iii	X
ejpam-3405	107	28	)	)	PUNCT
ejpam-3405	107	29	a	a	PRON
ejpam-3405	107	30	=	=	SYM
ejpam-3405	107	31	g	g	PROPN
ejpam-3405	107	32	,	,	PUNCT
ejpam-3405	107	33	b	b	NOUN
ejpam-3405	107	34	=	=	SYM
ejpam-3405	107	35	h	h	NOUN
ejpam-3405	107	36	and	and	CCONJ
ejpam-3405	107	37	r	r	PROPN
ejpam-3405	107	38	∈	∈	PROPN
ejpam-3405	107	39	{	{	PUNCT
ejpam-3405	107	40	cd−1	cd−1	PROPN
ejpam-3405	107	41	,	,	PUNCT
ejpam-3405	107	42	ce−1	ce−1	PROPN
ejpam-3405	107	43	,	,	PUNCT
ejpam-3405	107	44	ch−1	ch−1	PROPN
ejpam-3405	107	45	,	,	PUNCT
ejpam-3405	107	46	de−1	de−1	PROPN
ejpam-3405	107	47	,	,	PUNCT
ejpam-3405	107	48	dh−1	dh−1	PROPN
ejpam-3405	107	49	,	,	PUNCT
ejpam-3405	107	50	eh−1	eh−1	NOUN
ejpam-3405	107	51	}	}	PUNCT
ejpam-3405	107	52	proof	proof	NOUN
ejpam-3405	107	53	.	.	PUNCT
ejpam-3405	108	1	the	the	DET
ejpam-3405	108	2	result	result	NOUN
ejpam-3405	108	3	is	be	AUX
ejpam-3405	108	4	clear	clear	ADJ
ejpam-3405	108	5	from	from	ADP
ejpam-3405	108	6	lemma	lemma	PROPN
ejpam-3405	108	7	3	3	NUM
ejpam-3405	108	8	by	by	ADP
ejpam-3405	108	9	taking	take	VERB
ejpam-3405	108	10	the	the	DET
ejpam-3405	108	11	weight	weight	NOUN
ejpam-3405	108	12	function	function	NOUN
ejpam-3405	108	13	as	as	SCONJ
ejpam-3405	108	14	given	give	VERB
ejpam-3405	108	15	in	in	ADP
ejpam-3405	108	16	lemma	lemma	PROPN
ejpam-3405	108	17	3	3	NUM
ejpam-3405	108	18	,	,	PUNCT
ejpam-3405	108	19	part	part	NOUN
ejpam-3405	108	20	1	1	NUM
ejpam-3405	108	21	,	,	PUNCT
ejpam-3405	108	22	2	2	NUM
ejpam-3405	108	23	and	and	CCONJ
ejpam-3405	108	24	3	3	NUM
ejpam-3405	108	25	respectively	respectively	ADV
ejpam-3405	108	26	.	.	PUNCT
ejpam-3405	109	1	m.	m.	PROPN
ejpam-3405	109	2	fazeel	fazeel	PROPN
ejpam-3405	109	3	anwar	anwar	PROPN
ejpam-3405	109	4	,	,	PUNCT
ejpam-3405	109	5	mairaj	mairaj	ADJ
ejpam-3405	109	6	bibi	bibi	NOUN
ejpam-3405	109	7	,	,	PUNCT
ejpam-3405	109	8	m.	m.	PROPN
ejpam-3405	109	9	saeed	saeed	PROPN
ejpam-3405	109	10	akram	akram	PROPN
ejpam-3405	109	11	/	/	PUNCT
ejpam-3405	109	12	eur	eur	PROPN
ejpam-3405	109	13	.	.	PUNCT
ejpam-3405	110	1	j.	j.	PROPN
ejpam-3405	110	2	pure	pure	PROPN
ejpam-3405	110	3	appl	appl	PROPN
ejpam-3405	110	4	.	.	PROPN
ejpam-3405	110	5	math	math	PROPN
ejpam-3405	110	6	,	,	PUNCT
ejpam-3405	110	7	12	12	NUM
ejpam-3405	110	8	(	(	PUNCT
ejpam-3405	110	9	2	2	NUM
ejpam-3405	110	10	)	)	PUNCT
ejpam-3405	110	11	(	(	PUNCT
ejpam-3405	110	12	2019	2019	NUM
ejpam-3405	110	13	)	)	PUNCT
ejpam-3405	110	14	,	,	PUNCT
ejpam-3405	110	15	590	590	NUM
ejpam-3405	110	16	-	-	SYM
ejpam-3405	110	17	604	604	NUM
ejpam-3405	110	18	594	594	NUM
ejpam-3405	110	19	lemma	lemma	PROPN
ejpam-3405	110	20	3	3	NUM
ejpam-3405	110	21	.	.	PUNCT
ejpam-3405	111	1	the	the	DET
ejpam-3405	111	2	presentation	presentation	NOUN
ejpam-3405	111	3	p	p	X
ejpam-3405	111	4	=	=	PUNCT
ejpam-3405	111	5	〈	〈	PROPN
ejpam-3405	111	6	g	g	NOUN
ejpam-3405	111	7	,	,	PUNCT
ejpam-3405	111	8	t|s(t	t|s(t	PROPN
ejpam-3405	111	9	)	)	PUNCT
ejpam-3405	111	10	〉	〉	PROPN
ejpam-3405	111	11	,	,	PUNCT
ejpam-3405	111	12	where	where	SCONJ
ejpam-3405	111	13	s(t	s(t	NOUN
ejpam-3405	111	14	)	)	PUNCT
ejpam-3405	111	15	=	=	PUNCT
ejpam-3405	112	1	atbtctdtetft−1gthtit−1	atbtctdtetft−1gthtit−1	PROPN
ejpam-3405	112	2	is	be	AUX
ejpam-3405	112	3	aspherical	aspherical	ADJ
ejpam-3405	112	4	if	if	SCONJ
ejpam-3405	112	5	any	any	DET
ejpam-3405	112	6	one	one	NUM
ejpam-3405	112	7	of	of	ADP
ejpam-3405	112	8	the	the	DET
ejpam-3405	112	9	following	follow	VERB
ejpam-3405	112	10	holds	hold	VERB
ejpam-3405	112	11	:	:	PUNCT
ejpam-3405	112	12	(	(	PUNCT
ejpam-3405	112	13	i	i	NOUN
ejpam-3405	112	14	)	)	PUNCT
ejpam-3405	112	15	a	a	DET
ejpam-3405	112	16	=	=	SYM
ejpam-3405	112	17	g	g	PROPN
ejpam-3405	112	18	,	,	PUNCT
ejpam-3405	112	19	b	b	PROPN
ejpam-3405	112	20	=	=	SYM
ejpam-3405	112	21	c	c	PROPN
ejpam-3405	112	22	(	(	PUNCT
ejpam-3405	112	23	ii	ii	NOUN
ejpam-3405	112	24	)	)	PUNCT
ejpam-3405	112	25	a	a	DET
ejpam-3405	112	26	=	=	SYM
ejpam-3405	112	27	g	g	PROPN
ejpam-3405	112	28	,	,	PUNCT
ejpam-3405	112	29	b	b	X
ejpam-3405	113	1	=	=	SYM
ejpam-3405	113	2	d	d	PROPN
ejpam-3405	113	3	(	(	PUNCT
ejpam-3405	113	4	iii	iii	NOUN
ejpam-3405	113	5	)	)	PUNCT
ejpam-3405	113	6	a	a	DET
ejpam-3405	113	7	=	=	SYM
ejpam-3405	113	8	g	g	PROPN
ejpam-3405	113	9	,	,	PUNCT
ejpam-3405	113	10	b	b	NOUN
ejpam-3405	113	11	=	=	SYM
ejpam-3405	113	12	e	e	X
ejpam-3405	113	13	(	(	PUNCT
ejpam-3405	113	14	iv	iv	X
ejpam-3405	113	15	)	)	PUNCT
ejpam-3405	113	16	a	a	PRON
ejpam-3405	113	17	=	=	SYM
ejpam-3405	113	18	g	g	NOUN
ejpam-3405	113	19	,	,	PUNCT
ejpam-3405	113	20	c	c	NOUN
ejpam-3405	114	1	=	=	SYM
ejpam-3405	115	1	d	d	PROPN
ejpam-3405	115	2	(	(	PUNCT
ejpam-3405	115	3	v	v	NOUN
ejpam-3405	115	4	)	)	PUNCT
ejpam-3405	115	5	a	a	DET
ejpam-3405	115	6	=	=	SYM
ejpam-3405	115	7	g	g	NOUN
ejpam-3405	115	8	,	,	PUNCT
ejpam-3405	115	9	c	c	X
ejpam-3405	115	10	=	=	SYM
ejpam-3405	115	11	e	e	X
ejpam-3405	115	12	(	(	PUNCT
ejpam-3405	115	13	vi	vi	NOUN
ejpam-3405	115	14	)	)	PUNCT
ejpam-3405	115	15	a	a	DET
ejpam-3405	115	16	=	=	SYM
ejpam-3405	115	17	g	g	NOUN
ejpam-3405	115	18	,	,	PUNCT
ejpam-3405	115	19	c	c	NOUN
ejpam-3405	115	20	=	=	SYM
ejpam-3405	115	21	h	h	PROPN
ejpam-3405	115	22	(	(	PUNCT
ejpam-3405	115	23	vii	vii	PROPN
ejpam-3405	115	24	)	)	PUNCT
ejpam-3405	115	25	a	a	DET
ejpam-3405	115	26	=	=	SYM
ejpam-3405	115	27	g	g	NOUN
ejpam-3405	115	28	,	,	PUNCT
ejpam-3405	115	29	d	d	PROPN
ejpam-3405	115	30	=	=	SYM
ejpam-3405	115	31	e	e	X
ejpam-3405	115	32	(	(	PUNCT
ejpam-3405	115	33	viii	viii	PROPN
ejpam-3405	115	34	)	)	PUNCT
ejpam-3405	115	35	a	a	DET
ejpam-3405	115	36	=	=	SYM
ejpam-3405	115	37	g	g	NOUN
ejpam-3405	115	38	,	,	PUNCT
ejpam-3405	115	39	d	d	PROPN
ejpam-3405	115	40	=	=	SYM
ejpam-3405	115	41	h	h	PROPN
ejpam-3405	115	42	(	(	PUNCT
ejpam-3405	115	43	ix	ix	PROPN
ejpam-3405	115	44	)	)	PUNCT
ejpam-3405	115	45	a	a	DET
ejpam-3405	115	46	=	=	SYM
ejpam-3405	115	47	g	g	NOUN
ejpam-3405	115	48	,	,	PUNCT
ejpam-3405	115	49	e	e	X
ejpam-3405	115	50	=	=	SYM
ejpam-3405	115	51	h	h	PROPN
ejpam-3405	115	52	(	(	PUNCT
ejpam-3405	115	53	x	x	NOUN
ejpam-3405	115	54	)	)	PUNCT
ejpam-3405	115	55	b	b	NOUN
ejpam-3405	116	1	=	=	SYM
ejpam-3405	116	2	c	c	NOUN
ejpam-3405	116	3	,	,	PUNCT
ejpam-3405	116	4	d	d	NOUN
ejpam-3405	116	5	=	=	SYM
ejpam-3405	116	6	h	h	PROPN
ejpam-3405	116	7	(	(	PUNCT
ejpam-3405	116	8	xi	xi	PROPN
ejpam-3405	116	9	)	)	PUNCT
ejpam-3405	116	10	b	b	NOUN
ejpam-3405	116	11	=	=	SYM
ejpam-3405	116	12	c	c	X
ejpam-3405	116	13	,	,	PUNCT
ejpam-3405	116	14	e	e	X
ejpam-3405	116	15	=	=	SYM
ejpam-3405	116	16	h	h	PROPN
ejpam-3405	116	17	(	(	PUNCT
ejpam-3405	116	18	xii	xii	NOUN
ejpam-3405	116	19	)	)	PUNCT
ejpam-3405	116	20	b	b	NOUN
ejpam-3405	117	1	=	=	SYM
ejpam-3405	117	2	d	d	PROPN
ejpam-3405	117	3	,	,	PUNCT
ejpam-3405	117	4	c	c	X
ejpam-3405	117	5	=	=	SYM
ejpam-3405	117	6	e	e	X
ejpam-3405	117	7	(	(	PUNCT
ejpam-3405	117	8	xiii	xiii	PROPN
ejpam-3405	117	9	)	)	PUNCT
ejpam-3405	117	10	b	b	NOUN
ejpam-3405	118	1	=	=	SYM
ejpam-3405	118	2	d	d	PROPN
ejpam-3405	118	3	,	,	PUNCT
ejpam-3405	118	4	c	c	NOUN
ejpam-3405	118	5	=	=	SYM
ejpam-3405	118	6	h	h	PROPN
ejpam-3405	118	7	(	(	PUNCT
ejpam-3405	118	8	xiv	xiv	PROPN
ejpam-3405	118	9	)	)	PUNCT
ejpam-3405	118	10	b	b	PROPN
ejpam-3405	119	1	=	=	SYM
ejpam-3405	119	2	d	d	PROPN
ejpam-3405	119	3	,	,	PUNCT
ejpam-3405	119	4	e	e	X
ejpam-3405	119	5	=	=	SYM
ejpam-3405	119	6	h	h	PROPN
ejpam-3405	119	7	(	(	PUNCT
ejpam-3405	119	8	xv	xv	PROPN
ejpam-3405	119	9	)	)	PUNCT
ejpam-3405	119	10	b	b	NOUN
ejpam-3405	119	11	=	=	SYM
ejpam-3405	119	12	e	e	PROPN
ejpam-3405	119	13	,	,	PUNCT
ejpam-3405	119	14	c	c	NOUN
ejpam-3405	119	15	=	=	SYM
ejpam-3405	119	16	h	h	PROPN
ejpam-3405	119	17	(	(	PUNCT
ejpam-3405	119	18	xvi	xvi	PROPN
ejpam-3405	119	19	)	)	PUNCT
ejpam-3405	119	20	b	b	NOUN
ejpam-3405	119	21	=	=	SYM
ejpam-3405	119	22	h	h	PROPN
ejpam-3405	119	23	,	,	PUNCT
ejpam-3405	119	24	c	c	NOUN
ejpam-3405	120	1	=	=	SYM
ejpam-3405	120	2	d	d	PROPN
ejpam-3405	120	3	(	(	PUNCT
ejpam-3405	120	4	xvii	xvii	PROPN
ejpam-3405	120	5	)	)	PUNCT
ejpam-3405	120	6	b	b	NOUN
ejpam-3405	121	1	=	=	SYM
ejpam-3405	121	2	c	c	NOUN
ejpam-3405	121	3	,	,	PUNCT
ejpam-3405	121	4	d	d	NOUN
ejpam-3405	121	5	=	=	SYM
ejpam-3405	121	6	e	e	NOUN
ejpam-3405	121	7	proof	proof	NOUN
ejpam-3405	121	8	.	.	PUNCT
ejpam-3405	122	1	(	(	PUNCT
ejpam-3405	122	2	i	i	NOUN
ejpam-3405	122	3	)	)	PUNCT
ejpam-3405	122	4	in	in	ADP
ejpam-3405	122	5	this	this	DET
ejpam-3405	122	6	case	case	NOUN
ejpam-3405	122	7	∆	∆	PROPN
ejpam-3405	122	8	is	be	AUX
ejpam-3405	122	9	shown	show	VERB
ejpam-3405	122	10	in	in	ADP
ejpam-3405	122	11	figure	figure	NOUN
ejpam-3405	122	12	3	3	NUM
ejpam-3405	122	13	.	.	PUNCT
ejpam-3405	122	14	since	since	SCONJ
ejpam-3405	122	15	d∆(va	d∆(va	NOUN
ejpam-3405	122	16	)	)	PUNCT
ejpam-3405	122	17	=	=	SYM
ejpam-3405	122	18	d∆(vb	d∆(vb	NOUN
ejpam-3405	122	19	)	)	PUNCT
ejpam-3405	122	20	=	=	SYM
ejpam-3405	122	21	2	2	NUM
ejpam-3405	122	22	or	or	CCONJ
ejpam-3405	122	23	d∆(vb	d∆(vb	NOUN
ejpam-3405	122	24	)	)	PUNCT
ejpam-3405	123	1	=	=	SYM
ejpam-3405	123	2	d∆(vc	d∆(vc	NOUN
ejpam-3405	123	3	)	)	PUNCT
ejpam-3405	124	1	=	=	SYM
ejpam-3405	124	2	2	2	NUM
ejpam-3405	124	3	can	can	AUX
ejpam-3405	124	4	not	not	PART
ejpam-3405	124	5	occur	occur	VERB
ejpam-3405	124	6	therefore	therefore	ADV
ejpam-3405	124	7	it	it	PRON
ejpam-3405	124	8	can	can	AUX
ejpam-3405	124	9	be	be	AUX
ejpam-3405	124	10	assumed	assume	VERB
ejpam-3405	124	11	that	that	SCONJ
ejpam-3405	124	12	d∆(va	d∆(va	NOUN
ejpam-3405	124	13	)	)	PUNCT
ejpam-3405	124	14	=	=	PUNCT
ejpam-3405	124	15	d∆(vc	d∆(vc	NOUN
ejpam-3405	124	16	)	)	PUNCT
ejpam-3405	125	1	=	=	PUNCT
ejpam-3405	125	2	d∆(vg	d∆(vg	NOUN
ejpam-3405	125	3	)	)	PUNCT
ejpam-3405	125	4	=	=	SYM
ejpam-3405	125	5	2	2	NUM
ejpam-3405	125	6	as	as	SCONJ
ejpam-3405	125	7	shown	show	VERB
ejpam-3405	125	8	in	in	ADP
ejpam-3405	125	9	figure	figure	NOUN
ejpam-3405	125	10	3	3	NUM
ejpam-3405	125	11	.	.	PUNCT
ejpam-3405	126	1	in	in	ADP
ejpam-3405	126	2	this	this	DET
ejpam-3405	126	3	case	case	NOUN
ejpam-3405	126	4	c(∆	c(∆	PROPN
ejpam-3405	126	5	)	)	PUNCT
ejpam-3405	126	6	≤	≤	NOUN
ejpam-3405	126	7	0	0	NUM
ejpam-3405	126	8	.	.	PUNCT
ejpam-3405	126	9	m.	m.	PROPN
ejpam-3405	126	10	fazeel	fazeel	PROPN
ejpam-3405	126	11	anwar	anwar	PROPN
ejpam-3405	126	12	,	,	PUNCT
ejpam-3405	126	13	mairaj	mairaj	ADJ
ejpam-3405	126	14	bibi	bibi	NOUN
ejpam-3405	126	15	,	,	PUNCT
ejpam-3405	126	16	m.	m.	PROPN
ejpam-3405	126	17	saeed	saeed	PROPN
ejpam-3405	126	18	akram	akram	PROPN
ejpam-3405	126	19	/	/	PUNCT
ejpam-3405	126	20	eur	eur	PROPN
ejpam-3405	126	21	.	.	PUNCT
ejpam-3405	127	1	j.	j.	PROPN
ejpam-3405	127	2	pure	pure	PROPN
ejpam-3405	127	3	appl	appl	PROPN
ejpam-3405	127	4	.	.	PROPN
ejpam-3405	127	5	math	math	PROPN
ejpam-3405	127	6	,	,	PUNCT
ejpam-3405	127	7	12	12	NUM
ejpam-3405	127	8	(	(	PUNCT
ejpam-3405	127	9	2	2	NUM
ejpam-3405	127	10	)	)	PUNCT
ejpam-3405	127	11	(	(	PUNCT
ejpam-3405	127	12	2019	2019	NUM
ejpam-3405	127	13	)	)	PUNCT
ejpam-3405	127	14	,	,	PUNCT
ejpam-3405	127	15	590	590	NUM
ejpam-3405	127	16	-	-	SYM
ejpam-3405	127	17	604	604	NUM
ejpam-3405	127	18	595	595	NUM
ejpam-3405	127	19	a	a	DET
ejpam-3405	127	20	b	b	NOUN
ejpam-3405	127	21	c	c	NOUN
ejpam-3405	127	22	d	d	X
ejpam-3405	127	23	ef	ef	PROPN
ejpam-3405	127	24	g	g	NOUN
ejpam-3405	127	25	h	h	NOUN
ejpam-3405	128	1	i	i	PRON
ejpam-3405	128	2	c	c	VERB
ejpam-3405	128	3	g	g	NOUN
ejpam-3405	128	4	a	a	DET
ejpam-3405	128	5	b	b	NOUN
ejpam-3405	128	6	a	a	DET
ejpam-3405	128	7	b	b	NOUN
ejpam-3405	128	8	c	c	NOUN
ejpam-3405	128	9	d	d	X
ejpam-3405	128	10	ef	ef	PROPN
ejpam-3405	129	1	g	g	NOUN
ejpam-3405	129	2	h	h	NOUN
ejpam-3405	130	1	i	i	PRON
ejpam-3405	130	2	g	g	VERB
ejpam-3405	130	3	a	a	DET
ejpam-3405	130	4	b	b	NUM
ejpam-3405	130	5	figure	figure	NOUN
ejpam-3405	130	6	3	3	NUM
ejpam-3405	130	7	:	:	PUNCT
ejpam-3405	130	8	region	region	NOUN
ejpam-3405	130	9	∆	∆	PROPN
ejpam-3405	130	10	(	(	PUNCT
ejpam-3405	130	11	ii	ii	NOUN
ejpam-3405	130	12	)	)	PUNCT
ejpam-3405	130	13	in	in	ADP
ejpam-3405	130	14	this	this	DET
ejpam-3405	130	15	case	case	NOUN
ejpam-3405	131	1	∆	∆	PROPN
ejpam-3405	131	2	is	be	AUX
ejpam-3405	131	3	shown	show	VERB
ejpam-3405	131	4	in	in	ADP
ejpam-3405	131	5	figure	figure	NOUN
ejpam-3405	131	6	4	4	NUM
ejpam-3405	131	7	.	.	PUNCT
ejpam-3405	131	8	since	since	SCONJ
ejpam-3405	131	9	degree	degree	NOUN
ejpam-3405	131	10	of	of	ADP
ejpam-3405	131	11	vertices	vertex	NOUN
ejpam-3405	131	12	va	va	NOUN
ejpam-3405	131	13	and	and	CCONJ
ejpam-3405	131	14	vb	vb	NOUN
ejpam-3405	131	15	can	can	AUX
ejpam-3405	131	16	not	not	PART
ejpam-3405	131	17	be	be	AUX
ejpam-3405	131	18	2	2	NUM
ejpam-3405	131	19	together	together	ADV
ejpam-3405	131	20	so	so	SCONJ
ejpam-3405	131	21	there	there	PRON
ejpam-3405	131	22	are	be	VERB
ejpam-3405	131	23	the	the	DET
ejpam-3405	131	24	following	follow	VERB
ejpam-3405	131	25	two	two	NUM
ejpam-3405	131	26	cases	case	NOUN
ejpam-3405	131	27	to	to	PART
ejpam-3405	131	28	consider	consider	VERB
ejpam-3405	131	29	:	:	PUNCT
ejpam-3405	131	30	(	(	PUNCT
ejpam-3405	131	31	a	a	X
ejpam-3405	131	32	)	)	PUNCT
ejpam-3405	131	33	d∆(va	d∆(va	NOUN
ejpam-3405	131	34	)	)	PUNCT
ejpam-3405	131	35	=	=	PUNCT
ejpam-3405	132	1	d∆(vd	d∆(vd	ADJ
ejpam-3405	132	2	)	)	PUNCT
ejpam-3405	132	3	=	=	PUNCT
ejpam-3405	132	4	d∆(vg	d∆(vg	NOUN
ejpam-3405	132	5	)	)	PUNCT
ejpam-3405	132	6	=	=	SYM
ejpam-3405	132	7	2	2	NUM
ejpam-3405	132	8	;	;	PUNCT
ejpam-3405	132	9	(	(	PUNCT
ejpam-3405	132	10	b	b	X
ejpam-3405	132	11	)	)	PUNCT
ejpam-3405	132	12	d∆(vb	d∆(vb	NOUN
ejpam-3405	132	13	)	)	PUNCT
ejpam-3405	133	1	=	=	PUNCT
ejpam-3405	133	2	d∆(vd	d∆(vd	ADJ
ejpam-3405	133	3	)	)	PUNCT
ejpam-3405	133	4	=	=	PUNCT
ejpam-3405	133	5	d∆(vg	d∆(vg	NOUN
ejpam-3405	133	6	)	)	PUNCT
ejpam-3405	133	7	=	=	SYM
ejpam-3405	134	1	2	2	X
ejpam-3405	134	2	.	.	PUNCT
ejpam-3405	134	3	as	as	SCONJ
ejpam-3405	134	4	shown	show	VERB
ejpam-3405	134	5	in	in	ADP
ejpam-3405	134	6	figure	figure	NOUN
ejpam-3405	134	7	4	4	NUM
ejpam-3405	134	8	.	.	PUNCT
ejpam-3405	135	1	in	in	ADP
ejpam-3405	135	2	both	both	DET
ejpam-3405	135	3	of	of	ADP
ejpam-3405	135	4	these	these	DET
ejpam-3405	135	5	cases	case	NOUN
ejpam-3405	135	6	c(∆	c(∆	NOUN
ejpam-3405	135	7	)	)	PUNCT
ejpam-3405	135	8	≤	≤	NOUN
ejpam-3405	135	9	0	0	NUM
ejpam-3405	135	10	.	.	PUNCT
ejpam-3405	136	1	a	a	DET
ejpam-3405	136	2	b	b	NOUN
ejpam-3405	136	3	c	c	NOUN
ejpam-3405	136	4	d	d	X
ejpam-3405	136	5	ef	ef	PROPN
ejpam-3405	136	6	g	g	NOUN
ejpam-3405	136	7	h	h	NOUN
ejpam-3405	137	1	i	i	NOUN
ejpam-3405	138	1	d	d	X
ejpam-3405	138	2	g	g	ADP
ejpam-3405	138	3	a	a	DET
ejpam-3405	138	4	b	b	NOUN
ejpam-3405	138	5	a	a	DET
ejpam-3405	138	6	b	b	NOUN
ejpam-3405	138	7	c	c	NOUN
ejpam-3405	138	8	d	d	X
ejpam-3405	138	9	ef	ef	PROPN
ejpam-3405	138	10	g	g	NOUN
ejpam-3405	138	11	h	h	NOUN
ejpam-3405	139	1	i	i	PRON
ejpam-3405	139	2	g	g	VERB
ejpam-3405	139	3	a	a	DET
ejpam-3405	139	4	b	b	NOUN
ejpam-3405	139	5	a	a	DET
ejpam-3405	139	6	b	b	NOUN
ejpam-3405	139	7	c	c	NOUN
ejpam-3405	139	8	d	d	X
ejpam-3405	139	9	ef	ef	PROPN
ejpam-3405	140	1	g	g	NOUN
ejpam-3405	140	2	h	h	NOUN
ejpam-3405	141	1	i	i	NOUN
ejpam-3405	141	2	d	d	PROPN
ejpam-3405	141	3	a	a	DET
ejpam-3405	141	4	b	b	X
ejpam-3405	141	5	figure	figure	NOUN
ejpam-3405	141	6	4	4	NUM
ejpam-3405	141	7	:	:	PUNCT
ejpam-3405	141	8	region	region	NOUN
ejpam-3405	141	9	∆	∆	PROPN
ejpam-3405	141	10	(	(	PUNCT
ejpam-3405	141	11	iii	iii	NOUN
ejpam-3405	141	12	)	)	PUNCT
ejpam-3405	141	13	in	in	ADP
ejpam-3405	141	14	this	this	DET
ejpam-3405	141	15	case	case	NOUN
ejpam-3405	141	16	∆	∆	PROPN
ejpam-3405	141	17	is	be	AUX
ejpam-3405	141	18	shown	show	VERB
ejpam-3405	141	19	in	in	ADP
ejpam-3405	141	20	figure	figure	NOUN
ejpam-3405	141	21	5	5	NUM
ejpam-3405	141	22	.	.	PUNCT
ejpam-3405	142	1	since	since	SCONJ
ejpam-3405	142	2	degree	degree	NOUN
ejpam-3405	142	3	of	of	ADP
ejpam-3405	142	4	vertices	vertex	NOUN
ejpam-3405	142	5	va	va	NOUN
ejpam-3405	142	6	and	and	CCONJ
ejpam-3405	142	7	vb	vb	NOUN
ejpam-3405	142	8	can	can	AUX
ejpam-3405	142	9	not	not	PART
ejpam-3405	142	10	be	be	AUX
ejpam-3405	142	11	2	2	NUM
ejpam-3405	142	12	together	together	ADV
ejpam-3405	142	13	so	so	SCONJ
ejpam-3405	142	14	there	there	PRON
ejpam-3405	142	15	are	be	VERB
ejpam-3405	142	16	the	the	DET
ejpam-3405	142	17	following	follow	VERB
ejpam-3405	142	18	two	two	NUM
ejpam-3405	142	19	cases	case	NOUN
ejpam-3405	142	20	to	to	PART
ejpam-3405	142	21	consider	consider	VERB
ejpam-3405	142	22	:	:	PUNCT
ejpam-3405	142	23	m.	m.	NOUN
ejpam-3405	142	24	fazeel	fazeel	PROPN
ejpam-3405	142	25	anwar	anwar	PROPN
ejpam-3405	142	26	,	,	PUNCT
ejpam-3405	142	27	mairaj	mairaj	ADJ
ejpam-3405	142	28	bibi	bibi	NOUN
ejpam-3405	142	29	,	,	PUNCT
ejpam-3405	142	30	m.	m.	PROPN
ejpam-3405	142	31	saeed	saeed	PROPN
ejpam-3405	142	32	akram	akram	PROPN
ejpam-3405	142	33	/	/	PUNCT
ejpam-3405	142	34	eur	eur	PROPN
ejpam-3405	142	35	.	.	PUNCT
ejpam-3405	143	1	j.	j.	PROPN
ejpam-3405	143	2	pure	pure	PROPN
ejpam-3405	143	3	appl	appl	PROPN
ejpam-3405	143	4	.	.	PROPN
ejpam-3405	143	5	math	math	PROPN
ejpam-3405	143	6	,	,	PUNCT
ejpam-3405	143	7	12	12	NUM
ejpam-3405	143	8	(	(	PUNCT
ejpam-3405	143	9	2	2	NUM
ejpam-3405	143	10	)	)	PUNCT
ejpam-3405	143	11	(	(	PUNCT
ejpam-3405	143	12	2019	2019	NUM
ejpam-3405	143	13	)	)	PUNCT
ejpam-3405	143	14	,	,	PUNCT
ejpam-3405	143	15	590	590	NUM
ejpam-3405	143	16	-	-	SYM
ejpam-3405	143	17	604	604	NUM
ejpam-3405	143	18	596	596	NUM
ejpam-3405	143	19	(	(	PUNCT
ejpam-3405	143	20	a	a	PRON
ejpam-3405	143	21	)	)	PUNCT
ejpam-3405	143	22	d∆(va	d∆(va	NOUN
ejpam-3405	143	23	)	)	PUNCT
ejpam-3405	143	24	=	=	SYM
ejpam-3405	143	25	d∆(ve	d∆(ve	NOUN
ejpam-3405	143	26	)	)	PUNCT
ejpam-3405	143	27	=	=	SYM
ejpam-3405	143	28	d∆(vg	d∆(vg	NOUN
ejpam-3405	143	29	)	)	PUNCT
ejpam-3405	143	30	=	=	SYM
ejpam-3405	143	31	2	2	NUM
ejpam-3405	143	32	;	;	PUNCT
ejpam-3405	143	33	(	(	PUNCT
ejpam-3405	143	34	b	b	X
ejpam-3405	143	35	)	)	PUNCT
ejpam-3405	143	36	d∆(vb	d∆(vb	NOUN
ejpam-3405	143	37	)	)	PUNCT
ejpam-3405	143	38	=	=	SYM
ejpam-3405	143	39	d∆(ve	d∆(ve	NOUN
ejpam-3405	143	40	)	)	PUNCT
ejpam-3405	143	41	=	=	SYM
ejpam-3405	143	42	d∆(vg	d∆(vg	NOUN
ejpam-3405	143	43	)	)	PUNCT
ejpam-3405	143	44	=	=	SYM
ejpam-3405	144	1	2	2	X
ejpam-3405	144	2	.	.	PUNCT
ejpam-3405	144	3	as	as	SCONJ
ejpam-3405	144	4	shown	show	VERB
ejpam-3405	144	5	in	in	ADP
ejpam-3405	144	6	figure	figure	NOUN
ejpam-3405	144	7	5	5	NUM
ejpam-3405	144	8	.	.	PUNCT
ejpam-3405	145	1	in	in	ADP
ejpam-3405	145	2	both	both	DET
ejpam-3405	145	3	of	of	ADP
ejpam-3405	145	4	these	these	DET
ejpam-3405	145	5	cases	case	NOUN
ejpam-3405	145	6	c(∆	c(∆	NOUN
ejpam-3405	145	7	)	)	PUNCT
ejpam-3405	145	8	≤	≤	NOUN
ejpam-3405	145	9	0	0	NUM
ejpam-3405	145	10	.	.	PUNCT
ejpam-3405	146	1	a	a	DET
ejpam-3405	146	2	b	b	NOUN
ejpam-3405	146	3	c	c	NOUN
ejpam-3405	146	4	d	d	X
ejpam-3405	146	5	ef	ef	PROPN
ejpam-3405	146	6	g	g	NOUN
ejpam-3405	146	7	h	h	NOUN
ejpam-3405	147	1	i	i	NOUN
ejpam-3405	147	2	e	e	VERB
ejpam-3405	147	3	g	g	ADP
ejpam-3405	147	4	a	a	DET
ejpam-3405	147	5	b	b	NOUN
ejpam-3405	147	6	a	a	DET
ejpam-3405	147	7	b	b	NOUN
ejpam-3405	147	8	c	c	NOUN
ejpam-3405	147	9	d	d	X
ejpam-3405	147	10	ef	ef	PROPN
ejpam-3405	148	1	g	g	NOUN
ejpam-3405	149	1	h	h	NOUN
ejpam-3405	150	1	i	i	PRON
ejpam-3405	150	2	g	g	VERB
ejpam-3405	150	3	a	a	DET
ejpam-3405	150	4	b	b	NOUN
ejpam-3405	150	5	a	a	DET
ejpam-3405	150	6	b	b	NOUN
ejpam-3405	150	7	c	c	NOUN
ejpam-3405	150	8	d	d	X
ejpam-3405	150	9	ef	ef	PROPN
ejpam-3405	151	1	g	g	NOUN
ejpam-3405	151	2	h	h	NOUN
ejpam-3405	152	1	i	i	NOUN
ejpam-3405	152	2	e	e	VERB
ejpam-3405	152	3	a	a	DET
ejpam-3405	152	4	b	b	NUM
ejpam-3405	152	5	figure	figure	NOUN
ejpam-3405	152	6	5	5	NUM
ejpam-3405	152	7	:	:	PUNCT
ejpam-3405	152	8	region	region	NOUN
ejpam-3405	152	9	∆	∆	PROPN
ejpam-3405	152	10	(	(	PUNCT
ejpam-3405	152	11	iv	iv	X
ejpam-3405	152	12	)	)	PUNCT
ejpam-3405	152	13	in	in	ADP
ejpam-3405	152	14	this	this	DET
ejpam-3405	152	15	case	case	NOUN
ejpam-3405	152	16	∆	∆	PROPN
ejpam-3405	152	17	is	be	AUX
ejpam-3405	152	18	shown	show	VERB
ejpam-3405	152	19	in	in	ADP
ejpam-3405	152	20	figure	figure	NOUN
ejpam-3405	152	21	6	6	NUM
ejpam-3405	152	22	.	.	PUNCT
ejpam-3405	153	1	since	since	SCONJ
ejpam-3405	153	2	degree	degree	NOUN
ejpam-3405	153	3	of	of	ADP
ejpam-3405	153	4	vertices	vertex	NOUN
ejpam-3405	153	5	va	va	NOUN
ejpam-3405	153	6	and	and	CCONJ
ejpam-3405	153	7	vb	vb	NOUN
ejpam-3405	153	8	can	can	AUX
ejpam-3405	153	9	not	not	PART
ejpam-3405	153	10	be	be	AUX
ejpam-3405	153	11	2	2	NUM
ejpam-3405	153	12	together	together	ADV
ejpam-3405	153	13	so	so	SCONJ
ejpam-3405	153	14	there	there	PRON
ejpam-3405	153	15	are	be	VERB
ejpam-3405	153	16	the	the	DET
ejpam-3405	153	17	following	follow	VERB
ejpam-3405	153	18	two	two	NUM
ejpam-3405	153	19	cases	case	NOUN
ejpam-3405	153	20	to	to	PART
ejpam-3405	153	21	consider	consider	VERB
ejpam-3405	153	22	:	:	PUNCT
ejpam-3405	153	23	(	(	PUNCT
ejpam-3405	153	24	a	a	X
ejpam-3405	153	25	)	)	PUNCT
ejpam-3405	153	26	d∆(va	d∆(va	NOUN
ejpam-3405	153	27	)	)	PUNCT
ejpam-3405	154	1	=	=	PUNCT
ejpam-3405	154	2	d∆(vc	d∆(vc	NOUN
ejpam-3405	154	3	)	)	PUNCT
ejpam-3405	155	1	=	=	PUNCT
ejpam-3405	155	2	d∆(vg	d∆(vg	NOUN
ejpam-3405	155	3	)	)	PUNCT
ejpam-3405	155	4	=	=	SYM
ejpam-3405	155	5	2	2	NUM
ejpam-3405	155	6	;	;	PUNCT
ejpam-3405	155	7	(	(	PUNCT
ejpam-3405	155	8	b	b	X
ejpam-3405	155	9	)	)	PUNCT
ejpam-3405	155	10	d∆(va	d∆(va	NOUN
ejpam-3405	155	11	)	)	PUNCT
ejpam-3405	155	12	=	=	PUNCT
ejpam-3405	156	1	d∆(vd	d∆(vd	ADJ
ejpam-3405	156	2	)	)	PUNCT
ejpam-3405	156	3	=	=	PUNCT
ejpam-3405	156	4	d∆(vg	d∆(vg	NOUN
ejpam-3405	156	5	)	)	PUNCT
ejpam-3405	156	6	=	=	SYM
ejpam-3405	157	1	2	2	X
ejpam-3405	157	2	.	.	PUNCT
ejpam-3405	157	3	as	as	SCONJ
ejpam-3405	157	4	shown	show	VERB
ejpam-3405	157	5	in	in	ADP
ejpam-3405	157	6	figure	figure	NOUN
ejpam-3405	157	7	6	6	NUM
ejpam-3405	157	8	.	.	PUNCT
ejpam-3405	158	1	in	in	ADP
ejpam-3405	158	2	both	both	PRON
ejpam-3405	158	3	of	of	ADP
ejpam-3405	158	4	these	these	DET
ejpam-3405	158	5	cases	case	NOUN
ejpam-3405	158	6	c(∆	c(∆	NOUN
ejpam-3405	158	7	)	)	PUNCT
ejpam-3405	158	8	≤	≤	NOUN
ejpam-3405	158	9	0	0	NUM
ejpam-3405	158	10	.	.	PUNCT
ejpam-3405	158	11	m.	m.	PROPN
ejpam-3405	158	12	fazeel	fazeel	PROPN
ejpam-3405	158	13	anwar	anwar	PROPN
ejpam-3405	158	14	,	,	PUNCT
ejpam-3405	158	15	mairaj	mairaj	ADJ
ejpam-3405	158	16	bibi	bibi	NOUN
ejpam-3405	158	17	,	,	PUNCT
ejpam-3405	158	18	m.	m.	PROPN
ejpam-3405	158	19	saeed	saeed	PROPN
ejpam-3405	158	20	akram	akram	PROPN
ejpam-3405	158	21	/	/	PUNCT
ejpam-3405	158	22	eur	eur	PROPN
ejpam-3405	158	23	.	.	PUNCT
ejpam-3405	159	1	j.	j.	PROPN
ejpam-3405	159	2	pure	pure	PROPN
ejpam-3405	159	3	appl	appl	PROPN
ejpam-3405	159	4	.	.	PROPN
ejpam-3405	159	5	math	math	PROPN
ejpam-3405	159	6	,	,	PUNCT
ejpam-3405	159	7	12	12	NUM
ejpam-3405	159	8	(	(	PUNCT
ejpam-3405	159	9	2	2	NUM
ejpam-3405	159	10	)	)	PUNCT
ejpam-3405	159	11	(	(	PUNCT
ejpam-3405	159	12	2019	2019	NUM
ejpam-3405	159	13	)	)	PUNCT
ejpam-3405	159	14	,	,	PUNCT
ejpam-3405	159	15	590	590	NUM
ejpam-3405	159	16	-	-	SYM
ejpam-3405	159	17	604	604	NUM
ejpam-3405	159	18	597	597	NUM
ejpam-3405	159	19	a	a	DET
ejpam-3405	159	20	b	b	NOUN
ejpam-3405	159	21	c	c	NOUN
ejpam-3405	159	22	d	d	X
ejpam-3405	159	23	ef	ef	PROPN
ejpam-3405	159	24	g	g	NOUN
ejpam-3405	159	25	h	h	NOUN
ejpam-3405	160	1	i	i	NOUN
ejpam-3405	161	1	d	d	X
ejpam-3405	161	2	g	g	NOUN
ejpam-3405	161	3	a	a	DET
ejpam-3405	161	4	c	c	NOUN
ejpam-3405	161	5	a	a	DET
ejpam-3405	161	6	b	b	NOUN
ejpam-3405	161	7	c	c	NOUN
ejpam-3405	161	8	d	d	X
ejpam-3405	161	9	ef	ef	PROPN
ejpam-3405	161	10	g	g	NOUN
ejpam-3405	161	11	h	h	NOUN
ejpam-3405	162	1	i	i	PRON
ejpam-3405	162	2	g	g	VERB
ejpam-3405	162	3	a	a	PRON
ejpam-3405	162	4	a	a	DET
ejpam-3405	162	5	b	b	NOUN
ejpam-3405	162	6	c	c	NOUN
ejpam-3405	162	7	d	d	X
ejpam-3405	162	8	ef	ef	PROPN
ejpam-3405	163	1	g	g	PROPN
ejpam-3405	163	2	h	h	NOUN
ejpam-3405	164	1	i	i	PRON
ejpam-3405	164	2	a	a	PROPN
ejpam-3405	165	1	d	d	X
ejpam-3405	165	2	c	c	NOUN
ejpam-3405	165	3	g	g	NOUN
ejpam-3405	165	4	figure	figure	NOUN
ejpam-3405	165	5	6	6	NUM
ejpam-3405	165	6	:	:	PUNCT
ejpam-3405	165	7	region	region	NOUN
ejpam-3405	165	8	∆	∆	PROPN
ejpam-3405	165	9	(	(	PUNCT
ejpam-3405	165	10	v	v	NOUN
ejpam-3405	165	11	)	)	PUNCT
ejpam-3405	165	12	in	in	ADP
ejpam-3405	165	13	this	this	DET
ejpam-3405	165	14	case	case	NOUN
ejpam-3405	165	15	∆	∆	PROPN
ejpam-3405	165	16	is	be	AUX
ejpam-3405	165	17	shown	show	VERB
ejpam-3405	165	18	in	in	ADP
ejpam-3405	165	19	figure	figure	NOUN
ejpam-3405	165	20	7	7	NUM
ejpam-3405	165	21	.	.	PUNCT
ejpam-3405	166	1	here	here	ADV
ejpam-3405	166	2	d∆(va	d∆(va	NOUN
ejpam-3405	166	3	)	)	PUNCT
ejpam-3405	166	4	=	=	PUNCT
ejpam-3405	166	5	d∆(vc	d∆(vc	NOUN
ejpam-3405	166	6	)	)	PUNCT
ejpam-3405	166	7	=	=	SYM
ejpam-3405	166	8	d∆(ve	d∆(ve	NOUN
ejpam-3405	166	9	)	)	PUNCT
ejpam-3405	166	10	=	=	SYM
ejpam-3405	167	1	d∆(vg	d∆(vg	NOUN
ejpam-3405	167	2	)	)	PUNCT
ejpam-3405	168	1	=	=	SYM
ejpam-3405	168	2	2	2	NUM
ejpam-3405	168	3	which	which	PRON
ejpam-3405	168	4	implies	imply	VERB
ejpam-3405	168	5	l∆(va	l∆(va	NOUN
ejpam-3405	168	6	)	)	PUNCT
ejpam-3405	169	1	=	=	SYM
ejpam-3405	169	2	ag−1	ag−1	NOUN
ejpam-3405	169	3	,	,	PUNCT
ejpam-3405	169	4	l∆(vc	l∆(vc	PROPN
ejpam-3405	169	5	)	)	PUNCT
ejpam-3405	170	1	=	=	SYM
ejpam-3405	170	2	ce−1	ce−1	PROPN
ejpam-3405	170	3	,	,	PUNCT
ejpam-3405	170	4	l∆(ve	l∆(ve	PROPN
ejpam-3405	170	5	)	)	PUNCT
ejpam-3405	171	1	=	=	SYM
ejpam-3405	171	2	ec−1	ec−1	NOUN
ejpam-3405	171	3	ans	an	NOUN
ejpam-3405	171	4	l∆(vg	l∆(vg	NOUN
ejpam-3405	171	5	)	)	PUNCT
ejpam-3405	172	1	=	=	VERB
ejpam-3405	172	2	ga−1	ga−1	NOUN
ejpam-3405	172	3	as	as	SCONJ
ejpam-3405	172	4	shown	show	VERB
ejpam-3405	172	5	in	in	ADP
ejpam-3405	172	6	figure	figure	NOUN
ejpam-3405	172	7	7	7	NUM
ejpam-3405	172	8	.	.	PUNCT
ejpam-3405	173	1	in	in	ADP
ejpam-3405	173	2	order	order	NOUN
ejpam-3405	173	3	to	to	PART
ejpam-3405	173	4	have	have	AUX
ejpam-3405	173	5	positive	positive	ADJ
ejpam-3405	173	6	curvature	curvature	NOUN
ejpam-3405	173	7	the	the	DET
ejpam-3405	173	8	remaining	remain	VERB
ejpam-3405	173	9	vertices	vertex	NOUN
ejpam-3405	173	10	must	must	AUX
ejpam-3405	173	11	be	be	AUX
ejpam-3405	173	12	of	of	ADP
ejpam-3405	173	13	degree	degree	NOUN
ejpam-3405	173	14	3	3	NUM
ejpam-3405	173	15	.	.	X
ejpam-3405	173	16	observe	observe	VERB
ejpam-3405	173	17	that	that	DET
ejpam-3405	173	18	l∆(va	l∆(va	NOUN
ejpam-3405	173	19	)	)	PUNCT
ejpam-3405	174	1	=	=	SYM
ejpam-3405	174	2	ag−1	ag−1	NOUN
ejpam-3405	174	3	and	and	CCONJ
ejpam-3405	174	4	l∆(vc	l∆(vc	NOUN
ejpam-3405	174	5	)	)	PUNCT
ejpam-3405	175	1	=	=	NOUN
ejpam-3405	175	2	ce−1	ce−1	PROPN
ejpam-3405	175	3	implies	imply	VERB
ejpam-3405	175	4	that	that	SCONJ
ejpam-3405	175	5	l∆(vb	l∆(vb	NOUN
ejpam-3405	175	6	)	)	PUNCT
ejpam-3405	176	1	=	=	PUNCT
ejpam-3405	176	2	h−1bd−1w	h−1bd−1w	VERB
ejpam-3405	176	3	where	where	SCONJ
ejpam-3405	176	4	w	w	PROPN
ejpam-3405	176	5	∈	∈	PROPN
ejpam-3405	176	6	{	{	PUNCT
ejpam-3405	176	7	b	b	NOUN
ejpam-3405	176	8	,	,	PUNCT
ejpam-3405	176	9	c	c	NOUN
ejpam-3405	176	10	,	,	PUNCT
ejpam-3405	176	11	d	d	NOUN
ejpam-3405	176	12	,	,	PUNCT
ejpam-3405	176	13	e	e	NOUN
ejpam-3405	176	14	,	,	PUNCT
ejpam-3405	176	15	h	h	NOUN
ejpam-3405	176	16	}	}	PUNCT
ejpam-3405	176	17	which	which	PRON
ejpam-3405	176	18	implies	imply	VERB
ejpam-3405	176	19	d∆(vb	d∆(vb	NOUN
ejpam-3405	176	20	)	)	PUNCT
ejpam-3405	176	21	>	>	X
ejpam-3405	177	1	3	3	X
ejpam-3405	177	2	.	.	X
ejpam-3405	177	3	notice	notice	VERB
ejpam-3405	177	4	that	that	SCONJ
ejpam-3405	177	5	l∆(ve	l∆(ve	NOUN
ejpam-3405	177	6	)	)	PUNCT
ejpam-3405	177	7	=	=	SYM
ejpam-3405	177	8	ec−1	ec−1	NOUN
ejpam-3405	177	9	and	and	CCONJ
ejpam-3405	177	10	l∆(vg	l∆(vg	NOUN
ejpam-3405	177	11	)	)	PUNCT
ejpam-3405	178	1	=	=	SYM
ejpam-3405	178	2	ga−1	ga−1	NOUN
ejpam-3405	178	3	implies	imply	VERB
ejpam-3405	178	4	that	that	PRON
ejpam-3405	178	5	l∆(vf	l∆(vf	ADJ
ejpam-3405	178	6	)	)	PUNCT
ejpam-3405	178	7	=	=	PUNCT
ejpam-3405	178	8	d−1fi−1w	d−1fi−1w	NOUN
ejpam-3405	178	9	where	where	SCONJ
ejpam-3405	178	10	w	w	PROPN
ejpam-3405	178	11	∈	∈	PROPN
ejpam-3405	178	12	{	{	PUNCT
ejpam-3405	178	13	b	b	NOUN
ejpam-3405	178	14	,	,	PUNCT
ejpam-3405	178	15	c	c	NOUN
ejpam-3405	178	16	,	,	PUNCT
ejpam-3405	178	17	d	d	NOUN
ejpam-3405	178	18	,	,	PUNCT
ejpam-3405	178	19	e	e	NOUN
ejpam-3405	178	20	,	,	PUNCT
ejpam-3405	178	21	h	h	NOUN
ejpam-3405	178	22	}	}	PUNCT
ejpam-3405	178	23	which	which	PRON
ejpam-3405	178	24	implies	imply	VERB
ejpam-3405	178	25	d∆(vf	d∆(vf	NOUN
ejpam-3405	178	26	)	)	PUNCT
ejpam-3405	178	27	>	>	X
ejpam-3405	179	1	3	3	X
ejpam-3405	179	2	.	.	PUNCT
ejpam-3405	179	3	since	since	SCONJ
ejpam-3405	179	4	d∆(vb	d∆(vb	PROPN
ejpam-3405	179	5	)	)	PUNCT
ejpam-3405	179	6	>	>	X
ejpam-3405	179	7	3	3	NUM
ejpam-3405	179	8	and	and	CCONJ
ejpam-3405	179	9	d∆(vf	d∆(vf	ADJ
ejpam-3405	179	10	)	)	PUNCT
ejpam-3405	179	11	>	>	X
ejpam-3405	179	12	3	3	NUM
ejpam-3405	179	13	so	so	ADV
ejpam-3405	179	14	c(∆	c(∆	NOUN
ejpam-3405	179	15	)	)	PUNCT
ejpam-3405	179	16	≤	≤	NOUN
ejpam-3405	179	17	0	0	NUM
ejpam-3405	179	18	.	.	PUNCT
ejpam-3405	180	1	a	a	DET
ejpam-3405	180	2	b	b	NOUN
ejpam-3405	180	3	c	c	NOUN
ejpam-3405	180	4	d	d	X
ejpam-3405	180	5	ef	ef	PROPN
ejpam-3405	180	6	g	g	NOUN
ejpam-3405	180	7	h	h	NOUN
ejpam-3405	181	1	i	i	PRON
ejpam-3405	181	2	c	c	VERB
ejpam-3405	181	3	g	g	NOUN
ejpam-3405	181	4	a	a	DET
ejpam-3405	181	5	e	e	NOUN
ejpam-3405	181	6	a	a	PRON
ejpam-3405	181	7	b	b	NOUN
ejpam-3405	181	8	c	c	NOUN
ejpam-3405	181	9	d	d	X
ejpam-3405	181	10	ef	ef	PROPN
ejpam-3405	182	1	g	g	NOUN
ejpam-3405	182	2	h	h	NOUN
ejpam-3405	183	1	i	i	PRON
ejpam-3405	183	2	g	g	VERB
ejpam-3405	183	3	a	a	DET
ejpam-3405	183	4	e	e	NOUN
ejpam-3405	183	5	c	c	NOUN
ejpam-3405	184	1	d	d	NOUN
ejpam-3405	184	2	i	i	PRON
ejpam-3405	184	3	d	d	NOUN
ejpam-3405	184	4	h	h	NOUN
ejpam-3405	184	5	figure	figure	VERB
ejpam-3405	184	6	7	7	NUM
ejpam-3405	184	7	:	:	PUNCT
ejpam-3405	184	8	region	region	NOUN
ejpam-3405	184	9	∆	∆	PROPN
ejpam-3405	184	10	(	(	PUNCT
ejpam-3405	184	11	vi	vi	NOUN
ejpam-3405	184	12	)	)	PUNCT
ejpam-3405	184	13	in	in	ADP
ejpam-3405	184	14	this	this	DET
ejpam-3405	184	15	case	case	NOUN
ejpam-3405	184	16	∆	∆	PROPN
ejpam-3405	184	17	is	be	AUX
ejpam-3405	184	18	shown	show	VERB
ejpam-3405	184	19	in	in	ADP
ejpam-3405	184	20	figure	figure	NOUN
ejpam-3405	184	21	8	8	NUM
ejpam-3405	184	22	.	.	PUNCT
ejpam-3405	185	1	since	since	SCONJ
ejpam-3405	185	2	degree	degree	NOUN
ejpam-3405	185	3	of	of	ADP
ejpam-3405	185	4	vertices	vertex	NOUN
ejpam-3405	185	5	vg	vg	ADV
ejpam-3405	185	6	and	and	CCONJ
ejpam-3405	185	7	vh	vh	PROPN
ejpam-3405	185	8	can	can	AUX
ejpam-3405	185	9	not	not	PART
ejpam-3405	185	10	be	be	AUX
ejpam-3405	185	11	2	2	NUM
ejpam-3405	185	12	together	together	ADV
ejpam-3405	185	13	so	so	SCONJ
ejpam-3405	185	14	there	there	PRON
ejpam-3405	185	15	are	be	VERB
ejpam-3405	185	16	the	the	DET
ejpam-3405	185	17	following	follow	VERB
ejpam-3405	185	18	two	two	NUM
ejpam-3405	185	19	cases	case	NOUN
ejpam-3405	185	20	to	to	PART
ejpam-3405	185	21	consider	consider	VERB
ejpam-3405	185	22	:	:	PUNCT
ejpam-3405	185	23	m.	m.	NOUN
ejpam-3405	185	24	fazeel	fazeel	PROPN
ejpam-3405	185	25	anwar	anwar	PROPN
ejpam-3405	185	26	,	,	PUNCT
ejpam-3405	185	27	mairaj	mairaj	ADJ
ejpam-3405	185	28	bibi	bibi	NOUN
ejpam-3405	185	29	,	,	PUNCT
ejpam-3405	185	30	m.	m.	PROPN
ejpam-3405	185	31	saeed	saeed	PROPN
ejpam-3405	185	32	akram	akram	PROPN
ejpam-3405	185	33	/	/	PUNCT
ejpam-3405	185	34	eur	eur	PROPN
ejpam-3405	185	35	.	.	PUNCT
ejpam-3405	186	1	j.	j.	PROPN
ejpam-3405	186	2	pure	pure	PROPN
ejpam-3405	186	3	appl	appl	PROPN
ejpam-3405	186	4	.	.	PROPN
ejpam-3405	186	5	math	math	PROPN
ejpam-3405	186	6	,	,	PUNCT
ejpam-3405	186	7	12	12	NUM
ejpam-3405	186	8	(	(	PUNCT
ejpam-3405	186	9	2	2	NUM
ejpam-3405	186	10	)	)	PUNCT
ejpam-3405	186	11	(	(	PUNCT
ejpam-3405	186	12	2019	2019	NUM
ejpam-3405	186	13	)	)	PUNCT
ejpam-3405	186	14	,	,	PUNCT
ejpam-3405	186	15	590	590	NUM
ejpam-3405	186	16	-	-	SYM
ejpam-3405	186	17	604	604	NUM
ejpam-3405	186	18	598	598	NUM
ejpam-3405	186	19	(	(	PUNCT
ejpam-3405	186	20	a	a	PRON
ejpam-3405	186	21	)	)	PUNCT
ejpam-3405	186	22	d∆(va	d∆(va	NOUN
ejpam-3405	186	23	)	)	PUNCT
ejpam-3405	186	24	=	=	PUNCT
ejpam-3405	186	25	d∆(vc	d∆(vc	NOUN
ejpam-3405	186	26	)	)	PUNCT
ejpam-3405	187	1	=	=	PUNCT
ejpam-3405	187	2	d∆(vg	d∆(vg	NOUN
ejpam-3405	187	3	)	)	PUNCT
ejpam-3405	187	4	=	=	SYM
ejpam-3405	187	5	2	2	NUM
ejpam-3405	187	6	;	;	PUNCT
ejpam-3405	187	7	(	(	PUNCT
ejpam-3405	187	8	b	b	X
ejpam-3405	187	9	)	)	PUNCT
ejpam-3405	187	10	d∆(va	d∆(va	NOUN
ejpam-3405	187	11	)	)	PUNCT
ejpam-3405	187	12	=	=	PUNCT
ejpam-3405	188	1	d∆(vc	d∆(vc	NOUN
ejpam-3405	188	2	)	)	PUNCT
ejpam-3405	188	3	=	=	SYM
ejpam-3405	188	4	d∆(vh	d∆(vh	X
ejpam-3405	188	5	)	)	PUNCT
ejpam-3405	188	6	=	=	SYM
ejpam-3405	189	1	2	2	X
ejpam-3405	189	2	.	.	PUNCT
ejpam-3405	189	3	as	as	SCONJ
ejpam-3405	189	4	shown	show	VERB
ejpam-3405	189	5	in	in	ADP
ejpam-3405	189	6	figure	figure	NOUN
ejpam-3405	189	7	8	8	NUM
ejpam-3405	189	8	.	.	PUNCT
ejpam-3405	190	1	in	in	ADP
ejpam-3405	190	2	both	both	DET
ejpam-3405	190	3	of	of	ADP
ejpam-3405	190	4	these	these	DET
ejpam-3405	190	5	cases	case	NOUN
ejpam-3405	190	6	c(∆	c(∆	NOUN
ejpam-3405	190	7	)	)	PUNCT
ejpam-3405	190	8	≤	≤	NOUN
ejpam-3405	190	9	0	0	NUM
ejpam-3405	190	10	.	.	PUNCT
ejpam-3405	191	1	c	c	PROPN
ejpam-3405	191	2	a	a	DET
ejpam-3405	191	3	b	b	PROPN
ejpam-3405	191	4	c	c	NOUN
ejpam-3405	191	5	d	d	X
ejpam-3405	191	6	ef	ef	PROPN
ejpam-3405	191	7	g	g	PROPN
ejpam-3405	191	8	h	h	NOUN
ejpam-3405	192	1	i	i	PRON
ejpam-3405	192	2	h	h	VERB
ejpam-3405	192	3	g	g	VERB
ejpam-3405	193	1	a	a	PRON
ejpam-3405	193	2	a	a	DET
ejpam-3405	193	3	b	b	NOUN
ejpam-3405	193	4	c	c	NOUN
ejpam-3405	193	5	d	d	X
ejpam-3405	193	6	ef	ef	PROPN
ejpam-3405	193	7	g	g	NOUN
ejpam-3405	193	8	h	h	NOUN
ejpam-3405	194	1	i	i	PRON
ejpam-3405	194	2	g	g	VERB
ejpam-3405	194	3	a	a	DET
ejpam-3405	194	4	a	a	DET
ejpam-3405	194	5	b	b	NOUN
ejpam-3405	194	6	c	c	NOUN
ejpam-3405	194	7	d	d	X
ejpam-3405	194	8	ef	ef	PROPN
ejpam-3405	195	1	g	g	PROPN
ejpam-3405	195	2	h	h	NOUN
ejpam-3405	196	1	i	i	PRON
ejpam-3405	196	2	h	h	VERB
ejpam-3405	197	1	h	h	NOUN
ejpam-3405	197	2	g	g	PROPN
ejpam-3405	197	3	c	c	PROPN
ejpam-3405	197	4	figure	figure	NOUN
ejpam-3405	197	5	8	8	NUM
ejpam-3405	197	6	:	:	PUNCT
ejpam-3405	197	7	region	region	NOUN
ejpam-3405	197	8	∆	∆	PROPN
ejpam-3405	197	9	(	(	PUNCT
ejpam-3405	197	10	vii	vii	PROPN
ejpam-3405	197	11	)	)	PUNCT
ejpam-3405	197	12	in	in	ADP
ejpam-3405	197	13	this	this	DET
ejpam-3405	197	14	case	case	NOUN
ejpam-3405	197	15	∆	∆	PROPN
ejpam-3405	197	16	is	be	AUX
ejpam-3405	197	17	shown	show	VERB
ejpam-3405	197	18	in	in	ADP
ejpam-3405	197	19	figure	figure	NOUN
ejpam-3405	197	20	9	9	NUM
ejpam-3405	197	21	.	.	PUNCT
ejpam-3405	198	1	since	since	SCONJ
ejpam-3405	198	2	degree	degree	NOUN
ejpam-3405	198	3	of	of	ADP
ejpam-3405	198	4	vertices	vertex	NOUN
ejpam-3405	198	5	vd	vd	NOUN
ejpam-3405	198	6	and	and	CCONJ
ejpam-3405	198	7	ve	ve	AUX
ejpam-3405	198	8	can	can	AUX
ejpam-3405	198	9	not	not	PART
ejpam-3405	198	10	be	be	AUX
ejpam-3405	198	11	2	2	NUM
ejpam-3405	198	12	together	together	ADV
ejpam-3405	198	13	so	so	SCONJ
ejpam-3405	198	14	there	there	PRON
ejpam-3405	198	15	are	be	VERB
ejpam-3405	198	16	the	the	DET
ejpam-3405	198	17	following	follow	VERB
ejpam-3405	198	18	two	two	NUM
ejpam-3405	198	19	cases	case	NOUN
ejpam-3405	198	20	to	to	PART
ejpam-3405	198	21	consider	consider	VERB
ejpam-3405	198	22	:	:	PUNCT
ejpam-3405	198	23	(	(	PUNCT
ejpam-3405	198	24	a	a	X
ejpam-3405	198	25	)	)	PUNCT
ejpam-3405	198	26	d∆(va	d∆(va	NOUN
ejpam-3405	198	27	)	)	PUNCT
ejpam-3405	198	28	=	=	PUNCT
ejpam-3405	199	1	d∆(vd	d∆(vd	ADJ
ejpam-3405	199	2	)	)	PUNCT
ejpam-3405	199	3	=	=	PUNCT
ejpam-3405	199	4	d∆(vg	d∆(vg	NOUN
ejpam-3405	199	5	)	)	PUNCT
ejpam-3405	199	6	=	=	SYM
ejpam-3405	199	7	2	2	NUM
ejpam-3405	199	8	;	;	PUNCT
ejpam-3405	199	9	(	(	PUNCT
ejpam-3405	199	10	b	b	X
ejpam-3405	199	11	)	)	PUNCT
ejpam-3405	199	12	d∆(va	d∆(va	NOUN
ejpam-3405	199	13	)	)	PUNCT
ejpam-3405	199	14	=	=	SYM
ejpam-3405	199	15	d∆(ve	d∆(ve	NOUN
ejpam-3405	199	16	)	)	PUNCT
ejpam-3405	199	17	=	=	SYM
ejpam-3405	199	18	d∆(vg	d∆(vg	NOUN
ejpam-3405	199	19	)	)	PUNCT
ejpam-3405	199	20	=	=	SYM
ejpam-3405	200	1	2	2	X
ejpam-3405	200	2	.	.	PUNCT
ejpam-3405	200	3	as	as	SCONJ
ejpam-3405	200	4	shown	show	VERB
ejpam-3405	200	5	in	in	ADP
ejpam-3405	200	6	figure	figure	NOUN
ejpam-3405	200	7	9	9	NUM
ejpam-3405	200	8	.	.	PUNCT
ejpam-3405	201	1	in	in	ADP
ejpam-3405	201	2	both	both	DET
ejpam-3405	201	3	of	of	ADP
ejpam-3405	201	4	these	these	DET
ejpam-3405	201	5	cases	case	NOUN
ejpam-3405	201	6	c(∆	c(∆	NOUN
ejpam-3405	201	7	)	)	PUNCT
ejpam-3405	201	8	≤	≤	NOUN
ejpam-3405	201	9	0	0	NUM
ejpam-3405	201	10	.	.	PUNCT
ejpam-3405	202	1	a	a	DET
ejpam-3405	202	2	b	b	NOUN
ejpam-3405	202	3	c	c	NOUN
ejpam-3405	202	4	d	d	X
ejpam-3405	202	5	ef	ef	PROPN
ejpam-3405	202	6	g	g	NOUN
ejpam-3405	202	7	h	h	NOUN
ejpam-3405	203	1	i	i	NOUN
ejpam-3405	204	1	d	d	X
ejpam-3405	204	2	g	g	NOUN
ejpam-3405	204	3	a	a	DET
ejpam-3405	204	4	e	e	NOUN
ejpam-3405	204	5	a	a	PRON
ejpam-3405	204	6	b	b	NOUN
ejpam-3405	204	7	c	c	NOUN
ejpam-3405	204	8	d	d	X
ejpam-3405	204	9	ef	ef	PROPN
ejpam-3405	204	10	g	g	NOUN
ejpam-3405	204	11	h	h	NOUN
ejpam-3405	205	1	i	i	PRON
ejpam-3405	205	2	g	g	VERB
ejpam-3405	205	3	a	a	PRON
ejpam-3405	205	4	a	a	DET
ejpam-3405	205	5	b	b	NOUN
ejpam-3405	205	6	c	c	NOUN
ejpam-3405	205	7	d	d	X
ejpam-3405	205	8	ef	ef	PROPN
ejpam-3405	206	1	g	g	PROPN
ejpam-3405	206	2	h	h	NOUN
ejpam-3405	207	1	i	i	PRON
ejpam-3405	207	2	a	a	PROPN
ejpam-3405	208	1	d	d	X
ejpam-3405	208	2	e	e	ADP
ejpam-3405	208	3	g	g	PROPN
ejpam-3405	208	4	figure	figure	NOUN
ejpam-3405	208	5	9	9	NUM
ejpam-3405	208	6	:	:	PUNCT
ejpam-3405	208	7	region	region	NOUN
ejpam-3405	208	8	∆	∆	PROPN
ejpam-3405	208	9	(	(	PUNCT
ejpam-3405	208	10	viii	viii	NOUN
ejpam-3405	208	11	)	)	PUNCT
ejpam-3405	208	12	in	in	ADP
ejpam-3405	208	13	this	this	DET
ejpam-3405	208	14	case	case	NOUN
ejpam-3405	208	15	∆	∆	PROPN
ejpam-3405	208	16	is	be	AUX
ejpam-3405	208	17	shown	show	VERB
ejpam-3405	208	18	in	in	ADP
ejpam-3405	208	19	figure	figure	NOUN
ejpam-3405	208	20	10	10	NUM
ejpam-3405	208	21	.	.	PUNCT
ejpam-3405	209	1	since	since	SCONJ
ejpam-3405	209	2	degree	degree	NOUN
ejpam-3405	209	3	of	of	ADP
ejpam-3405	209	4	vertices	vertex	NOUN
ejpam-3405	209	5	vg	vg	ADV
ejpam-3405	209	6	and	and	CCONJ
ejpam-3405	209	7	vh	vh	PROPN
ejpam-3405	209	8	can	can	AUX
ejpam-3405	209	9	not	not	PART
ejpam-3405	209	10	be	be	AUX
ejpam-3405	209	11	2	2	NUM
ejpam-3405	209	12	together	together	ADV
ejpam-3405	209	13	so	so	SCONJ
ejpam-3405	209	14	there	there	PRON
ejpam-3405	209	15	are	be	VERB
ejpam-3405	209	16	the	the	DET
ejpam-3405	209	17	following	follow	VERB
ejpam-3405	209	18	two	two	NUM
ejpam-3405	209	19	cases	case	NOUN
ejpam-3405	209	20	to	to	PART
ejpam-3405	209	21	consider	consider	VERB
ejpam-3405	209	22	:	:	PUNCT
ejpam-3405	209	23	(	(	PUNCT
ejpam-3405	209	24	a	a	X
ejpam-3405	209	25	)	)	PUNCT
ejpam-3405	209	26	d∆(va	d∆(va	NOUN
ejpam-3405	209	27	)	)	PUNCT
ejpam-3405	209	28	=	=	PUNCT
ejpam-3405	209	29	d∆(vd	d∆(vd	ADJ
ejpam-3405	209	30	)	)	PUNCT
ejpam-3405	209	31	=	=	PUNCT
ejpam-3405	209	32	d∆(vg	d∆(vg	NOUN
ejpam-3405	209	33	)	)	PUNCT
ejpam-3405	209	34	=	=	SYM
ejpam-3405	209	35	2	2	NUM
ejpam-3405	209	36	;	;	PUNCT
ejpam-3405	209	37	m.	m.	NOUN
ejpam-3405	209	38	fazeel	fazeel	PROPN
ejpam-3405	209	39	anwar	anwar	PROPN
ejpam-3405	209	40	,	,	PUNCT
ejpam-3405	209	41	mairaj	mairaj	ADJ
ejpam-3405	209	42	bibi	bibi	NOUN
ejpam-3405	209	43	,	,	PUNCT
ejpam-3405	209	44	m.	m.	PROPN
ejpam-3405	209	45	saeed	saeed	PROPN
ejpam-3405	209	46	akram	akram	PROPN
ejpam-3405	209	47	/	/	PUNCT
ejpam-3405	209	48	eur	eur	PROPN
ejpam-3405	209	49	.	.	PUNCT
ejpam-3405	210	1	j.	j.	PROPN
ejpam-3405	210	2	pure	pure	PROPN
ejpam-3405	210	3	appl	appl	PROPN
ejpam-3405	210	4	.	.	PROPN
ejpam-3405	210	5	math	math	PROPN
ejpam-3405	210	6	,	,	PUNCT
ejpam-3405	210	7	12	12	NUM
ejpam-3405	210	8	(	(	PUNCT
ejpam-3405	210	9	2	2	NUM
ejpam-3405	210	10	)	)	PUNCT
ejpam-3405	210	11	(	(	PUNCT
ejpam-3405	210	12	2019	2019	NUM
ejpam-3405	210	13	)	)	PUNCT
ejpam-3405	210	14	,	,	PUNCT
ejpam-3405	210	15	590	590	NUM
ejpam-3405	210	16	-	-	SYM
ejpam-3405	210	17	604	604	NUM
ejpam-3405	210	18	599	599	NUM
ejpam-3405	210	19	(	(	PUNCT
ejpam-3405	210	20	b	b	NOUN
ejpam-3405	210	21	)	)	PUNCT
ejpam-3405	210	22	d∆(va	d∆(va	NOUN
ejpam-3405	210	23	)	)	PUNCT
ejpam-3405	210	24	=	=	PUNCT
ejpam-3405	210	25	d∆(vd	d∆(vd	ADJ
ejpam-3405	210	26	)	)	PUNCT
ejpam-3405	210	27	=	=	SYM
ejpam-3405	210	28	d∆(vh	d∆(vh	X
ejpam-3405	210	29	)	)	PUNCT
ejpam-3405	210	30	=	=	SYM
ejpam-3405	211	1	2	2	X
ejpam-3405	211	2	.	.	PUNCT
ejpam-3405	211	3	as	as	SCONJ
ejpam-3405	211	4	shown	show	VERB
ejpam-3405	211	5	in	in	ADP
ejpam-3405	211	6	figure	figure	NOUN
ejpam-3405	211	7	10	10	NUM
ejpam-3405	211	8	.	.	PUNCT
ejpam-3405	212	1	in	in	ADP
ejpam-3405	212	2	both	both	DET
ejpam-3405	212	3	of	of	ADP
ejpam-3405	212	4	these	these	DET
ejpam-3405	212	5	cases	case	NOUN
ejpam-3405	212	6	c(∆	c(∆	NOUN
ejpam-3405	212	7	)	)	PUNCT
ejpam-3405	212	8	≤	≤	NOUN
ejpam-3405	212	9	0	0	NUM
ejpam-3405	212	10	.	.	PUNCT
ejpam-3405	213	1	d	d	X
ejpam-3405	213	2	a	a	DET
ejpam-3405	213	3	b	b	NOUN
ejpam-3405	213	4	c	c	NOUN
ejpam-3405	213	5	d	d	X
ejpam-3405	213	6	ef	ef	PROPN
ejpam-3405	213	7	g	g	PROPN
ejpam-3405	213	8	h	h	NOUN
ejpam-3405	214	1	i	i	PRON
ejpam-3405	214	2	h	h	VERB
ejpam-3405	214	3	g	g	VERB
ejpam-3405	215	1	a	a	PRON
ejpam-3405	215	2	a	a	DET
ejpam-3405	215	3	b	b	NOUN
ejpam-3405	215	4	c	c	NOUN
ejpam-3405	215	5	d	d	X
ejpam-3405	215	6	ef	ef	PROPN
ejpam-3405	215	7	g	g	NOUN
ejpam-3405	215	8	h	h	NOUN
ejpam-3405	216	1	i	i	PRON
ejpam-3405	216	2	g	g	VERB
ejpam-3405	216	3	a	a	DET
ejpam-3405	216	4	a	a	DET
ejpam-3405	216	5	b	b	NOUN
ejpam-3405	216	6	c	c	NOUN
ejpam-3405	216	7	d	d	X
ejpam-3405	216	8	ef	ef	PROPN
ejpam-3405	217	1	g	g	PROPN
ejpam-3405	217	2	h	h	NOUN
ejpam-3405	218	1	i	i	PRON
ejpam-3405	218	2	h	h	VERB
ejpam-3405	219	1	h	h	NOUN
ejpam-3405	219	2	g	g	NOUN
ejpam-3405	219	3	d	d	PRON
ejpam-3405	219	4	figure	figure	NOUN
ejpam-3405	219	5	10	10	NUM
ejpam-3405	219	6	:	:	PUNCT
ejpam-3405	219	7	region	region	NOUN
ejpam-3405	219	8	∆	∆	PROPN
ejpam-3405	219	9	(	(	PUNCT
ejpam-3405	219	10	ix	ix	INTJ
ejpam-3405	219	11	)	)	PUNCT
ejpam-3405	219	12	in	in	ADP
ejpam-3405	219	13	this	this	DET
ejpam-3405	219	14	case	case	NOUN
ejpam-3405	219	15	∆	∆	PROPN
ejpam-3405	219	16	is	be	AUX
ejpam-3405	219	17	shown	show	VERB
ejpam-3405	219	18	in	in	ADP
ejpam-3405	219	19	figure	figure	NOUN
ejpam-3405	219	20	11	11	NUM
ejpam-3405	219	21	.	.	PUNCT
ejpam-3405	220	1	since	since	SCONJ
ejpam-3405	220	2	degree	degree	NOUN
ejpam-3405	220	3	of	of	ADP
ejpam-3405	220	4	vertices	vertex	NOUN
ejpam-3405	220	5	vg	vg	ADV
ejpam-3405	220	6	and	and	CCONJ
ejpam-3405	220	7	vh	vh	PROPN
ejpam-3405	220	8	can	can	AUX
ejpam-3405	220	9	not	not	PART
ejpam-3405	220	10	be	be	AUX
ejpam-3405	220	11	2	2	NUM
ejpam-3405	220	12	together	together	ADV
ejpam-3405	220	13	so	so	SCONJ
ejpam-3405	220	14	there	there	PRON
ejpam-3405	220	15	are	be	VERB
ejpam-3405	220	16	the	the	DET
ejpam-3405	220	17	following	follow	VERB
ejpam-3405	220	18	two	two	NUM
ejpam-3405	220	19	cases	case	NOUN
ejpam-3405	220	20	to	to	PART
ejpam-3405	220	21	consider	consider	VERB
ejpam-3405	220	22	:	:	PUNCT
ejpam-3405	220	23	(	(	PUNCT
ejpam-3405	220	24	a	a	X
ejpam-3405	220	25	)	)	PUNCT
ejpam-3405	220	26	d∆(va	d∆(va	NOUN
ejpam-3405	220	27	)	)	PUNCT
ejpam-3405	220	28	=	=	SYM
ejpam-3405	220	29	d∆(ve	d∆(ve	NOUN
ejpam-3405	220	30	)	)	PUNCT
ejpam-3405	221	1	=	=	SYM
ejpam-3405	221	2	d∆(vg	d∆(vg	NOUN
ejpam-3405	221	3	)	)	PUNCT
ejpam-3405	221	4	=	=	SYM
ejpam-3405	221	5	2	2	NUM
ejpam-3405	221	6	;	;	PUNCT
ejpam-3405	221	7	(	(	PUNCT
ejpam-3405	221	8	b	b	X
ejpam-3405	221	9	)	)	PUNCT
ejpam-3405	221	10	d∆(va	d∆(va	NOUN
ejpam-3405	221	11	)	)	PUNCT
ejpam-3405	221	12	=	=	SYM
ejpam-3405	221	13	d∆(ve	d∆(ve	NOUN
ejpam-3405	221	14	)	)	PUNCT
ejpam-3405	221	15	=	=	SYM
ejpam-3405	221	16	d∆(vh	d∆(vh	X
ejpam-3405	221	17	)	)	PUNCT
ejpam-3405	221	18	=	=	SYM
ejpam-3405	222	1	2	2	X
ejpam-3405	222	2	.	.	PUNCT
ejpam-3405	222	3	as	as	SCONJ
ejpam-3405	222	4	shown	show	VERB
ejpam-3405	222	5	in	in	ADP
ejpam-3405	222	6	figure	figure	NOUN
ejpam-3405	222	7	11	11	NUM
ejpam-3405	222	8	.	.	PUNCT
ejpam-3405	223	1	in	in	ADP
ejpam-3405	223	2	both	both	DET
ejpam-3405	223	3	of	of	ADP
ejpam-3405	223	4	these	these	DET
ejpam-3405	223	5	cases	case	NOUN
ejpam-3405	223	6	c(∆	c(∆	NOUN
ejpam-3405	223	7	)	)	PUNCT
ejpam-3405	223	8	≤	≤	NOUN
ejpam-3405	223	9	0	0	NUM
ejpam-3405	223	10	.	.	PUNCT
ejpam-3405	224	1	e	e	X
ejpam-3405	224	2	a	a	DET
ejpam-3405	224	3	b	b	X
ejpam-3405	224	4	c	c	NOUN
ejpam-3405	224	5	d	d	X
ejpam-3405	224	6	ef	ef	PROPN
ejpam-3405	224	7	g	g	PROPN
ejpam-3405	224	8	h	h	NOUN
ejpam-3405	225	1	i	i	PRON
ejpam-3405	225	2	h	h	VERB
ejpam-3405	225	3	g	g	VERB
ejpam-3405	226	1	a	a	PRON
ejpam-3405	226	2	a	a	DET
ejpam-3405	226	3	b	b	NOUN
ejpam-3405	226	4	c	c	NOUN
ejpam-3405	226	5	d	d	X
ejpam-3405	226	6	ef	ef	PROPN
ejpam-3405	226	7	g	g	NOUN
ejpam-3405	226	8	h	h	NOUN
ejpam-3405	227	1	i	i	PRON
ejpam-3405	227	2	g	g	VERB
ejpam-3405	227	3	a	a	DET
ejpam-3405	227	4	a	a	DET
ejpam-3405	227	5	b	b	NOUN
ejpam-3405	227	6	c	c	NOUN
ejpam-3405	227	7	d	d	X
ejpam-3405	227	8	ef	ef	PROPN
ejpam-3405	228	1	g	g	PROPN
ejpam-3405	228	2	h	h	NOUN
ejpam-3405	229	1	i	i	PRON
ejpam-3405	229	2	h	h	VERB
ejpam-3405	230	1	h	h	NOUN
ejpam-3405	230	2	g	g	PROPN
ejpam-3405	230	3	e	e	NOUN
ejpam-3405	230	4	figure	figure	NOUN
ejpam-3405	230	5	11	11	NUM
ejpam-3405	230	6	:	:	PUNCT
ejpam-3405	230	7	region	region	NOUN
ejpam-3405	230	8	∆	∆	PROPN
ejpam-3405	230	9	(	(	PUNCT
ejpam-3405	230	10	x	x	X
ejpam-3405	230	11	)	)	PUNCT
ejpam-3405	230	12	in	in	ADP
ejpam-3405	230	13	this	this	DET
ejpam-3405	230	14	case	case	NOUN
ejpam-3405	230	15	∆	∆	PROPN
ejpam-3405	230	16	is	be	AUX
ejpam-3405	230	17	shown	show	VERB
ejpam-3405	230	18	in	in	ADP
ejpam-3405	230	19	figure	figure	NOUN
ejpam-3405	230	20	12	12	NUM
ejpam-3405	230	21	.	.	PUNCT
ejpam-3405	231	1	since	since	SCONJ
ejpam-3405	231	2	d∆(vb	d∆(vb	PROPN
ejpam-3405	231	3	)	)	PUNCT
ejpam-3405	231	4	=	=	SYM
ejpam-3405	231	5	d∆(vc	d∆(vc	NOUN
ejpam-3405	231	6	)	)	PUNCT
ejpam-3405	232	1	=	=	SYM
ejpam-3405	232	2	2	2	NUM
ejpam-3405	232	3	or	or	CCONJ
ejpam-3405	232	4	d∆(vc	d∆(vc	VERB
ejpam-3405	232	5	)	)	PUNCT
ejpam-3405	233	1	=	=	PUNCT
ejpam-3405	233	2	d∆(vd	d∆(vd	ADJ
ejpam-3405	233	3	)	)	PUNCT
ejpam-3405	233	4	=	=	SYM
ejpam-3405	233	5	2	2	NUM
ejpam-3405	233	6	can	can	AUX
ejpam-3405	233	7	not	not	PART
ejpam-3405	233	8	occur	occur	VERB
ejpam-3405	233	9	therefore	therefore	ADV
ejpam-3405	233	10	it	it	PRON
ejpam-3405	233	11	can	can	AUX
ejpam-3405	233	12	be	be	AUX
ejpam-3405	233	13	assumed	assume	VERB
ejpam-3405	233	14	that	that	SCONJ
ejpam-3405	233	15	d∆(vb	d∆(vb	NOUN
ejpam-3405	233	16	)	)	PUNCT
ejpam-3405	234	1	=	=	PUNCT
ejpam-3405	234	2	d∆(vd	d∆(vd	ADJ
ejpam-3405	234	3	)	)	PUNCT
ejpam-3405	234	4	=	=	SYM
ejpam-3405	234	5	d∆(vh	d∆(vh	X
ejpam-3405	234	6	)	)	PUNCT
ejpam-3405	234	7	=	=	SYM
ejpam-3405	234	8	2	2	NUM
ejpam-3405	234	9	as	as	SCONJ
ejpam-3405	234	10	shown	show	VERB
ejpam-3405	234	11	in	in	ADP
ejpam-3405	234	12	figure	figure	NOUN
ejpam-3405	234	13	12	12	NUM
ejpam-3405	234	14	.	.	PUNCT
ejpam-3405	235	1	in	in	ADP
ejpam-3405	235	2	this	this	DET
ejpam-3405	235	3	case	case	NOUN
ejpam-3405	235	4	c(∆	c(∆	PROPN
ejpam-3405	235	5	)	)	PUNCT
ejpam-3405	235	6	≤	≤	NOUN
ejpam-3405	235	7	0	0	NUM
ejpam-3405	235	8	.	.	PUNCT
ejpam-3405	235	9	m.	m.	PROPN
ejpam-3405	235	10	fazeel	fazeel	PROPN
ejpam-3405	235	11	anwar	anwar	PROPN
ejpam-3405	235	12	,	,	PUNCT
ejpam-3405	235	13	mairaj	mairaj	ADJ
ejpam-3405	235	14	bibi	bibi	NOUN
ejpam-3405	235	15	,	,	PUNCT
ejpam-3405	235	16	m.	m.	PROPN
ejpam-3405	235	17	saeed	saeed	PROPN
ejpam-3405	235	18	akram	akram	PROPN
ejpam-3405	235	19	/	/	PUNCT
ejpam-3405	235	20	eur	eur	PROPN
ejpam-3405	235	21	.	.	PUNCT
ejpam-3405	236	1	j.	j.	PROPN
ejpam-3405	236	2	pure	pure	PROPN
ejpam-3405	236	3	appl	appl	PROPN
ejpam-3405	236	4	.	.	PROPN
ejpam-3405	236	5	math	math	PROPN
ejpam-3405	236	6	,	,	PUNCT
ejpam-3405	236	7	12	12	NUM
ejpam-3405	236	8	(	(	PUNCT
ejpam-3405	236	9	2	2	NUM
ejpam-3405	236	10	)	)	PUNCT
ejpam-3405	236	11	(	(	PUNCT
ejpam-3405	236	12	2019	2019	NUM
ejpam-3405	236	13	)	)	PUNCT
ejpam-3405	236	14	,	,	PUNCT
ejpam-3405	236	15	590	590	NUM
ejpam-3405	236	16	-	-	SYM
ejpam-3405	236	17	604	604	NUM
ejpam-3405	236	18	600	600	NUM
ejpam-3405	236	19	a	a	DET
ejpam-3405	236	20	b	b	NOUN
ejpam-3405	236	21	c	c	NOUN
ejpam-3405	236	22	d	d	X
ejpam-3405	236	23	ef	ef	PROPN
ejpam-3405	236	24	g	g	NOUN
ejpam-3405	236	25	h	h	NOUN
ejpam-3405	237	1	i	i	NOUN
ejpam-3405	237	2	c	c	NOUN
ejpam-3405	237	3	h	h	NOUN
ejpam-3405	238	1	d	d	NOUN
ejpam-3405	238	2	b	b	PROPN
ejpam-3405	238	3	a	a	DET
ejpam-3405	238	4	b	b	NOUN
ejpam-3405	238	5	c	c	NOUN
ejpam-3405	238	6	d	d	X
ejpam-3405	238	7	ef	ef	PROPN
ejpam-3405	238	8	g	g	NOUN
ejpam-3405	238	9	h	h	NOUN
ejpam-3405	239	1	i	i	NOUN
ejpam-3405	239	2	c	c	NOUN
ejpam-3405	239	3	h	h	NOUN
ejpam-3405	240	1	d	d	NOUN
ejpam-3405	240	2	figure	figure	NOUN
ejpam-3405	240	3	12	12	NUM
ejpam-3405	240	4	:	:	PUNCT
ejpam-3405	240	5	region	region	NOUN
ejpam-3405	240	6	∆	∆	PROPN
ejpam-3405	240	7	(	(	PUNCT
ejpam-3405	240	8	xi	xi	NOUN
ejpam-3405	240	9	)	)	PUNCT
ejpam-3405	240	10	in	in	ADP
ejpam-3405	240	11	this	this	DET
ejpam-3405	240	12	case	case	NOUN
ejpam-3405	240	13	∆	∆	PROPN
ejpam-3405	240	14	is	be	AUX
ejpam-3405	240	15	shown	show	VERB
ejpam-3405	240	16	in	in	ADP
ejpam-3405	240	17	figure	figure	NOUN
ejpam-3405	240	18	13	13	NUM
ejpam-3405	240	19	.	.	PUNCT
ejpam-3405	241	1	since	since	SCONJ
ejpam-3405	241	2	degree	degree	NOUN
ejpam-3405	241	3	of	of	ADP
ejpam-3405	241	4	vertices	vertex	NOUN
ejpam-3405	241	5	vb	vb	NOUN
ejpam-3405	241	6	and	and	CCONJ
ejpam-3405	241	7	vc	vc	PROPN
ejpam-3405	241	8	can	can	AUX
ejpam-3405	241	9	not	not	PART
ejpam-3405	241	10	be	be	AUX
ejpam-3405	241	11	2	2	NUM
ejpam-3405	241	12	together	together	ADV
ejpam-3405	241	13	so	so	SCONJ
ejpam-3405	241	14	there	there	PRON
ejpam-3405	241	15	are	be	VERB
ejpam-3405	241	16	the	the	DET
ejpam-3405	241	17	following	follow	VERB
ejpam-3405	241	18	two	two	NUM
ejpam-3405	241	19	cases	case	NOUN
ejpam-3405	241	20	to	to	PART
ejpam-3405	241	21	consider	consider	VERB
ejpam-3405	241	22	:	:	PUNCT
ejpam-3405	241	23	(	(	PUNCT
ejpam-3405	241	24	a	a	X
ejpam-3405	241	25	)	)	PUNCT
ejpam-3405	241	26	d∆(vb	d∆(vb	NOUN
ejpam-3405	241	27	)	)	PUNCT
ejpam-3405	241	28	=	=	SYM
ejpam-3405	241	29	d∆(ve	d∆(ve	NOUN
ejpam-3405	241	30	)	)	PUNCT
ejpam-3405	241	31	=	=	SYM
ejpam-3405	241	32	d∆(vh	d∆(vh	X
ejpam-3405	241	33	)	)	PUNCT
ejpam-3405	241	34	=	=	SYM
ejpam-3405	241	35	2	2	NUM
ejpam-3405	241	36	;	;	PUNCT
ejpam-3405	241	37	(	(	PUNCT
ejpam-3405	241	38	b	b	X
ejpam-3405	241	39	)	)	PUNCT
ejpam-3405	241	40	d∆(vc	d∆(vc	NOUN
ejpam-3405	241	41	)	)	PUNCT
ejpam-3405	241	42	=	=	SYM
ejpam-3405	241	43	d∆(ve	d∆(ve	NOUN
ejpam-3405	241	44	)	)	PUNCT
ejpam-3405	241	45	=	=	SYM
ejpam-3405	241	46	d∆(vh	d∆(vh	X
ejpam-3405	241	47	)	)	PUNCT
ejpam-3405	241	48	=	=	SYM
ejpam-3405	242	1	2	2	X
ejpam-3405	242	2	.	.	PUNCT
ejpam-3405	242	3	as	as	SCONJ
ejpam-3405	242	4	shown	show	VERB
ejpam-3405	242	5	in	in	ADP
ejpam-3405	242	6	figure	figure	NOUN
ejpam-3405	242	7	13	13	NUM
ejpam-3405	242	8	.	.	PUNCT
ejpam-3405	243	1	in	in	ADP
ejpam-3405	243	2	both	both	DET
ejpam-3405	243	3	of	of	ADP
ejpam-3405	243	4	these	these	DET
ejpam-3405	243	5	cases	case	NOUN
ejpam-3405	243	6	c(∆	c(∆	NOUN
ejpam-3405	243	7	)	)	PUNCT
ejpam-3405	243	8	≤	≤	NOUN
ejpam-3405	243	9	0	0	NUM
ejpam-3405	243	10	.	.	PUNCT
ejpam-3405	244	1	e	e	X
ejpam-3405	244	2	a	a	DET
ejpam-3405	244	3	b	b	X
ejpam-3405	244	4	c	c	NOUN
ejpam-3405	244	5	d	d	X
ejpam-3405	244	6	ef	ef	PROPN
ejpam-3405	244	7	g	g	PROPN
ejpam-3405	244	8	h	h	NOUN
ejpam-3405	245	1	i	i	PRON
ejpam-3405	245	2	h	h	VERB
ejpam-3405	246	1	c	c	NOUN
ejpam-3405	246	2	b	b	PROPN
ejpam-3405	246	3	a	a	DET
ejpam-3405	246	4	b	b	NOUN
ejpam-3405	246	5	c	c	NOUN
ejpam-3405	246	6	d	d	X
ejpam-3405	246	7	ef	ef	PROPN
ejpam-3405	246	8	g	g	PROPN
ejpam-3405	246	9	h	h	NOUN
ejpam-3405	247	1	i	i	PRON
ejpam-3405	247	2	a	a	DET
ejpam-3405	247	3	b	b	X
ejpam-3405	247	4	c	c	NOUN
ejpam-3405	247	5	d	d	X
ejpam-3405	247	6	ef	ef	PROPN
ejpam-3405	248	1	g	g	PROPN
ejpam-3405	248	2	h	h	NOUN
ejpam-3405	249	1	i	i	PRON
ejpam-3405	249	2	h	h	VERB
ejpam-3405	249	3	h	h	NOUN
ejpam-3405	249	4	e	e	NOUN
ejpam-3405	249	5	e	e	PROPN
ejpam-3405	249	6	c	c	PROPN
ejpam-3405	249	7	b	b	PROPN
ejpam-3405	249	8	figure	figure	NOUN
ejpam-3405	249	9	13	13	NUM
ejpam-3405	249	10	:	:	PUNCT
ejpam-3405	249	11	region	region	NOUN
ejpam-3405	249	12	∆	∆	PROPN
ejpam-3405	249	13	(	(	PUNCT
ejpam-3405	249	14	xii	xii	NOUN
ejpam-3405	249	15	)	)	PUNCT
ejpam-3405	249	16	in	in	ADP
ejpam-3405	249	17	this	this	DET
ejpam-3405	249	18	case	case	NOUN
ejpam-3405	249	19	∆	∆	PROPN
ejpam-3405	249	20	is	be	AUX
ejpam-3405	249	21	shown	show	VERB
ejpam-3405	249	22	in	in	ADP
ejpam-3405	249	23	figure	figure	NOUN
ejpam-3405	249	24	14	14	NUM
ejpam-3405	249	25	.	.	PUNCT
ejpam-3405	250	1	since	since	SCONJ
ejpam-3405	250	2	d∆(vb	d∆(vb	PROPN
ejpam-3405	250	3	)	)	PUNCT
ejpam-3405	250	4	=	=	SYM
ejpam-3405	250	5	d∆(vc	d∆(vc	NOUN
ejpam-3405	250	6	)	)	PUNCT
ejpam-3405	251	1	=	=	SYM
ejpam-3405	251	2	2	2	NUM
ejpam-3405	251	3	or	or	CCONJ
ejpam-3405	251	4	d∆(vc	d∆(vc	VERB
ejpam-3405	251	5	)	)	PUNCT
ejpam-3405	252	1	=	=	PUNCT
ejpam-3405	252	2	d∆(vd	d∆(vd	ADJ
ejpam-3405	252	3	)	)	PUNCT
ejpam-3405	252	4	=	=	SYM
ejpam-3405	252	5	2	2	NUM
ejpam-3405	252	6	or	or	CCONJ
ejpam-3405	252	7	d∆(vd	d∆(vd	ADJ
ejpam-3405	252	8	)	)	PUNCT
ejpam-3405	252	9	=	=	SYM
ejpam-3405	252	10	d∆(ve	d∆(ve	NOUN
ejpam-3405	252	11	)	)	PUNCT
ejpam-3405	252	12	=	=	SYM
ejpam-3405	252	13	2	2	NUM
ejpam-3405	252	14	can	can	AUX
ejpam-3405	252	15	not	not	PART
ejpam-3405	252	16	occur	occur	VERB
ejpam-3405	252	17	therefore	therefore	ADV
ejpam-3405	252	18	c(∆	c(∆	PROPN
ejpam-3405	252	19	)	)	PUNCT
ejpam-3405	252	20	≤	≤	NOUN
ejpam-3405	252	21	0	0	NUM
ejpam-3405	252	22	.	.	PUNCT
ejpam-3405	252	23	m.	m.	PROPN
ejpam-3405	252	24	fazeel	fazeel	PROPN
ejpam-3405	252	25	anwar	anwar	PROPN
ejpam-3405	252	26	,	,	PUNCT
ejpam-3405	252	27	mairaj	mairaj	ADJ
ejpam-3405	252	28	bibi	bibi	NOUN
ejpam-3405	252	29	,	,	PUNCT
ejpam-3405	252	30	m.	m.	PROPN
ejpam-3405	252	31	saeed	saeed	PROPN
ejpam-3405	252	32	akram	akram	PROPN
ejpam-3405	252	33	/	/	PUNCT
ejpam-3405	252	34	eur	eur	PROPN
ejpam-3405	252	35	.	.	PUNCT
ejpam-3405	253	1	j.	j.	PROPN
ejpam-3405	253	2	pure	pure	PROPN
ejpam-3405	253	3	appl	appl	PROPN
ejpam-3405	253	4	.	.	PROPN
ejpam-3405	253	5	math	math	PROPN
ejpam-3405	253	6	,	,	PUNCT
ejpam-3405	253	7	12	12	NUM
ejpam-3405	253	8	(	(	PUNCT
ejpam-3405	253	9	2	2	NUM
ejpam-3405	253	10	)	)	PUNCT
ejpam-3405	253	11	(	(	PUNCT
ejpam-3405	253	12	2019	2019	NUM
ejpam-3405	253	13	)	)	PUNCT
ejpam-3405	253	14	,	,	PUNCT
ejpam-3405	253	15	590	590	NUM
ejpam-3405	253	16	-	-	SYM
ejpam-3405	253	17	604	604	NUM
ejpam-3405	253	18	601	601	NUM
ejpam-3405	253	19	a	a	DET
ejpam-3405	253	20	b	b	NOUN
ejpam-3405	253	21	c	c	NOUN
ejpam-3405	253	22	d	d	X
ejpam-3405	253	23	ef	ef	PROPN
ejpam-3405	254	1	g	g	NOUN
ejpam-3405	254	2	h	h	NOUN
ejpam-3405	255	1	i	i	NOUN
ejpam-3405	255	2	c	c	NOUN
ejpam-3405	255	3	h	h	NOUN
ejpam-3405	256	1	d	d	NOUN
ejpam-3405	256	2	b	b	X
ejpam-3405	256	3	figure	figure	NOUN
ejpam-3405	256	4	14	14	NUM
ejpam-3405	256	5	:	:	PUNCT
ejpam-3405	256	6	region	region	NOUN
ejpam-3405	256	7	∆	∆	PROPN
ejpam-3405	256	8	(	(	PUNCT
ejpam-3405	256	9	xiii	xiii	PROPN
ejpam-3405	256	10	)	)	PUNCT
ejpam-3405	256	11	in	in	ADP
ejpam-3405	256	12	this	this	DET
ejpam-3405	256	13	case	case	NOUN
ejpam-3405	256	14	∆	∆	PROPN
ejpam-3405	256	15	is	be	AUX
ejpam-3405	256	16	shown	show	VERB
ejpam-3405	256	17	in	in	ADP
ejpam-3405	256	18	figure	figure	NOUN
ejpam-3405	256	19	15	15	NUM
ejpam-3405	256	20	.	.	PUNCT
ejpam-3405	257	1	since	since	SCONJ
ejpam-3405	257	2	d∆(vb	d∆(vb	PROPN
ejpam-3405	257	3	)	)	PUNCT
ejpam-3405	257	4	=	=	SYM
ejpam-3405	257	5	d∆(vc	d∆(vc	NOUN
ejpam-3405	257	6	)	)	PUNCT
ejpam-3405	258	1	=	=	SYM
ejpam-3405	258	2	2	2	NUM
ejpam-3405	258	3	or	or	CCONJ
ejpam-3405	258	4	d∆(vc	d∆(vc	VERB
ejpam-3405	258	5	)	)	PUNCT
ejpam-3405	259	1	=	=	PUNCT
ejpam-3405	259	2	d∆(vd	d∆(vd	ADJ
ejpam-3405	259	3	)	)	PUNCT
ejpam-3405	259	4	=	=	SYM
ejpam-3405	259	5	2	2	NUM
ejpam-3405	259	6	can	can	AUX
ejpam-3405	259	7	not	not	PART
ejpam-3405	259	8	occur	occur	VERB
ejpam-3405	259	9	therefore	therefore	ADV
ejpam-3405	259	10	it	it	PRON
ejpam-3405	259	11	can	can	AUX
ejpam-3405	259	12	be	be	AUX
ejpam-3405	259	13	assumed	assume	VERB
ejpam-3405	259	14	that	that	SCONJ
ejpam-3405	259	15	d∆(vb	d∆(vb	NOUN
ejpam-3405	259	16	)	)	PUNCT
ejpam-3405	260	1	=	=	PUNCT
ejpam-3405	260	2	d∆(vd	d∆(vd	ADJ
ejpam-3405	260	3	)	)	PUNCT
ejpam-3405	260	4	=	=	SYM
ejpam-3405	260	5	d∆(vh	d∆(vh	X
ejpam-3405	260	6	)	)	PUNCT
ejpam-3405	260	7	=	=	SYM
ejpam-3405	260	8	2	2	NUM
ejpam-3405	260	9	as	as	SCONJ
ejpam-3405	260	10	shown	show	VERB
ejpam-3405	260	11	in	in	ADP
ejpam-3405	260	12	figure	figure	NOUN
ejpam-3405	260	13	15	15	NUM
ejpam-3405	260	14	.	.	PUNCT
ejpam-3405	261	1	in	in	ADP
ejpam-3405	261	2	this	this	DET
ejpam-3405	261	3	case	case	NOUN
ejpam-3405	261	4	c(∆	c(∆	PROPN
ejpam-3405	261	5	)	)	PUNCT
ejpam-3405	261	6	≤	≤	NOUN
ejpam-3405	261	7	0	0	NUM
ejpam-3405	261	8	.	.	PUNCT
ejpam-3405	262	1	a	a	DET
ejpam-3405	262	2	b	b	NOUN
ejpam-3405	262	3	c	c	NOUN
ejpam-3405	262	4	d	d	X
ejpam-3405	262	5	ef	ef	PROPN
ejpam-3405	262	6	g	g	NOUN
ejpam-3405	262	7	h	h	NOUN
ejpam-3405	263	1	i	i	NOUN
ejpam-3405	264	1	d	d	PROPN
ejpam-3405	264	2	b	b	X
ejpam-3405	264	3	c	c	NOUN
ejpam-3405	264	4	h	h	NOUN
ejpam-3405	265	1	a	a	DET
ejpam-3405	265	2	b	b	NOUN
ejpam-3405	265	3	c	c	NOUN
ejpam-3405	265	4	d	d	X
ejpam-3405	265	5	ef	ef	PROPN
ejpam-3405	265	6	g	g	NOUN
ejpam-3405	265	7	h	h	NOUN
ejpam-3405	266	1	i	i	NOUN
ejpam-3405	266	2	d	d	PROPN
ejpam-3405	266	3	b	b	X
ejpam-3405	266	4	c	c	X
ejpam-3405	266	5	figure	figure	NOUN
ejpam-3405	266	6	15	15	NUM
ejpam-3405	266	7	:	:	PUNCT
ejpam-3405	266	8	region	region	NOUN
ejpam-3405	266	9	∆	∆	PROPN
ejpam-3405	266	10	(	(	PUNCT
ejpam-3405	266	11	xiv	xiv	PROPN
ejpam-3405	266	12	)	)	PUNCT
ejpam-3405	266	13	in	in	ADP
ejpam-3405	266	14	this	this	DET
ejpam-3405	266	15	case	case	NOUN
ejpam-3405	266	16	∆	∆	PROPN
ejpam-3405	266	17	is	be	AUX
ejpam-3405	266	18	shown	show	VERB
ejpam-3405	266	19	in	in	ADP
ejpam-3405	266	20	figure	figure	NOUN
ejpam-3405	266	21	16	16	NUM
ejpam-3405	266	22	.	.	PUNCT
ejpam-3405	267	1	since	since	SCONJ
ejpam-3405	267	2	degree	degree	NOUN
ejpam-3405	267	3	of	of	ADP
ejpam-3405	267	4	vertices	vertex	NOUN
ejpam-3405	267	5	vd	vd	NOUN
ejpam-3405	267	6	and	and	CCONJ
ejpam-3405	267	7	ve	ve	AUX
ejpam-3405	267	8	can	can	AUX
ejpam-3405	267	9	not	not	PART
ejpam-3405	267	10	be	be	AUX
ejpam-3405	267	11	2	2	NUM
ejpam-3405	267	12	together	together	ADV
ejpam-3405	267	13	so	so	SCONJ
ejpam-3405	267	14	there	there	PRON
ejpam-3405	267	15	are	be	VERB
ejpam-3405	267	16	the	the	DET
ejpam-3405	267	17	following	follow	VERB
ejpam-3405	267	18	two	two	NUM
ejpam-3405	267	19	cases	case	NOUN
ejpam-3405	267	20	to	to	PART
ejpam-3405	267	21	consider	consider	VERB
ejpam-3405	267	22	:	:	PUNCT
ejpam-3405	267	23	(	(	PUNCT
ejpam-3405	267	24	a	a	X
ejpam-3405	267	25	)	)	PUNCT
ejpam-3405	267	26	d∆(vb	d∆(vb	NOUN
ejpam-3405	267	27	)	)	PUNCT
ejpam-3405	268	1	=	=	PUNCT
ejpam-3405	268	2	d∆(vd	d∆(vd	ADJ
ejpam-3405	268	3	)	)	PUNCT
ejpam-3405	268	4	=	=	SYM
ejpam-3405	268	5	d∆(vh	d∆(vh	X
ejpam-3405	268	6	)	)	PUNCT
ejpam-3405	268	7	=	=	SYM
ejpam-3405	268	8	2	2	NUM
ejpam-3405	268	9	;	;	PUNCT
ejpam-3405	268	10	(	(	PUNCT
ejpam-3405	268	11	b	b	X
ejpam-3405	268	12	)	)	PUNCT
ejpam-3405	268	13	d∆(vb	d∆(vb	NOUN
ejpam-3405	268	14	)	)	PUNCT
ejpam-3405	268	15	=	=	SYM
ejpam-3405	268	16	d∆(ve	d∆(ve	NOUN
ejpam-3405	268	17	)	)	PUNCT
ejpam-3405	268	18	=	=	SYM
ejpam-3405	268	19	d∆(vh	d∆(vh	X
ejpam-3405	268	20	)	)	PUNCT
ejpam-3405	268	21	=	=	SYM
ejpam-3405	269	1	2	2	X
ejpam-3405	269	2	.	.	PUNCT
ejpam-3405	269	3	as	as	SCONJ
ejpam-3405	269	4	shown	show	VERB
ejpam-3405	269	5	in	in	ADP
ejpam-3405	269	6	figure	figure	NOUN
ejpam-3405	269	7	16	16	NUM
ejpam-3405	269	8	.	.	PUNCT
ejpam-3405	270	1	in	in	ADP
ejpam-3405	270	2	both	both	PRON
ejpam-3405	270	3	of	of	ADP
ejpam-3405	270	4	these	these	DET
ejpam-3405	270	5	cases	case	NOUN
ejpam-3405	270	6	c(∆	c(∆	NOUN
ejpam-3405	270	7	)	)	PUNCT
ejpam-3405	270	8	≤	≤	NOUN
ejpam-3405	270	9	0	0	NUM
ejpam-3405	270	10	.	.	PUNCT
ejpam-3405	270	11	m.	m.	PROPN
ejpam-3405	270	12	fazeel	fazeel	PROPN
ejpam-3405	270	13	anwar	anwar	PROPN
ejpam-3405	270	14	,	,	PUNCT
ejpam-3405	270	15	mairaj	mairaj	ADJ
ejpam-3405	270	16	bibi	bibi	NOUN
ejpam-3405	270	17	,	,	PUNCT
ejpam-3405	270	18	m.	m.	PROPN
ejpam-3405	270	19	saeed	saeed	PROPN
ejpam-3405	270	20	akram	akram	PROPN
ejpam-3405	270	21	/	/	PUNCT
ejpam-3405	270	22	eur	eur	PROPN
ejpam-3405	270	23	.	.	PUNCT
ejpam-3405	271	1	j.	j.	PROPN
ejpam-3405	271	2	pure	pure	PROPN
ejpam-3405	271	3	appl	appl	PROPN
ejpam-3405	271	4	.	.	PROPN
ejpam-3405	271	5	math	math	PROPN
ejpam-3405	271	6	,	,	PUNCT
ejpam-3405	271	7	12	12	NUM
ejpam-3405	271	8	(	(	PUNCT
ejpam-3405	271	9	2	2	NUM
ejpam-3405	271	10	)	)	PUNCT
ejpam-3405	271	11	(	(	PUNCT
ejpam-3405	271	12	2019	2019	NUM
ejpam-3405	271	13	)	)	PUNCT
ejpam-3405	271	14	,	,	PUNCT
ejpam-3405	271	15	590	590	NUM
ejpam-3405	271	16	-	-	SYM
ejpam-3405	271	17	604	604	NUM
ejpam-3405	271	18	602	602	NUM
ejpam-3405	271	19	e	e	NOUN
ejpam-3405	271	20	a	a	DET
ejpam-3405	271	21	b	b	NOUN
ejpam-3405	271	22	c	c	NOUN
ejpam-3405	271	23	d	d	X
ejpam-3405	271	24	ef	ef	PROPN
ejpam-3405	271	25	g	g	PROPN
ejpam-3405	271	26	h	h	NOUN
ejpam-3405	272	1	i	i	PRON
ejpam-3405	272	2	h	h	VERB
ejpam-3405	273	1	d	d	NOUN
ejpam-3405	273	2	b	b	PROPN
ejpam-3405	273	3	a	a	DET
ejpam-3405	273	4	b	b	NOUN
ejpam-3405	273	5	c	c	NOUN
ejpam-3405	273	6	d	d	X
ejpam-3405	273	7	ef	ef	PROPN
ejpam-3405	273	8	g	g	PROPN
ejpam-3405	273	9	h	h	NOUN
ejpam-3405	274	1	i	i	PRON
ejpam-3405	274	2	a	a	DET
ejpam-3405	274	3	b	b	X
ejpam-3405	274	4	c	c	NOUN
ejpam-3405	274	5	d	d	X
ejpam-3405	274	6	ef	ef	PROPN
ejpam-3405	275	1	g	g	NOUN
ejpam-3405	275	2	h	h	NOUN
ejpam-3405	276	1	i	i	NOUN
ejpam-3405	276	2	b	b	NOUN
ejpam-3405	276	3	h	h	NOUN
ejpam-3405	276	4	e	e	NOUN
ejpam-3405	276	5	e	e	X
ejpam-3405	276	6	d	d	X
ejpam-3405	276	7	d	d	X
ejpam-3405	276	8	figure	figure	NOUN
ejpam-3405	276	9	16	16	NUM
ejpam-3405	276	10	:	:	PUNCT
ejpam-3405	276	11	region	region	NOUN
ejpam-3405	276	12	∆	∆	PROPN
ejpam-3405	276	13	(	(	PUNCT
ejpam-3405	276	14	xv	xv	PROPN
ejpam-3405	276	15	)	)	PUNCT
ejpam-3405	276	16	in	in	ADP
ejpam-3405	276	17	this	this	DET
ejpam-3405	276	18	case	case	NOUN
ejpam-3405	276	19	∆	∆	PROPN
ejpam-3405	276	20	is	be	AUX
ejpam-3405	276	21	shown	show	VERB
ejpam-3405	276	22	in	in	ADP
ejpam-3405	276	23	figure	figure	NOUN
ejpam-3405	276	24	17	17	NUM
ejpam-3405	276	25	.	.	PUNCT
ejpam-3405	277	1	since	since	SCONJ
ejpam-3405	277	2	degree	degree	NOUN
ejpam-3405	277	3	of	of	ADP
ejpam-3405	277	4	vertices	vertex	NOUN
ejpam-3405	277	5	vb	vb	NOUN
ejpam-3405	277	6	and	and	CCONJ
ejpam-3405	277	7	vc	vc	PROPN
ejpam-3405	277	8	can	can	AUX
ejpam-3405	277	9	not	not	PART
ejpam-3405	277	10	be	be	AUX
ejpam-3405	277	11	2	2	NUM
ejpam-3405	277	12	together	together	ADV
ejpam-3405	277	13	so	so	SCONJ
ejpam-3405	277	14	there	there	PRON
ejpam-3405	277	15	are	be	VERB
ejpam-3405	277	16	the	the	DET
ejpam-3405	277	17	following	follow	VERB
ejpam-3405	277	18	two	two	NUM
ejpam-3405	277	19	cases	case	NOUN
ejpam-3405	277	20	to	to	PART
ejpam-3405	277	21	consider	consider	VERB
ejpam-3405	277	22	:	:	PUNCT
ejpam-3405	277	23	(	(	PUNCT
ejpam-3405	277	24	a	a	X
ejpam-3405	277	25	)	)	PUNCT
ejpam-3405	277	26	d∆(vb	d∆(vb	NOUN
ejpam-3405	277	27	)	)	PUNCT
ejpam-3405	277	28	=	=	SYM
ejpam-3405	277	29	d∆(ve	d∆(ve	NOUN
ejpam-3405	277	30	)	)	PUNCT
ejpam-3405	278	1	=	=	SYM
ejpam-3405	278	2	d∆(vh	d∆(vh	X
ejpam-3405	278	3	)	)	PUNCT
ejpam-3405	278	4	=	=	SYM
ejpam-3405	278	5	2	2	NUM
ejpam-3405	278	6	;	;	PUNCT
ejpam-3405	278	7	(	(	PUNCT
ejpam-3405	278	8	b	b	X
ejpam-3405	278	9	)	)	PUNCT
ejpam-3405	278	10	d∆(vc	d∆(vc	NOUN
ejpam-3405	278	11	)	)	PUNCT
ejpam-3405	279	1	=	=	SYM
ejpam-3405	279	2	d∆(ve	d∆(ve	NOUN
ejpam-3405	279	3	)	)	PUNCT
ejpam-3405	279	4	=	=	SYM
ejpam-3405	279	5	d∆(vh	d∆(vh	X
ejpam-3405	279	6	)	)	PUNCT
ejpam-3405	279	7	=	=	SYM
ejpam-3405	280	1	2	2	X
ejpam-3405	280	2	.	.	PUNCT
ejpam-3405	280	3	as	as	SCONJ
ejpam-3405	280	4	shown	show	VERB
ejpam-3405	280	5	in	in	ADP
ejpam-3405	280	6	figure	figure	NOUN
ejpam-3405	280	7	17	17	NUM
ejpam-3405	280	8	.	.	PUNCT
ejpam-3405	281	1	in	in	ADP
ejpam-3405	281	2	both	both	DET
ejpam-3405	281	3	of	of	ADP
ejpam-3405	281	4	these	these	DET
ejpam-3405	281	5	cases	case	NOUN
ejpam-3405	281	6	c(∆	c(∆	NOUN
ejpam-3405	281	7	)	)	PUNCT
ejpam-3405	281	8	≤	≤	NOUN
ejpam-3405	281	9	0	0	NUM
ejpam-3405	281	10	.	.	PUNCT
ejpam-3405	282	1	c	c	PROPN
ejpam-3405	282	2	a	a	DET
ejpam-3405	282	3	b	b	PROPN
ejpam-3405	282	4	c	c	NOUN
ejpam-3405	282	5	d	d	X
ejpam-3405	282	6	ef	ef	PROPN
ejpam-3405	282	7	g	g	NOUN
ejpam-3405	282	8	h	h	NOUN
ejpam-3405	283	1	i	i	NOUN
ejpam-3405	283	2	b	b	PROPN
ejpam-3405	283	3	e	e	NOUN
ejpam-3405	283	4	h	h	NOUN
ejpam-3405	283	5	a	a	DET
ejpam-3405	283	6	b	b	NOUN
ejpam-3405	283	7	c	c	NOUN
ejpam-3405	283	8	d	d	X
ejpam-3405	283	9	ef	ef	PROPN
ejpam-3405	283	10	g	g	PROPN
ejpam-3405	283	11	h	h	NOUN
ejpam-3405	284	1	i	i	PRON
ejpam-3405	284	2	a	a	DET
ejpam-3405	284	3	b	b	X
ejpam-3405	284	4	c	c	NOUN
ejpam-3405	284	5	d	d	X
ejpam-3405	284	6	ef	ef	PROPN
ejpam-3405	285	1	g	g	NOUN
ejpam-3405	285	2	h	h	NOUN
ejpam-3405	286	1	i	i	NOUN
ejpam-3405	286	2	b	b	PROPN
ejpam-3405	286	3	b	b	NOUN
ejpam-3405	286	4	c	c	NOUN
ejpam-3405	286	5	c	c	NOUN
ejpam-3405	286	6	e	e	NOUN
ejpam-3405	286	7	h	h	NOUN
ejpam-3405	286	8	figure	figure	VERB
ejpam-3405	286	9	17	17	NUM
ejpam-3405	286	10	:	:	PUNCT
ejpam-3405	286	11	region	region	NOUN
ejpam-3405	286	12	∆	∆	PROPN
ejpam-3405	286	13	(	(	PUNCT
ejpam-3405	286	14	xvi	xvi	NOUN
ejpam-3405	286	15	)	)	PUNCT
ejpam-3405	286	16	in	in	ADP
ejpam-3405	286	17	this	this	DET
ejpam-3405	286	18	case	case	NOUN
ejpam-3405	286	19	∆	∆	PROPN
ejpam-3405	286	20	is	be	AUX
ejpam-3405	286	21	shown	show	VERB
ejpam-3405	286	22	in	in	ADP
ejpam-3405	286	23	figure	figure	NOUN
ejpam-3405	286	24	18	18	NUM
ejpam-3405	286	25	.	.	PUNCT
ejpam-3405	287	1	since	since	SCONJ
ejpam-3405	287	2	d∆(vb	d∆(vb	PROPN
ejpam-3405	287	3	)	)	PUNCT
ejpam-3405	287	4	=	=	SYM
ejpam-3405	287	5	d∆(vc	d∆(vc	NOUN
ejpam-3405	287	6	)	)	PUNCT
ejpam-3405	288	1	=	=	SYM
ejpam-3405	288	2	2	2	NUM
ejpam-3405	288	3	or	or	CCONJ
ejpam-3405	288	4	d∆(vc	d∆(vc	VERB
ejpam-3405	288	5	)	)	PUNCT
ejpam-3405	289	1	=	=	PUNCT
ejpam-3405	289	2	d∆(vd	d∆(vd	ADJ
ejpam-3405	289	3	)	)	PUNCT
ejpam-3405	289	4	=	=	SYM
ejpam-3405	289	5	2	2	NUM
ejpam-3405	289	6	can	can	AUX
ejpam-3405	289	7	not	not	PART
ejpam-3405	289	8	occur	occur	VERB
ejpam-3405	289	9	therefore	therefore	ADV
ejpam-3405	289	10	it	it	PRON
ejpam-3405	289	11	can	can	AUX
ejpam-3405	289	12	be	be	AUX
ejpam-3405	289	13	assumed	assume	VERB
ejpam-3405	289	14	that	that	SCONJ
ejpam-3405	289	15	d∆(vb	d∆(vb	NOUN
ejpam-3405	289	16	)	)	PUNCT
ejpam-3405	290	1	=	=	PUNCT
ejpam-3405	290	2	d∆(vd	d∆(vd	ADJ
ejpam-3405	290	3	)	)	PUNCT
ejpam-3405	290	4	=	=	SYM
ejpam-3405	290	5	d∆(vh	d∆(vh	X
ejpam-3405	290	6	)	)	PUNCT
ejpam-3405	290	7	=	=	SYM
ejpam-3405	290	8	2	2	NUM
ejpam-3405	290	9	as	as	SCONJ
ejpam-3405	290	10	shown	show	VERB
ejpam-3405	290	11	in	in	ADP
ejpam-3405	290	12	figure	figure	NOUN
ejpam-3405	290	13	18	18	NUM
ejpam-3405	290	14	.	.	PUNCT
ejpam-3405	291	1	in	in	ADP
ejpam-3405	291	2	this	this	DET
ejpam-3405	291	3	case	case	NOUN
ejpam-3405	291	4	c(∆	c(∆	PROPN
ejpam-3405	291	5	)	)	PUNCT
ejpam-3405	291	6	≤	≤	NOUN
ejpam-3405	291	7	0	0	NUM
ejpam-3405	291	8	.	.	PUNCT
ejpam-3405	291	9	references	reference	NOUN
ejpam-3405	291	10	603	603	NUM
ejpam-3405	291	11	a	a	DET
ejpam-3405	291	12	b	b	NOUN
ejpam-3405	291	13	c	c	NOUN
ejpam-3405	291	14	d	d	X
ejpam-3405	291	15	ef	ef	PROPN
ejpam-3405	292	1	g	g	PROPN
ejpam-3405	292	2	h	h	NOUN
ejpam-3405	293	1	i	i	PRON
ejpam-3405	293	2	h	h	VERB
ejpam-3405	294	1	c	c	NOUN
ejpam-3405	294	2	b	b	PROPN
ejpam-3405	295	1	d	d	X
ejpam-3405	295	2	a	a	DET
ejpam-3405	295	3	b	b	NOUN
ejpam-3405	295	4	c	c	NOUN
ejpam-3405	295	5	d	d	X
ejpam-3405	295	6	ef	ef	PROPN
ejpam-3405	295	7	g	g	PROPN
ejpam-3405	295	8	h	h	NOUN
ejpam-3405	296	1	i	i	PRON
ejpam-3405	296	2	h	h	VERB
ejpam-3405	296	3	c	c	NOUN
ejpam-3405	296	4	b	b	PROPN
ejpam-3405	296	5	figure	figure	NOUN
ejpam-3405	296	6	18	18	NUM
ejpam-3405	296	7	:	:	PUNCT
ejpam-3405	296	8	region	region	NOUN
ejpam-3405	296	9	∆	∆	PROPN
ejpam-3405	296	10	(	(	PUNCT
ejpam-3405	296	11	xvii	xvii	PROPN
ejpam-3405	296	12	)	)	PUNCT
ejpam-3405	296	13	in	in	ADP
ejpam-3405	296	14	this	this	DET
ejpam-3405	296	15	case	case	NOUN
ejpam-3405	296	16	∆	∆	PROPN
ejpam-3405	296	17	is	be	AUX
ejpam-3405	296	18	shown	show	VERB
ejpam-3405	296	19	in	in	ADP
ejpam-3405	296	20	figure	figure	NOUN
ejpam-3405	296	21	19	19	NUM
ejpam-3405	296	22	.	.	PUNCT
ejpam-3405	297	1	since	since	SCONJ
ejpam-3405	297	2	d∆(vb	d∆(vb	PROPN
ejpam-3405	297	3	)	)	PUNCT
ejpam-3405	297	4	=	=	SYM
ejpam-3405	297	5	d∆(vc	d∆(vc	NOUN
ejpam-3405	297	6	)	)	PUNCT
ejpam-3405	298	1	=	=	SYM
ejpam-3405	298	2	2	2	NUM
ejpam-3405	298	3	or	or	CCONJ
ejpam-3405	298	4	d∆(vc	d∆(vc	VERB
ejpam-3405	298	5	)	)	PUNCT
ejpam-3405	299	1	=	=	PUNCT
ejpam-3405	299	2	d∆(vd	d∆(vd	ADJ
ejpam-3405	299	3	)	)	PUNCT
ejpam-3405	299	4	=	=	SYM
ejpam-3405	299	5	2	2	NUM
ejpam-3405	299	6	or	or	CCONJ
ejpam-3405	299	7	d∆(vd	d∆(vd	ADJ
ejpam-3405	299	8	)	)	PUNCT
ejpam-3405	299	9	=	=	SYM
ejpam-3405	299	10	d∆(ve	d∆(ve	NOUN
ejpam-3405	299	11	)	)	PUNCT
ejpam-3405	299	12	=	=	SYM
ejpam-3405	299	13	2	2	NUM
ejpam-3405	299	14	can	can	AUX
ejpam-3405	299	15	not	not	PART
ejpam-3405	299	16	occur	occur	VERB
ejpam-3405	299	17	therefore	therefore	ADV
ejpam-3405	299	18	c(∆	c(∆	PROPN
ejpam-3405	299	19	)	)	PUNCT
ejpam-3405	299	20	≤	≤	NOUN
ejpam-3405	299	21	0	0	NUM
ejpam-3405	299	22	.	.	PUNCT
ejpam-3405	300	1	a	a	DET
ejpam-3405	300	2	b	b	NOUN
ejpam-3405	300	3	c	c	NOUN
ejpam-3405	300	4	d	d	X
ejpam-3405	300	5	ef	ef	PROPN
ejpam-3405	300	6	g	g	NOUN
ejpam-3405	300	7	h	h	NOUN
ejpam-3405	301	1	i	i	NOUN
ejpam-3405	302	1	d	d	X
ejpam-3405	302	2	e	e	PROPN
ejpam-3405	302	3	c	c	NOUN
ejpam-3405	302	4	b	b	PROPN
ejpam-3405	302	5	figure	figure	NOUN
ejpam-3405	302	6	19	19	NUM
ejpam-3405	302	7	:	:	PUNCT
ejpam-3405	302	8	region	region	NOUN
ejpam-3405	302	9	∆	∆	PROPN
ejpam-3405	302	10	remark	remark	NOUN
ejpam-3405	302	11	1	1	NUM
ejpam-3405	302	12	.	.	PUNCT
ejpam-3405	303	1	it	it	PRON
ejpam-3405	303	2	is	be	AUX
ejpam-3405	303	3	worth	worth	ADJ
ejpam-3405	303	4	mentioning	mention	VERB
ejpam-3405	303	5	here	here	ADV
ejpam-3405	303	6	that	that	SCONJ
ejpam-3405	303	7	a	a	DET
ejpam-3405	303	8	few	few	ADJ
ejpam-3405	303	9	of	of	ADP
ejpam-3405	303	10	the	the	DET
ejpam-3405	303	11	cases	case	NOUN
ejpam-3405	303	12	still	still	ADV
ejpam-3405	303	13	remain	remain	VERB
ejpam-3405	303	14	open	open	ADJ
ejpam-3405	303	15	for	for	ADP
ejpam-3405	303	16	this	this	DET
ejpam-3405	303	17	equation	equation	NOUN
ejpam-3405	303	18	.	.	PUNCT
ejpam-3405	304	1	these	these	DET
ejpam-3405	304	2	cases	case	NOUN
ejpam-3405	304	3	are	be	AUX
ejpam-3405	304	4	extremely	extremely	ADV
ejpam-3405	304	5	technical	technical	ADJ
ejpam-3405	304	6	in	in	ADP
ejpam-3405	304	7	detail	detail	NOUN
ejpam-3405	304	8	and	and	CCONJ
ejpam-3405	304	9	will	will	AUX
ejpam-3405	304	10	be	be	AUX
ejpam-3405	304	11	considered	consider	VERB
ejpam-3405	304	12	in	in	ADP
ejpam-3405	304	13	a	a	DET
ejpam-3405	304	14	different	different	ADJ
ejpam-3405	304	15	article	article	NOUN
ejpam-3405	304	16	.	.	PUNCT
ejpam-3405	305	1	references	reference	NOUN
ejpam-3405	305	2	[	[	X
ejpam-3405	305	3	1	1	NUM
ejpam-3405	305	4	]	]	X
ejpam-3405	305	5	m	m	PROPN
ejpam-3405	305	6	f	f	PROPN
ejpam-3405	305	7	anwar	anwar	PROPN
ejpam-3405	305	8	,	,	PUNCT
ejpam-3405	305	9	m	m	VERB
ejpam-3405	305	10	bibi	bibi	NOUN
ejpam-3405	305	11	,	,	PUNCT
ejpam-3405	305	12	and	and	CCONJ
ejpam-3405	305	13	m	m	PROPN
ejpam-3405	305	14	s	s	PROPN
ejpam-3405	305	15	akram	akram	NOUN
ejpam-3405	305	16	.	.	PUNCT
ejpam-3405	306	1	on	on	ADP
ejpam-3405	306	2	solvability	solvability	NOUN
ejpam-3405	306	3	of	of	ADP
ejpam-3405	306	4	certain	certain	ADJ
ejpam-3405	306	5	equations	equation	NOUN
ejpam-3405	306	6	of	of	ADP
ejpam-3405	306	7	arbitrary	arbitrary	ADJ
ejpam-3405	306	8	length	length	NOUN
ejpam-3405	306	9	over	over	ADP
ejpam-3405	306	10	torsion	torsion	NOUN
ejpam-3405	306	11	-	-	PUNCT
ejpam-3405	306	12	free	free	ADJ
ejpam-3405	306	13	groups	group	NOUN
ejpam-3405	306	14	.	.	PUNCT
ejpam-3405	307	1	preprint	preprint	NOUN
ejpam-3405	307	2	,	,	PUNCT
ejpam-3405	307	3	2019	2019	NUM
ejpam-3405	307	4	.	.	PUNCT
ejpam-3405	308	1	[	[	X
ejpam-3405	308	2	2	2	NUM
ejpam-3405	308	3	]	]	X
ejpam-3405	308	4	m	m	PROPN
ejpam-3405	308	5	f	f	PROPN
ejpam-3405	308	6	anwar	anwar	PROPN
ejpam-3405	308	7	,	,	PUNCT
ejpam-3405	308	8	m	m	VERB
ejpam-3405	308	9	bibi	bibi	NOUN
ejpam-3405	308	10	,	,	PUNCT
ejpam-3405	308	11	and	and	CCONJ
ejpam-3405	308	12	s	s	VERB
ejpam-3405	308	13	iqbal	iqbal	ADJ
ejpam-3405	308	14	.	.	PUNCT
ejpam-3405	309	1	on	on	ADP
ejpam-3405	309	2	certain	certain	ADJ
ejpam-3405	309	3	equations	equation	NOUN
ejpam-3405	309	4	of	of	ADP
ejpam-3405	309	5	arbitrary	arbitrary	ADJ
ejpam-3405	309	6	length	length	NOUN
ejpam-3405	309	7	over	over	ADP
ejpam-3405	309	8	torsion	torsion	NOUN
ejpam-3405	309	9	-	-	PUNCT
ejpam-3405	309	10	free	free	ADJ
ejpam-3405	309	11	groups	group	NOUN
ejpam-3405	309	12	.	.	PUNCT
ejpam-3405	310	1	preprint	preprint	NOUN
ejpam-3405	310	2	,	,	PUNCT
ejpam-3405	310	3	2019	2019	NUM
ejpam-3405	310	4	.	.	PUNCT
ejpam-3405	311	1	[	[	X
ejpam-3405	311	2	3	3	NUM
ejpam-3405	311	3	]	]	X
ejpam-3405	311	4	m	m	VERB
ejpam-3405	311	5	bibi	bibi	NOUN
ejpam-3405	311	6	.	.	PUNCT
ejpam-3405	312	1	equations	equation	NOUN
ejpam-3405	312	2	of	of	ADP
ejpam-3405	312	3	length	length	NOUN
ejpam-3405	312	4	seven	seven	NUM
ejpam-3405	312	5	over	over	ADP
ejpam-3405	312	6	torsion	torsion	NOUN
ejpam-3405	312	7	free	free	ADJ
ejpam-3405	312	8	groups	group	NOUN
ejpam-3405	312	9	.	.	PUNCT
ejpam-3405	313	1	phd	phd	NOUN
ejpam-3405	313	2	thesis	thesis	PROPN
ejpam-3405	313	3	,	,	PUNCT
ejpam-3405	313	4	university	university	NOUN
ejpam-3405	313	5	of	of	ADP
ejpam-3405	313	6	notingham	notingham	NOUN
ejpam-3405	313	7	,	,	PUNCT
ejpam-3405	313	8	2013	2013	NUM
ejpam-3405	313	9	.	.	PUNCT
ejpam-3405	314	1	references	reference	NOUN
ejpam-3405	314	2	604	604	NUM
ejpam-3405	314	3	[	[	X
ejpam-3405	314	4	4	4	NUM
ejpam-3405	314	5	]	]	SYM
ejpam-3405	314	6	m	m	VERB
ejpam-3405	314	7	bibi	bibi	NOUN
ejpam-3405	314	8	,	,	PUNCT
ejpam-3405	314	9	m	m	PROPN
ejpam-3405	314	10	f	f	PROPN
ejpam-3405	314	11	anwar	anwar	PROPN
ejpam-3405	314	12	,	,	PUNCT
ejpam-3405	314	13	s	s	PART
ejpam-3405	314	14	iqbal	iqbal	NOUN
ejpam-3405	314	15	,	,	PUNCT
ejpam-3405	314	16	and	and	CCONJ
ejpam-3405	314	17	m	m	PROPN
ejpam-3405	314	18	s	s	PROPN
ejpam-3405	314	19	akram	akram	NOUN
ejpam-3405	314	20	.	.	PUNCT
ejpam-3405	315	1	solution	solution	NOUN
ejpam-3405	315	2	of	of	ADP
ejpam-3405	315	3	a	a	DET
ejpam-3405	315	4	non	non	ADJ
ejpam-3405	315	5	-	-	ADJ
ejpam-3405	315	6	singular	singular	ADJ
ejpam-3405	315	7	equation	equation	NOUN
ejpam-3405	315	8	of	of	ADP
ejpam-3405	315	9	length	length	NOUN
ejpam-3405	315	10	8	8	NUM
ejpam-3405	315	11	over	over	ADP
ejpam-3405	315	12	torsion	torsion	NOUN
ejpam-3405	315	13	free	free	ADJ
ejpam-3405	315	14	groups	group	NOUN
ejpam-3405	315	15	.	.	PUNCT
ejpam-3405	316	1	preprint	preprint	NOUN
ejpam-3405	316	2	,	,	PUNCT
ejpam-3405	316	3	2019	2019	NUM
ejpam-3405	316	4	.	.	PUNCT
ejpam-3405	317	1	[	[	X
ejpam-3405	317	2	5	5	NUM
ejpam-3405	317	3	]	]	PUNCT
ejpam-3405	317	4	m	m	VERB
ejpam-3405	317	5	bibi	bibi	NOUN
ejpam-3405	317	6	and	and	CCONJ
ejpam-3405	317	7	m	m	AUX
ejpam-3405	317	8	edjvet	edjvet	NOUN
ejpam-3405	317	9	.	.	PUNCT
ejpam-3405	318	1	solving	solve	VERB
ejpam-3405	318	2	equations	equation	NOUN
ejpam-3405	318	3	of	of	ADP
ejpam-3405	318	4	length	length	NOUN
ejpam-3405	318	5	seven	seven	NUM
ejpam-3405	318	6	over	over	ADP
ejpam-3405	318	7	torsion	torsion	NOUN
ejpam-3405	318	8	-	-	PUNCT
ejpam-3405	318	9	free	free	ADJ
ejpam-3405	318	10	groups	group	NOUN
ejpam-3405	318	11	.	.	PUNCT
ejpam-3405	319	1	journal	journal	PROPN
ejpam-3405	319	2	of	of	ADP
ejpam-3405	319	3	group	group	PROPN
ejpam-3405	319	4	theory	theory	NOUN
ejpam-3405	319	5	,	,	PUNCT
ejpam-3405	319	6	21(1):147–164	21(1):147–164	NOUN
ejpam-3405	319	7	,	,	PUNCT
ejpam-3405	319	8	2018	2018	NUM
ejpam-3405	319	9	.	.	PUNCT
ejpam-3405	320	1	[	[	X
ejpam-3405	320	2	6	6	NUM
ejpam-3405	320	3	]	]	PUNCT
ejpam-3405	320	4	w	w	ADP
ejpam-3405	320	5	a	a	DET
ejpam-3405	320	6	bogley	bogley	NOUN
ejpam-3405	320	7	and	and	CCONJ
ejpam-3405	320	8	s	s	NOUN
ejpam-3405	320	9	j	j	NOUN
ejpam-3405	320	10	pride	pride	NOUN
ejpam-3405	320	11	.	.	PUNCT
ejpam-3405	321	1	aspherical	aspherical	ADJ
ejpam-3405	321	2	relative	relative	ADJ
ejpam-3405	321	3	presentations	presentation	NOUN
ejpam-3405	321	4	.	.	PUNCT
ejpam-3405	322	1	proceedings	proceeding	NOUN
ejpam-3405	322	2	of	of	ADP
ejpam-3405	322	3	the	the	DET
ejpam-3405	322	4	edinburgh	edinburgh	PROPN
ejpam-3405	322	5	mathematical	mathematical	PROPN
ejpam-3405	322	6	society	society	NOUN
ejpam-3405	322	7	,	,	PUNCT
ejpam-3405	322	8	35	35	NUM
ejpam-3405	322	9	,	,	PUNCT
ejpam-3405	322	10	1992	1992	NUM
ejpam-3405	322	11	.	.	PUNCT
ejpam-3405	323	1	[	[	X
ejpam-3405	323	2	7	7	NUM
ejpam-3405	323	3	]	]	SYM
ejpam-3405	323	4	s	s	PART
ejpam-3405	323	5	d	d	X
ejpam-3405	323	6	brodski	brodski	PROPN
ejpam-3405	323	7	and	and	CCONJ
ejpam-3405	323	8	j	j	PROPN
ejpam-3405	323	9	howie	howie	PROPN
ejpam-3405	323	10	.	.	PUNCT
ejpam-3405	324	1	one	one	NUM
ejpam-3405	324	2	-	-	PUNCT
ejpam-3405	324	3	relator	relator	NOUN
ejpam-3405	324	4	products	product	NOUN
ejpam-3405	324	5	of	of	ADP
ejpam-3405	324	6	torsion	torsion	NOUN
ejpam-3405	324	7	-	-	PUNCT
ejpam-3405	324	8	free	free	ADJ
ejpam-3405	324	9	groups	group	NOUN
ejpam-3405	324	10	.	.	PUNCT
ejpam-3405	325	1	glasgow	glasgow	PROPN
ejpam-3405	325	2	mathematical	mathematical	ADJ
ejpam-3405	325	3	journal	journal	NOUN
ejpam-3405	325	4	,	,	PUNCT
ejpam-3405	325	5	35(1):99–104	35(1):99–104	PROPN
ejpam-3405	325	6	,	,	PUNCT
ejpam-3405	325	7	1993	1993	NUM
ejpam-3405	325	8	.	.	PUNCT
ejpam-3405	326	1	[	[	X
ejpam-3405	326	2	8	8	NUM
ejpam-3405	326	3	]	]	X
ejpam-3405	326	4	j	j	PROPN
ejpam-3405	326	5	howie	howie	NOUN
ejpam-3405	326	6	.	.	PUNCT
ejpam-3405	327	1	the	the	DET
ejpam-3405	327	2	solution	solution	NOUN
ejpam-3405	327	3	of	of	ADP
ejpam-3405	327	4	length	length	NOUN
ejpam-3405	327	5	three	three	NUM
ejpam-3405	327	6	equations	equation	NOUN
ejpam-3405	327	7	over	over	ADP
ejpam-3405	327	8	groups	group	NOUN
ejpam-3405	327	9	.	.	PUNCT
ejpam-3405	328	1	proceedings	proceeding	NOUN
ejpam-3405	328	2	of	of	ADP
ejpam-3405	328	3	the	the	DET
ejpam-3405	328	4	edinburgh	edinburgh	PROPN
ejpam-3405	328	5	mathematical	mathematical	PROPN
ejpam-3405	328	6	society	society	NOUN
ejpam-3405	328	7	,	,	PUNCT
ejpam-3405	328	8	26(2):89–96	26(2):89–96	NUM
ejpam-3405	328	9	,	,	PUNCT
ejpam-3405	328	10	1983	1983	NUM
ejpam-3405	328	11	.	.	PUNCT
ejpam-3405	329	1	[	[	X
ejpam-3405	329	2	9	9	NUM
ejpam-3405	329	3	]	]	SYM
ejpam-3405	329	4	s	s	PART
ejpam-3405	329	5	v	v	ADP
ejpam-3405	329	6	ivanov	ivanov	NOUN
ejpam-3405	329	7	and	and	CCONJ
ejpam-3405	329	8	a	a	DET
ejpam-3405	329	9	a	a	DET
ejpam-3405	329	10	klyachko	klyachko	ADJ
ejpam-3405	329	11	.	.	PUNCT
ejpam-3405	330	1	solving	solve	VERB
ejpam-3405	330	2	equations	equation	NOUN
ejpam-3405	330	3	of	of	ADP
ejpam-3405	330	4	length	length	NOUN
ejpam-3405	330	5	at	at	ADP
ejpam-3405	330	6	most	most	ADV
ejpam-3405	330	7	six	six	NUM
ejpam-3405	330	8	over	over	ADP
ejpam-3405	330	9	torsionfree	torsionfree	ADJ
ejpam-3405	330	10	groups	group	NOUN
ejpam-3405	330	11	.	.	PUNCT
ejpam-3405	331	1	journal	journal	PROPN
ejpam-3405	331	2	od	od	PROPN
ejpam-3405	331	3	group	group	PROPN
ejpam-3405	331	4	theory	theory	NOUN
ejpam-3405	331	5	,	,	PUNCT
ejpam-3405	331	6	3(3):329–337	3(3):329–337	NOUN
ejpam-3405	331	7	,	,	PUNCT
ejpam-3405	331	8	2000	2000	NUM
ejpam-3405	331	9	.	.	PUNCT
ejpam-3405	332	1	[	[	X
ejpam-3405	332	2	10	10	NUM
ejpam-3405	332	3	]	]	SYM
ejpam-3405	332	4	s	s	PROPN
ejpam-3405	332	5	k	k	PROPN
ejpam-3405	332	6	kim	kim	PROPN
ejpam-3405	332	7	.	.	PUNCT
ejpam-3405	333	1	on	on	ADP
ejpam-3405	333	2	the	the	DET
ejpam-3405	333	3	asphericity	asphericity	NOUN
ejpam-3405	333	4	of	of	ADP
ejpam-3405	333	5	length-6	length-6	PROPN
ejpam-3405	333	6	relative	relative	ADJ
ejpam-3405	333	7	presentations	presentation	NOUN
ejpam-3405	333	8	with	with	ADP
ejpam-3405	333	9	torsion	torsion	NOUN
ejpam-3405	333	10	-	-	PUNCT
ejpam-3405	333	11	free	free	ADJ
ejpam-3405	333	12	coefficients	coefficient	NOUN
ejpam-3405	333	13	.	.	PUNCT
ejpam-3405	334	1	proceedings	proceeding	NOUN
ejpam-3405	334	2	of	of	ADP
ejpam-3405	334	3	the	the	DET
ejpam-3405	334	4	edinburgh	edinburgh	PROPN
ejpam-3405	334	5	mathematical	mathematical	PROPN
ejpam-3405	334	6	society	society	NOUN
ejpam-3405	334	7	,	,	PUNCT
ejpam-3405	334	8	51(1):201–214	51(1):201–214	NUM
ejpam-3405	334	9	,	,	PUNCT
ejpam-3405	334	10	2008	2008	NUM
ejpam-3405	334	11	.	.	PUNCT
ejpam-3405	335	1	[	[	X
ejpam-3405	335	2	11	11	NUM
ejpam-3405	335	3	]	]	X
ejpam-3405	335	4	f	f	PROPN
ejpam-3405	335	5	levin	levin	PROPN
ejpam-3405	335	6	.	.	PUNCT
ejpam-3405	336	1	solutions	solution	NOUN
ejpam-3405	336	2	of	of	ADP
ejpam-3405	336	3	equations	equation	NOUN
ejpam-3405	336	4	over	over	ADP
ejpam-3405	336	5	groups	group	NOUN
ejpam-3405	336	6	.	.	PUNCT
ejpam-3405	337	1	bulletin	bulletin	NOUN
ejpam-3405	337	2	of	of	ADP
ejpam-3405	337	3	american	american	PROPN
ejpam-3405	337	4	mathematical	mathematical	PROPN
ejpam-3405	337	5	society	society	NOUN
ejpam-3405	337	6	,	,	PUNCT
ejpam-3405	337	7	68	68	NUM
ejpam-3405	337	8	,	,	PUNCT
ejpam-3405	337	9	1962	1962	NUM
ejpam-3405	337	10	.	.	PUNCT
ejpam-3405	338	1	[	[	X
ejpam-3405	338	2	12	12	NUM
ejpam-3405	338	3	]	]	X
ejpam-3405	338	4	m	m	VERB
ejpam-3405	338	5	i	i	NOUN
ejpam-3405	338	6	prishchepov	prishchepov	NOUN
ejpam-3405	338	7	.	.	PUNCT
ejpam-3405	339	1	on	on	ADP
ejpam-3405	339	2	small	small	ADJ
ejpam-3405	339	3	length	length	NOUN
ejpam-3405	339	4	equations	equation	NOUN
ejpam-3405	339	5	over	over	ADP
ejpam-3405	339	6	torsion	torsion	NOUN
ejpam-3405	339	7	-	-	PUNCT
ejpam-3405	339	8	free	free	ADJ
ejpam-3405	339	9	groups	group	NOUN
ejpam-3405	339	10	.	.	PUNCT
ejpam-3405	340	1	international	international	ADJ
ejpam-3405	340	2	journal	journal	NOUN
ejpam-3405	340	3	of	of	ADP
ejpam-3405	340	4	algebra	algebra	NOUN
ejpam-3405	340	5	and	and	CCONJ
ejpam-3405	340	6	computation	computation	NOUN
ejpam-3405	340	7	,	,	PUNCT
ejpam-3405	340	8	4(4):575–589	4(4):575–589	PROPN
ejpam-3405	340	9	,	,	PUNCT
ejpam-3405	340	10	1994	1994	NUM
ejpam-3405	340	11	.	.	PUNCT