id	sid	tid	token	lemma	pos
ejpam-1809	1	1	european	european	PROPN
ejpam-1809	1	2	journal	journal	PROPN
ejpam-1809	1	3	of	of	ADP
ejpam-1809	1	4	pure	pure	ADJ
ejpam-1809	1	5	and	and	CCONJ
ejpam-1809	1	6	applied	apply	VERB
ejpam-1809	1	7	mathematics	mathematic	NOUN
ejpam-1809	1	8	vol	vol	NOUN
ejpam-1809	1	9	.	.	PROPN
ejpam-1809	2	1	6	6	NUM
ejpam-1809	2	2	,	,	PUNCT
ejpam-1809	2	3	no	no	INTJ
ejpam-1809	2	4	.	.	NOUN
ejpam-1809	2	5	3	3	NUM
ejpam-1809	2	6	,	,	PUNCT
ejpam-1809	2	7	2013	2013	NUM
ejpam-1809	2	8	,	,	PUNCT
ejpam-1809	2	9	335	335	NUM
ejpam-1809	2	10	-	-	SYM
ejpam-1809	2	11	339	339	NUM
ejpam-1809	2	12	issn	issn	PROPN
ejpam-1809	2	13	1307	1307	NUM
ejpam-1809	2	14	-	-	SYM
ejpam-1809	2	15	5543	5543	NUM
ejpam-1809	2	16	–	–	PUNCT
ejpam-1809	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1809	2	18	finiteness	finitenes	VERB
ejpam-1809	2	19	conditions	condition	NOUN
ejpam-1809	2	20	for	for	ADP
ejpam-1809	2	21	unions	union	NOUN
ejpam-1809	2	22	of	of	ADP
ejpam-1809	2	23	two	two	NUM
ejpam-1809	2	24	semigroups	semigroup	NOUN
ejpam-1809	2	25	and	and	CCONJ
ejpam-1809	2	26	ranks	rank	NOUN
ejpam-1809	2	27	of	of	ADP
ejpam-1809	2	28	b(g	b(g	PROPN
ejpam-1809	2	29	,	,	PUNCT
ejpam-1809	2	30	n	n	CCONJ
ejpam-1809	2	31	)	)	PUNCT
ejpam-1809	2	32	melis	melis	PROPN
ejpam-1809	2	33	minisker	minisker	PROPN
ejpam-1809	2	34	mustafa	mustafa	PROPN
ejpam-1809	2	35	kemal	kemal	PROPN
ejpam-1809	2	36	university	university	PROPN
ejpam-1809	2	37	,	,	PUNCT
ejpam-1809	2	38	faculty	faculty	NOUN
ejpam-1809	2	39	of	of	ADP
ejpam-1809	2	40	education	education	NOUN
ejpam-1809	2	41	,	,	PUNCT
ejpam-1809	2	42	antakya	antakya	NOUN
ejpam-1809	2	43	-	-	PUNCT
ejpam-1809	2	44	hatay	hatay	NOUN
ejpam-1809	2	45	abstract	abstract	NOUN
ejpam-1809	2	46	.	.	PUNCT
ejpam-1809	3	1	in	in	ADP
ejpam-1809	3	2	this	this	DET
ejpam-1809	3	3	paper	paper	NOUN
ejpam-1809	3	4	we	we	PRON
ejpam-1809	3	5	try	try	VERB
ejpam-1809	3	6	to	to	PART
ejpam-1809	3	7	find	find	VERB
ejpam-1809	3	8	the	the	DET
ejpam-1809	3	9	finiteness	finiteness	ADJ
ejpam-1809	3	10	conditions	condition	NOUN
ejpam-1809	3	11	for	for	ADP
ejpam-1809	3	12	union	union	NOUN
ejpam-1809	3	13	of	of	ADP
ejpam-1809	3	14	two	two	NUM
ejpam-1809	3	15	finite	finite	ADJ
ejpam-1809	3	16	semigroups	semigroup	NOUN
ejpam-1809	3	17	with	with	ADP
ejpam-1809	3	18	a	a	DET
ejpam-1809	3	19	specially	specially	ADV
ejpam-1809	3	20	defined	define	VERB
ejpam-1809	3	21	binary	binary	ADJ
ejpam-1809	3	22	equation	equation	NOUN
ejpam-1809	3	23	.	.	PUNCT
ejpam-1809	4	1	moreover	moreover	ADV
ejpam-1809	4	2	we	we	PRON
ejpam-1809	4	3	find	find	VERB
ejpam-1809	4	4	the	the	DET
ejpam-1809	4	5	ranks	rank	NOUN
ejpam-1809	4	6	of	of	ADP
ejpam-1809	4	7	the	the	DET
ejpam-1809	4	8	semigroup	semigroup	PROPN
ejpam-1809	4	9	b(g	b(g	PROPN
ejpam-1809	4	10	,	,	PUNCT
ejpam-1809	4	11	n	n	CCONJ
ejpam-1809	4	12	)	)	PUNCT
ejpam-1809	4	13	.	.	PUNCT
ejpam-1809	5	1	2010	2010	NUM
ejpam-1809	5	2	mathematics	mathematic	NOUN
ejpam-1809	5	3	subject	subject	NOUN
ejpam-1809	5	4	classifications	classification	NOUN
ejpam-1809	5	5	:	:	PUNCT
ejpam-1809	5	6	20m05	20m05	NUM
ejpam-1809	5	7	key	key	ADJ
ejpam-1809	5	8	words	word	NOUN
ejpam-1809	5	9	and	and	CCONJ
ejpam-1809	5	10	phrases	phrase	NOUN
ejpam-1809	5	11	:	:	PUNCT
ejpam-1809	5	12	finiteness	finiteness	ADJ
ejpam-1809	5	13	conditions	condition	NOUN
ejpam-1809	5	14	,	,	PUNCT
ejpam-1809	5	15	ranks	rank	NOUN
ejpam-1809	5	16	,	,	PUNCT
ejpam-1809	5	17	union	union	NOUN
ejpam-1809	5	18	1	1	NUM
ejpam-1809	5	19	.	.	PUNCT
ejpam-1809	6	1	introduction	introduction	NOUN
ejpam-1809	6	2	finiteness	finiteness	NOUN
ejpam-1809	6	3	conditions	condition	NOUN
ejpam-1809	6	4	of	of	ADP
ejpam-1809	6	5	semigroups	semigroup	NOUN
ejpam-1809	6	6	(	(	PUNCT
ejpam-1809	6	7	the	the	DET
ejpam-1809	6	8	properties	property	NOUN
ejpam-1809	6	9	of	of	ADP
ejpam-1809	6	10	semigroups	semigroup	NOUN
ejpam-1809	6	11	which	which	PRON
ejpam-1809	6	12	all	all	PRON
ejpam-1809	6	13	finite	finite	VERB
ejpam-1809	6	14	semigroups	semigroup	NOUN
ejpam-1809	6	15	have	have	AUX
ejpam-1809	6	16	)	)	PUNCT
ejpam-1809	6	17	have	have	AUX
ejpam-1809	6	18	been	be	AUX
ejpam-1809	6	19	considered	consider	VERB
ejpam-1809	6	20	for	for	ADP
ejpam-1809	6	21	certain	certain	ADJ
ejpam-1809	6	22	classes	class	NOUN
ejpam-1809	6	23	of	of	ADP
ejpam-1809	6	24	semigroup	semigroup	ADJ
ejpam-1809	6	25	constructions	construction	NOUN
ejpam-1809	6	26	.	.	PUNCT
ejpam-1809	7	1	(	(	PUNCT
ejpam-1809	7	2	for	for	ADP
ejpam-1809	7	3	examples	example	NOUN
ejpam-1809	7	4	see	see	VERB
ejpam-1809	7	5	[	[	X
ejpam-1809	7	6	1	1	NUM
ejpam-1809	7	7	,	,	PUNCT
ejpam-1809	7	8	2	2	NUM
ejpam-1809	7	9	]	]	PUNCT
ejpam-1809	7	10	)	)	PUNCT
ejpam-1809	7	11	.	.	PUNCT
ejpam-1809	8	1	in	in	ADP
ejpam-1809	8	2	this	this	DET
ejpam-1809	8	3	paper	paper	NOUN
ejpam-1809	8	4	periodicity	periodicity	NOUN
ejpam-1809	8	5	,	,	PUNCT
ejpam-1809	8	6	residual	residual	ADJ
ejpam-1809	8	7	finiteness	finiteness	NOUN
ejpam-1809	8	8	and	and	CCONJ
ejpam-1809	8	9	solvability	solvability	NOUN
ejpam-1809	8	10	of	of	ADP
ejpam-1809	8	11	word	word	NOUN
ejpam-1809	8	12	problem	problem	NOUN
ejpam-1809	8	13	of	of	ADP
ejpam-1809	8	14	union	union	NOUN
ejpam-1809	8	15	of	of	ADP
ejpam-1809	8	16	two	two	NUM
ejpam-1809	8	17	finite	finite	NOUN
ejpam-1809	8	18	semigroups	semigroup	NOUN
ejpam-1809	8	19	are	be	AUX
ejpam-1809	8	20	determined	determine	VERB
ejpam-1809	8	21	.	.	PUNCT
ejpam-1809	9	1	let	let	VERB
ejpam-1809	9	2	s	s	PRON
ejpam-1809	9	3	and	and	CCONJ
ejpam-1809	9	4	t	t	PROPN
ejpam-1809	9	5	be	be	AUX
ejpam-1809	9	6	two	two	NUM
ejpam-1809	9	7	finite	finite	ADJ
ejpam-1809	9	8	semigroups	semigroup	NOUN
ejpam-1809	9	9	with	with	ADP
ejpam-1809	9	10	empty	empty	ADJ
ejpam-1809	9	11	intersection	intersection	NOUN
ejpam-1809	9	12	.	.	PUNCT
ejpam-1809	10	1	we	we	PRON
ejpam-1809	10	2	define	define	VERB
ejpam-1809	10	3	a	a	DET
ejpam-1809	10	4	binary	binary	ADJ
ejpam-1809	10	5	equation	equation	NOUN
ejpam-1809	10	6	on	on	ADP
ejpam-1809	10	7	s	s	PROPN
ejpam-1809	10	8	∪	∪	ADJ
ejpam-1809	10	9	t	t	PROPN
ejpam-1809	10	10	as	as	SCONJ
ejpam-1809	10	11	follows	follow	VERB
ejpam-1809	10	12	:	:	PUNCT
ejpam-1809	10	13	if	if	SCONJ
ejpam-1809	10	14	s1	s1	PROPN
ejpam-1809	10	15	∈	∈	PROPN
ejpam-1809	10	16	s	s	PART
ejpam-1809	10	17	and	and	CCONJ
ejpam-1809	10	18	s2	s2	PROPN
ejpam-1809	10	19	∈	∈	PROPN
ejpam-1809	10	20	s	s	PART
ejpam-1809	10	21	then	then	ADV
ejpam-1809	10	22	s1.s2	s1.s2	PROPN
ejpam-1809	10	23	is	be	AUX
ejpam-1809	10	24	considered	consider	VERB
ejpam-1809	10	25	as	as	ADP
ejpam-1809	10	26	the	the	DET
ejpam-1809	10	27	same	same	ADJ
ejpam-1809	10	28	operation	operation	NOUN
ejpam-1809	10	29	defined	define	VERB
ejpam-1809	10	30	on	on	ADP
ejpam-1809	10	31	s.	s.	PROPN
ejpam-1809	10	32	if	if	SCONJ
ejpam-1809	10	33	t1	t1	PROPN
ejpam-1809	10	34	∈	∈	PROPN
ejpam-1809	10	35	t	t	PROPN
ejpam-1809	10	36	and	and	CCONJ
ejpam-1809	10	37	t2	t2	PROPN
ejpam-1809	10	38	∈	∈	PROPN
ejpam-1809	10	39	t	t	NOUN
ejpam-1809	10	40	then	then	ADV
ejpam-1809	10	41	t1.t2	t1.t2	PROPN
ejpam-1809	10	42	is	be	AUX
ejpam-1809	10	43	considered	consider	VERB
ejpam-1809	10	44	as	as	ADP
ejpam-1809	10	45	the	the	DET
ejpam-1809	10	46	same	same	ADJ
ejpam-1809	10	47	operation	operation	NOUN
ejpam-1809	10	48	defined	define	VERB
ejpam-1809	10	49	on	on	ADP
ejpam-1809	10	50	t	t	PROPN
ejpam-1809	10	51	.	.	PUNCT
ejpam-1809	11	1	if	if	SCONJ
ejpam-1809	11	2	s	s	VERB
ejpam-1809	11	3	∈	∈	PROPN
ejpam-1809	11	4	s	s	X
ejpam-1809	11	5	and	and	CCONJ
ejpam-1809	11	6	t	t	PROPN
ejpam-1809	11	7	∈	∈	PROPN
ejpam-1809	12	1	t	t	PROPN
ejpam-1809	12	2	then	then	ADV
ejpam-1809	12	3	st	st	PROPN
ejpam-1809	12	4	=	=	NOUN
ejpam-1809	12	5	ts	ts	PROPN
ejpam-1809	12	6	=	=	PUNCT
ejpam-1809	12	7	t.	t.	PROPN
ejpam-1809	12	8	in	in	ADP
ejpam-1809	13	1	[	[	X
ejpam-1809	13	2	3	3	X
ejpam-1809	13	3	]	]	X
ejpam-1809	13	4	it	it	PRON
ejpam-1809	13	5	is	be	AUX
ejpam-1809	13	6	shown	show	VERB
ejpam-1809	13	7	that	that	SCONJ
ejpam-1809	13	8	any	any	DET
ejpam-1809	13	9	finitely	finitely	ADV
ejpam-1809	13	10	presented	present	VERB
ejpam-1809	13	11	semigroup	semigroup	PROPN
ejpam-1809	13	12	s	s	VERB
ejpam-1809	13	13	is	be	AUX
ejpam-1809	13	14	embedded	embed	VERB
ejpam-1809	13	15	into	into	ADP
ejpam-1809	13	16	an	an	DET
ejpam-1809	13	17	inefficient	inefficient	ADJ
ejpam-1809	13	18	semigroup	semigroup	NOUN
ejpam-1809	13	19	,	,	PUNCT
ejpam-1809	13	20	namely	namely	ADV
ejpam-1809	13	21	,	,	PUNCT
ejpam-1809	13	22	the	the	DET
ejpam-1809	13	23	semigroup	semigroup	PROPN
ejpam-1809	13	24	s∪sln	s∪sln	PROPN
ejpam-1809	13	25	where	where	SCONJ
ejpam-1809	13	26	sln	sln	PROPN
ejpam-1809	13	27	is	be	AUX
ejpam-1809	13	28	the	the	DET
ejpam-1809	13	29	free	free	ADJ
ejpam-1809	13	30	semilattice	semilattice	NOUN
ejpam-1809	13	31	of	of	ADP
ejpam-1809	13	32	rank	rank	PROPN
ejpam-1809	13	33	n.	n.	PROPN
ejpam-1809	13	34	let	let	VERB
ejpam-1809	13	35	s	s	PRON
ejpam-1809	13	36	be	be	AUX
ejpam-1809	13	37	a	a	DET
ejpam-1809	13	38	finite	finite	ADJ
ejpam-1809	13	39	semigroup	semigroup	NOUN
ejpam-1809	13	40	.	.	PUNCT
ejpam-1809	14	1	a	a	DET
ejpam-1809	14	2	subset	subset	ADJ
ejpam-1809	14	3	u	u	NOUN
ejpam-1809	14	4	of	of	ADP
ejpam-1809	14	5	s	s	PROPN
ejpam-1809	14	6	is	be	AUX
ejpam-1809	14	7	called	call	VERB
ejpam-1809	14	8	independent	independent	ADJ
ejpam-1809	14	9	if	if	SCONJ
ejpam-1809	14	10	,	,	PUNCT
ejpam-1809	14	11	for	for	ADP
ejpam-1809	14	12	every	every	DET
ejpam-1809	14	13	u	u	NOUN
ejpam-1809	14	14	in	in	ADP
ejpam-1809	14	15	u	u	PROPN
ejpam-1809	14	16	,	,	PUNCT
ejpam-1809	14	17	the	the	DET
ejpam-1809	14	18	element	element	NOUN
ejpam-1809	14	19	u	u	NOUN
ejpam-1809	14	20	does	do	AUX
ejpam-1809	14	21	not	not	PART
ejpam-1809	14	22	belong	belong	VERB
ejpam-1809	14	23	to	to	ADP
ejpam-1809	14	24	the	the	DET
ejpam-1809	14	25	semigroup	semigroup	NOUN
ejpam-1809	14	26	<	<	X
ejpam-1809	14	27	u	u	PRON
ejpam-1809	14	28	\{u	\{u	ADV
ejpam-1809	14	29	}	}	PUNCT
ejpam-1809	14	30	>	>	X
ejpam-1809	14	31	generated	generate	VERB
ejpam-1809	14	32	by	by	ADP
ejpam-1809	14	33	the	the	DET
ejpam-1809	14	34	remaining	remain	VERB
ejpam-1809	14	35	elements	element	NOUN
ejpam-1809	14	36	of	of	ADP
ejpam-1809	14	37	u	u	NOUN
ejpam-1809	14	38	(	(	PUNCT
ejpam-1809	14	39	see	see	VERB
ejpam-1809	14	40	[	[	X
ejpam-1809	14	41	4	4	NUM
ejpam-1809	14	42	]	]	NUM
ejpam-1809	14	43	)	)	PUNCT
ejpam-1809	14	44	.	.	PUNCT
ejpam-1809	15	1	in	in	ADP
ejpam-1809	15	2	[	[	X
ejpam-1809	15	3	5	5	NUM
ejpam-1809	15	4	]	]	X
ejpam-1809	15	5	howie	howie	NOUN
ejpam-1809	15	6	and	and	CCONJ
ejpam-1809	15	7	ribeiro	ribeiro	PROPN
ejpam-1809	15	8	introduced	introduce	VERB
ejpam-1809	15	9	r1(s	r1(s	NOUN
ejpam-1809	15	10	)	)	PUNCT
ejpam-1809	15	11	,	,	PUNCT
ejpam-1809	15	12	r2(s	r2(s	NOUN
ejpam-1809	15	13	)	)	PUNCT
ejpam-1809	15	14	,	,	PUNCT
ejpam-1809	15	15	r3(s	r3(s	PROPN
ejpam-1809	15	16	)	)	PUNCT
ejpam-1809	15	17	,	,	PUNCT
ejpam-1809	15	18	r4(s	r4(s	PROPN
ejpam-1809	15	19	)	)	PUNCT
ejpam-1809	15	20	and	and	CCONJ
ejpam-1809	15	21	r5(s	r5(	NOUN
ejpam-1809	15	22	)	)	PUNCT
ejpam-1809	15	23	defined	define	VERB
ejpam-1809	15	24	as	as	SCONJ
ejpam-1809	15	25	follows	follow	VERB
ejpam-1809	15	26	:	:	PUNCT
ejpam-1809	15	27	•	•	NUM
ejpam-1809	15	28	r1(s	r1(s	NOUN
ejpam-1809	15	29	)	)	PUNCT
ejpam-1809	15	30	=	=	SYM
ejpam-1809	15	31	max{k	max{k	NOUN
ejpam-1809	15	32	:	:	PUNCT
ejpam-1809	15	33	every	every	DET
ejpam-1809	15	34	subset	subset	ADJ
ejpam-1809	15	35	u	u	NOUN
ejpam-1809	15	36	of	of	ADP
ejpam-1809	15	37	s	s	PRON
ejpam-1809	15	38	of	of	ADP
ejpam-1809	15	39	cardinality	cardinality	PROPN
ejpam-1809	15	40	k	k	PROPN
ejpam-1809	15	41	is	be	AUX
ejpam-1809	15	42	independent	independent	ADJ
ejpam-1809	15	43	}	}	PUNCT
ejpam-1809	15	44	•	•	NUM
ejpam-1809	15	45	r2(s	r2(s	NOUN
ejpam-1809	15	46	)	)	PUNCT
ejpam-1809	16	1	=	=	NOUN
ejpam-1809	16	2	min{k	min{k	NOUN
ejpam-1809	16	3	:	:	PUNCT
ejpam-1809	16	4	there	there	PRON
ejpam-1809	16	5	exists	exist	VERB
ejpam-1809	16	6	a	a	DET
ejpam-1809	16	7	subset	subset	ADJ
ejpam-1809	16	8	u	u	NOUN
ejpam-1809	16	9	of	of	ADP
ejpam-1809	16	10	s	s	PRON
ejpam-1809	16	11	of	of	ADP
ejpam-1809	16	12	cardinality	cardinality	PROPN
ejpam-1809	16	13	k	k	PROPN
ejpam-1809	16	14	which	which	PRON
ejpam-1809	16	15	generates	generate	VERB
ejpam-1809	16	16	s	s	PART
ejpam-1809	16	17	}	}	PUNCT
ejpam-1809	16	18	email	email	NOUN
ejpam-1809	16	19	addresses	address	NOUN
ejpam-1809	16	20	:	:	PUNCT
ejpam-1809	17	1	melisminisker@hotmail.com	melisminisker@hotmail.com	X
ejpam-1809	17	2	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1809	17	3	335	335	NUM
ejpam-1809	18	1	c	c	X
ejpam-1809	18	2	©	©	PROPN
ejpam-1809	18	3	2013	2013	NUM
ejpam-1809	18	4	ejpam	ejpam	NOUN
ejpam-1809	18	5	all	all	DET
ejpam-1809	18	6	rights	right	NOUN
ejpam-1809	18	7	reserved	reserve	VERB
ejpam-1809	18	8	.	.	PUNCT
ejpam-1809	19	1	m.	m.	NOUN
ejpam-1809	19	2	minisker	minisker	PROPN
ejpam-1809	19	3	/	/	SYM
ejpam-1809	19	4	eur	eur	PROPN
ejpam-1809	19	5	.	.	PUNCT
ejpam-1809	20	1	j.	j.	PROPN
ejpam-1809	20	2	pure	pure	PROPN
ejpam-1809	20	3	appl	appl	PROPN
ejpam-1809	20	4	.	.	PROPN
ejpam-1809	20	5	math	math	PROPN
ejpam-1809	20	6	,	,	PUNCT
ejpam-1809	20	7	6	6	NUM
ejpam-1809	20	8	(	(	PUNCT
ejpam-1809	20	9	2013	2013	NUM
ejpam-1809	20	10	)	)	PUNCT
ejpam-1809	20	11	,	,	PUNCT
ejpam-1809	20	12	335	335	NUM
ejpam-1809	20	13	-	-	SYM
ejpam-1809	20	14	339	339	NUM
ejpam-1809	20	15	336	336	NUM
ejpam-1809	20	16	•	•	NUM
ejpam-1809	20	17	r3(s	r3(s	PROPN
ejpam-1809	20	18	)	)	PUNCT
ejpam-1809	20	19	=	=	SYM
ejpam-1809	20	20	max{k	max{k	NOUN
ejpam-1809	20	21	:	:	PUNCT
ejpam-1809	20	22	there	there	PRON
ejpam-1809	20	23	exists	exist	VERB
ejpam-1809	20	24	a	a	DET
ejpam-1809	20	25	subset	subset	ADJ
ejpam-1809	20	26	u	u	NOUN
ejpam-1809	20	27	of	of	ADP
ejpam-1809	20	28	s	s	PRON
ejpam-1809	20	29	of	of	ADP
ejpam-1809	20	30	cardinality	cardinality	PROPN
ejpam-1809	20	31	k	k	PROPN
ejpam-1809	20	32	which	which	PRON
ejpam-1809	20	33	is	be	AUX
ejpam-1809	20	34	independent	independent	ADJ
ejpam-1809	20	35	and	and	CCONJ
ejpam-1809	20	36	which	which	PRON
ejpam-1809	20	37	generates	generate	VERB
ejpam-1809	20	38	s	s	NOUN
ejpam-1809	20	39	}	}	PUNCT
ejpam-1809	20	40	•	•	NUM
ejpam-1809	20	41	r4(s	r4(s	NOUN
ejpam-1809	20	42	)	)	PUNCT
ejpam-1809	20	43	=	=	SYM
ejpam-1809	20	44	max{k	max{k	NOUN
ejpam-1809	20	45	:	:	PUNCT
ejpam-1809	20	46	there	there	PRON
ejpam-1809	20	47	exists	exist	VERB
ejpam-1809	20	48	a	a	DET
ejpam-1809	20	49	subset	subset	ADJ
ejpam-1809	20	50	u	u	NOUN
ejpam-1809	20	51	of	of	ADP
ejpam-1809	20	52	s	s	PRON
ejpam-1809	20	53	of	of	ADP
ejpam-1809	20	54	cardinality	cardinality	PROPN
ejpam-1809	20	55	k	k	PROPN
ejpam-1809	20	56	which	which	PRON
ejpam-1809	20	57	is	be	AUX
ejpam-1809	20	58	independent	independent	ADJ
ejpam-1809	20	59	}	}	PUNCT
ejpam-1809	20	60	•	•	NUM
ejpam-1809	20	61	r5(s	r5(s	NOUN
ejpam-1809	20	62	)	)	PUNCT
ejpam-1809	20	63	=	=	NOUN
ejpam-1809	20	64	min{k	min{k	NOUN
ejpam-1809	20	65	:	:	PUNCT
ejpam-1809	20	66	every	every	DET
ejpam-1809	20	67	subset	subset	ADJ
ejpam-1809	20	68	u	u	NOUN
ejpam-1809	20	69	of	of	ADP
ejpam-1809	20	70	s	s	PRON
ejpam-1809	20	71	of	of	ADP
ejpam-1809	20	72	cardinality	cardinality	PROPN
ejpam-1809	20	73	k	k	PROPN
ejpam-1809	20	74	generates	generate	VERB
ejpam-1809	20	75	s	s	PART
ejpam-1809	20	76	}	}	PUNCT
ejpam-1809	20	77	generally	generally	ADV
ejpam-1809	20	78	in	in	ADP
ejpam-1809	20	79	[	[	X
ejpam-1809	20	80	5	5	NUM
ejpam-1809	20	81	]	]	PUNCT
ejpam-1809	20	82	,	,	PUNCT
ejpam-1809	20	83	r1(s	r1(s	NOUN
ejpam-1809	20	84	)	)	PUNCT
ejpam-1809	20	85	is	be	AUX
ejpam-1809	20	86	small	small	ADJ
ejpam-1809	20	87	rank	rank	NOUN
ejpam-1809	20	88	,	,	PUNCT
ejpam-1809	20	89	r2(s	r2(s	NOUN
ejpam-1809	20	90	)	)	PUNCT
ejpam-1809	20	91	is	be	AUX
ejpam-1809	20	92	lower	low	ADJ
ejpam-1809	20	93	rank	rank	NOUN
ejpam-1809	20	94	,	,	PUNCT
ejpam-1809	20	95	r3(s	r3(s	PROPN
ejpam-1809	20	96	)	)	PUNCT
ejpam-1809	20	97	is	be	AUX
ejpam-1809	20	98	intermediate	intermediate	ADJ
ejpam-1809	20	99	rank	rank	NOUN
ejpam-1809	20	100	,	,	PUNCT
ejpam-1809	20	101	r4(s	r4(s	NOUN
ejpam-1809	20	102	)	)	PUNCT
ejpam-1809	20	103	is	be	AUX
ejpam-1809	20	104	upper	upper	ADJ
ejpam-1809	20	105	rank	rank	NOUN
ejpam-1809	20	106	and	and	CCONJ
ejpam-1809	20	107	r5(s	r5(s	X
ejpam-1809	20	108	)	)	PUNCT
ejpam-1809	21	1	is	be	AUX
ejpam-1809	21	2	large	large	ADJ
ejpam-1809	21	3	rank	rank	NOUN
ejpam-1809	21	4	.	.	PUNCT
ejpam-1809	22	1	in	in	ADP
ejpam-1809	22	2	[	[	X
ejpam-1809	22	3	5	5	NUM
ejpam-1809	22	4	]	]	PUNCT
ejpam-1809	22	5	r5(cn	r5(cn	PROPN
ejpam-1809	22	6	)	)	PUNCT
ejpam-1809	22	7	,	,	PUNCT
ejpam-1809	22	8	r5(tn	r5(tn	PROPN
ejpam-1809	22	9	)	)	PUNCT
ejpam-1809	22	10	and	and	CCONJ
ejpam-1809	22	11	r5(b(g	r5(b(g	NOUN
ejpam-1809	22	12	,	,	PUNCT
ejpam-1809	22	13	n	n	CCONJ
ejpam-1809	22	14	)	)	PUNCT
ejpam-1809	22	15	)	)	PUNCT
ejpam-1809	22	16	are	be	AUX
ejpam-1809	22	17	given	give	VERB
ejpam-1809	22	18	.	.	PUNCT
ejpam-1809	23	1	here	here	ADV
ejpam-1809	23	2	cn	cn	PROPN
ejpam-1809	23	3	is	be	AUX
ejpam-1809	23	4	the	the	DET
ejpam-1809	23	5	cyclic	cyclic	ADJ
ejpam-1809	23	6	group	group	NOUN
ejpam-1809	23	7	of	of	ADP
ejpam-1809	23	8	order	order	NOUN
ejpam-1809	23	9	n	n	CCONJ
ejpam-1809	23	10	,	,	PUNCT
ejpam-1809	23	11	tn	tn	PROPN
ejpam-1809	23	12	is	be	AUX
ejpam-1809	23	13	the	the	DET
ejpam-1809	23	14	full	full	ADJ
ejpam-1809	23	15	transformation	transformation	NOUN
ejpam-1809	23	16	semigroup	semigroup	NOUN
ejpam-1809	23	17	and	and	CCONJ
ejpam-1809	23	18	b(g	b(g	PROPN
ejpam-1809	23	19	,	,	PUNCT
ejpam-1809	23	20	n	n	CCONJ
ejpam-1809	23	21	)	)	PUNCT
ejpam-1809	23	22	is	be	AUX
ejpam-1809	23	23	a	a	DET
ejpam-1809	23	24	brandt	brandt	PROPN
ejpam-1809	23	25	semigroup	semigroup	PROPN
ejpam-1809	23	26	.	.	PUNCT
ejpam-1809	24	1	in	in	ADP
ejpam-1809	24	2	[	[	X
ejpam-1809	24	3	5	5	X
ejpam-1809	24	4	]	]	PUNCT
ejpam-1809	24	5	it	it	PRON
ejpam-1809	24	6	is	be	AUX
ejpam-1809	24	7	also	also	ADV
ejpam-1809	24	8	shown	show	VERB
ejpam-1809	24	9	that	that	SCONJ
ejpam-1809	24	10	all	all	DET
ejpam-1809	24	11	five	five	NUM
ejpam-1809	24	12	ranks	rank	NOUN
ejpam-1809	24	13	of	of	ADP
ejpam-1809	24	14	the	the	DET
ejpam-1809	24	15	aperiodic	aperiodic	ADJ
ejpam-1809	24	16	brandt	brandt	PROPN
ejpam-1809	24	17	semigroup	semigroup	PROPN
ejpam-1809	24	18	bn	bn	PROPN
ejpam-1809	24	19	are	be	AUX
ejpam-1809	24	20	different	different	ADJ
ejpam-1809	24	21	.	.	PUNCT
ejpam-1809	25	1	in	in	ADP
ejpam-1809	25	2	this	this	DET
ejpam-1809	25	3	paper	paper	NOUN
ejpam-1809	25	4	we	we	PRON
ejpam-1809	25	5	examine	examine	VERB
ejpam-1809	25	6	r1(b(g	r1(b(g	NOUN
ejpam-1809	25	7	,	,	PUNCT
ejpam-1809	25	8	n	n	CCONJ
ejpam-1809	25	9	)	)	PUNCT
ejpam-1809	25	10	)	)	PUNCT
ejpam-1809	25	11	,	,	PUNCT
ejpam-1809	25	12	r2(b(g	r2(b(g	NOUN
ejpam-1809	25	13	,	,	PUNCT
ejpam-1809	25	14	n	n	CCONJ
ejpam-1809	25	15	)	)	PUNCT
ejpam-1809	25	16	)	)	PUNCT
ejpam-1809	25	17	,	,	PUNCT
ejpam-1809	25	18	r3(b(g	r3(b(g	NOUN
ejpam-1809	25	19	,	,	PUNCT
ejpam-1809	25	20	n	n	CCONJ
ejpam-1809	25	21	)	)	PUNCT
ejpam-1809	25	22	)	)	PUNCT
ejpam-1809	25	23	and	and	CCONJ
ejpam-1809	25	24	r4(b(g	r4(b(g	NOUN
ejpam-1809	25	25	,	,	PUNCT
ejpam-1809	25	26	n	n	CCONJ
ejpam-1809	25	27	)	)	PUNCT
ejpam-1809	25	28	)	)	PUNCT
ejpam-1809	25	29	.	.	PUNCT
ejpam-1809	26	1	2	2	X
ejpam-1809	26	2	.	.	X
ejpam-1809	26	3	periodicity	periodicity	NOUN
ejpam-1809	26	4	recall	recall	VERB
ejpam-1809	26	5	that	that	SCONJ
ejpam-1809	26	6	a	a	DET
ejpam-1809	26	7	semigroup	semigroup	NOUN
ejpam-1809	26	8	s	s	VERB
ejpam-1809	26	9	is	be	AUX
ejpam-1809	26	10	periodic	periodic	ADJ
ejpam-1809	26	11	if	if	SCONJ
ejpam-1809	26	12	,	,	PUNCT
ejpam-1809	26	13	for	for	SCONJ
ejpam-1809	26	14	each	each	DET
ejpam-1809	26	15	s	s	X
ejpam-1809	26	16	∈	∈	PROPN
ejpam-1809	26	17	s	s	VERB
ejpam-1809	26	18	the	the	DET
ejpam-1809	26	19	monogenic	monogenic	ADJ
ejpam-1809	26	20	semigroup	semigroup	NOUN
ejpam-1809	26	21	generated	generate	VERB
ejpam-1809	26	22	by	by	ADP
ejpam-1809	26	23	s	s	PROPN
ejpam-1809	26	24	is	be	AUX
ejpam-1809	26	25	finite	finite	ADJ
ejpam-1809	26	26	,	,	PUNCT
ejpam-1809	26	27	or	or	CCONJ
ejpam-1809	26	28	equivalently	equivalently	ADV
ejpam-1809	26	29	there	there	PRON
ejpam-1809	26	30	exists	exist	VERB
ejpam-1809	26	31	positive	positive	ADJ
ejpam-1809	26	32	integers	integer	NOUN
ejpam-1809	26	33	m	m	VERB
ejpam-1809	26	34	and	and	CCONJ
ejpam-1809	26	35	n	n	PROPN
ejpam-1809	26	36	(	(	PUNCT
ejpam-1809	26	37	depending	depend	VERB
ejpam-1809	26	38	on	on	ADP
ejpam-1809	26	39	s	s	NOUN
ejpam-1809	26	40	)	)	PUNCT
ejpam-1809	27	1	such	such	ADJ
ejpam-1809	27	2	that	that	SCONJ
ejpam-1809	27	3	sm	sm	PROPN
ejpam-1809	27	4	=	=	SYM
ejpam-1809	27	5	sn	sn	PROPN
ejpam-1809	27	6	.	.	PUNCT
ejpam-1809	27	7	theorem	theorem	NOUN
ejpam-1809	27	8	1	1	NUM
ejpam-1809	27	9	.	.	PUNCT
ejpam-1809	28	1	let	let	VERB
ejpam-1809	28	2	s	s	PRON
ejpam-1809	28	3	and	and	CCONJ
ejpam-1809	28	4	t	t	PROPN
ejpam-1809	28	5	be	be	AUX
ejpam-1809	28	6	finite	finite	ADJ
ejpam-1809	28	7	semigroups	semigroup	NOUN
ejpam-1809	28	8	.	.	PUNCT
ejpam-1809	29	1	then	then	ADV
ejpam-1809	29	2	s	s	VERB
ejpam-1809	29	3	and	and	CCONJ
ejpam-1809	29	4	t	t	PROPN
ejpam-1809	29	5	are	be	AUX
ejpam-1809	29	6	periodic	periodic	ADJ
ejpam-1809	29	7	if	if	SCONJ
ejpam-1809	29	8	and	and	CCONJ
ejpam-1809	29	9	only	only	ADV
ejpam-1809	29	10	if	if	SCONJ
ejpam-1809	29	11	s	s	X
ejpam-1809	29	12	∪	∪	ADJ
ejpam-1809	29	13	t	t	PROPN
ejpam-1809	29	14	is	be	AUX
ejpam-1809	29	15	periodic	periodic	ADJ
ejpam-1809	29	16	.	.	PUNCT
ejpam-1809	30	1	proof	proof	NOUN
ejpam-1809	30	2	.	.	PUNCT
ejpam-1809	31	1	(	(	PUNCT
ejpam-1809	31	2	⇒	⇒	NOUN
ejpam-1809	31	3	)	)	PUNCT
ejpam-1809	31	4	let	let	VERB
ejpam-1809	31	5	s	s	PRON
ejpam-1809	31	6	and	and	CCONJ
ejpam-1809	31	7	t	t	PROPN
ejpam-1809	31	8	be	be	AUX
ejpam-1809	31	9	periodic	periodic	ADJ
ejpam-1809	31	10	.	.	PUNCT
ejpam-1809	32	1	let	let	VERB
ejpam-1809	32	2	x	x	PUNCT
ejpam-1809	32	3	∈	∈	NOUN
ejpam-1809	32	4	s	s	VERB
ejpam-1809	32	5	∪	∪	ADJ
ejpam-1809	32	6	t	t	NOUN
ejpam-1809	32	7	.	.	PUNCT
ejpam-1809	33	1	then	then	ADV
ejpam-1809	33	2	x	x	X
ejpam-1809	33	3	∈	∈	PROPN
ejpam-1809	33	4	s	s	PART
ejpam-1809	33	5	or	or	CCONJ
ejpam-1809	33	6	x	x	PROPN
ejpam-1809	33	7	∈	∈	PROPN
ejpam-1809	33	8	t	t	NOUN
ejpam-1809	33	9	.	.	PUNCT
ejpam-1809	34	1	if	if	SCONJ
ejpam-1809	34	2	x	x	PUNCT
ejpam-1809	34	3	∈	∈	PROPN
ejpam-1809	34	4	s	s	NOUN
ejpam-1809	34	5	,	,	PUNCT
ejpam-1809	34	6	since	since	SCONJ
ejpam-1809	34	7	s	s	NOUN
ejpam-1809	34	8	is	be	AUX
ejpam-1809	34	9	periodic	periodic	ADJ
ejpam-1809	34	10	there	there	ADV
ejpam-1809	34	11	exists	exist	VERB
ejpam-1809	34	12	∃m	∃m	PROPN
ejpam-1809	34	13	,	,	PUNCT
ejpam-1809	34	14	n	n	PROPN
ejpam-1809	34	15	∈	∈	PROPN
ejpam-1809	34	16	n	n	PRON
ejpam-1809	34	17	such	such	ADJ
ejpam-1809	34	18	that	that	PRON
ejpam-1809	34	19	xm	xm	PROPN
ejpam-1809	35	1	=	=	SYM
ejpam-1809	36	1	xn	xn	PROPN
ejpam-1809	36	2	.	.	PUNCT
ejpam-1809	37	1	if	if	SCONJ
ejpam-1809	37	2	x	x	SYM
ejpam-1809	37	3	∈	∈	PROPN
ejpam-1809	37	4	t	t	NOUN
ejpam-1809	37	5	,	,	PUNCT
ejpam-1809	37	6	since	since	SCONJ
ejpam-1809	37	7	t	t	PROPN
ejpam-1809	37	8	is	be	AUX
ejpam-1809	37	9	periodic	periodic	ADJ
ejpam-1809	37	10	there	there	ADV
ejpam-1809	37	11	exists	exist	VERB
ejpam-1809	37	12	∃k	∃k	PROPN
ejpam-1809	37	13	,	,	PUNCT
ejpam-1809	37	14	l	l	NOUN
ejpam-1809	37	15	∈	∈	PROPN
ejpam-1809	37	16	n	n	PRON
ejpam-1809	37	17	such	such	ADJ
ejpam-1809	37	18	that	that	SCONJ
ejpam-1809	37	19	xk	xk	PROPN
ejpam-1809	38	1	=	=	PUNCT
ejpam-1809	38	2	x	x	X
ejpam-1809	38	3	l	l	NOUN
ejpam-1809	38	4	.	.	PUNCT
ejpam-1809	39	1	so	so	ADV
ejpam-1809	39	2	s	s	X
ejpam-1809	39	3	∪	∪	PROPN
ejpam-1809	39	4	t	t	PROPN
ejpam-1809	39	5	is	be	AUX
ejpam-1809	39	6	periodic	periodic	ADJ
ejpam-1809	39	7	.	.	PUNCT
ejpam-1809	40	1	(	(	PUNCT
ejpam-1809	40	2	⇐	⇐	NOUN
ejpam-1809	40	3	)	)	PUNCT
ejpam-1809	40	4	let	let	VERB
ejpam-1809	40	5	s	s	PRON
ejpam-1809	40	6	∪	∪	VERB
ejpam-1809	40	7	t	t	PROPN
ejpam-1809	40	8	be	be	AUX
ejpam-1809	40	9	periodic	periodic	ADJ
ejpam-1809	40	10	.	.	PUNCT
ejpam-1809	41	1	let	let	VERB
ejpam-1809	41	2	x	x	SYM
ejpam-1809	41	3	∈	∈	PROPN
ejpam-1809	41	4	s.	s.	PROPN
ejpam-1809	41	5	since	since	SCONJ
ejpam-1809	41	6	s	s	PRON
ejpam-1809	41	7	⊆	⊆	NUM
ejpam-1809	41	8	s	s	NOUN
ejpam-1809	41	9	∪	∪	NOUN
ejpam-1809	41	10	t	t	NOUN
ejpam-1809	41	11	we	we	PRON
ejpam-1809	41	12	have	have	VERB
ejpam-1809	41	13	x	x	X
ejpam-1809	41	14	∈	∈	NOUN
ejpam-1809	41	15	s	s	PART
ejpam-1809	41	16	∪	∪	ADJ
ejpam-1809	41	17	t	t	NOUN
ejpam-1809	41	18	.	.	PUNCT
ejpam-1809	42	1	since	since	SCONJ
ejpam-1809	42	2	s	s	PROPN
ejpam-1809	42	3	∪	∪	PROPN
ejpam-1809	42	4	t	t	PROPN
ejpam-1809	42	5	is	be	AUX
ejpam-1809	42	6	periodic	periodic	ADJ
ejpam-1809	42	7	there	there	ADV
ejpam-1809	42	8	exists	exist	VERB
ejpam-1809	42	9	∃k1	∃k1	NOUN
ejpam-1809	42	10	,	,	PUNCT
ejpam-1809	42	11	k2	k2	PROPN
ejpam-1809	42	12	∈	∈	PROPN
ejpam-1809	42	13	n	n	PRON
ejpam-1809	42	14	such	such	ADJ
ejpam-1809	42	15	that	that	DET
ejpam-1809	42	16	xk1	xk1	PROPN
ejpam-1809	42	17	=	=	PUNCT
ejpam-1809	42	18	xk2	xk2	NOUN
ejpam-1809	42	19	.	.	PUNCT
ejpam-1809	43	1	we	we	PRON
ejpam-1809	43	2	obtain	obtain	VERB
ejpam-1809	43	3	s	s	PART
ejpam-1809	43	4	is	be	AUX
ejpam-1809	43	5	periodic	periodic	ADJ
ejpam-1809	43	6	.	.	PUNCT
ejpam-1809	44	1	let	let	VERB
ejpam-1809	44	2	y	y	PROPN
ejpam-1809	44	3	∈	∈	PROPN
ejpam-1809	44	4	t	t	PROPN
ejpam-1809	44	5	.	.	PUNCT
ejpam-1809	45	1	since	since	SCONJ
ejpam-1809	45	2	t	t	PROPN
ejpam-1809	45	3	⊆	⊆	NUM
ejpam-1809	45	4	s	s	PART
ejpam-1809	45	5	∪	∪	NOUN
ejpam-1809	45	6	t	t	NOUN
ejpam-1809	45	7	we	we	PRON
ejpam-1809	45	8	have	have	VERB
ejpam-1809	45	9	y	y	PROPN
ejpam-1809	45	10	∈	∈	PROPN
ejpam-1809	45	11	s	s	PART
ejpam-1809	45	12	∪	∪	PROPN
ejpam-1809	45	13	t	t	NOUN
ejpam-1809	45	14	.	.	PUNCT
ejpam-1809	46	1	since	since	SCONJ
ejpam-1809	46	2	s	s	PROPN
ejpam-1809	46	3	∪	∪	PROPN
ejpam-1809	46	4	t	t	PROPN
ejpam-1809	46	5	is	be	AUX
ejpam-1809	46	6	periodic	periodic	ADJ
ejpam-1809	46	7	there	there	ADV
ejpam-1809	46	8	exists	exist	VERB
ejpam-1809	46	9	∃k3	∃k3	NOUN
ejpam-1809	46	10	,	,	PUNCT
ejpam-1809	46	11	k4	k4	PROPN
ejpam-1809	46	12	∈	∈	PROPN
ejpam-1809	46	13	n	n	PRON
ejpam-1809	46	14	such	such	ADJ
ejpam-1809	46	15	that	that	SCONJ
ejpam-1809	46	16	yk3	yk3	PROPN
ejpam-1809	46	17	=	=	PUNCT
ejpam-1809	46	18	yk4	yk4	PROPN
ejpam-1809	46	19	.	.	PUNCT
ejpam-1809	47	1	thus	thus	ADV
ejpam-1809	47	2	t	t	PROPN
ejpam-1809	47	3	is	be	AUX
ejpam-1809	47	4	also	also	ADV
ejpam-1809	47	5	periodic	periodic	ADJ
ejpam-1809	47	6	.	.	PUNCT
ejpam-1809	48	1	3	3	X
ejpam-1809	48	2	.	.	X
ejpam-1809	48	3	residual	residual	ADJ
ejpam-1809	48	4	finiteness	finiteness	NOUN
ejpam-1809	48	5	we	we	PRON
ejpam-1809	48	6	call	call	VERB
ejpam-1809	48	7	a	a	DET
ejpam-1809	48	8	semigroup	semigroup	NOUN
ejpam-1809	48	9	residually	residually	ADV
ejpam-1809	48	10	finite	finite	VERB
ejpam-1809	48	11	if	if	SCONJ
ejpam-1809	48	12	,	,	PUNCT
ejpam-1809	48	13	for	for	ADP
ejpam-1809	48	14	each	each	DET
ejpam-1809	48	15	pair	pair	NOUN
ejpam-1809	48	16	s	s	PART
ejpam-1809	48	17	6=	6=	PROPN
ejpam-1809	48	18	t	t	PROPN
ejpam-1809	48	19	∈	∈	PROPN
ejpam-1809	48	20	s	s	VERB
ejpam-1809	48	21	there	there	PRON
ejpam-1809	48	22	exists	exist	VERB
ejpam-1809	48	23	a	a	DET
ejpam-1809	48	24	homomorphism	homomorphism	NOUN
ejpam-1809	48	25	φ	φ	NUM
ejpam-1809	48	26	from	from	ADP
ejpam-1809	48	27	s	s	PRON
ejpam-1809	48	28	onto	onto	ADP
ejpam-1809	48	29	a	a	DET
ejpam-1809	48	30	finite	finite	ADJ
ejpam-1809	48	31	semigroup	semigroup	NOUN
ejpam-1809	49	1	such	such	ADJ
ejpam-1809	49	2	that	that	SCONJ
ejpam-1809	49	3	φ(s	φ(	VERB
ejpam-1809	49	4	)	)	PUNCT
ejpam-1809	49	5	6=	6=	ADP
ejpam-1809	49	6	φ(t	φ(t	PROPN
ejpam-1809	49	7	)	)	PUNCT
ejpam-1809	49	8	,	,	PUNCT
ejpam-1809	49	9	or	or	CCONJ
ejpam-1809	49	10	equivalently	equivalently	ADV
ejpam-1809	49	11	,	,	PUNCT
ejpam-1809	49	12	there	there	PRON
ejpam-1809	49	13	exists	exist	VERB
ejpam-1809	49	14	a	a	DET
ejpam-1809	49	15	congruance	congruance	NOUN
ejpam-1809	49	16	ρ	ρ	NOUN
ejpam-1809	49	17	with	with	ADP
ejpam-1809	49	18	finite	finite	ADJ
ejpam-1809	49	19	index	index	NOUN
ejpam-1809	49	20	(	(	PUNCT
ejpam-1809	49	21	that	that	PRON
ejpam-1809	49	22	is	is	ADV
ejpam-1809	49	23	ρ	ρ	NOUN
ejpam-1809	49	24	has	have	VERB
ejpam-1809	49	25	finitely	finitely	ADV
ejpam-1809	49	26	many	many	ADJ
ejpam-1809	49	27	equivalence	equivalence	NOUN
ejpam-1809	49	28	classes	class	NOUN
ejpam-1809	49	29	)	)	PUNCT
ejpam-1809	49	30	such	such	ADJ
ejpam-1809	49	31	that	that	SCONJ
ejpam-1809	49	32	(	(	PUNCT
ejpam-1809	49	33	s	s	PROPN
ejpam-1809	49	34	,	,	PUNCT
ejpam-1809	49	35	t	t	PROPN
ejpam-1809	49	36	)	)	PUNCT
ejpam-1809	49	37	/∈	/∈	PUNCT
ejpam-1809	50	1	ρ	ρ	PROPN
ejpam-1809	50	2	.	.	PUNCT
ejpam-1809	51	1	(	(	PUNCT
ejpam-1809	51	2	residual	residual	ADJ
ejpam-1809	51	3	finiteness	finiteness	NOUN
ejpam-1809	51	4	of	of	ADP
ejpam-1809	51	5	completely	completely	ADV
ejpam-1809	51	6	(	(	PUNCT
ejpam-1809	51	7	0)-simple	0)-simple	NUM
ejpam-1809	51	8	semigroups	semigroup	NOUN
ejpam-1809	51	9	,	,	PUNCT
ejpam-1809	51	10	which	which	PRON
ejpam-1809	51	11	are	be	AUX
ejpam-1809	51	12	rees	rees	PROPN
ejpam-1809	51	13	matrix	matrix	NOUN
ejpam-1809	51	14	semigroups	semigroup	NOUN
ejpam-1809	51	15	m[g	m[g	NOUN
ejpam-1809	51	16	;	;	PUNCT
ejpam-1809	51	17	i	i	PRON
ejpam-1809	51	18	,	,	PUNCT
ejpam-1809	51	19	j	j	PROPN
ejpam-1809	51	20	,	,	PUNCT
ejpam-1809	51	21	p	p	X
ejpam-1809	51	22	]	]	X
ejpam-1809	51	23	over	over	ADP
ejpam-1809	51	24	groups	group	NOUN
ejpam-1809	51	25	was	be	AUX
ejpam-1809	51	26	investigated	investigate	VERB
ejpam-1809	51	27	in	in	ADP
ejpam-1809	51	28	[	[	X
ejpam-1809	51	29	2	2	NUM
ejpam-1809	51	30	]	]	PUNCT
ejpam-1809	51	31	.	.	PUNCT
ejpam-1809	51	32	)	)	PUNCT
ejpam-1809	52	1	theorem	theorem	VERB
ejpam-1809	52	2	2	2	NUM
ejpam-1809	52	3	.	.	PUNCT
ejpam-1809	53	1	s	s	PART
ejpam-1809	54	1	∪	∪	PROPN
ejpam-1809	54	2	t	t	PROPN
ejpam-1809	54	3	is	be	AUX
ejpam-1809	54	4	residually	residually	ADV
ejpam-1809	54	5	finite	finite	ADJ
ejpam-1809	54	6	if	if	SCONJ
ejpam-1809	54	7	and	and	CCONJ
ejpam-1809	54	8	only	only	ADV
ejpam-1809	54	9	if	if	SCONJ
ejpam-1809	54	10	s	s	PRON
ejpam-1809	54	11	and	and	CCONJ
ejpam-1809	54	12	t	t	PROPN
ejpam-1809	54	13	are	be	AUX
ejpam-1809	54	14	residually	residually	ADV
ejpam-1809	54	15	finite	finite	ADJ
ejpam-1809	54	16	.	.	PUNCT
ejpam-1809	55	1	proof	proof	NOUN
ejpam-1809	55	2	.	.	PUNCT
ejpam-1809	56	1	(	(	PUNCT
ejpam-1809	56	2	⇒	⇒	NOUN
ejpam-1809	56	3	)	)	PUNCT
ejpam-1809	56	4	assume	assume	VERB
ejpam-1809	56	5	that	that	SCONJ
ejpam-1809	56	6	s∪t	s∪t	NOUN
ejpam-1809	56	7	is	be	AUX
ejpam-1809	56	8	residually	residually	ADV
ejpam-1809	56	9	finite	finite	ADJ
ejpam-1809	56	10	.	.	PUNCT
ejpam-1809	57	1	since	since	SCONJ
ejpam-1809	57	2	s	s	PROPN
ejpam-1809	57	3	and	and	CCONJ
ejpam-1809	57	4	t	t	PROPN
ejpam-1809	57	5	are	be	AUX
ejpam-1809	57	6	subsemigroups	subsemigroup	NOUN
ejpam-1809	57	7	of	of	ADP
ejpam-1809	57	8	s∪t	s∪t	NOUN
ejpam-1809	57	9	then	then	ADV
ejpam-1809	57	10	s	s	PRON
ejpam-1809	57	11	and	and	CCONJ
ejpam-1809	57	12	t	t	PROPN
ejpam-1809	57	13	are	be	AUX
ejpam-1809	57	14	residually	residually	ADV
ejpam-1809	57	15	finite	finite	ADJ
ejpam-1809	57	16	.	.	PUNCT
ejpam-1809	58	1	(	(	PUNCT
ejpam-1809	58	2	⇐	⇐	ADJ
ejpam-1809	58	3	)	)	PUNCT
ejpam-1809	58	4	assume	assume	VERB
ejpam-1809	58	5	that	that	SCONJ
ejpam-1809	58	6	s	s	VERB
ejpam-1809	58	7	and	and	CCONJ
ejpam-1809	58	8	t	t	PROPN
ejpam-1809	58	9	are	be	AUX
ejpam-1809	58	10	residually	residually	ADV
ejpam-1809	58	11	finite	finite	ADJ
ejpam-1809	58	12	semigroups	semigroup	NOUN
ejpam-1809	58	13	.	.	PUNCT
ejpam-1809	59	1	we	we	PRON
ejpam-1809	59	2	will	will	AUX
ejpam-1809	59	3	show	show	VERB
ejpam-1809	59	4	that	that	DET
ejpam-1809	59	5	s∪t	s∪t	NOUN
ejpam-1809	59	6	is	be	AUX
ejpam-1809	59	7	residually	residually	ADV
ejpam-1809	59	8	finite	finite	ADJ
ejpam-1809	59	9	.	.	PUNCT
ejpam-1809	60	1	let	let	VERB
ejpam-1809	60	2	s1	s1	NOUN
ejpam-1809	60	3	,	,	PUNCT
ejpam-1809	60	4	s2	s2	PROPN
ejpam-1809	60	5	∈	∈	PROPN
ejpam-1809	60	6	s∪t	s∪t	NOUN
ejpam-1809	60	7	and	and	CCONJ
ejpam-1809	60	8	s1	s1	PROPN
ejpam-1809	60	9	6=	6=	NUM
ejpam-1809	60	10	s2	s2	PROPN
ejpam-1809	60	11	.	.	PUNCT
ejpam-1809	61	1	since	since	SCONJ
ejpam-1809	61	2	s	s	NOUN
ejpam-1809	61	3	is	be	AUX
ejpam-1809	61	4	residually	residually	ADV
ejpam-1809	61	5	finite	finite	ADJ
ejpam-1809	61	6	there	there	PRON
ejpam-1809	61	7	is	be	VERB
ejpam-1809	61	8	a	a	DET
ejpam-1809	61	9	finite	finite	NOUN
ejpam-1809	61	10	semigroup	semigroup	PROPN
ejpam-1809	61	11	k	k	PROPN
ejpam-1809	61	12	and	and	CCONJ
ejpam-1809	61	13	an	an	PRON
ejpam-1809	61	14	onto	onto	ADP
ejpam-1809	61	15	homomorphism	homomorphism	PROPN
ejpam-1809	61	16	φ	φ	NOUN
ejpam-1809	61	17	:	:	PUNCT
ejpam-1809	61	18	s→	s→	X
ejpam-1809	62	1	k	k	PROPN
ejpam-1809	62	2	such	such	ADJ
ejpam-1809	62	3	that	that	DET
ejpam-1809	62	4	φ(s1	φ(s1	NOUN
ejpam-1809	62	5	)	)	PUNCT
ejpam-1809	62	6	6=	6=	ADP
ejpam-1809	62	7	φ(s2	φ(s2	NOUN
ejpam-1809	62	8	)	)	PUNCT
ejpam-1809	62	9	.	.	PUNCT
ejpam-1809	63	1	let	let	VERB
ejpam-1809	63	2	ψ	ψ	X
ejpam-1809	63	3	:	:	PUNCT
ejpam-1809	63	4	s	s	VERB
ejpam-1809	63	5	∪	∪	PROPN
ejpam-1809	63	6	t	t	PROPN
ejpam-1809	63	7	→	→	SYM
ejpam-1809	63	8	k	k	X
ejpam-1809	63	9	∪	∪	X
ejpam-1809	63	10	{	{	PUNCT
ejpam-1809	63	11	0	0	NUM
ejpam-1809	63	12	}	}	PUNCT
ejpam-1809	63	13	.	.	PUNCT
ejpam-1809	64	1	if	if	SCONJ
ejpam-1809	64	2	x	x	PUNCT
ejpam-1809	64	3	∈	∈	PROPN
ejpam-1809	64	4	s	s	PART
ejpam-1809	64	5	m.	m.	NOUN
ejpam-1809	64	6	minisker	minisker	PROPN
ejpam-1809	64	7	/	/	SYM
ejpam-1809	64	8	eur	eur	PROPN
ejpam-1809	64	9	.	.	PUNCT
ejpam-1809	65	1	j.	j.	PROPN
ejpam-1809	65	2	pure	pure	PROPN
ejpam-1809	65	3	appl	appl	PROPN
ejpam-1809	65	4	.	.	PROPN
ejpam-1809	65	5	math	math	PROPN
ejpam-1809	65	6	,	,	PUNCT
ejpam-1809	65	7	6	6	NUM
ejpam-1809	65	8	(	(	PUNCT
ejpam-1809	65	9	2013	2013	NUM
ejpam-1809	65	10	)	)	PUNCT
ejpam-1809	65	11	,	,	PUNCT
ejpam-1809	65	12	335	335	NUM
ejpam-1809	65	13	-	-	SYM
ejpam-1809	65	14	339	339	NUM
ejpam-1809	65	15	337	337	NUM
ejpam-1809	65	16	let	let	VERB
ejpam-1809	65	17	ψ(x	ψ(x	NOUN
ejpam-1809	65	18	)	)	PUNCT
ejpam-1809	65	19	=	=	SYM
ejpam-1809	66	1	φ(x	φ(x	NOUN
ejpam-1809	66	2	)	)	PUNCT
ejpam-1809	66	3	and	and	CCONJ
ejpam-1809	66	4	if	if	SCONJ
ejpam-1809	66	5	x	x	SYM
ejpam-1809	66	6	∈	∈	PROPN
ejpam-1809	66	7	t	t	NOUN
ejpam-1809	66	8	let	let	VERB
ejpam-1809	66	9	ψ(x	ψ(x	NOUN
ejpam-1809	66	10	)	)	PUNCT
ejpam-1809	66	11	=	=	SYM
ejpam-1809	67	1	0	0	X
ejpam-1809	67	2	.	.	PUNCT
ejpam-1809	67	3	then	then	ADV
ejpam-1809	67	4	ψ(s1	ψ(s1	VERB
ejpam-1809	67	5	)	)	PUNCT
ejpam-1809	68	1	=	=	SYM
ejpam-1809	68	2	φ(s1	φ(s1	NOUN
ejpam-1809	68	3	)	)	PUNCT
ejpam-1809	68	4	6=	6=	SYM
ejpam-1809	68	5	φ(s2	φ(s2	NOUN
ejpam-1809	68	6	)	)	PUNCT
ejpam-1809	68	7	=	=	SYM
ejpam-1809	68	8	ψ(s2	ψ(s2	NOUN
ejpam-1809	68	9	)	)	PUNCT
ejpam-1809	68	10	.	.	PUNCT
ejpam-1809	69	1	if	if	SCONJ
ejpam-1809	69	2	s1	s1	NOUN
ejpam-1809	69	3	,	,	PUNCT
ejpam-1809	69	4	s2	s2	NOUN
ejpam-1809	69	5	∈	∈	PROPN
ejpam-1809	69	6	s	s	PART
ejpam-1809	69	7	then	then	ADV
ejpam-1809	69	8	ψ(s1s2	ψ(s1s2	ADJ
ejpam-1809	69	9	)	)	PUNCT
ejpam-1809	69	10	=	=	SYM
ejpam-1809	69	11	φ(s1s2	φ(s1s2	PROPN
ejpam-1809	69	12	)	)	PUNCT
ejpam-1809	69	13	=	=	SYM
ejpam-1809	69	14	φ(s1).φ(s2	φ(s1).φ(s2	NOUN
ejpam-1809	69	15	)	)	PUNCT
ejpam-1809	69	16	.	.	PUNCT
ejpam-1809	70	1	if	if	SCONJ
ejpam-1809	70	2	t1	t1	NOUN
ejpam-1809	70	3	,	,	PUNCT
ejpam-1809	70	4	t2	t2	PROPN
ejpam-1809	70	5	∈	∈	PROPN
ejpam-1809	70	6	t	t	PROPN
ejpam-1809	70	7	then	then	ADV
ejpam-1809	70	8	ψ(t1	ψ(t1	VERB
ejpam-1809	70	9	t2	t2	NOUN
ejpam-1809	70	10	)	)	PUNCT
ejpam-1809	71	1	=	=	SYM
ejpam-1809	71	2	0	0	X
ejpam-1809	71	3	=	=	PUNCT
ejpam-1809	71	4	ψ(t1).ψ(t2	ψ(t1).ψ(t2	X
ejpam-1809	71	5	)	)	PUNCT
ejpam-1809	71	6	=	=	SYM
ejpam-1809	71	7	0.0	0.0	NUM
ejpam-1809	71	8	.	.	PUNCT
ejpam-1809	72	1	if	if	SCONJ
ejpam-1809	72	2	s	s	VERB
ejpam-1809	72	3	∈	∈	PROPN
ejpam-1809	72	4	s	s	X
ejpam-1809	72	5	and	and	CCONJ
ejpam-1809	72	6	t	t	PROPN
ejpam-1809	72	7	∈	∈	PROPN
ejpam-1809	72	8	t	t	PROPN
ejpam-1809	72	9	then	then	ADV
ejpam-1809	72	10	ψ(st	ψ(st	NOUN
ejpam-1809	72	11	)	)	PUNCT
ejpam-1809	72	12	=	=	SYM
ejpam-1809	72	13	ψ(t	ψ(t	PROPN
ejpam-1809	72	14	)	)	PUNCT
ejpam-1809	72	15	=	=	SYM
ejpam-1809	72	16	0	0	NUM
ejpam-1809	72	17	=	=	NUM
ejpam-1809	72	18	ψ(s)ψ(t	ψ(s)ψ(t	X
ejpam-1809	72	19	)	)	PUNCT
ejpam-1809	72	20	.	.	PUNCT
ejpam-1809	73	1	so	so	ADV
ejpam-1809	73	2	ψ	ψ	NOUN
ejpam-1809	73	3	is	be	AUX
ejpam-1809	73	4	an	an	PRON
ejpam-1809	73	5	onto	onto	ADP
ejpam-1809	73	6	homomorphism	homomorphism	NOUN
ejpam-1809	73	7	.	.	PUNCT
ejpam-1809	74	1	let	let	AUX
ejpam-1809	74	2	t1	t1	NOUN
ejpam-1809	74	3	,	,	PUNCT
ejpam-1809	74	4	t2	t2	PROPN
ejpam-1809	74	5	∈	∈	PROPN
ejpam-1809	74	6	s	s	PART
ejpam-1809	74	7	∪	∪	ADJ
ejpam-1809	74	8	t	t	NOUN
ejpam-1809	74	9	and	and	CCONJ
ejpam-1809	74	10	t1	t1	NOUN
ejpam-1809	74	11	6=	6=	PROPN
ejpam-1809	75	1	t2	t2	PROPN
ejpam-1809	76	1	.	.	PUNCT
ejpam-1809	77	1	since	since	SCONJ
ejpam-1809	77	2	t	t	PROPN
ejpam-1809	77	3	is	be	AUX
ejpam-1809	77	4	residually	residually	ADV
ejpam-1809	77	5	finite	finite	ADJ
ejpam-1809	77	6	there	there	PRON
ejpam-1809	77	7	is	be	VERB
ejpam-1809	77	8	a	a	DET
ejpam-1809	77	9	finite	finite	NOUN
ejpam-1809	77	10	semigroup	semigroup	PROPN
ejpam-1809	77	11	l	l	PROPN
ejpam-1809	77	12	and	and	CCONJ
ejpam-1809	77	13	an	an	PRON
ejpam-1809	77	14	onto	onto	ADP
ejpam-1809	77	15	homomorphism	homomorphism	NOUN
ejpam-1809	77	16	θ	θ	PROPN
ejpam-1809	77	17	:	:	PUNCT
ejpam-1809	77	18	t	t	PROPN
ejpam-1809	77	19	→	→	SYM
ejpam-1809	77	20	l	l	NOUN
ejpam-1809	77	21	such	such	ADJ
ejpam-1809	77	22	that	that	DET
ejpam-1809	77	23	θ(t1	θ(t1	NOUN
ejpam-1809	77	24	)	)	PUNCT
ejpam-1809	77	25	6=	6=	ADP
ejpam-1809	77	26	θ(t2	θ(t2	NOUN
ejpam-1809	77	27	)	)	PUNCT
ejpam-1809	77	28	.	.	PUNCT
ejpam-1809	78	1	we	we	PRON
ejpam-1809	78	2	define	define	VERB
ejpam-1809	78	3	α	α	NOUN
ejpam-1809	78	4	:	:	PUNCT
ejpam-1809	78	5	s	s	VERB
ejpam-1809	78	6	∪	∪	ADP
ejpam-1809	78	7	t	t	PROPN
ejpam-1809	78	8	→	→	SYM
ejpam-1809	78	9	l	l	NOUN
ejpam-1809	78	10	∪	∪	X
ejpam-1809	78	11	{	{	PUNCT
ejpam-1809	78	12	1	1	NUM
ejpam-1809	78	13	}	}	PUNCT
ejpam-1809	78	14	as	as	SCONJ
ejpam-1809	78	15	follows	follow	VERB
ejpam-1809	78	16	.	.	PUNCT
ejpam-1809	79	1	if	if	SCONJ
ejpam-1809	79	2	x	x	PUNCT
ejpam-1809	79	3	∈	∈	PROPN
ejpam-1809	79	4	s	s	AUX
ejpam-1809	79	5	let	let	VERB
ejpam-1809	79	6	α(x	α(x	NOUN
ejpam-1809	79	7	)	)	PUNCT
ejpam-1809	79	8	=	=	SYM
ejpam-1809	79	9	1	1	NUM
ejpam-1809	79	10	and	and	CCONJ
ejpam-1809	79	11	if	if	SCONJ
ejpam-1809	79	12	x	x	SYM
ejpam-1809	79	13	∈	∈	PROPN
ejpam-1809	79	14	t	t	NOUN
ejpam-1809	79	15	let	let	VERB
ejpam-1809	79	16	α(x	α(x	NOUN
ejpam-1809	79	17	)	)	PUNCT
ejpam-1809	79	18	=	=	SYM
ejpam-1809	79	19	θ(x	θ(x	PROPN
ejpam-1809	79	20	)	)	PUNCT
ejpam-1809	79	21	.	.	PUNCT
ejpam-1809	80	1	it	it	PRON
ejpam-1809	80	2	is	be	AUX
ejpam-1809	80	3	clear	clear	ADJ
ejpam-1809	80	4	that	that	SCONJ
ejpam-1809	80	5	α(t1	α(t1	NOUN
ejpam-1809	80	6	)	)	PUNCT
ejpam-1809	80	7	=	=	PUNCT
ejpam-1809	80	8	θ(t1	θ(t1	NOUN
ejpam-1809	80	9	)	)	PUNCT
ejpam-1809	80	10	6=	6=	ADP
ejpam-1809	80	11	θ(t2	θ(t2	NOUN
ejpam-1809	80	12	)	)	PUNCT
ejpam-1809	80	13	=	=	SYM
ejpam-1809	80	14	α(t2	α(t2	NUM
ejpam-1809	80	15	)	)	PUNCT
ejpam-1809	80	16	.	.	PUNCT
ejpam-1809	81	1	if	if	SCONJ
ejpam-1809	81	2	s1	s1	NOUN
ejpam-1809	81	3	,	,	PUNCT
ejpam-1809	81	4	s2	s2	NOUN
ejpam-1809	81	5	∈	∈	PROPN
ejpam-1809	81	6	s	s	VERB
ejpam-1809	81	7	then	then	ADV
ejpam-1809	81	8	α(s1s2	α(s1s2	VERB
ejpam-1809	81	9	)	)	PUNCT
ejpam-1809	81	10	=	=	SYM
ejpam-1809	81	11	α(s1).α(s2	α(s1).α(s2	X
ejpam-1809	81	12	)	)	PUNCT
ejpam-1809	81	13	=	=	SYM
ejpam-1809	82	1	1.1	1.1	NUM
ejpam-1809	82	2	=	=	SYM
ejpam-1809	82	3	1	1	X
ejpam-1809	82	4	.	.	PUNCT
ejpam-1809	83	1	if	if	SCONJ
ejpam-1809	83	2	t1	t1	NOUN
ejpam-1809	83	3	,	,	PUNCT
ejpam-1809	83	4	t2	t2	PROPN
ejpam-1809	83	5	∈	∈	PROPN
ejpam-1809	83	6	t	t	PROPN
ejpam-1809	83	7	then	then	ADV
ejpam-1809	83	8	α(t1	α(t1	PROPN
ejpam-1809	83	9	t2	t2	PROPN
ejpam-1809	83	10	)	)	PUNCT
ejpam-1809	84	1	=	=	SYM
ejpam-1809	84	2	θ(t1	θ(t1	NOUN
ejpam-1809	84	3	t2	t2	NOUN
ejpam-1809	84	4	)	)	PUNCT
ejpam-1809	84	5	=	=	SYM
ejpam-1809	84	6	θ(t1).θ(t2	θ(t1).θ(t2	NOUN
ejpam-1809	84	7	)	)	PUNCT
ejpam-1809	84	8	.	.	PUNCT
ejpam-1809	85	1	if	if	SCONJ
ejpam-1809	85	2	s	s	VERB
ejpam-1809	85	3	∈	∈	PROPN
ejpam-1809	85	4	s	s	X
ejpam-1809	85	5	and	and	CCONJ
ejpam-1809	85	6	t	t	PROPN
ejpam-1809	85	7	∈	∈	PROPN
ejpam-1809	85	8	t	t	PROPN
ejpam-1809	85	9	then	then	ADV
ejpam-1809	85	10	α(st	α(st	NOUN
ejpam-1809	85	11	)	)	PUNCT
ejpam-1809	85	12	=	=	SYM
ejpam-1809	85	13	α(t	α(t	PROPN
ejpam-1809	85	14	)	)	PUNCT
ejpam-1809	85	15	=	=	SYM
ejpam-1809	85	16	θ(t	θ(t	PROPN
ejpam-1809	85	17	)	)	PUNCT
ejpam-1809	85	18	=	=	SYM
ejpam-1809	85	19	α(s).α(t	α(s).α(t	X
ejpam-1809	85	20	)	)	PUNCT
ejpam-1809	85	21	=	=	SYM
ejpam-1809	85	22	1.θ(t	1.θ(t	NUM
ejpam-1809	85	23	)	)	PUNCT
ejpam-1809	85	24	.	.	PUNCT
ejpam-1809	86	1	so	so	ADV
ejpam-1809	86	2	α	α	PRON
ejpam-1809	86	3	is	be	AUX
ejpam-1809	86	4	an	an	PRON
ejpam-1809	86	5	onto	onto	ADP
ejpam-1809	86	6	homomorphism	homomorphism	NOUN
ejpam-1809	86	7	.	.	PUNCT
ejpam-1809	87	1	let	let	VERB
ejpam-1809	87	2	s	s	NOUN
ejpam-1809	87	3	,	,	PUNCT
ejpam-1809	87	4	t	t	PROPN
ejpam-1809	87	5	∈	∈	PROPN
ejpam-1809	87	6	s	s	PART
ejpam-1809	87	7	∪	∪	ADJ
ejpam-1809	87	8	t	t	PROPN
ejpam-1809	87	9	and	and	CCONJ
ejpam-1809	87	10	s	s	PROPN
ejpam-1809	87	11	6=	6=	PROPN
ejpam-1809	87	12	t.	t.	NOUN
ejpam-1809	87	13	we	we	PRON
ejpam-1809	87	14	define	define	VERB
ejpam-1809	87	15	µ	µ	X
ejpam-1809	87	16	:	:	PUNCT
ejpam-1809	87	17	s	s	VERB
ejpam-1809	87	18	∪	∪	PROPN
ejpam-1809	87	19	t	t	NOUN
ejpam-1809	87	20	→	→	SYM
ejpam-1809	87	21	r2	r2	PROPN
ejpam-1809	87	22	=	=	PUNCT
ejpam-1809	87	23	{	{	PUNCT
ejpam-1809	87	24	a	a	DET
ejpam-1809	87	25	,	,	PUNCT
ejpam-1809	87	26	b	b	NOUN
ejpam-1809	87	27	}	}	PUNCT
ejpam-1809	87	28	.	.	PUNCT
ejpam-1809	88	1	here	here	ADV
ejpam-1809	88	2	r2	r2	PROPN
ejpam-1809	88	3	=	=	PUNCT
ejpam-1809	88	4	{	{	PUNCT
ejpam-1809	88	5	a	a	DET
ejpam-1809	88	6	,	,	PUNCT
ejpam-1809	88	7	b	b	NOUN
ejpam-1809	88	8	}	}	PUNCT
ejpam-1809	88	9	is	be	AUX
ejpam-1809	88	10	the	the	DET
ejpam-1809	88	11	right	right	ADJ
ejpam-1809	88	12	zero	zero	NUM
ejpam-1809	88	13	semigroup	semigroup	NOUN
ejpam-1809	88	14	with	with	ADP
ejpam-1809	88	15	2	2	NUM
ejpam-1809	88	16	elements	element	NOUN
ejpam-1809	88	17	and	and	CCONJ
ejpam-1809	88	18	ab	ab	NOUN
ejpam-1809	88	19	=	=	SYM
ejpam-1809	88	20	b	b	PROPN
ejpam-1809	88	21	,	,	PUNCT
ejpam-1809	88	22	ba	ba	X
ejpam-1809	89	1	=	=	PUNCT
ejpam-1809	89	2	a.	a.	NOUN
ejpam-1809	89	3	if	if	SCONJ
ejpam-1809	89	4	s	s	VERB
ejpam-1809	89	5	∈	∈	PROPN
ejpam-1809	89	6	s	s	AUX
ejpam-1809	89	7	let	let	VERB
ejpam-1809	89	8	µ(s	µ(	NOUN
ejpam-1809	89	9	)	)	PUNCT
ejpam-1809	89	10	=	=	SYM
ejpam-1809	90	1	a	a	NOUN
ejpam-1809	91	1	and	and	CCONJ
ejpam-1809	91	2	if	if	SCONJ
ejpam-1809	91	3	t	t	PROPN
ejpam-1809	91	4	∈	∈	PROPN
ejpam-1809	91	5	t	t	PROPN
ejpam-1809	91	6	let	let	VERB
ejpam-1809	91	7	µ(t	µ(t	VERB
ejpam-1809	91	8	)	)	PUNCT
ejpam-1809	92	1	=	=	SYM
ejpam-1809	92	2	b.	b.	NOUN
ejpam-1809	92	3	we	we	PRON
ejpam-1809	92	4	have	have	VERB
ejpam-1809	92	5	µ(s	µ(	NOUN
ejpam-1809	92	6	)	)	PUNCT
ejpam-1809	92	7	=	=	SYM
ejpam-1809	92	8	a	a	PRON
ejpam-1809	92	9	6=	6=	X
ejpam-1809	92	10	µ(t	µ(t	ADJ
ejpam-1809	92	11	)	)	PUNCT
ejpam-1809	93	1	=	=	SYM
ejpam-1809	93	2	b.	b.	PROPN
ejpam-1809	93	3	if	if	SCONJ
ejpam-1809	93	4	s1	s1	PROPN
ejpam-1809	93	5	,	,	PUNCT
ejpam-1809	93	6	s2	s2	PROPN
ejpam-1809	93	7	∈	∈	PROPN
ejpam-1809	93	8	s	s	VERB
ejpam-1809	93	9	then	then	ADV
ejpam-1809	93	10	µ(s1s2	µ(s1s2	ADV
ejpam-1809	93	11	)	)	PUNCT
ejpam-1809	93	12	=	=	SYM
ejpam-1809	93	13	a	a	DET
ejpam-1809	93	14	=	=	PUNCT
ejpam-1809	93	15	µ(s1).µ(s2	µ(s1).µ(s2	NOUN
ejpam-1809	93	16	)	)	PUNCT
ejpam-1809	93	17	=	=	SYM
ejpam-1809	93	18	a.a	a.a	PROPN
ejpam-1809	93	19	=	=	PROPN
ejpam-1809	93	20	a.	a.	NOUN
ejpam-1809	93	21	if	if	SCONJ
ejpam-1809	93	22	t1	t1	PROPN
ejpam-1809	93	23	,	,	PUNCT
ejpam-1809	93	24	t2	t2	PROPN
ejpam-1809	93	25	∈	∈	PROPN
ejpam-1809	93	26	t	t	PROPN
ejpam-1809	93	27	then	then	ADV
ejpam-1809	93	28	µ(t1	µ(t1	NOUN
ejpam-1809	93	29	t2	t2	PROPN
ejpam-1809	93	30	)	)	PUNCT
ejpam-1809	94	1	=	=	SYM
ejpam-1809	94	2	b	b	X
ejpam-1809	94	3	=	=	SYM
ejpam-1809	94	4	µ(t1).µ(t2	µ(t1).µ(t2	ADV
ejpam-1809	94	5	)	)	PUNCT
ejpam-1809	94	6	=	=	SYM
ejpam-1809	94	7	b.b	b.b	PROPN
ejpam-1809	94	8	=	=	PROPN
ejpam-1809	94	9	b.	b.	PROPN
ejpam-1809	95	1	if	if	SCONJ
ejpam-1809	95	2	s	s	VERB
ejpam-1809	95	3	∈	∈	PROPN
ejpam-1809	95	4	s	s	X
ejpam-1809	95	5	and	and	CCONJ
ejpam-1809	95	6	t	t	PROPN
ejpam-1809	95	7	∈	∈	PROPN
ejpam-1809	95	8	t	t	PROPN
ejpam-1809	95	9	then	then	ADV
ejpam-1809	95	10	µ(st	µ(st	NUM
ejpam-1809	95	11	)	)	PUNCT
ejpam-1809	95	12	=	=	SYM
ejpam-1809	95	13	µ(t	µ(t	ADJ
ejpam-1809	95	14	)	)	PUNCT
ejpam-1809	95	15	=	=	SYM
ejpam-1809	95	16	b	b	X
ejpam-1809	95	17	=	=	SYM
ejpam-1809	95	18	µ(s)µ(t	µ(s)µ(t	PROPN
ejpam-1809	95	19	)	)	PUNCT
ejpam-1809	95	20	=	=	SYM
ejpam-1809	95	21	a.b	a.b	PROPN
ejpam-1809	95	22	=	=	SYM
ejpam-1809	95	23	b.	b.	PROPN
ejpam-1809	95	24	thus	thus	ADV
ejpam-1809	95	25	µ	µ	X
ejpam-1809	95	26	is	be	AUX
ejpam-1809	95	27	an	an	PRON
ejpam-1809	95	28	onto	onto	ADP
ejpam-1809	95	29	homomorphism	homomorphism	NOUN
ejpam-1809	95	30	.	.	PUNCT
ejpam-1809	96	1	4	4	X
ejpam-1809	96	2	.	.	X
ejpam-1809	96	3	solvable	solvable	ADJ
ejpam-1809	96	4	word	word	NOUN
ejpam-1809	96	5	problem	problem	NOUN
ejpam-1809	96	6	a	a	DET
ejpam-1809	96	7	semigroup	semigroup	NOUN
ejpam-1809	96	8	s	s	NOUN
ejpam-1809	96	9	is	be	AUX
ejpam-1809	96	10	said	say	VERB
ejpam-1809	96	11	to	to	PART
ejpam-1809	96	12	have	have	VERB
ejpam-1809	96	13	a	a	DET
ejpam-1809	96	14	solvable	solvable	ADJ
ejpam-1809	96	15	word	word	NOUN
ejpam-1809	96	16	problem	problem	NOUN
ejpam-1809	96	17	with	with	ADP
ejpam-1809	96	18	respect	respect	NOUN
ejpam-1809	96	19	to	to	ADP
ejpam-1809	96	20	a	a	DET
ejpam-1809	96	21	generating	generating	NOUN
ejpam-1809	96	22	set	set	NOUN
ejpam-1809	96	23	a	a	PRON
ejpam-1809	96	24	if	if	SCONJ
ejpam-1809	96	25	there	there	PRON
ejpam-1809	96	26	exists	exist	VERB
ejpam-1809	96	27	a	a	DET
ejpam-1809	96	28	algorithm	algorithm	NOUN
ejpam-1809	96	29	which	which	PRON
ejpam-1809	96	30	,	,	PUNCT
ejpam-1809	96	31	for	for	ADP
ejpam-1809	96	32	any	any	DET
ejpam-1809	96	33	two	two	NUM
ejpam-1809	96	34	words	word	NOUN
ejpam-1809	96	35	u	u	NOUN
ejpam-1809	96	36	,	,	PUNCT
ejpam-1809	96	37	v	v	PROPN
ejpam-1809	96	38	∈	∈	PROPN
ejpam-1809	96	39	a+	a+	PUNCT
ejpam-1809	96	40	,	,	PUNCT
ejpam-1809	96	41	decides	decide	VERB
ejpam-1809	96	42	whether	whether	SCONJ
ejpam-1809	96	43	the	the	DET
ejpam-1809	96	44	relation	relation	NOUN
ejpam-1809	96	45	u	u	NOUN
ejpam-1809	96	46	=	=	NOUN
ejpam-1809	96	47	v	v	NOUN
ejpam-1809	96	48	holds	hold	VERB
ejpam-1809	96	49	in	in	ADP
ejpam-1809	96	50	s	s	PRON
ejpam-1809	96	51	or	or	CCONJ
ejpam-1809	96	52	not	not	PART
ejpam-1809	96	53	.	.	PUNCT
ejpam-1809	97	1	it	it	PRON
ejpam-1809	97	2	is	be	AUX
ejpam-1809	97	3	a	a	DET
ejpam-1809	97	4	well	well	ADV
ejpam-1809	97	5	-	-	PUNCT
ejpam-1809	97	6	known	know	VERB
ejpam-1809	97	7	fact	fact	NOUN
ejpam-1809	97	8	that	that	SCONJ
ejpam-1809	97	9	,	,	PUNCT
ejpam-1809	97	10	for	for	ADP
ejpam-1809	97	11	a	a	DET
ejpam-1809	97	12	finitely	finitely	ADV
ejpam-1809	97	13	generated	generate	VERB
ejpam-1809	97	14	semigroup	semigroup	PROPN
ejpam-1809	97	15	s	s	PROPN
ejpam-1809	97	16	,	,	PUNCT
ejpam-1809	97	17	the	the	DET
ejpam-1809	97	18	solvability	solvability	NOUN
ejpam-1809	97	19	of	of	ADP
ejpam-1809	97	20	the	the	DET
ejpam-1809	97	21	word	word	NOUN
ejpam-1809	97	22	problem	problem	NOUN
ejpam-1809	97	23	does	do	AUX
ejpam-1809	97	24	not	not	PART
ejpam-1809	97	25	depend	depend	VERB
ejpam-1809	97	26	on	on	ADP
ejpam-1809	97	27	the	the	DET
ejpam-1809	97	28	choice	choice	NOUN
ejpam-1809	97	29	of	of	ADP
ejpam-1809	97	30	the	the	DET
ejpam-1809	97	31	finite	finite	NOUN
ejpam-1809	97	32	generating	generating	NOUN
ejpam-1809	97	33	set	set	NOUN
ejpam-1809	97	34	for	for	ADP
ejpam-1809	97	35	s.	s.	PROPN
ejpam-1809	97	36	thus	thus	ADV
ejpam-1809	97	37	we	we	PRON
ejpam-1809	97	38	say	say	VERB
ejpam-1809	97	39	that	that	SCONJ
ejpam-1809	97	40	a	a	DET
ejpam-1809	97	41	semigroup	semigroup	NOUN
ejpam-1809	97	42	s	s	PART
ejpam-1809	97	43	has	have	VERB
ejpam-1809	97	44	a	a	DET
ejpam-1809	97	45	solvable	solvable	ADJ
ejpam-1809	97	46	word	word	NOUN
ejpam-1809	97	47	problem	problem	NOUN
ejpam-1809	97	48	with	with	ADP
ejpam-1809	97	49	respect	respect	NOUN
ejpam-1809	97	50	to	to	ADP
ejpam-1809	97	51	any	any	DET
ejpam-1809	97	52	finite	finite	NOUN
ejpam-1809	97	53	generating	generating	NOUN
ejpam-1809	97	54	set	set	NOUN
ejpam-1809	97	55	.	.	PUNCT
ejpam-1809	98	1	theorem	theorem	NOUN
ejpam-1809	98	2	3	3	NUM
ejpam-1809	98	3	.	.	NOUN
ejpam-1809	98	4	s∪t	s∪t	NOUN
ejpam-1809	98	5	has	have	VERB
ejpam-1809	98	6	solvable	solvable	ADJ
ejpam-1809	98	7	word	word	NOUN
ejpam-1809	98	8	problem	problem	NOUN
ejpam-1809	98	9	if	if	SCONJ
ejpam-1809	98	10	and	and	CCONJ
ejpam-1809	98	11	only	only	ADV
ejpam-1809	98	12	if	if	SCONJ
ejpam-1809	98	13	s	s	PRON
ejpam-1809	98	14	and	and	CCONJ
ejpam-1809	98	15	t	t	PROPN
ejpam-1809	98	16	have	have	VERB
ejpam-1809	98	17	solvable	solvable	ADJ
ejpam-1809	98	18	word	word	NOUN
ejpam-1809	98	19	problem	problem	NOUN
ejpam-1809	98	20	.	.	PUNCT
ejpam-1809	99	1	proof	proof	NOUN
ejpam-1809	99	2	.	.	PUNCT
ejpam-1809	100	1	(	(	PUNCT
ejpam-1809	100	2	⇒	⇒	NOUN
ejpam-1809	100	3	)	)	PUNCT
ejpam-1809	100	4	let	let	VERB
ejpam-1809	100	5	s	s	PRON
ejpam-1809	100	6	∪	∪	VERB
ejpam-1809	100	7	t	t	PROPN
ejpam-1809	100	8	have	have	VERB
ejpam-1809	100	9	solvable	solvable	ADJ
ejpam-1809	100	10	word	word	NOUN
ejpam-1809	100	11	problem	problem	NOUN
ejpam-1809	100	12	.	.	PUNCT
ejpam-1809	101	1	since	since	SCONJ
ejpam-1809	101	2	s	s	PROPN
ejpam-1809	101	3	and	and	CCONJ
ejpam-1809	101	4	t	t	PROPN
ejpam-1809	101	5	are	be	AUX
ejpam-1809	101	6	finitely	finitely	ADV
ejpam-1809	101	7	generated	generate	VERB
ejpam-1809	101	8	,	,	PUNCT
ejpam-1809	101	9	let	let	VERB
ejpam-1809	101	10	y1	y1	INTJ
ejpam-1809	101	11	be	be	AUX
ejpam-1809	101	12	generating	generate	VERB
ejpam-1809	101	13	set	set	NOUN
ejpam-1809	101	14	of	of	ADP
ejpam-1809	101	15	s	s	PRON
ejpam-1809	101	16	and	and	CCONJ
ejpam-1809	101	17	y2	y2	PROPN
ejpam-1809	101	18	be	be	AUX
ejpam-1809	101	19	generating	generate	VERB
ejpam-1809	101	20	set	set	NOUN
ejpam-1809	101	21	of	of	ADP
ejpam-1809	101	22	t	t	PROPN
ejpam-1809	101	23	.	.	PUNCT
ejpam-1809	102	1	then	then	ADV
ejpam-1809	102	2	y1	y1	NOUN
ejpam-1809	102	3	∪	∪	ADP
ejpam-1809	102	4	y2	y2	PROPN
ejpam-1809	102	5	is	be	AUX
ejpam-1809	102	6	a	a	DET
ejpam-1809	102	7	generating	generate	VERB
ejpam-1809	102	8	set	set	NOUN
ejpam-1809	102	9	for	for	ADP
ejpam-1809	102	10	s	s	NOUN
ejpam-1809	102	11	∪	∪	PROPN
ejpam-1809	102	12	t	t	NOUN
ejpam-1809	102	13	.	.	PUNCT
ejpam-1809	103	1	let	let	VERB
ejpam-1809	103	2	w1	w1	NOUN
ejpam-1809	103	3	,	,	PUNCT
ejpam-1809	103	4	w2	w2	NOUN
ejpam-1809	103	5	∈	∈	PROPN
ejpam-1809	103	6	y+1	y+1	PRON
ejpam-1809	103	7	.	.	PUNCT
ejpam-1809	104	1	since	since	SCONJ
ejpam-1809	104	2	w1	w1	NOUN
ejpam-1809	104	3	,	,	PUNCT
ejpam-1809	104	4	w2	w2	NOUN
ejpam-1809	104	5	∈	∈	PROPN
ejpam-1809	104	6	y+1	y+1	PRON
ejpam-1809	104	7	⊆	⊆	NUM
ejpam-1809	104	8	(	(	PUNCT
ejpam-1809	104	9	y1	y1	NOUN
ejpam-1809	104	10	∪	∪	ADJ
ejpam-1809	104	11	y2)+	y2)+	NOUN
ejpam-1809	104	12	and	and	CCONJ
ejpam-1809	104	13	since	since	SCONJ
ejpam-1809	104	14	s	s	NOUN
ejpam-1809	104	15	∪	∪	ADP
ejpam-1809	104	16	t	t	PROPN
ejpam-1809	104	17	has	have	VERB
ejpam-1809	104	18	solvable	solvable	ADJ
ejpam-1809	104	19	word	word	NOUN
ejpam-1809	104	20	problem	problem	NOUN
ejpam-1809	104	21	there	there	PRON
ejpam-1809	104	22	exists	exist	VERB
ejpam-1809	104	23	an	an	DET
ejpam-1809	104	24	algorithm	algorithm	NOUN
ejpam-1809	104	25	which	which	PRON
ejpam-1809	104	26	decides	decide	VERB
ejpam-1809	104	27	whether	whether	SCONJ
ejpam-1809	104	28	w1	w1	NOUN
ejpam-1809	104	29	=	=	SYM
ejpam-1809	104	30	w2	w2	NOUN
ejpam-1809	104	31	holds	hold	VERB
ejpam-1809	104	32	in	in	ADP
ejpam-1809	104	33	s∪	s∪	PROPN
ejpam-1809	104	34	t	t	PROPN
ejpam-1809	104	35	.	.	PUNCT
ejpam-1809	105	1	since	since	SCONJ
ejpam-1809	105	2	w1	w1	NOUN
ejpam-1809	105	3	,	,	PUNCT
ejpam-1809	105	4	w2	w2	NOUN
ejpam-1809	105	5	∈	∈	PROPN
ejpam-1809	105	6	y+1	y+1	PROPN
ejpam-1809	105	7	and	and	CCONJ
ejpam-1809	105	8	y1	y1	PROPN
ejpam-1809	105	9	is	be	AUX
ejpam-1809	105	10	a	a	DET
ejpam-1809	105	11	generating	generate	VERB
ejpam-1809	105	12	set	set	NOUN
ejpam-1809	105	13	for	for	ADP
ejpam-1809	105	14	s	s	PROPN
ejpam-1809	105	15	,	,	PUNCT
ejpam-1809	105	16	the	the	DET
ejpam-1809	105	17	algorithm	algorithm	NOUN
ejpam-1809	105	18	decides	decide	VERB
ejpam-1809	105	19	whether	whether	SCONJ
ejpam-1809	105	20	w1	w1	NOUN
ejpam-1809	105	21	=	=	SYM
ejpam-1809	105	22	w2	w2	NOUN
ejpam-1809	105	23	holds	hold	VERB
ejpam-1809	105	24	in	in	ADP
ejpam-1809	105	25	s.	s.	PROPN
ejpam-1809	106	1	so	so	PROPN
ejpam-1809	106	2	s	s	PROPN
ejpam-1809	106	3	has	have	VERB
ejpam-1809	106	4	a	a	DET
ejpam-1809	106	5	solvable	solvable	ADJ
ejpam-1809	106	6	word	word	NOUN
ejpam-1809	106	7	problem	problem	NOUN
ejpam-1809	106	8	.	.	PUNCT
ejpam-1809	107	1	similarly	similarly	ADV
ejpam-1809	107	2	it	it	PRON
ejpam-1809	107	3	is	be	AUX
ejpam-1809	107	4	shown	show	VERB
ejpam-1809	107	5	that	that	SCONJ
ejpam-1809	107	6	t	t	PROPN
ejpam-1809	107	7	has	have	VERB
ejpam-1809	107	8	a	a	DET
ejpam-1809	107	9	solvable	solvable	ADJ
ejpam-1809	107	10	word	word	NOUN
ejpam-1809	107	11	problem	problem	NOUN
ejpam-1809	107	12	.	.	PUNCT
ejpam-1809	108	1	(	(	PUNCT
ejpam-1809	108	2	⇐	⇐	ADJ
ejpam-1809	108	3	)	)	PUNCT
ejpam-1809	108	4	assume	assume	VERB
ejpam-1809	108	5	that	that	SCONJ
ejpam-1809	108	6	s	s	VERB
ejpam-1809	108	7	and	and	CCONJ
ejpam-1809	108	8	t	t	PROPN
ejpam-1809	108	9	have	have	VERB
ejpam-1809	108	10	solvable	solvable	ADJ
ejpam-1809	108	11	word	word	NOUN
ejpam-1809	108	12	problem	problem	NOUN
ejpam-1809	108	13	.	.	PUNCT
ejpam-1809	109	1	let	let	VERB
ejpam-1809	109	2	x	x	PRON
ejpam-1809	109	3	be	be	AUX
ejpam-1809	109	4	a	a	DET
ejpam-1809	109	5	finite	finite	NOUN
ejpam-1809	109	6	generating	generating	NOUN
ejpam-1809	109	7	set	set	NOUN
ejpam-1809	109	8	for	for	ADP
ejpam-1809	109	9	s	s	NOUN
ejpam-1809	109	10	∪	∪	PROPN
ejpam-1809	109	11	t	t	NOUN
ejpam-1809	109	12	.	.	PUNCT
ejpam-1809	110	1	then	then	ADV
ejpam-1809	110	2	x1	x1	PROPN
ejpam-1809	110	3	=	=	PUNCT
ejpam-1809	111	1	x	x	SYM
ejpam-1809	111	2	∩	∩	X
ejpam-1809	111	3	s	s	PART
ejpam-1809	111	4	and	and	CCONJ
ejpam-1809	111	5	x2	x2	PROPN
ejpam-1809	112	1	=	=	SYM
ejpam-1809	112	2	x	x	NOUN
ejpam-1809	112	3	∩	∩	PROPN
ejpam-1809	112	4	t	t	PROPN
ejpam-1809	112	5	are	be	AUX
ejpam-1809	112	6	generating	generate	VERB
ejpam-1809	112	7	sets	set	NOUN
ejpam-1809	112	8	for	for	ADP
ejpam-1809	112	9	s	s	NOUN
ejpam-1809	112	10	and	and	CCONJ
ejpam-1809	112	11	t	t	PROPN
ejpam-1809	112	12	.	.	PUNCT
ejpam-1809	113	1	the	the	DET
ejpam-1809	113	2	set	set	NOUN
ejpam-1809	113	3	z	z	NOUN
ejpam-1809	113	4	=	=	SYM
ejpam-1809	113	5	{	{	PUNCT
ejpam-1809	113	6	x1	x1	NOUN
ejpam-1809	113	7	x2	x2	NOUN
ejpam-1809	113	8	=	=	SYM
ejpam-1809	113	9	x2	x2	PROPN
ejpam-1809	113	10	,	,	PUNCT
ejpam-1809	113	11	x2	x2	PROPN
ejpam-1809	113	12	x1	x1	PROPN
ejpam-1809	114	1	=	=	PUNCT
ejpam-1809	114	2	x2	x2	PROPN
ejpam-1809	115	1	|	|	INTJ
ejpam-1809	115	2	x1	x1	PROPN
ejpam-1809	115	3	∈	∈	PROPN
ejpam-1809	116	1	x1	x1	PROPN
ejpam-1809	116	2	,	,	PUNCT
ejpam-1809	116	3	x2	x2	PROPN
ejpam-1809	116	4	∈	∈	PROPN
ejpam-1809	116	5	x2	x2	PROPN
ejpam-1809	116	6	}	}	PUNCT
ejpam-1809	116	7	is	be	AUX
ejpam-1809	116	8	finite	finite	ADJ
ejpam-1809	116	9	.	.	PUNCT
ejpam-1809	117	1	for	for	ADP
ejpam-1809	117	2	w1	w1	NOUN
ejpam-1809	117	3	,	,	PUNCT
ejpam-1809	117	4	w2	w2	NOUN
ejpam-1809	117	5	∈	∈	PROPN
ejpam-1809	117	6	x+	x+	X
ejpam-1809	117	7	,	,	PUNCT
ejpam-1809	117	8	if	if	SCONJ
ejpam-1809	117	9	we	we	PRON
ejpam-1809	117	10	apply	apply	VERB
ejpam-1809	117	11	some	some	DET
ejpam-1809	117	12	necessary	necessary	ADJ
ejpam-1809	117	13	relations	relation	NOUN
ejpam-1809	117	14	from	from	ADP
ejpam-1809	117	15	z	z	NOUN
ejpam-1809	117	16	we	we	PRON
ejpam-1809	117	17	obtain	obtain	VERB
ejpam-1809	117	18	w1	w1	NOUN
ejpam-1809	117	19	,	,	PUNCT
ejpam-1809	117	20	w2	w2	NOUN
ejpam-1809	117	21	∈	∈	PROPN
ejpam-1809	117	22	x+	x+	PUNCT
ejpam-1809	117	23	such	such	ADJ
ejpam-1809	117	24	that	that	DET
ejpam-1809	117	25	w1	w1	NOUN
ejpam-1809	117	26	=	=	SYM
ejpam-1809	117	27	w′1	w′1	NOUN
ejpam-1809	117	28	and	and	CCONJ
ejpam-1809	117	29	w2	w2	NOUN
ejpam-1809	117	30	=	=	SYM
ejpam-1809	117	31	w′2	w′2	PROPN
ejpam-1809	117	32	holds	hold	VERB
ejpam-1809	117	33	in	in	ADP
ejpam-1809	117	34	t	t	PROPN
ejpam-1809	117	35	.	.	PUNCT
ejpam-1809	118	1	w′i	w′i	PROPN
ejpam-1809	118	2	∈	∈	PROPN
ejpam-1809	118	3	x+1	x+1	PROPN
ejpam-1809	118	4	(	(	PUNCT
ejpam-1809	118	5	i	i	NOUN
ejpam-1809	118	6	=	=	SYM
ejpam-1809	118	7	1,2	1,2	NUM
ejpam-1809	118	8	)	)	PUNCT
ejpam-1809	118	9	or	or	CCONJ
ejpam-1809	118	10	w′i	w′i	PROPN
ejpam-1809	118	11	∈	∈	PROPN
ejpam-1809	118	12	x+2	x+2	X
ejpam-1809	119	1	(	(	PUNCT
ejpam-1809	119	2	i	i	NOUN
ejpam-1809	119	3	=	=	NOUN
ejpam-1809	119	4	1	1	NUM
ejpam-1809	119	5	,	,	PUNCT
ejpam-1809	119	6	2	2	NUM
ejpam-1809	119	7	)	)	PUNCT
ejpam-1809	119	8	.	.	PUNCT
ejpam-1809	120	1	if	if	SCONJ
ejpam-1809	120	2	w′1	w′1	PROPN
ejpam-1809	120	3	and	and	CCONJ
ejpam-1809	120	4	w′2	w′2	NOUN
ejpam-1809	120	5	are	be	AUX
ejpam-1809	120	6	not	not	PART
ejpam-1809	120	7	elements	element	NOUN
ejpam-1809	120	8	of	of	ADP
ejpam-1809	120	9	the	the	DET
ejpam-1809	120	10	same	same	ADJ
ejpam-1809	120	11	free	free	ADJ
ejpam-1809	120	12	semigroup	semigroup	NOUN
ejpam-1809	120	13	x+i	x+i	PROPN
ejpam-1809	121	1	(	(	PUNCT
ejpam-1809	121	2	i	i	NOUN
ejpam-1809	121	3	=	=	NOUN
ejpam-1809	121	4	1	1	NUM
ejpam-1809	121	5	,	,	PUNCT
ejpam-1809	121	6	2	2	NUM
ejpam-1809	121	7	)	)	PUNCT
ejpam-1809	121	8	then	then	ADV
ejpam-1809	121	9	w′1	w′1	X
ejpam-1809	121	10	=	=	NOUN
ejpam-1809	121	11	w′2	w′2	NOUN
ejpam-1809	121	12	does	do	AUX
ejpam-1809	121	13	not	not	PART
ejpam-1809	121	14	hold	hold	VERB
ejpam-1809	121	15	in	in	ADP
ejpam-1809	121	16	s∪t	s∪t	NOUN
ejpam-1809	121	17	.	.	PUNCT
ejpam-1809	122	1	if	if	SCONJ
ejpam-1809	122	2	w′1	w′1	PROPN
ejpam-1809	122	3	and	and	CCONJ
ejpam-1809	122	4	w′2	w′2	NOUN
ejpam-1809	122	5	are	be	AUX
ejpam-1809	122	6	in	in	ADP
ejpam-1809	122	7	the	the	DET
ejpam-1809	122	8	same	same	ADJ
ejpam-1809	122	9	free	free	ADJ
ejpam-1809	122	10	semigroup	semigroup	NOUN
ejpam-1809	122	11	x+i	x+i	PROPN
ejpam-1809	123	1	(	(	PUNCT
ejpam-1809	123	2	i	i	NOUN
ejpam-1809	123	3	=	=	SYM
ejpam-1809	123	4	1,2	1,2	NUM
ejpam-1809	123	5	)	)	PUNCT
ejpam-1809	123	6	there	there	PRON
ejpam-1809	123	7	exists	exist	VERB
ejpam-1809	123	8	an	an	DET
ejpam-1809	123	9	algorithm	algorithm	NOUN
ejpam-1809	123	10	which	which	PRON
ejpam-1809	123	11	decides	decide	VERB
ejpam-1809	123	12	whether	whether	SCONJ
ejpam-1809	123	13	the	the	DET
ejpam-1809	123	14	relation	relation	NOUN
ejpam-1809	123	15	w′1	w′1	NOUN
ejpam-1809	123	16	=	=	PUNCT
ejpam-1809	123	17	w′2	w′2	PROPN
ejpam-1809	123	18	holds	hold	VERB
ejpam-1809	123	19	in	in	ADP
ejpam-1809	123	20	s	s	PRON
ejpam-1809	123	21	or	or	CCONJ
ejpam-1809	123	22	t	t	PROPN
ejpam-1809	123	23	.	.	PUNCT
ejpam-1809	124	1	because	because	SCONJ
ejpam-1809	124	2	s	s	PRON
ejpam-1809	124	3	and	and	CCONJ
ejpam-1809	124	4	t	t	PROPN
ejpam-1809	124	5	have	have	VERB
ejpam-1809	124	6	solvable	solvable	ADJ
ejpam-1809	124	7	word	word	NOUN
ejpam-1809	124	8	problem	problem	NOUN
ejpam-1809	124	9	.	.	PUNCT
ejpam-1809	125	1	so	so	ADV
ejpam-1809	125	2	s	s	X
ejpam-1809	125	3	∪	∪	PROPN
ejpam-1809	125	4	t	t	PROPN
ejpam-1809	125	5	has	have	VERB
ejpam-1809	125	6	solvable	solvable	ADJ
ejpam-1809	125	7	word	word	NOUN
ejpam-1809	125	8	problem	problem	NOUN
ejpam-1809	125	9	.	.	PUNCT
ejpam-1809	126	1	m.	m.	NOUN
ejpam-1809	126	2	minisker	minisker	PROPN
ejpam-1809	126	3	/	/	SYM
ejpam-1809	126	4	eur	eur	PROPN
ejpam-1809	126	5	.	.	PUNCT
ejpam-1809	127	1	j.	j.	PROPN
ejpam-1809	127	2	pure	pure	PROPN
ejpam-1809	127	3	appl	appl	PROPN
ejpam-1809	127	4	.	.	PROPN
ejpam-1809	127	5	math	math	PROPN
ejpam-1809	127	6	,	,	PUNCT
ejpam-1809	127	7	6	6	NUM
ejpam-1809	127	8	(	(	PUNCT
ejpam-1809	127	9	2013	2013	NUM
ejpam-1809	127	10	)	)	PUNCT
ejpam-1809	127	11	,	,	PUNCT
ejpam-1809	127	12	335	335	NUM
ejpam-1809	127	13	-	-	SYM
ejpam-1809	127	14	339	339	NUM
ejpam-1809	127	15	338	338	NUM
ejpam-1809	127	16	5	5	NUM
ejpam-1809	127	17	.	.	PUNCT
ejpam-1809	127	18	ranks	rank	NOUN
ejpam-1809	127	19	of	of	ADP
ejpam-1809	127	20	b(g	b(g	PROPN
ejpam-1809	127	21	,	,	PUNCT
ejpam-1809	127	22	n	n	CCONJ
ejpam-1809	127	23	)	)	PUNCT
ejpam-1809	127	24	the	the	DET
ejpam-1809	127	25	semigroup	semigroup	PROPN
ejpam-1809	127	26	b(g	b(g	PROPN
ejpam-1809	127	27	,	,	PUNCT
ejpam-1809	127	28	n	n	CCONJ
ejpam-1809	127	29	)	)	PUNCT
ejpam-1809	127	30	=	=	PRON
ejpam-1809	127	31	{	{	PUNCT
ejpam-1809	127	32	1	1	NUM
ejpam-1809	127	33	,	,	PUNCT
ejpam-1809	127	34	2	2	NUM
ejpam-1809	127	35	,	,	PUNCT
ejpam-1809	127	36	.	.	PUNCT
ejpam-1809	127	37	.	.	PUNCT
ejpam-1809	128	1	.	.	PUNCT
ejpam-1809	129	1	,	,	PUNCT
ejpam-1809	129	2	n	n	CCONJ
ejpam-1809	129	3	}	}	PUNCT
ejpam-1809	129	4	×	×	NOUN
ejpam-1809	129	5	g	g	PROPN
ejpam-1809	129	6	×	×	NOUN
ejpam-1809	129	7	{	{	PUNCT
ejpam-1809	129	8	1	1	NUM
ejpam-1809	129	9	,	,	PUNCT
ejpam-1809	129	10	2	2	NUM
ejpam-1809	129	11	,	,	PUNCT
ejpam-1809	129	12	.	.	PUNCT
ejpam-1809	129	13	.	.	PUNCT
ejpam-1809	130	1	.	.	PUNCT
ejpam-1809	131	1	,	,	PUNCT
ejpam-1809	131	2	n	n	CCONJ
ejpam-1809	131	3	}	}	PUNCT
ejpam-1809	131	4	∪	∪	X
ejpam-1809	131	5	{	{	PUNCT
ejpam-1809	131	6	0	0	NUM
ejpam-1809	131	7	}	}	PUNCT
ejpam-1809	131	8	is	be	AUX
ejpam-1809	131	9	the	the	DET
ejpam-1809	131	10	brandt	brandt	PROPN
ejpam-1809	131	11	semigroup	semigroup	PROPN
ejpam-1809	131	12	.	.	PUNCT
ejpam-1809	132	1	the	the	DET
ejpam-1809	132	2	binary	binary	PROPN
ejpam-1809	132	3	operation	operation	NOUN
ejpam-1809	132	4	on	on	ADP
ejpam-1809	132	5	b(g	b(g	PROPN
ejpam-1809	132	6	,	,	PUNCT
ejpam-1809	132	7	n	n	CCONJ
ejpam-1809	132	8	)	)	PUNCT
ejpam-1809	132	9	is	be	AUX
ejpam-1809	132	10	defined	define	VERB
ejpam-1809	132	11	as	as	ADP
ejpam-1809	132	12	follows	follow	VERB
ejpam-1809	132	13	(	(	PUNCT
ejpam-1809	132	14	i	i	NOUN
ejpam-1809	132	15	,	,	PUNCT
ejpam-1809	132	16	a	a	PRON
ejpam-1809	132	17	,	,	PUNCT
ejpam-1809	132	18	j).(k	j).(k	PROPN
ejpam-1809	132	19	,	,	PUNCT
ejpam-1809	132	20	b	b	NOUN
ejpam-1809	132	21	,	,	PUNCT
ejpam-1809	132	22	l	l	NOUN
ejpam-1809	132	23	)	)	PUNCT
ejpam-1809	132	24	=	=	SYM
ejpam-1809	132	25	(	(	PUNCT
ejpam-1809	132	26	i	i	PROPN
ejpam-1809	132	27	,	,	PUNCT
ejpam-1809	132	28	ab	ab	PROPN
ejpam-1809	132	29	,	,	PUNCT
ejpam-1809	132	30	l	l	NOUN
ejpam-1809	132	31	)	)	PUNCT
ejpam-1809	133	1	if	if	SCONJ
ejpam-1809	133	2	j	j	PROPN
ejpam-1809	133	3	=	=	SYM
ejpam-1809	133	4	k	k	PROPN
ejpam-1809	133	5	0	0	PUNCT
ejpam-1809	134	1	if	if	SCONJ
ejpam-1809	134	2	j	j	PROPN
ejpam-1809	134	3	6=	6=	PROPN
ejpam-1809	134	4	k	k	PROPN
ejpam-1809	134	5	0.(i	0.(i	PROPN
ejpam-1809	134	6	,	,	PUNCT
ejpam-1809	134	7	a	a	PRON
ejpam-1809	134	8	,	,	PUNCT
ejpam-1809	134	9	j	j	NOUN
ejpam-1809	134	10	)	)	PUNCT
ejpam-1809	134	11	=	=	PUNCT
ejpam-1809	134	12	(	(	PUNCT
ejpam-1809	134	13	i	i	NOUN
ejpam-1809	134	14	,	,	PUNCT
ejpam-1809	134	15	a	a	PRON
ejpam-1809	134	16	,	,	PUNCT
ejpam-1809	134	17	j).0=	j).0=	X
ejpam-1809	134	18	0.0=	0.0=	PROPN
ejpam-1809	134	19	0	0	PUNCT
ejpam-1809	134	20	in	in	ADP
ejpam-1809	134	21	[	[	X
ejpam-1809	134	22	5	5	NUM
ejpam-1809	134	23	]	]	SYM
ejpam-1809	134	24	r5(b(g	r5(b(g	NOUN
ejpam-1809	134	25	,	,	PUNCT
ejpam-1809	134	26	n	n	CCONJ
ejpam-1809	134	27	)	)	PUNCT
ejpam-1809	134	28	)	)	PUNCT
ejpam-1809	134	29	is	be	AUX
ejpam-1809	134	30	given	give	VERB
ejpam-1809	134	31	.	.	PUNCT
ejpam-1809	135	1	now	now	ADV
ejpam-1809	135	2	we	we	PRON
ejpam-1809	135	3	define	define	VERB
ejpam-1809	135	4	other	other	ADJ
ejpam-1809	135	5	ranks	rank	NOUN
ejpam-1809	135	6	of	of	ADP
ejpam-1809	135	7	b(g	b(g	PROPN
ejpam-1809	135	8	,	,	PUNCT
ejpam-1809	135	9	n	n	CCONJ
ejpam-1809	135	10	)	)	PUNCT
ejpam-1809	135	11	.	.	PUNCT
ejpam-1809	136	1	lemma	lemma	PROPN
ejpam-1809	136	2	1	1	X
ejpam-1809	136	3	.	.	PUNCT
ejpam-1809	137	1	let	let	VERB
ejpam-1809	137	2	b(g	b(g	PROPN
ejpam-1809	137	3	,	,	PUNCT
ejpam-1809	137	4	n	n	CCONJ
ejpam-1809	137	5	)	)	PUNCT
ejpam-1809	137	6	be	be	AUX
ejpam-1809	137	7	the	the	DET
ejpam-1809	137	8	brandt	brandt	PROPN
ejpam-1809	137	9	semigroup	semigroup	PROPN
ejpam-1809	137	10	.	.	PUNCT
ejpam-1809	138	1	let	let	VERB
ejpam-1809	138	2	a	a	PRON
ejpam-1809	138	3	be	be	AUX
ejpam-1809	138	4	the	the	DET
ejpam-1809	138	5	minimum	minimum	NOUN
ejpam-1809	138	6	generating	generating	NOUN
ejpam-1809	138	7	set	set	NOUN
ejpam-1809	138	8	of	of	ADP
ejpam-1809	138	9	g.	g.	PROPN
ejpam-1809	138	10	then	then	ADV
ejpam-1809	138	11	r1(b(g	r1(b(g	NOUN
ejpam-1809	138	12	,	,	PUNCT
ejpam-1809	138	13	n	n	CCONJ
ejpam-1809	138	14	)	)	PUNCT
ejpam-1809	138	15	)	)	PUNCT
ejpam-1809	139	1	=	=	SYM
ejpam-1809	139	2	1	1	NUM
ejpam-1809	139	3	,	,	PUNCT
ejpam-1809	139	4	r2(b(g	r2(b(g	NOUN
ejpam-1809	139	5	,	,	PUNCT
ejpam-1809	139	6	n	n	CCONJ
ejpam-1809	139	7	)	)	PUNCT
ejpam-1809	139	8	)	)	PUNCT
ejpam-1809	140	1	=	=	SYM
ejpam-1809	140	2	2n.|a|	2n.|a|	PROPN
ejpam-1809	140	3	and	and	CCONJ
ejpam-1809	140	4	r3(b(g	r3(b(g	NOUN
ejpam-1809	140	5	,	,	PUNCT
ejpam-1809	140	6	n	n	CCONJ
ejpam-1809	140	7	)	)	PUNCT
ejpam-1809	140	8	)	)	PUNCT
ejpam-1809	141	1	=	=	SYM
ejpam-1809	141	2	2n.|a|	2n.|a|	X
ejpam-1809	141	3	.	.	PUNCT
ejpam-1809	141	4	proof	proof	NOUN
ejpam-1809	141	5	.	.	PUNCT
ejpam-1809	142	1	let	let	VERB
ejpam-1809	142	2	a	a	PRON
ejpam-1809	142	3	be	be	AUX
ejpam-1809	142	4	the	the	DET
ejpam-1809	142	5	minimum	minimum	NOUN
ejpam-1809	142	6	generating	generating	NOUN
ejpam-1809	142	7	set	set	NOUN
ejpam-1809	142	8	of	of	ADP
ejpam-1809	142	9	g.	g.	PROPN
ejpam-1809	142	10	we	we	PRON
ejpam-1809	142	11	show	show	VERB
ejpam-1809	142	12	the	the	DET
ejpam-1809	142	13	set	set	NOUN
ejpam-1809	142	14	b	b	NOUN
ejpam-1809	142	15	=	=	PRON
ejpam-1809	142	16	{	{	PUNCT
ejpam-1809	142	17	(	(	PUNCT
ejpam-1809	142	18	1	1	NUM
ejpam-1809	142	19	,	,	PUNCT
ejpam-1809	142	20	a	a	DET
ejpam-1809	142	21	,	,	PUNCT
ejpam-1809	142	22	j	j	PROPN
ejpam-1809	142	23	)	)	PUNCT
ejpam-1809	142	24	,	,	PUNCT
ejpam-1809	142	25	(	(	PUNCT
ejpam-1809	142	26	i	i	PRON
ejpam-1809	142	27	,	,	PUNCT
ejpam-1809	142	28	a	a	PRON
ejpam-1809	142	29	,	,	PUNCT
ejpam-1809	142	30	1)|a	1)|a	NUM
ejpam-1809	142	31	∈	∈	PROPN
ejpam-1809	142	32	a	a	PRON
ejpam-1809	142	33	,	,	PUNCT
ejpam-1809	142	34	1≤	1≤	NUM
ejpam-1809	142	35	i	i	PROPN
ejpam-1809	142	36	≤	≤	PROPN
ejpam-1809	142	37	n	n	CCONJ
ejpam-1809	142	38	,	,	PUNCT
ejpam-1809	142	39	1≤	1≤	NUM
ejpam-1809	142	40	j	j	PROPN
ejpam-1809	142	41	≤	≤	PROPN
ejpam-1809	142	42	n	n	CCONJ
ejpam-1809	142	43	}	}	PUNCT
ejpam-1809	142	44	is	be	AUX
ejpam-1809	142	45	the	the	DET
ejpam-1809	142	46	minimum	minimum	NOUN
ejpam-1809	142	47	generating	generating	NOUN
ejpam-1809	142	48	set	set	NOUN
ejpam-1809	142	49	for	for	ADP
ejpam-1809	142	50	b(g	b(g	PROPN
ejpam-1809	142	51	,	,	PUNCT
ejpam-1809	142	52	n	n	CCONJ
ejpam-1809	142	53	)	)	PUNCT
ejpam-1809	142	54	.	.	PUNCT
ejpam-1809	143	1	for	for	ADP
ejpam-1809	143	2	(	(	PUNCT
ejpam-1809	143	3	i	i	PROPN
ejpam-1809	143	4	,	,	PUNCT
ejpam-1809	143	5	g	g	PROPN
ejpam-1809	143	6	,	,	PUNCT
ejpam-1809	143	7	j	j	NOUN
ejpam-1809	143	8	)	)	PUNCT
ejpam-1809	143	9	∈	∈	PROPN
ejpam-1809	143	10	b(g	b(g	PROPN
ejpam-1809	143	11	,	,	PUNCT
ejpam-1809	143	12	n	n	CCONJ
ejpam-1809	143	13	)	)	PUNCT
ejpam-1809	143	14	we	we	PRON
ejpam-1809	143	15	have	have	VERB
ejpam-1809	143	16	(	(	PUNCT
ejpam-1809	143	17	i	i	PRON
ejpam-1809	143	18	,	,	PUNCT
ejpam-1809	143	19	g	g	PROPN
ejpam-1809	143	20	,	,	PUNCT
ejpam-1809	143	21	j	j	PROPN
ejpam-1809	143	22	)	)	PUNCT
ejpam-1809	143	23	=	=	PUNCT
ejpam-1809	144	1	(	(	PUNCT
ejpam-1809	144	2	i	i	PROPN
ejpam-1809	144	3	,	,	PUNCT
ejpam-1809	144	4	a1	a1	PROPN
ejpam-1809	144	5	,	,	PUNCT
ejpam-1809	144	6	1).(1	1).(1	NUM
ejpam-1809	144	7	,	,	PUNCT
ejpam-1809	144	8	a2	a2	PROPN
ejpam-1809	144	9	,	,	PUNCT
ejpam-1809	144	10	1).(1	1).(1	NUM
ejpam-1809	144	11	,	,	PUNCT
ejpam-1809	144	12	a3	a3	NOUN
ejpam-1809	144	13	,	,	PUNCT
ejpam-1809	144	14	1	1	NUM
ejpam-1809	144	15	)	)	PUNCT
ejpam-1809	144	16	.	.	PUNCT
ejpam-1809	144	17	.	.	PUNCT
ejpam-1809	144	18	.	.	PUNCT
ejpam-1809	145	1	(	(	PUNCT
ejpam-1809	145	2	1	1	NUM
ejpam-1809	145	3	,	,	PUNCT
ejpam-1809	145	4	am	be	AUX
ejpam-1809	145	5	,	,	PUNCT
ejpam-1809	145	6	j	j	PROPN
ejpam-1809	145	7	)	)	PUNCT
ejpam-1809	145	8	,	,	PUNCT
ejpam-1809	145	9	(	(	PUNCT
ejpam-1809	145	10	ai	ai	VERB
ejpam-1809	145	11	∈	∈	PROPN
ejpam-1809	145	12	a	a	PRON
ejpam-1809	145	13	,	,	PUNCT
ejpam-1809	145	14	i	i	NOUN
ejpam-1809	145	15	=	=	NOUN
ejpam-1809	145	16	1	1	NUM
ejpam-1809	145	17	,	,	PUNCT
ejpam-1809	145	18	2	2	NUM
ejpam-1809	145	19	,	,	PUNCT
ejpam-1809	145	20	.	.	PUNCT
ejpam-1809	145	21	.	.	PUNCT
ejpam-1809	145	22	.	.	PUNCT
ejpam-1809	146	1	m	m	X
ejpam-1809	146	2	)	)	PUNCT
ejpam-1809	146	3	.	.	PUNCT
ejpam-1809	147	1	so	so	ADV
ejpam-1809	147	2	b	b	PROPN
ejpam-1809	147	3	is	be	AUX
ejpam-1809	147	4	a	a	DET
ejpam-1809	147	5	generating	generate	VERB
ejpam-1809	147	6	set	set	NOUN
ejpam-1809	147	7	for	for	ADP
ejpam-1809	147	8	b(g	b(g	PROPN
ejpam-1809	147	9	,	,	PUNCT
ejpam-1809	147	10	n	n	CCONJ
ejpam-1809	147	11	)	)	PUNCT
ejpam-1809	147	12	.	.	PUNCT
ejpam-1809	148	1	let	let	VERB
ejpam-1809	148	2	c	c	PRON
ejpam-1809	148	3	be	be	AUX
ejpam-1809	148	4	a	a	DET
ejpam-1809	148	5	generating	generate	VERB
ejpam-1809	148	6	set	set	NOUN
ejpam-1809	148	7	for	for	ADP
ejpam-1809	148	8	b(g	b(g	PROPN
ejpam-1809	148	9	,	,	PUNCT
ejpam-1809	148	10	n	n	CCONJ
ejpam-1809	148	11	)	)	PUNCT
ejpam-1809	148	12	.	.	PUNCT
ejpam-1809	149	1	since	since	SCONJ
ejpam-1809	149	2	(	(	PUNCT
ejpam-1809	149	3	i	i	PRON
ejpam-1809	149	4	,	,	PUNCT
ejpam-1809	149	5	a	a	PRON
ejpam-1809	149	6	,	,	PUNCT
ejpam-1809	149	7	1	1	NUM
ejpam-1809	149	8	)	)	PUNCT
ejpam-1809	149	9	=	=	SYM
ejpam-1809	149	10	(	(	PUNCT
ejpam-1809	149	11	i	i	NOUN
ejpam-1809	149	12	,	,	PUNCT
ejpam-1809	149	13	a	a	PRON
ejpam-1809	149	14	,	,	PUNCT
ejpam-1809	149	15	1).(1	1).(1	NUM
ejpam-1809	149	16	,	,	PUNCT
ejpam-1809	149	17	1,1)(a	1,1)(a	NUM
ejpam-1809	149	18	∈	∈	PROPN
ejpam-1809	149	19	a	a	NOUN
ejpam-1809	149	20	)	)	PUNCT
ejpam-1809	149	21	and	and	CCONJ
ejpam-1809	149	22	(	(	PUNCT
ejpam-1809	149	23	1,1	1,1	NUM
ejpam-1809	149	24	,	,	PUNCT
ejpam-1809	149	25	j	j	NOUN
ejpam-1809	149	26	)	)	PUNCT
ejpam-1809	149	27	=	=	PUNCT
ejpam-1809	149	28	(	(	PUNCT
ejpam-1809	149	29	1	1	NUM
ejpam-1809	149	30	,	,	PUNCT
ejpam-1809	149	31	1,1).(1	1,1).(1	NUM
ejpam-1809	149	32	,	,	PUNCT
ejpam-1809	149	33	1	1	NUM
ejpam-1809	149	34	,	,	PUNCT
ejpam-1809	149	35	j	j	NOUN
ejpam-1809	149	36	)	)	PUNCT
ejpam-1809	149	37	.	.	PUNCT
ejpam-1809	150	1	so	so	ADV
ejpam-1809	150	2	we	we	PRON
ejpam-1809	150	3	have	have	VERB
ejpam-1809	150	4	b	b	NUM
ejpam-1809	150	5	⊆	⊆	NUM
ejpam-1809	150	6	c	c	NOUN
ejpam-1809	150	7	.	.	PUNCT
ejpam-1809	151	1	thus	thus	ADV
ejpam-1809	151	2	b	b	X
ejpam-1809	151	3	is	be	AUX
ejpam-1809	151	4	the	the	DET
ejpam-1809	151	5	minimum	minimum	NOUN
ejpam-1809	151	6	generating	generating	NOUN
ejpam-1809	151	7	set	set	NOUN
ejpam-1809	151	8	for	for	ADP
ejpam-1809	151	9	b(g	b(g	PROPN
ejpam-1809	151	10	,	,	PUNCT
ejpam-1809	151	11	n	n	CCONJ
ejpam-1809	151	12	)	)	PUNCT
ejpam-1809	151	13	.	.	PUNCT
ejpam-1809	152	1	we	we	PRON
ejpam-1809	152	2	have	have	VERB
ejpam-1809	152	3	r2(b(g	r2(b(g	NOUN
ejpam-1809	152	4	,	,	PUNCT
ejpam-1809	152	5	n	n	CCONJ
ejpam-1809	152	6	)	)	PUNCT
ejpam-1809	152	7	)	)	PUNCT
ejpam-1809	153	1	=	=	SYM
ejpam-1809	153	2	2n.|a|	2n.|a|	X
ejpam-1809	153	3	.	.	PUNCT
ejpam-1809	154	1	let	let	VERB
ejpam-1809	154	2	d	d	PRON
ejpam-1809	154	3	be	be	AUX
ejpam-1809	154	4	a	a	DET
ejpam-1809	154	5	generating	generate	VERB
ejpam-1809	154	6	set	set	NOUN
ejpam-1809	154	7	for	for	ADP
ejpam-1809	154	8	b(g	b(g	PROPN
ejpam-1809	154	9	,	,	PUNCT
ejpam-1809	154	10	n	n	CCONJ
ejpam-1809	154	11	)	)	PUNCT
ejpam-1809	154	12	and	and	CCONJ
ejpam-1809	154	13	assume	assume	VERB
ejpam-1809	154	14	that	that	SCONJ
ejpam-1809	154	15	d	d	NOUN
ejpam-1809	154	16	is	be	AUX
ejpam-1809	154	17	independent	independent	ADJ
ejpam-1809	154	18	.	.	PUNCT
ejpam-1809	155	1	since	since	SCONJ
ejpam-1809	155	2	d	d	PROPN
ejpam-1809	155	3	is	be	AUX
ejpam-1809	155	4	a	a	DET
ejpam-1809	155	5	generating	generate	VERB
ejpam-1809	155	6	set	set	NOUN
ejpam-1809	155	7	and	and	CCONJ
ejpam-1809	155	8	b	b	NOUN
ejpam-1809	155	9	is	be	AUX
ejpam-1809	155	10	the	the	DET
ejpam-1809	155	11	minimum	minimum	NOUN
ejpam-1809	155	12	generating	generating	NOUN
ejpam-1809	155	13	set	set	NOUN
ejpam-1809	155	14	then	then	ADV
ejpam-1809	155	15	b	b	PROPN
ejpam-1809	155	16	⊆	⊆	NUM
ejpam-1809	155	17	d.	d.	PROPN
ejpam-1809	155	18	let	let	VERB
ejpam-1809	155	19	(	(	PUNCT
ejpam-1809	155	20	i′	i′	NOUN
ejpam-1809	155	21	,	,	PUNCT
ejpam-1809	155	22	g	g	NOUN
ejpam-1809	155	23	,	,	PUNCT
ejpam-1809	155	24	j′	j′	PROPN
ejpam-1809	155	25	)	)	PUNCT
ejpam-1809	156	1	∈	∈	PROPN
ejpam-1809	156	2	d	d	X
ejpam-1809	156	3	b.	b.	PROPN
ejpam-1809	156	4	let	let	VERB
ejpam-1809	156	5	g	g	NOUN
ejpam-1809	156	6	=	=	VERB
ejpam-1809	156	7	a′1a′2	a′1a′2	NOUN
ejpam-1809	156	8	.	.	PUNCT
ejpam-1809	156	9	.	.	PUNCT
ejpam-1809	156	10	.	.	PUNCT
ejpam-1809	157	1	a′l(a	a′l(a	PROPN
ejpam-1809	157	2	′	′	NUM
ejpam-1809	158	1	i	i	PRON
ejpam-1809	158	2	∈	∈	VERB
ejpam-1809	158	3	a	a	PRON
ejpam-1809	158	4	)	)	PUNCT
ejpam-1809	158	5	.	.	PUNCT
ejpam-1809	159	1	then	then	ADV
ejpam-1809	159	2	(	(	PUNCT
ejpam-1809	159	3	i′	i′	NOUN
ejpam-1809	159	4	,	,	PUNCT
ejpam-1809	159	5	g	g	NOUN
ejpam-1809	159	6	,	,	PUNCT
ejpam-1809	159	7	j′	j′	PROPN
ejpam-1809	159	8	)	)	PUNCT
ejpam-1809	160	1	=	=	SYM
ejpam-1809	160	2	(	(	PUNCT
ejpam-1809	160	3	i′	i′	NOUN
ejpam-1809	160	4	,	,	PUNCT
ejpam-1809	160	5	a′1	a′1	PROPN
ejpam-1809	160	6	,	,	PUNCT
ejpam-1809	160	7	1).(1	1).(1	NUM
ejpam-1809	160	8	,	,	PUNCT
ejpam-1809	160	9	a′2	a′2	PRON
ejpam-1809	160	10	,	,	PUNCT
ejpam-1809	160	11	1)(1	1)(1	NUM
ejpam-1809	160	12	,	,	PUNCT
ejpam-1809	160	13	a′3	a′3	NOUN
ejpam-1809	160	14	,	,	PUNCT
ejpam-1809	160	15	1	1	NUM
ejpam-1809	160	16	)	)	PUNCT
ejpam-1809	160	17	.	.	PUNCT
ejpam-1809	160	18	.	.	PUNCT
ejpam-1809	160	19	.	.	PUNCT
ejpam-1809	161	1	(	(	PUNCT
ejpam-1809	161	2	1	1	NUM
ejpam-1809	161	3	,	,	PUNCT
ejpam-1809	161	4	a′l	a′l	NOUN
ejpam-1809	161	5	,	,	PUNCT
ejpam-1809	161	6	j′	j′	PROPN
ejpam-1809	161	7	)	)	PUNCT
ejpam-1809	161	8	.	.	PUNCT
ejpam-1809	162	1	this	this	PRON
ejpam-1809	162	2	contradicts	contradict	VERB
ejpam-1809	162	3	with	with	ADP
ejpam-1809	162	4	the	the	DET
ejpam-1809	162	5	assumption	assumption	NOUN
ejpam-1809	162	6	of	of	ADP
ejpam-1809	162	7	d	d	PROPN
ejpam-1809	162	8	to	to	PART
ejpam-1809	162	9	be	be	AUX
ejpam-1809	162	10	independent	independent	ADJ
ejpam-1809	162	11	.	.	PUNCT
ejpam-1809	163	1	so	so	ADV
ejpam-1809	163	2	b	b	PROPN
ejpam-1809	163	3	is	be	AUX
ejpam-1809	163	4	the	the	DET
ejpam-1809	163	5	unique	unique	ADJ
ejpam-1809	163	6	independent	independent	ADJ
ejpam-1809	163	7	generating	generating	NOUN
ejpam-1809	163	8	subset	subset	NOUN
ejpam-1809	163	9	of	of	ADP
ejpam-1809	163	10	b(g	b(g	PROPN
ejpam-1809	163	11	,	,	PUNCT
ejpam-1809	163	12	n	n	CCONJ
ejpam-1809	163	13	)	)	PUNCT
ejpam-1809	163	14	.	.	PUNCT
ejpam-1809	164	1	thus	thus	ADV
ejpam-1809	164	2	r3(b(g	r3(b(g	NUM
ejpam-1809	164	3	,	,	PUNCT
ejpam-1809	164	4	n	n	CCONJ
ejpam-1809	164	5	)	)	PUNCT
ejpam-1809	164	6	)	)	PUNCT
ejpam-1809	165	1	=	=	SYM
ejpam-1809	165	2	2n.|a|	2n.|a|	X
ejpam-1809	165	3	.	.	PUNCT
ejpam-1809	166	1	let	let	VERB
ejpam-1809	166	2	(	(	PUNCT
ejpam-1809	166	3	i	i	NOUN
ejpam-1809	166	4	,	,	PUNCT
ejpam-1809	166	5	g	g	PROPN
ejpam-1809	166	6	,	,	PUNCT
ejpam-1809	166	7	j	j	NOUN
ejpam-1809	166	8	)	)	PUNCT
ejpam-1809	166	9	∈	∈	PROPN
ejpam-1809	166	10	b(g	b(g	PROPN
ejpam-1809	166	11	,	,	PUNCT
ejpam-1809	166	12	n	n	CCONJ
ejpam-1809	166	13	)	)	PUNCT
ejpam-1809	166	14	.	.	PUNCT
ejpam-1809	167	1	if	if	SCONJ
ejpam-1809	167	2	i	i	PRON
ejpam-1809	167	3	=	=	SYM
ejpam-1809	167	4	j	j	PROPN
ejpam-1809	167	5	then	then	ADV
ejpam-1809	167	6	(	(	PUNCT
ejpam-1809	167	7	i	i	NOUN
ejpam-1809	167	8	,	,	PUNCT
ejpam-1809	167	9	g	g	NOUN
ejpam-1809	167	10	,	,	PUNCT
ejpam-1809	167	11	j).(i	j).(i	PROPN
ejpam-1809	167	12	,	,	PUNCT
ejpam-1809	167	13	g	g	PROPN
ejpam-1809	167	14	,	,	PUNCT
ejpam-1809	167	15	j	j	NOUN
ejpam-1809	167	16	)	)	PUNCT
ejpam-1809	167	17	=	=	PUNCT
ejpam-1809	167	18	(	(	PUNCT
ejpam-1809	167	19	i	i	PROPN
ejpam-1809	167	20	,	,	PUNCT
ejpam-1809	167	21	g2	g2	PROPN
ejpam-1809	167	22	,	,	PUNCT
ejpam-1809	167	23	j	j	PROPN
ejpam-1809	167	24	)	)	PUNCT
ejpam-1809	167	25	6=	6=	PROPN
ejpam-1809	168	1	(	(	PUNCT
ejpam-1809	168	2	i	i	PRON
ejpam-1809	168	3	,	,	PUNCT
ejpam-1809	168	4	g	g	PROPN
ejpam-1809	168	5	,	,	PUNCT
ejpam-1809	168	6	j	j	PROPN
ejpam-1809	168	7	)	)	PUNCT
ejpam-1809	168	8	unless	unless	SCONJ
ejpam-1809	168	9	g2	g2	PROPN
ejpam-1809	168	10	=	=	PUNCT
ejpam-1809	168	11	g.	g.	PROPN
ejpam-1809	169	1	if	if	SCONJ
ejpam-1809	169	2	i	i	PRON
ejpam-1809	169	3	6=	6=	PROPN
ejpam-1809	169	4	j	j	PROPN
ejpam-1809	169	5	then	then	ADV
ejpam-1809	169	6	(	(	PUNCT
ejpam-1809	169	7	i	i	NOUN
ejpam-1809	169	8	,	,	PUNCT
ejpam-1809	169	9	g	g	NOUN
ejpam-1809	169	10	,	,	PUNCT
ejpam-1809	169	11	j).(i	j).(i	PROPN
ejpam-1809	169	12	,	,	PUNCT
ejpam-1809	169	13	g	g	PROPN
ejpam-1809	169	14	,	,	PUNCT
ejpam-1809	169	15	j	j	NOUN
ejpam-1809	169	16	)	)	PUNCT
ejpam-1809	169	17	=	=	SYM
ejpam-1809	169	18	0	0	X
ejpam-1809	169	19	.	.	PUNCT
ejpam-1809	170	1	so	so	ADV
ejpam-1809	170	2	b(g	b(g	PROPN
ejpam-1809	170	3	,	,	PUNCT
ejpam-1809	170	4	n	n	CCONJ
ejpam-1809	170	5	)	)	PUNCT
ejpam-1809	170	6	is	be	AUX
ejpam-1809	170	7	not	not	PART
ejpam-1809	170	8	a	a	DET
ejpam-1809	170	9	band	band	NOUN
ejpam-1809	170	10	.	.	PUNCT
ejpam-1809	171	1	since	since	SCONJ
ejpam-1809	171	2	r2(b(g	r2(b(g	NOUN
ejpam-1809	171	3	,	,	PUNCT
ejpam-1809	171	4	n	n	CCONJ
ejpam-1809	171	5	)	)	PUNCT
ejpam-1809	171	6	)	)	PUNCT
ejpam-1809	171	7	6=|	6=|	NUM
ejpam-1809	171	8	b(g	b(g	NOUN
ejpam-1809	171	9	,	,	PUNCT
ejpam-1809	171	10	n	n	CCONJ
ejpam-1809	171	11	)	)	PUNCT
ejpam-1809	171	12	|	|	ADV
ejpam-1809	171	13	then	then	ADV
ejpam-1809	171	14	b(g	b(g	PROPN
ejpam-1809	171	15	,	,	PUNCT
ejpam-1809	171	16	n	n	CCONJ
ejpam-1809	171	17	)	)	PUNCT
ejpam-1809	171	18	is	be	AUX
ejpam-1809	171	19	not	not	PART
ejpam-1809	171	20	royal	royal	ADJ
ejpam-1809	171	21	.	.	PUNCT
ejpam-1809	172	1	(	(	PUNCT
ejpam-1809	172	2	see	see	VERB
ejpam-1809	172	3	[	[	X
ejpam-1809	172	4	5	5	NUM
ejpam-1809	172	5	]	]	PUNCT
ejpam-1809	172	6	)	)	PUNCT
ejpam-1809	172	7	so	so	SCONJ
ejpam-1809	172	8	r1(b(g	r1(b(g	NOUN
ejpam-1809	172	9	,	,	PUNCT
ejpam-1809	172	10	n	n	CCONJ
ejpam-1809	172	11	)	)	PUNCT
ejpam-1809	172	12	)	)	PUNCT
ejpam-1809	173	1	=	=	PUNCT
ejpam-1809	173	2	1	1	X
ejpam-1809	173	3	.	.	PUNCT
ejpam-1809	173	4	in	in	ADP
ejpam-1809	173	5	the	the	DET
ejpam-1809	173	6	following	follow	VERB
ejpam-1809	173	7	theorem	theorem	NOUN
ejpam-1809	173	8	we	we	PRON
ejpam-1809	173	9	determine	determine	VERB
ejpam-1809	173	10	r4(b(g	r4(b(g	NOUN
ejpam-1809	173	11	,	,	PUNCT
ejpam-1809	173	12	n	n	CCONJ
ejpam-1809	173	13	)	)	PUNCT
ejpam-1809	173	14	)	)	PUNCT
ejpam-1809	173	15	.	.	PUNCT
ejpam-1809	174	1	theorem	theorem	ADJ
ejpam-1809	174	2	4	4	NUM
ejpam-1809	174	3	.	.	PUNCT
ejpam-1809	175	1	let	let	VERB
ejpam-1809	175	2	b(g	b(g	PROPN
ejpam-1809	175	3	,	,	PUNCT
ejpam-1809	175	4	n	n	CCONJ
ejpam-1809	175	5	)	)	PUNCT
ejpam-1809	175	6	be	be	AUX
ejpam-1809	175	7	a	a	DET
ejpam-1809	175	8	brandt	brandt	PROPN
ejpam-1809	175	9	semigroup	semigroup	PROPN
ejpam-1809	175	10	.	.	PUNCT
ejpam-1809	176	1	let	let	VERB
ejpam-1809	176	2	r4(g	r4(g	X
ejpam-1809	176	3	)	)	PUNCT
ejpam-1809	177	1	=	=	VERB
ejpam-1809	177	2	k.	k.	PROPN
ejpam-1809	178	1	then	then	ADV
ejpam-1809	178	2	r4(b(g	r4(b(g	PROPN
ejpam-1809	178	3	,	,	PUNCT
ejpam-1809	178	4	n	n	CCONJ
ejpam-1809	178	5	)	)	PUNCT
ejpam-1809	178	6	)	)	PUNCT
ejpam-1809	179	1	=	=	PUNCT
ejpam-1809	179	2	k+	k+	NOUN
ejpam-1809	179	3	1	1	X
ejpam-1809	179	4	.	.	X
ejpam-1809	180	1	proof	proof	NOUN
ejpam-1809	180	2	.	.	PUNCT
ejpam-1809	181	1	let	let	VERB
ejpam-1809	181	2	u	u	PRON
ejpam-1809	181	3	be	be	AUX
ejpam-1809	181	4	the	the	DET
ejpam-1809	181	5	maximum	maximum	ADJ
ejpam-1809	181	6	independent	independent	ADJ
ejpam-1809	181	7	subset	subset	NOUN
ejpam-1809	181	8	of	of	ADP
ejpam-1809	181	9	g.	g.	PROPN
ejpam-1809	181	10	since	since	SCONJ
ejpam-1809	181	11	r4(g	r4(g	PART
ejpam-1809	181	12	)	)	PUNCT
ejpam-1809	181	13	=	=	VERB
ejpam-1809	182	1	k	k	PROPN
ejpam-1809	182	2	then	then	ADV
ejpam-1809	182	3	|	|	ADV
ejpam-1809	182	4	u	u	PRON
ejpam-1809	182	5	|=	|=	PUNCT
ejpam-1809	182	6	k.	k.	ADV
ejpam-1809	182	7	we	we	PRON
ejpam-1809	182	8	will	will	AUX
ejpam-1809	182	9	show	show	VERB
ejpam-1809	182	10	that	that	SCONJ
ejpam-1809	182	11	u	u	NOUN
ejpam-1809	182	12	′	′	NOUN
ejpam-1809	182	13	=	=	SYM
ejpam-1809	182	14	{	{	PUNCT
ejpam-1809	182	15	(	(	PUNCT
ejpam-1809	182	16	1	1	NUM
ejpam-1809	182	17	,	,	PUNCT
ejpam-1809	182	18	u	u	NOUN
ejpam-1809	182	19	,	,	PUNCT
ejpam-1809	182	20	1)|u	1)|u	NUM
ejpam-1809	182	21	∈	∈	NOUN
ejpam-1809	182	22	u}∪{0	u}∪{0	NOUN
ejpam-1809	182	23	}	}	PUNCT
ejpam-1809	182	24	is	be	AUX
ejpam-1809	182	25	the	the	DET
ejpam-1809	182	26	maximum	maximum	ADJ
ejpam-1809	182	27	independent	independent	ADJ
ejpam-1809	182	28	subset	subset	NOUN
ejpam-1809	182	29	of	of	ADP
ejpam-1809	182	30	b(g	b(g	PROPN
ejpam-1809	182	31	,	,	PUNCT
ejpam-1809	182	32	n	n	CCONJ
ejpam-1809	182	33	)	)	PUNCT
ejpam-1809	182	34	.	.	PUNCT
ejpam-1809	183	1	let	let	VERB
ejpam-1809	183	2	(	(	PUNCT
ejpam-1809	183	3	1	1	NUM
ejpam-1809	183	4	,	,	PUNCT
ejpam-1809	183	5	u	u	NOUN
ejpam-1809	183	6	,	,	PUNCT
ejpam-1809	183	7	1	1	NUM
ejpam-1809	183	8	)	)	PUNCT
ejpam-1809	183	9	=	=	SYM
ejpam-1809	183	10	(	(	PUNCT
ejpam-1809	183	11	1	1	NUM
ejpam-1809	183	12	,	,	PUNCT
ejpam-1809	183	13	u1	u1	NOUN
ejpam-1809	183	14	,	,	PUNCT
ejpam-1809	183	15	1).(1	1).(1	NUM
ejpam-1809	183	16	,	,	PUNCT
ejpam-1809	183	17	u2	u2	NOUN
ejpam-1809	183	18	,	,	PUNCT
ejpam-1809	183	19	1)(u1	1)(u1	NUM
ejpam-1809	183	20	,	,	PUNCT
ejpam-1809	183	21	u2	u2	PROPN
ejpam-1809	183	22	∈	∈	PROPN
ejpam-1809	183	23	u	u	NOUN
ejpam-1809	183	24	)	)	PUNCT
ejpam-1809	183	25	.	.	PUNCT
ejpam-1809	184	1	then	then	ADV
ejpam-1809	184	2	u=	u=	ADV
ejpam-1809	184	3	u1.u2	u1.u2	PROPN
ejpam-1809	184	4	.	.	PUNCT
ejpam-1809	185	1	since	since	SCONJ
ejpam-1809	185	2	u	u	NOUN
ejpam-1809	185	3	is	be	AUX
ejpam-1809	185	4	independent	independent	ADJ
ejpam-1809	185	5	then	then	ADV
ejpam-1809	185	6	u=	u=	ADJ
ejpam-1809	185	7	u1	u1	NOUN
ejpam-1809	185	8	or	or	CCONJ
ejpam-1809	185	9	u	u	NOUN
ejpam-1809	185	10	=	=	PROPN
ejpam-1809	185	11	u2	u2	PROPN
ejpam-1809	185	12	.	.	PUNCT
ejpam-1809	186	1	we	we	PRON
ejpam-1809	186	2	obtain	obtain	VERB
ejpam-1809	186	3	u	u	NOUN
ejpam-1809	186	4	′	′	NOUN
ejpam-1809	186	5	is	be	AUX
ejpam-1809	186	6	independent	independent	ADJ
ejpam-1809	186	7	.	.	PUNCT
ejpam-1809	187	1	let	let	VERB
ejpam-1809	187	2	u	u	PRON
ejpam-1809	187	3	′′	′′	PROPN
ejpam-1809	187	4	⊆	⊆	PROPN
ejpam-1809	187	5	b(g	b(g	PROPN
ejpam-1809	187	6	,	,	PUNCT
ejpam-1809	187	7	n	n	CCONJ
ejpam-1809	187	8	)	)	PUNCT
ejpam-1809	187	9	be	be	AUX
ejpam-1809	187	10	another	another	DET
ejpam-1809	187	11	independent	independent	ADJ
ejpam-1809	187	12	set	set	NOUN
ejpam-1809	187	13	.	.	PUNCT
ejpam-1809	188	1	we	we	PRON
ejpam-1809	188	2	have	have	VERB
ejpam-1809	188	3	u	u	NOUN
ejpam-1809	188	4	′	′	NOUN
ejpam-1809	188	5	∪	∪	ADV
ejpam-1809	188	6	(	(	PUNCT
ejpam-1809	188	7	s\u	s\u	NOUN
ejpam-1809	188	8	′	′	NUM
ejpam-1809	188	9	)	)	PUNCT
ejpam-1809	189	1	=	=	PRON
ejpam-1809	189	2	s	s	NOUN
ejpam-1809	189	3	=	=	PUNCT
ejpam-1809	189	4	b(g	b(g	PROPN
ejpam-1809	189	5	,	,	PUNCT
ejpam-1809	189	6	n	n	CCONJ
ejpam-1809	189	7	)	)	PUNCT
ejpam-1809	189	8	.	.	PUNCT
ejpam-1809	190	1	let	let	VERB
ejpam-1809	190	2	s	s	PRON
ejpam-1809	190	3	∈	∈	PROPN
ejpam-1809	190	4	s\u	s\u	NOUN
ejpam-1809	190	5	′.	′.	NOUN
ejpam-1809	190	6	let	let	VERB
ejpam-1809	190	7	s	s	PRON
ejpam-1809	190	8	=	=	PUNCT
ejpam-1809	190	9	(	(	PUNCT
ejpam-1809	190	10	i	i	NOUN
ejpam-1809	190	11	,	,	PUNCT
ejpam-1809	190	12	g	g	PROPN
ejpam-1809	190	13	,	,	PUNCT
ejpam-1809	190	14	j)(1≤	j)(1≤	PROPN
ejpam-1809	190	15	i	i	PROPN
ejpam-1809	190	16	≤	≤	PROPN
ejpam-1809	190	17	n	n	CCONJ
ejpam-1809	190	18	,	,	PUNCT
ejpam-1809	190	19	g	g	PROPN
ejpam-1809	190	20	∈	∈	PROPN
ejpam-1809	190	21	g\u	g\u	PROPN
ejpam-1809	190	22	,	,	PUNCT
ejpam-1809	190	23	1≤	1≤	NUM
ejpam-1809	190	24	j	j	PROPN
ejpam-1809	190	25	≤	≤	PROPN
ejpam-1809	190	26	n	n	CCONJ
ejpam-1809	190	27	)	)	PUNCT
ejpam-1809	190	28	.	.	PUNCT
ejpam-1809	191	1	since	since	SCONJ
ejpam-1809	191	2	g	g	PROPN
ejpam-1809	191	3	∈	∈	PROPN
ejpam-1809	191	4	g\u	g\u	NOUN
ejpam-1809	191	5	then	then	ADV
ejpam-1809	191	6	g	g	NOUN
ejpam-1809	191	7	=	=	NOUN
ejpam-1809	191	8	g1.g2(g1	g1.g2(g1	NOUN
ejpam-1809	191	9	,	,	PUNCT
ejpam-1809	191	10	g2	g2	PROPN
ejpam-1809	191	11	∈	∈	PROPN
ejpam-1809	191	12	g	g	PROPN
ejpam-1809	191	13	,	,	PUNCT
ejpam-1809	191	14	g1	g1	PROPN
ejpam-1809	191	15	6=	6=	ADP
ejpam-1809	191	16	g	g	PROPN
ejpam-1809	191	17	,	,	PUNCT
ejpam-1809	191	18	g2	g2	PROPN
ejpam-1809	191	19	6=	6=	PRON
ejpam-1809	191	20	g	g	NOUN
ejpam-1809	191	21	)	)	PUNCT
ejpam-1809	191	22	.	.	PUNCT
ejpam-1809	192	1	we	we	PRON
ejpam-1809	192	2	have	have	VERB
ejpam-1809	192	3	(	(	PUNCT
ejpam-1809	192	4	i	i	PRON
ejpam-1809	192	5	,	,	PUNCT
ejpam-1809	192	6	g	g	PROPN
ejpam-1809	192	7	,	,	PUNCT
ejpam-1809	192	8	j	j	PROPN
ejpam-1809	192	9	)	)	PUNCT
ejpam-1809	192	10	=	=	PUNCT
ejpam-1809	193	1	(	(	PUNCT
ejpam-1809	193	2	i	i	PROPN
ejpam-1809	193	3	,	,	PUNCT
ejpam-1809	193	4	g1	g1	PROPN
ejpam-1809	193	5	,	,	PUNCT
ejpam-1809	193	6	j	j	PROPN
ejpam-1809	193	7	)	)	PUNCT
ejpam-1809	193	8	.	.	PUNCT
ejpam-1809	194	1	(	(	PUNCT
ejpam-1809	194	2	j	j	PROPN
ejpam-1809	194	3	,	,	PUNCT
ejpam-1809	194	4	g2	g2	PROPN
ejpam-1809	194	5	,	,	PUNCT
ejpam-1809	194	6	j	j	PROPN
ejpam-1809	194	7	)	)	PUNCT
ejpam-1809	194	8	and	and	CCONJ
ejpam-1809	194	9	u	u	NOUN
ejpam-1809	194	10	′′	′′	PROPN
ejpam-1809	194	11	=	=	SYM
ejpam-1809	194	12	(	(	PUNCT
ejpam-1809	194	13	(	(	PUNCT
ejpam-1809	194	14	u	u	NOUN
ejpam-1809	194	15	′∪{0})∩u	′∪{0})∩u	VERB
ejpam-1809	194	16	′′)∪	′′)∪	NOUN
ejpam-1809	194	17	(	(	PUNCT
ejpam-1809	194	18	u	u	NOUN
ejpam-1809	194	19	′′∩	′′∩	NOUN
ejpam-1809	194	20	(	(	PUNCT
ejpam-1809	194	21	s\u	s\u	PROPN
ejpam-1809	194	22	′	′	NUM
ejpam-1809	194	23	)	)	PUNCT
ejpam-1809	194	24	)	)	PUNCT
ejpam-1809	194	25	.	.	PUNCT
ejpam-1809	195	1	since	since	SCONJ
ejpam-1809	195	2	the	the	DET
ejpam-1809	195	3	elements	element	NOUN
ejpam-1809	195	4	of	of	ADP
ejpam-1809	195	5	s\(u	s\(u	PROPN
ejpam-1809	195	6	′∪{0	′∪{0	NOUN
ejpam-1809	195	7	}	}	PUNCT
ejpam-1809	195	8	)	)	PUNCT
ejpam-1809	195	9	can	can	AUX
ejpam-1809	195	10	be	be	AUX
ejpam-1809	195	11	written	write	VERB
ejpam-1809	195	12	references	reference	NOUN
ejpam-1809	195	13	339	339	NUM
ejpam-1809	195	14	as	as	ADP
ejpam-1809	195	15	a	a	DET
ejpam-1809	195	16	product	product	NOUN
ejpam-1809	195	17	of	of	ADP
ejpam-1809	195	18	two	two	NUM
ejpam-1809	195	19	elements	element	NOUN
ejpam-1809	195	20	.	.	PUNCT
ejpam-1809	196	1	so	so	ADV
ejpam-1809	196	2	u	u	PRON
ejpam-1809	196	3	′′	′′	PROPN
ejpam-1809	196	4	∩	∩	NOUN
ejpam-1809	196	5	(	(	PUNCT
ejpam-1809	196	6	s\(u	s\(u	NOUN
ejpam-1809	196	7	′	′	NUM
ejpam-1809	196	8	∪	∪	X
ejpam-1809	196	9	{	{	PUNCT
ejpam-1809	196	10	0	0	NUM
ejpam-1809	196	11	}	}	PUNCT
ejpam-1809	196	12	)	)	PUNCT
ejpam-1809	196	13	=	=	SYM
ejpam-1809	196	14	;	;	PUNCT
ejpam-1809	196	15	.	.	PUNCT
ejpam-1809	197	1	then	then	ADV
ejpam-1809	197	2	u	u	PROPN
ejpam-1809	197	3	′′	′′	PROPN
ejpam-1809	197	4	=	=	PUNCT
ejpam-1809	197	5	(	(	PUNCT
ejpam-1809	197	6	u	u	NOUN
ejpam-1809	197	7	′	′	NOUN
ejpam-1809	197	8	∪	∪	X
ejpam-1809	197	9	{	{	PUNCT
ejpam-1809	197	10	0})∩	0})∩	NOUN
ejpam-1809	197	11	u	u	NOUN
ejpam-1809	197	12	′′.	′′.	NOUN
ejpam-1809	197	13	so	so	SCONJ
ejpam-1809	197	14	u	u	PROPN
ejpam-1809	197	15	′′	′′	PROPN
ejpam-1809	197	16	⊆	⊆	NUM
ejpam-1809	197	17	(	(	PUNCT
ejpam-1809	197	18	u	u	NOUN
ejpam-1809	197	19	′	′	NOUN
ejpam-1809	197	20	∪	∪	X
ejpam-1809	197	21	{	{	PUNCT
ejpam-1809	197	22	0	0	NUM
ejpam-1809	197	23	}	}	PUNCT
ejpam-1809	197	24	)	)	PUNCT
ejpam-1809	197	25	.	.	PUNCT
ejpam-1809	198	1	we	we	PRON
ejpam-1809	198	2	obtain	obtain	VERB
ejpam-1809	198	3	u	u	NOUN
ejpam-1809	198	4	′	′	NOUN
ejpam-1809	198	5	∪	∪	X
ejpam-1809	198	6	{	{	PUNCT
ejpam-1809	198	7	0	0	NUM
ejpam-1809	198	8	}	}	PUNCT
ejpam-1809	198	9	is	be	AUX
ejpam-1809	198	10	the	the	DET
ejpam-1809	198	11	maximum	maximum	ADJ
ejpam-1809	198	12	independent	independent	ADJ
ejpam-1809	198	13	set	set	NOUN
ejpam-1809	198	14	.	.	PUNCT
ejpam-1809	199	1	so	so	ADV
ejpam-1809	199	2	r4(b(g	r4(b(g	PROPN
ejpam-1809	199	3	,	,	PUNCT
ejpam-1809	199	4	n	n	CCONJ
ejpam-1809	199	5	)	)	PUNCT
ejpam-1809	199	6	)	)	PUNCT
ejpam-1809	200	1	=	=	PUNCT
ejpam-1809	200	2	k+	k+	NOUN
ejpam-1809	200	3	1	1	X
ejpam-1809	200	4	.	.	PUNCT
ejpam-1809	201	1	the	the	DET
ejpam-1809	201	2	studies	study	NOUN
ejpam-1809	201	3	on	on	ADP
ejpam-1809	201	4	finiteness	finiteness	ADJ
ejpam-1809	201	5	conditions	condition	NOUN
ejpam-1809	201	6	of	of	ADP
ejpam-1809	201	7	semigroups	semigroup	NOUN
ejpam-1809	201	8	and	and	CCONJ
ejpam-1809	201	9	ranks	rank	NOUN
ejpam-1809	201	10	of	of	ADP
ejpam-1809	201	11	semigroups	semigroup	NOUN
ejpam-1809	201	12	may	may	AUX
ejpam-1809	201	13	be	be	AUX
ejpam-1809	201	14	expanded	expand	VERB
ejpam-1809	201	15	to	to	ADP
ejpam-1809	201	16	different	different	ADJ
ejpam-1809	201	17	classes	class	NOUN
ejpam-1809	201	18	of	of	ADP
ejpam-1809	201	19	semigroups	semigroup	NOUN
ejpam-1809	201	20	as	as	ADP
ejpam-1809	201	21	future	future	ADJ
ejpam-1809	201	22	work	work	NOUN
ejpam-1809	201	23	.	.	PUNCT
ejpam-1809	202	1	references	reference	NOUN
ejpam-1809	202	2	[	[	X
ejpam-1809	202	3	1	1	NUM
ejpam-1809	202	4	]	]	PUNCT
ejpam-1809	202	5	h.	h.	PROPN
ejpam-1809	202	6	ayık	ayık	PROPN
ejpam-1809	202	7	.	.	PUNCT
ejpam-1809	203	1	presentations	presentation	NOUN
ejpam-1809	203	2	and	and	CCONJ
ejpam-1809	203	3	efficiency	efficiency	NOUN
ejpam-1809	203	4	of	of	ADP
ejpam-1809	203	5	semigroups	semigroup	NOUN
ejpam-1809	203	6	.	.	PUNCT
ejpam-1809	204	1	phd	phd	NOUN
ejpam-1809	204	2	thesis	thesis	NOUN
ejpam-1809	204	3	,	,	PUNCT
ejpam-1809	204	4	1998	1998	NUM
ejpam-1809	204	5	.	.	PUNCT
ejpam-1809	205	1	[	[	X
ejpam-1809	205	2	2	2	X
ejpam-1809	205	3	]	]	PUNCT
ejpam-1809	205	4	h.	h.	PROPN
ejpam-1809	205	5	ayık	ayık	PROPN
ejpam-1809	205	6	.	.	PUNCT
ejpam-1809	206	1	on	on	ADP
ejpam-1809	206	2	finiteness	finiteness	ADJ
ejpam-1809	206	3	conditions	condition	NOUN
ejpam-1809	206	4	for	for	ADP
ejpam-1809	206	5	rees	ree	NOUN
ejpam-1809	206	6	matrix	matrix	NOUN
ejpam-1809	206	7	semigroups	semigroup	NOUN
ejpam-1809	206	8	.	.	PUNCT
ejpam-1809	207	1	czechoslovak	czechoslovak	ADJ
ejpam-1809	207	2	mathematical	mathematical	PROPN
ejpam-1809	207	3	journal	journal	NOUN
ejpam-1809	207	4	,	,	PUNCT
ejpam-1809	207	5	55	55	NUM
ejpam-1809	207	6	,	,	PUNCT
ejpam-1809	207	7	2005	2005	NUM
ejpam-1809	207	8	.	.	PUNCT
ejpam-1809	208	1	[	[	X
ejpam-1809	208	2	3	3	X
ejpam-1809	208	3	]	]	X
ejpam-1809	208	4	h.	h.	PROPN
ejpam-1809	208	5	ayık	ayık	PROPN
ejpam-1809	208	6	,	,	PUNCT
ejpam-1809	208	7	m.	m.	NOUN
ejpam-1809	208	8	minisker	minisker	NOUN
ejpam-1809	208	9	,	,	PUNCT
ejpam-1809	208	10	and	and	CCONJ
ejpam-1809	208	11	b.	b.	PROPN
ejpam-1809	208	12	vatansever	vatansever	PROPN
ejpam-1809	208	13	.	.	PUNCT
ejpam-1809	209	1	minimal	minimal	ADJ
ejpam-1809	209	2	presentations	presentation	NOUN
ejpam-1809	209	3	and	and	CCONJ
ejpam-1809	209	4	embedding	embed	VERB
ejpam-1809	209	5	into	into	ADP
ejpam-1809	209	6	inefficient	inefficient	ADJ
ejpam-1809	209	7	semigroups	semigroup	NOUN
ejpam-1809	209	8	.	.	PUNCT
ejpam-1809	210	1	algebra	algebra	NOUN
ejpam-1809	210	2	colloquium	colloquium	NOUN
ejpam-1809	210	3	,	,	PUNCT
ejpam-1809	210	4	12:59–65	12:59–65	PROPN
ejpam-1809	210	5	,	,	PUNCT
ejpam-1809	210	6	2005	2005	NUM
ejpam-1809	210	7	.	.	PUNCT
ejpam-1809	211	1	[	[	X
ejpam-1809	211	2	4	4	X
ejpam-1809	211	3	]	]	X
ejpam-1809	211	4	e.	e.	PROPN
ejpam-1809	211	5	giraldes	giraldes	PROPN
ejpam-1809	211	6	and	and	CCONJ
ejpam-1809	211	7	j.m	j.m	PROPN
ejpam-1809	211	8	.	.	PROPN
ejpam-1809	211	9	howie	howie	PROPN
ejpam-1809	211	10	.	.	PUNCT
ejpam-1809	212	1	semigroups	semigroup	NOUN
ejpam-1809	212	2	of	of	ADP
ejpam-1809	212	3	high	high	ADJ
ejpam-1809	212	4	rank	rank	NOUN
ejpam-1809	212	5	.	.	PUNCT
ejpam-1809	213	1	proceedings	proceeding	NOUN
ejpam-1809	213	2	of	of	ADP
ejpam-1809	213	3	the	the	DET
ejpam-1809	213	4	edinburgh	edinburgh	PROPN
ejpam-1809	213	5	mathematical	mathematical	PROPN
ejpam-1809	213	6	society	society	NOUN
ejpam-1809	213	7	,	,	PUNCT
ejpam-1809	213	8	28:13–34	28:13–34	NUM
ejpam-1809	213	9	,	,	PUNCT
ejpam-1809	213	10	1985	1985	NUM
ejpam-1809	213	11	.	.	PUNCT
ejpam-1809	214	1	[	[	X
ejpam-1809	214	2	5	5	NUM
ejpam-1809	214	3	]	]	X
ejpam-1809	214	4	j.m	j.m	PROPN
ejpam-1809	214	5	.	.	PROPN
ejpam-1809	214	6	howie	howie	NOUN
ejpam-1809	214	7	and	and	CCONJ
ejpam-1809	214	8	m.i.m	m.i.m	NOUN
ejpam-1809	214	9	.	.	PUNCT
ejpam-1809	215	1	ribeiro	ribeiro	PROPN
ejpam-1809	215	2	.	.	PROPN
ejpam-1809	215	3	rank	rank	PROPN
ejpam-1809	215	4	properties	property	NOUN
ejpam-1809	215	5	of	of	ADP
ejpam-1809	215	6	semigroups	semigroups	PROPN
ejpam-1809	215	7	ii	ii	PROPN
ejpam-1809	215	8	:	:	PUNCT
ejpam-1809	215	9	the	the	DET
ejpam-1809	215	10	small	small	ADJ
ejpam-1809	215	11	rank	rank	NOUN
ejpam-1809	215	12	and	and	CCONJ
ejpam-1809	215	13	the	the	DET
ejpam-1809	215	14	large	large	ADJ
ejpam-1809	215	15	rank	rank	NOUN
ejpam-1809	215	16	.	.	PUNCT
ejpam-1809	216	1	southeast	southeast	ADJ
ejpam-1809	216	2	asian	asian	ADJ
ejpam-1809	216	3	bulletin	bulletin	NOUN
ejpam-1809	216	4	of	of	ADP
ejpam-1809	216	5	mathematics	mathematic	NOUN
ejpam-1809	216	6	,	,	PUNCT
ejpam-1809	216	7	24:231–237	24:231–237	NUM
ejpam-1809	216	8	,	,	PUNCT
ejpam-1809	216	9	2000	2000	NUM
ejpam-1809	216	10	.	.	PUNCT