id	sid	tid	token	lemma	pos
ap-920	1	1	ap07_2-3.vp	ap07_2-3.vp	SYM
ap-920	1	2	1	1	NUM
ap-920	1	3	introduction	introduction	NOUN
ap-920	1	4	the	the	DET
ap-920	1	5	study	study	NOUN
ap-920	1	6	of	of	ADP
ap-920	1	7	factor	factor	NOUN
ap-920	1	8	complexity	complexity	NOUN
ap-920	1	9	,	,	PUNCT
ap-920	1	10	palindromic	palindromic	ADJ
ap-920	1	11	complexity	complexity	NOUN
ap-920	1	12	,	,	PUNCT
ap-920	1	13	balance	balance	NOUN
ap-920	1	14	property	property	NOUN
ap-920	1	15	,	,	PUNCT
ap-920	1	16	return	return	VERB
ap-920	1	17	words	word	NOUN
ap-920	1	18	,	,	PUNCT
ap-920	1	19	and	and	CCONJ
ap-920	1	20	the	the	DET
ap-920	1	21	recurrence	recurrence	NOUN
ap-920	1	22	function	function	NOUN
ap-920	1	23	of	of	ADP
ap-920	1	24	infinite	infinite	ADJ
ap-920	1	25	aperiodic	aperiodic	ADJ
ap-920	1	26	words	word	NOUN
ap-920	1	27	is	be	AUX
ap-920	1	28	an	an	DET
ap-920	1	29	interesting	interesting	ADJ
ap-920	1	30	combinatorial	combinatorial	ADJ
ap-920	1	31	problem	problem	NOUN
ap-920	1	32	.	.	PUNCT
ap-920	2	1	moreover	moreover	ADV
ap-920	2	2	,	,	PUNCT
ap-920	2	3	the	the	DET
ap-920	2	4	investigation	investigation	NOUN
ap-920	2	5	of	of	ADP
ap-920	2	6	infinite	infinite	ADJ
ap-920	2	7	words	word	NOUN
ap-920	2	8	coding	code	VERB
ap-920	2	9	�	�	PROPN
ap-920	2	10	-integers	-integer	NOUN
ap-920	2	11	�	�	PROPN
ap-920	2	12	�	�	PROPN
ap-920	2	13	,	,	PUNCT
ap-920	2	14	for	for	ADP
ap-920	2	15	�	�	PROPN
ap-920	2	16	being	be	AUX
ap-920	2	17	a	a	DET
ap-920	2	18	pisot	pisot	ADJ
ap-920	2	19	number	number	NOUN
ap-920	2	20	,	,	PUNCT
ap-920	2	21	can	can	AUX
ap-920	2	22	be	be	AUX
ap-920	2	23	interpreted	interpret	VERB
ap-920	2	24	as	as	ADP
ap-920	2	25	an	an	DET
ap-920	2	26	investigation	investigation	NOUN
ap-920	2	27	of	of	ADP
ap-920	2	28	one	one	NUM
ap-920	2	29	-	-	PUNCT
ap-920	2	30	dimensional	dimensional	ADJ
ap-920	2	31	quasicrystals	quasicrystal	NOUN
ap-920	2	32	.	.	PUNCT
ap-920	3	1	in	in	ADP
ap-920	3	2	this	this	DET
ap-920	3	3	paper	paper	NOUN
ap-920	3	4	,	,	PUNCT
ap-920	3	5	new	new	ADJ
ap-920	3	6	results	result	NOUN
ap-920	3	7	concerning	concern	VERB
ap-920	3	8	return	return	NOUN
ap-920	3	9	words	word	NOUN
ap-920	3	10	and	and	CCONJ
ap-920	3	11	recurrence	recurrence	NOUN
ap-920	3	12	function	function	NOUN
ap-920	3	13	will	will	AUX
ap-920	3	14	be	be	AUX
ap-920	3	15	presented	present	VERB
ap-920	3	16	.	.	PUNCT
ap-920	4	1	in	in	ADP
ap-920	4	2	general	general	ADJ
ap-920	4	3	,	,	PUNCT
ap-920	4	4	little	little	ADJ
ap-920	4	5	is	be	AUX
ap-920	4	6	known	know	VERB
ap-920	4	7	about	about	ADP
ap-920	4	8	return	return	NOUN
ap-920	4	9	words	word	NOUN
ap-920	4	10	.	.	PUNCT
ap-920	5	1	a	a	DET
ap-920	5	2	return	return	NOUN
ap-920	5	3	word	word	NOUN
ap-920	5	4	of	of	ADP
ap-920	5	5	factor	factor	NOUN
ap-920	5	6	w	w	PROPN
ap-920	5	7	of	of	ADP
ap-920	5	8	an	an	DET
ap-920	5	9	infinite	infinite	ADJ
ap-920	5	10	word	word	NOUN
ap-920	5	11	u	u	NOUN
ap-920	5	12	is	be	AUX
ap-920	5	13	any	any	DET
ap-920	5	14	word	word	NOUN
ap-920	5	15	which	which	PRON
ap-920	5	16	starts	start	VERB
ap-920	5	17	at	at	ADP
ap-920	5	18	some	some	DET
ap-920	5	19	occurrence	occurrence	NOUN
ap-920	5	20	of	of	ADP
ap-920	5	21	w	w	NOUN
ap-920	5	22	in	in	ADP
ap-920	5	23	u	u	NOUN
ap-920	5	24	and	and	CCONJ
ap-920	5	25	ends	end	VERB
ap-920	5	26	just	just	ADV
ap-920	5	27	before	before	ADP
ap-920	5	28	the	the	DET
ap-920	5	29	next	next	ADJ
ap-920	5	30	occurrence	occurrence	NOUN
ap-920	5	31	of	of	ADP
ap-920	5	32	w.	w.	PROPN
ap-920	5	33	vuillon	vuillon	PROPN
ap-920	6	1	[	[	X
ap-920	6	2	1	1	X
ap-920	6	3	]	]	PUNCT
ap-920	6	4	has	have	AUX
ap-920	6	5	shown	show	VERB
ap-920	6	6	that	that	SCONJ
ap-920	6	7	an	an	DET
ap-920	6	8	infinite	infinite	ADJ
ap-920	6	9	word	word	NOUN
ap-920	6	10	over	over	ADP
ap-920	6	11	a	a	DET
ap-920	6	12	bilateral	bilateral	ADJ
ap-920	6	13	alphabet	alphabet	NOUN
ap-920	6	14	is	be	AUX
ap-920	6	15	sturmian	sturmian	NOUN
ap-920	6	16	if	if	SCONJ
ap-920	6	17	and	and	CCONJ
ap-920	6	18	only	only	ADV
ap-920	6	19	if	if	SCONJ
ap-920	6	20	each	each	PRON
ap-920	6	21	of	of	ADP
ap-920	6	22	its	its	PRON
ap-920	6	23	factors	factor	NOUN
ap-920	6	24	has	have	VERB
ap-920	6	25	exactly	exactly	ADV
ap-920	6	26	two	two	NUM
ap-920	6	27	return	return	NOUN
ap-920	6	28	words	word	NOUN
ap-920	6	29	.	.	PUNCT
ap-920	7	1	justin	justin	NOUN
ap-920	7	2	and	and	CCONJ
ap-920	7	3	vuillon	vuillon	NOUN
ap-920	8	1	[	[	X
ap-920	8	2	2	2	NUM
ap-920	8	3	]	]	PUNCT
ap-920	8	4	proved	prove	VERB
ap-920	8	5	that	that	SCONJ
ap-920	8	6	each	each	DET
ap-920	8	7	factor	factor	NOUN
ap-920	8	8	of	of	ADP
ap-920	8	9	an	an	DET
ap-920	8	10	arnoux	arnoux	NOUN
ap-920	8	11	-	-	PUNCT
ap-920	8	12	rauzy	rauzy	NOUN
ap-920	8	13	word	word	NOUN
ap-920	8	14	of	of	ADP
ap-920	8	15	order	order	NOUN
ap-920	8	16	m	m	VERB
ap-920	8	17	has	have	VERB
ap-920	8	18	m	m	PROPN
ap-920	8	19	return	return	NOUN
ap-920	8	20	words	word	NOUN
ap-920	8	21	.	.	PUNCT
ap-920	9	1	moreover	moreover	ADV
ap-920	9	2	,	,	PUNCT
ap-920	9	3	vuillon	vuillon	PROPN
ap-920	9	4	proved	prove	VERB
ap-920	9	5	that	that	SCONJ
ap-920	9	6	each	each	DET
ap-920	9	7	factor	factor	NOUN
ap-920	9	8	of	of	ADP
ap-920	9	9	an	an	DET
ap-920	9	10	-interval	-interval	PROPN
ap-920	9	11	exchange	exchange	NOUN
ap-920	9	12	coding	code	VERB
ap-920	9	13	word	word	NOUN
ap-920	9	14	also	also	ADV
ap-920	9	15	has	have	AUX
ap-920	9	16	return	return	VERB
ap-920	9	17	words	word	NOUN
ap-920	9	18	.	.	PUNCT
ap-920	10	1	return	return	VERB
ap-920	10	2	words	word	NOUN
ap-920	10	3	in	in	ADP
ap-920	10	4	the	the	DET
ap-920	10	5	thue	thue	NOUN
ap-920	10	6	-	-	PUNCT
ap-920	10	7	morse	morse	NOUN
ap-920	10	8	sequence	sequence	NOUN
ap-920	10	9	and	and	CCONJ
ap-920	10	10	return	return	VERB
ap-920	10	11	words	word	NOUN
ap-920	10	12	in	in	ADP
ap-920	10	13	the	the	DET
ap-920	10	14	infinite	infinite	ADJ
ap-920	10	15	words	word	NOUN
ap-920	10	16	associated	associate	VERB
ap-920	10	17	with	with	ADP
ap-920	10	18	simple	simple	ADJ
ap-920	10	19	parry	parry	NOUN
ap-920	10	20	numbers	number	NOUN
ap-920	10	21	have	have	AUX
ap-920	10	22	been	be	AUX
ap-920	10	23	studied	study	VERB
ap-920	10	24	in	in	ADP
ap-920	10	25	[	[	X
ap-920	10	26	4	4	NUM
ap-920	10	27	]	]	PUNCT
ap-920	10	28	.	.	PUNCT
ap-920	11	1	even	even	ADV
ap-920	11	2	less	less	ADV
ap-920	11	3	is	be	AUX
ap-920	11	4	known	know	VERB
ap-920	11	5	about	about	ADP
ap-920	11	6	the	the	DET
ap-920	11	7	recurrence	recurrence	NOUN
ap-920	11	8	function	function	NOUN
ap-920	11	9	which	which	PRON
ap-920	11	10	,	,	PUNCT
ap-920	11	11	for	for	ADP
ap-920	11	12	an	an	DET
ap-920	11	13	infinite	infinite	ADJ
ap-920	11	14	uniformly	uniformly	ADV
ap-920	11	15	recurrent	recurrent	ADJ
ap-920	11	16	word	word	NOUN
ap-920	11	17	u	u	NOUN
ap-920	11	18	,	,	PUNCT
ap-920	11	19	determines	determine	VERB
ap-920	11	20	the	the	DET
ap-920	11	21	minimal	minimal	ADJ
ap-920	11	22	length	length	NOUN
ap-920	11	23	ru(n	ru(n	NOUN
ap-920	11	24	)	)	PUNCT
ap-920	11	25	such	such	ADJ
ap-920	11	26	that	that	SCONJ
ap-920	11	27	if	if	SCONJ
ap-920	11	28	we	we	PRON
ap-920	11	29	take	take	VERB
ap-920	11	30	any	any	DET
ap-920	11	31	subword	subword	NOUN
ap-920	11	32	of	of	ADP
ap-920	11	33	length	length	NOUN
ap-920	11	34	ru(n	ru(n	PROPN
ap-920	11	35	)	)	PUNCT
ap-920	11	36	of	of	ADP
ap-920	11	37	u	u	PROPN
ap-920	11	38	,	,	PUNCT
ap-920	11	39	we	we	PRON
ap-920	11	40	will	will	AUX
ap-920	11	41	find	find	VERB
ap-920	11	42	there	there	ADV
ap-920	11	43	all	all	DET
ap-920	11	44	the	the	DET
ap-920	11	45	factors	factor	NOUN
ap-920	11	46	of	of	ADP
ap-920	11	47	length	length	NOUN
ap-920	12	1	n.	n.	PROPN
ap-920	12	2	cassaigne	cassaigne	PROPN
ap-920	13	1	[	[	X
ap-920	13	2	5	5	NUM
ap-920	13	3	]	]	PUNCT
ap-920	13	4	determined	determine	VERB
ap-920	13	5	this	this	DET
ap-920	13	6	function	function	NOUN
ap-920	13	7	for	for	ADP
ap-920	13	8	sturmian	sturmian	ADJ
ap-920	13	9	words	word	NOUN
ap-920	13	10	taking	take	VERB
ap-920	13	11	into	into	ADP
ap-920	13	12	account	account	NOUN
ap-920	13	13	the	the	DET
ap-920	13	14	continued	continue	VERB
ap-920	13	15	fractions	fraction	NOUN
ap-920	13	16	of	of	ADP
ap-920	13	17	their	their	PRON
ap-920	13	18	slope	slope	NOUN
ap-920	13	19	and	and	CCONJ
ap-920	13	20	,	,	PUNCT
ap-920	13	21	in	in	ADP
ap-920	13	22	[	[	PUNCT
ap-920	13	23	6	6	NUM
ap-920	13	24	]	]	PUNCT
ap-920	13	25	,	,	PUNCT
ap-920	13	26	he	he	PRON
ap-920	13	27	given	give	VERB
ap-920	13	28	a	a	DET
ap-920	13	29	general	general	ADJ
ap-920	13	30	algorithm	algorithm	NOUN
ap-920	13	31	describing	describe	VERB
ap-920	13	32	how	how	SCONJ
ap-920	13	33	to	to	PART
ap-920	13	34	determine	determine	VERB
ap-920	13	35	the	the	DET
ap-920	13	36	recurrence	recurrence	NOUN
ap-920	13	37	function	function	NOUN
ap-920	13	38	if	if	SCONJ
ap-920	13	39	we	we	PRON
ap-920	13	40	know	know	VERB
ap-920	13	41	the	the	DET
ap-920	13	42	return	return	NOUN
ap-920	13	43	words	word	NOUN
ap-920	13	44	.	.	PUNCT
ap-920	14	1	this	this	DET
ap-920	14	2	algorithm	algorithm	NOUN
ap-920	14	3	will	will	AUX
ap-920	14	4	constitute	constitute	VERB
ap-920	14	5	the	the	DET
ap-920	14	6	headstone	headstone	NOUN
ap-920	14	7	of	of	ADP
ap-920	14	8	our	our	PRON
ap-920	14	9	further	further	ADJ
ap-920	14	10	results	result	NOUN
ap-920	14	11	.	.	PUNCT
ap-920	15	1	we	we	PRON
ap-920	15	2	will	will	AUX
ap-920	15	3	describe	describe	VERB
ap-920	15	4	the	the	DET
ap-920	15	5	cardinality	cardinality	NOUN
ap-920	15	6	of	of	ADP
ap-920	15	7	the	the	DET
ap-920	15	8	set	set	NOUN
ap-920	15	9	of	of	ADP
ap-920	15	10	return	return	NOUN
ap-920	15	11	words	word	NOUN
ap-920	15	12	for	for	ADP
ap-920	15	13	any	any	DET
ap-920	15	14	factor	factor	NOUN
ap-920	15	15	w	w	PROPN
ap-920	15	16	of	of	ADP
ap-920	15	17	the	the	DET
ap-920	15	18	infinite	infinite	ADJ
ap-920	15	19	word	word	NOUN
ap-920	15	20	u	u	NOUN
ap-920	15	21	�	�	PROPN
ap-920	15	22	associated	associate	VERB
ap-920	15	23	with	with	ADP
ap-920	15	24	quadratic	quadratic	ADJ
ap-920	15	25	non	non	ADJ
ap-920	15	26	-	-	ADJ
ap-920	15	27	simple	simple	ADJ
ap-920	15	28	parry	parry	NOUN
ap-920	15	29	(	(	PUNCT
ap-920	15	30	and	and	CCONJ
ap-920	15	31	,	,	PUNCT
ap-920	15	32	thus	thus	ADV
ap-920	15	33	pisot	pisot	ADJ
ap-920	15	34	)	)	PUNCT
ap-920	15	35	number	number	NOUN
ap-920	15	36	�	�	PROPN
ap-920	15	37	and	and	CCONJ
ap-920	15	38	,	,	PUNCT
ap-920	15	39	as	as	ADP
ap-920	15	40	a	a	DET
ap-920	15	41	consequence	consequence	NOUN
ap-920	15	42	,	,	PUNCT
ap-920	15	43	we	we	PRON
ap-920	15	44	will	will	AUX
ap-920	15	45	be	be	AUX
ap-920	15	46	able	able	ADJ
ap-920	15	47	to	to	PART
ap-920	15	48	deduce	deduce	VERB
ap-920	15	49	the	the	DET
ap-920	15	50	exact	exact	ADJ
ap-920	15	51	formula	formula	NOUN
ap-920	15	52	for	for	ADP
ap-920	15	53	the	the	DET
ap-920	15	54	recurrence	recurrence	NOUN
ap-920	15	55	function	function	NOUN
ap-920	15	56	.	.	PUNCT
ap-920	16	1	these	these	DET
ap-920	16	2	results	result	NOUN
ap-920	16	3	will	will	AUX
ap-920	16	4	complete	complete	VERB
ap-920	16	5	the	the	DET
ap-920	16	6	list	list	NOUN
ap-920	16	7	of	of	ADP
ap-920	16	8	properties	property	NOUN
ap-920	16	9	already	already	ADV
ap-920	16	10	studied	study	VERB
ap-920	16	11	:	:	PUNCT
ap-920	16	12	factor	factor	NOUN
ap-920	16	13	complexity	complexity	NOUN
ap-920	16	14	has	have	AUX
ap-920	16	15	been	be	AUX
ap-920	16	16	studied	study	VERB
ap-920	16	17	in	in	ADP
ap-920	16	18	[	[	PUNCT
ap-920	16	19	7	7	NUM
ap-920	16	20	]	]	PUNCT
ap-920	16	21	,	,	PUNCT
ap-920	16	22	palindromic	palindromic	ADJ
ap-920	16	23	complexity	complexity	NOUN
ap-920	16	24	is	be	AUX
ap-920	16	25	described	describe	VERB
ap-920	16	26	in	in	ADP
ap-920	16	27	[	[	X
ap-920	16	28	8	8	NUM
ap-920	16	29	]	]	PUNCT
ap-920	16	30	,	,	PUNCT
ap-920	16	31	and	and	CCONJ
ap-920	16	32	results	result	NOUN
ap-920	16	33	on	on	ADP
ap-920	16	34	balances	balance	NOUN
ap-920	16	35	can	can	AUX
ap-920	16	36	be	be	AUX
ap-920	16	37	found	find	VERB
ap-920	16	38	in	in	ADP
ap-920	16	39	[	[	X
ap-920	16	40	9	9	NUM
ap-920	16	41	]	]	SYM
ap-920	16	42	.	.	PUNCT
ap-920	17	1	2	2	NUM
ap-920	17	2	preliminaries	preliminary	NOUN
ap-920	17	3	first	first	ADV
ap-920	17	4	,	,	PUNCT
ap-920	17	5	let	let	VERB
ap-920	17	6	us	we	PRON
ap-920	17	7	introduce	introduce	VERB
ap-920	17	8	our	our	PRON
ap-920	17	9	“	"	PUNCT
ap-920	17	10	language	language	NOUN
ap-920	17	11	”	"	PUNCT
ap-920	17	12	,	,	PUNCT
ap-920	17	13	which	which	PRON
ap-920	17	14	will	will	AUX
ap-920	17	15	be	be	AUX
ap-920	17	16	used	use	VERB
ap-920	17	17	throughout	throughout	ADP
ap-920	17	18	this	this	DET
ap-920	17	19	paper	paper	NOUN
ap-920	17	20	.	.	PUNCT
ap-920	18	1	an	an	DET
ap-920	18	2	alphabet	alphabet	PROPN
ap-920	18	3	�	�	PROPN
ap-920	18	4	is	be	AUX
ap-920	18	5	a	a	DET
ap-920	18	6	finite	finite	ADJ
ap-920	18	7	set	set	NOUN
ap-920	18	8	of	of	ADP
ap-920	18	9	symbols	symbol	NOUN
ap-920	18	10	called	call	VERB
ap-920	18	11	letters	letter	NOUN
ap-920	18	12	.	.	PUNCT
ap-920	19	1	a	a	DET
ap-920	19	2	concatenation	concatenation	NOUN
ap-920	19	3	of	of	ADP
ap-920	19	4	letters	letter	NOUN
ap-920	19	5	is	be	AUX
ap-920	19	6	a	a	DET
ap-920	19	7	word	word	NOUN
ap-920	19	8	.	.	PUNCT
ap-920	20	1	the	the	DET
ap-920	20	2	length	length	NOUN
ap-920	20	3	of	of	ADP
ap-920	20	4	word	word	NOUN
ap-920	20	5	w	w	NOUN
ap-920	20	6	is	be	AUX
ap-920	20	7	denoted	denote	VERB
ap-920	20	8	by	by	ADP
ap-920	20	9	w	w	PROPN
ap-920	20	10	.	.	PUNCT
ap-920	21	1	the	the	DET
ap-920	21	2	set	set	PROPN
ap-920	21	3	�	�	PROPN
ap-920	21	4	*	*	PROPN
ap-920	21	5	of	of	ADP
ap-920	21	6	all	all	DET
ap-920	21	7	finite	finite	ADJ
ap-920	21	8	words	word	NOUN
ap-920	21	9	(	(	PUNCT
ap-920	21	10	including	include	VERB
ap-920	21	11	the	the	DET
ap-920	21	12	empty	empty	ADJ
ap-920	21	13	word	word	NOUN
ap-920	21	14	�	�	NOUN
ap-920	21	15	)	)	PUNCT
ap-920	21	16	provided	provide	VERB
ap-920	21	17	with	with	ADP
ap-920	21	18	the	the	DET
ap-920	21	19	operation	operation	NOUN
ap-920	21	20	of	of	ADP
ap-920	21	21	concatenation	concatenation	NOUN
ap-920	21	22	is	be	AUX
ap-920	21	23	a	a	DET
ap-920	21	24	free	free	ADJ
ap-920	21	25	monoid	monoid	NOUN
ap-920	21	26	.	.	PUNCT
ap-920	22	1	we	we	PRON
ap-920	22	2	will	will	AUX
ap-920	22	3	also	also	ADV
ap-920	22	4	deal	deal	VERB
ap-920	22	5	with	with	ADP
ap-920	22	6	right	right	ADV
ap-920	22	7	-	-	PUNCT
ap-920	22	8	sided	sided	ADJ
ap-920	22	9	infinite	infinite	ADJ
ap-920	22	10	words	word	NOUN
ap-920	22	11	u	u	X
ap-920	22	12	u	u	PROPN
ap-920	22	13	u	u	VERB
ap-920	22	14	u	u	NOUN
ap-920	22	15	�	�	PROPN
ap-920	22	16	0	0	NUM
ap-920	22	17	1	1	NUM
ap-920	22	18	2	2	NUM
ap-920	22	19	�	�	PROPN
ap-920	22	20	.	.	PUNCT
ap-920	23	1	a	a	DET
ap-920	23	2	finite	finite	ADJ
ap-920	23	3	word	word	NOUN
ap-920	23	4	w	w	NOUN
ap-920	23	5	is	be	AUX
ap-920	23	6	called	call	VERB
ap-920	23	7	a	a	DET
ap-920	23	8	factor	factor	NOUN
ap-920	23	9	of	of	ADP
ap-920	23	10	the	the	DET
ap-920	23	11	word	word	NOUN
ap-920	23	12	u	u	NOUN
ap-920	23	13	(	(	PUNCT
ap-920	23	14	finite	finite	NOUN
ap-920	23	15	or	or	CCONJ
ap-920	23	16	infinite	infinite	VERB
ap-920	23	17	)	)	PUNCT
ap-920	23	18	if	if	SCONJ
ap-920	23	19	there	there	PRON
ap-920	23	20	exist	exist	VERB
ap-920	23	21	a	a	DET
ap-920	23	22	finite	finite	ADJ
ap-920	23	23	word	word	NOUN
ap-920	23	24	w(1	w(1	PROPN
ap-920	23	25	)	)	PUNCT
ap-920	23	26	and	and	CCONJ
ap-920	23	27	a	a	DET
ap-920	23	28	word	word	NOUN
ap-920	23	29	w(2	w(2	NOUN
ap-920	23	30	)	)	PUNCT
ap-920	23	31	(	(	PUNCT
ap-920	23	32	finite	finite	NOUN
ap-920	23	33	or	or	CCONJ
ap-920	23	34	infinite	infinite	VERB
ap-920	23	35	)	)	PUNCT
ap-920	23	36	such	such	ADJ
ap-920	23	37	that	that	SCONJ
ap-920	23	38	u	u	PROPN
ap-920	23	39	w	w	PROPN
ap-920	23	40	ww	ww	PROPN
ap-920	23	41	�	�	PROPN
ap-920	23	42	(	(	PUNCT
ap-920	23	43	)	)	PUNCT
ap-920	23	44	(	(	PUNCT
ap-920	23	45	)	)	PUNCT
ap-920	23	46	1	1	NUM
ap-920	23	47	2	2	NUM
ap-920	23	48	.	.	PUNCT
ap-920	24	1	the	the	DET
ap-920	24	2	word	word	NOUN
ap-920	24	3	w	w	NOUN
ap-920	24	4	is	be	AUX
ap-920	24	5	a	a	DET
ap-920	24	6	prefix	prefix	NOUN
ap-920	24	7	of	of	ADP
ap-920	24	8	u	u	PRON
ap-920	24	9	if	if	SCONJ
ap-920	24	10	w	w	PROPN
ap-920	24	11	(	(	PUNCT
ap-920	24	12	)	)	SYM
ap-920	24	13	1	1	NUM
ap-920	24	14	�	�	PROPN
ap-920	24	15	�	�	PROPN
ap-920	24	16	and	and	CCONJ
ap-920	24	17	it	it	PRON
ap-920	24	18	is	be	AUX
ap-920	24	19	a	a	DET
ap-920	24	20	suffix	suffix	NOUN
ap-920	24	21	of	of	ADP
ap-920	24	22	u	u	PRON
ap-920	24	23	if	if	SCONJ
ap-920	24	24	w	w	PROPN
ap-920	24	25	(	(	PUNCT
ap-920	24	26	)	)	SYM
ap-920	24	27	2	2	NUM
ap-920	24	28	�	�	PROPN
ap-920	24	29	�	�	PROPN
ap-920	24	30	.	.	PUNCT
ap-920	25	1	a	a	DET
ap-920	25	2	concatenation	concatenation	NOUN
ap-920	25	3	of	of	ADP
ap-920	25	4	k	k	PROPN
ap-920	25	5	letters	letters	PROPN
ap-920	25	6	a	a	PRON
ap-920	25	7	(	(	PUNCT
ap-920	25	8	or	or	CCONJ
ap-920	25	9	words	word	NOUN
ap-920	25	10	a	a	PRON
ap-920	25	11	)	)	PUNCT
ap-920	25	12	will	will	AUX
ap-920	25	13	be	be	AUX
ap-920	25	14	denoted	denote	VERB
ap-920	25	15	by	by	ADP
ap-920	25	16	ak	ak	PROPN
ap-920	25	17	.	.	PUNCT
ap-920	25	18	the	the	DET
ap-920	25	19	language	language	NOUN
ap-920	25	20	of	of	ADP
ap-920	25	21	u	u	PROPN
ap-920	25	22	,	,	PUNCT
ap-920	25	23	�	�	PROPN
ap-920	25	24	(	(	PUNCT
ap-920	25	25	u	u	NOUN
ap-920	25	26	)	)	PUNCT
ap-920	25	27	,	,	PUNCT
ap-920	25	28	is	be	AUX
ap-920	25	29	the	the	DET
ap-920	25	30	set	set	NOUN
ap-920	25	31	of	of	ADP
ap-920	25	32	all	all	DET
ap-920	25	33	factors	factor	NOUN
ap-920	25	34	of	of	ADP
ap-920	25	35	a	a	DET
ap-920	25	36	word	word	NOUN
ap-920	25	37	u	u	NOUN
ap-920	25	38	,	,	PUNCT
ap-920	25	39	and	and	CCONJ
ap-920	25	40	�	�	PROPN
ap-920	25	41	n(u	n(u	PROPN
ap-920	25	42	)	)	PUNCT
ap-920	25	43	is	be	AUX
ap-920	25	44	the	the	DET
ap-920	25	45	set	set	NOUN
ap-920	25	46	of	of	ADP
ap-920	25	47	all	all	DET
ap-920	25	48	factors	factor	NOUN
ap-920	25	49	of	of	ADP
ap-920	25	50	u	u	NOUN
ap-920	25	51	of	of	ADP
ap-920	25	52	length	length	NOUN
ap-920	25	53	n.	n.	NOUN
ap-920	26	1	we	we	PRON
ap-920	26	2	say	say	VERB
ap-920	26	3	that	that	SCONJ
ap-920	26	4	a	a	DET
ap-920	26	5	letter	letter	NOUN
ap-920	26	6	a	a	DET
ap-920	26	7	�	�	PROPN
ap-920	26	8	�	�	PROPN
ap-920	26	9	is	be	AUX
ap-920	26	10	a	a	DET
ap-920	26	11	left	left	ADJ
ap-920	26	12	extension	extension	NOUN
ap-920	26	13	of	of	ADP
ap-920	26	14	a	a	DET
ap-920	26	15	factor	factor	NOUN
ap-920	26	16	w	w	PROPN
ap-920	26	17	u	u	PROPN
ap-920	26	18	�	�	PROPN
ap-920	26	19	�	�	PROPN
ap-920	26	20	(	(	PUNCT
ap-920	26	21	)	)	PUNCT
ap-920	26	22	if	if	SCONJ
ap-920	26	23	the	the	DET
ap-920	26	24	factor	factor	NOUN
ap-920	26	25	aw	aw	INTJ
ap-920	26	26	belongs	belong	VERB
ap-920	26	27	to	to	ADP
ap-920	26	28	the	the	DET
ap-920	26	29	language	language	NOUN
ap-920	26	30	�	�	PROPN
ap-920	26	31	(	(	PUNCT
ap-920	26	32	u	u	NOUN
ap-920	26	33	)	)	PUNCT
ap-920	26	34	and	and	CCONJ
ap-920	26	35	w	w	PROPN
ap-920	26	36	is	be	AUX
ap-920	26	37	left	leave	VERB
ap-920	26	38	special	special	ADJ
ap-920	26	39	if	if	SCONJ
ap-920	26	40	w	w	NOUN
ap-920	26	41	has	have	VERB
ap-920	26	42	at	at	ADV
ap-920	26	43	least	least	ADJ
ap-920	26	44	two	two	NUM
ap-920	26	45	left	left	ADJ
ap-920	26	46	extensions	extension	NOUN
ap-920	26	47	.	.	PUNCT
ap-920	27	1	right	right	ADJ
ap-920	27	2	extensions	extension	NOUN
ap-920	27	3	and	and	CCONJ
ap-920	27	4	right	right	ADJ
ap-920	27	5	special	special	ADJ
ap-920	27	6	factors	factor	NOUN
ap-920	27	7	are	be	AUX
ap-920	27	8	defined	define	VERB
ap-920	27	9	by	by	ADP
ap-920	27	10	analogy	analogy	NOUN
ap-920	27	11	.	.	PUNCT
ap-920	28	1	we	we	PRON
ap-920	28	2	call	call	VERB
ap-920	28	3	a	a	DET
ap-920	28	4	factor	factor	NOUN
ap-920	28	5	w	w	PROPN
ap-920	28	6	u	u	PROPN
ap-920	28	7	�	�	PROPN
ap-920	28	8	�	�	PROPN
ap-920	28	9	(	(	PUNCT
ap-920	28	10	)	)	PUNCT
ap-920	28	11	bispecial	bispecial	ADJ
ap-920	28	12	if	if	SCONJ
ap-920	28	13	it	it	PRON
ap-920	28	14	is	be	AUX
ap-920	28	15	left	leave	VERB
ap-920	28	16	special	special	ADJ
ap-920	28	17	and	and	CCONJ
ap-920	28	18	right	right	ADJ
ap-920	28	19	special	special	ADJ
ap-920	28	20	.	.	PUNCT
ap-920	29	1	a	a	DET
ap-920	29	2	mapping	mapping	NOUN
ap-920	29	3	�	�	NOUN
ap-920	29	4	on	on	ADP
ap-920	29	5	the	the	DET
ap-920	29	6	free	free	PROPN
ap-920	29	7	monoid	monoid	PROPN
ap-920	29	8	�	�	PROPN
ap-920	29	9	*	*	PROPN
ap-920	29	10	is	be	AUX
ap-920	29	11	called	call	VERB
ap-920	29	12	a	a	DET
ap-920	29	13	morphism	morphism	NOUN
ap-920	29	14	if	if	SCONJ
ap-920	29	15	�	�	PROPN
ap-920	29	16	�	�	PROPN
ap-920	29	17	�	�	PROPN
ap-920	29	18	(	(	PUNCT
ap-920	29	19	)	)	PUNCT
ap-920	29	20	(	(	PUNCT
ap-920	29	21	)	)	PUNCT
ap-920	29	22	(	(	PUNCT
ap-920	29	23	)	)	PUNCT
ap-920	29	24	vw	vw	PROPN
ap-920	29	25	v	v	PROPN
ap-920	29	26	w	w	PROPN
ap-920	29	27	�	�	PROPN
ap-920	29	28	for	for	ADP
ap-920	29	29	all	all	DET
ap-920	29	30	v	v	NOUN
ap-920	29	31	w	w	NOUN
ap-920	29	32	,	,	PUNCT
ap-920	29	33	*	*	ADJ
ap-920	29	34	�	�	PROPN
ap-920	29	35	�	�	PROPN
ap-920	29	36	.	.	PUNCT
ap-920	30	1	obviously	obviously	ADV
ap-920	30	2	,	,	PUNCT
ap-920	30	3	for	for	ADP
ap-920	30	4	determining	determine	VERB
ap-920	30	5	any	any	DET
ap-920	30	6	morphism	morphism	NOUN
ap-920	30	7	it	it	PRON
ap-920	30	8	suffices	suffice	VERB
ap-920	30	9	to	to	PART
ap-920	30	10	give	give	VERB
ap-920	30	11	�	�	PROPN
ap-920	30	12	(	(	PUNCT
ap-920	30	13	a	a	NOUN
ap-920	30	14	)	)	PUNCT
ap-920	30	15	for	for	ADP
ap-920	30	16	all	all	DET
ap-920	30	17	a	a	DET
ap-920	30	18	�	�	PROPN
ap-920	30	19	�	�	PROPN
ap-920	30	20	.	.	PUNCT
ap-920	31	1	the	the	DET
ap-920	31	2	action	action	NOUN
ap-920	31	3	of	of	ADP
ap-920	31	4	a	a	DET
ap-920	31	5	morphism	morphism	NOUN
ap-920	31	6	can	can	AUX
ap-920	31	7	be	be	AUX
ap-920	31	8	naturally	naturally	ADV
ap-920	31	9	extended	extend	VERB
ap-920	31	10	on	on	ADP
ap-920	31	11	right	right	ADV
ap-920	31	12	-	-	PUNCT
ap-920	31	13	sided	sided	ADJ
ap-920	31	14	infinite	infinite	ADJ
ap-920	31	15	words	word	NOUN
ap-920	31	16	by	by	ADP
ap-920	31	17	the	the	DET
ap-920	31	18	prescription	prescription	NOUN
ap-920	31	19	�	�	PROPN
ap-920	31	20	�	�	PROPN
ap-920	31	21	�	�	PROPN
ap-920	31	22	�	�	PROPN
ap-920	31	23	(	(	PUNCT
ap-920	31	24	)	)	PUNCT
ap-920	31	25	:	:	PUNCT
ap-920	31	26	(	(	PUNCT
ap-920	31	27	)	)	PUNCT
ap-920	31	28	(	(	PUNCT
ap-920	31	29	)	)	PUNCT
ap-920	32	1	(	(	PUNCT
ap-920	32	2	)	)	PUNCT
ap-920	32	3	u	u	NOUN
ap-920	32	4	u	u	PROPN
ap-920	32	5	u	u	X
ap-920	32	6	u	u	X
ap-920	32	7	u	u	NOUN
ap-920	32	8	u0	u0	ADJ
ap-920	32	9	1	1	NUM
ap-920	32	10	2	2	NUM
ap-920	32	11	0	0	NUM
ap-920	32	12	1	1	NUM
ap-920	32	13	2	2	NUM
ap-920	32	14	�	�	PROPN
ap-920	32	15	�	�	PROPN
ap-920	32	16	�	�	PROPN
ap-920	32	17	a	a	DET
ap-920	32	18	non	non	ADJ
ap-920	32	19	-	-	ADJ
ap-920	32	20	erasing	erase	VERB
ap-920	32	21	morphism	morphism	NOUN
ap-920	32	22	�	�	PROPN
ap-920	32	23	,	,	PUNCT
ap-920	32	24	for	for	ADP
ap-920	32	25	which	which	PRON
ap-920	32	26	there	there	PRON
ap-920	32	27	exists	exist	VERB
ap-920	32	28	a	a	DET
ap-920	32	29	letter	letter	NOUN
ap-920	32	30	a	a	DET
ap-920	32	31	�	�	NOUN
ap-920	32	32	�	�	PROPN
ap-920	32	33	such	such	ADJ
ap-920	32	34	that	that	DET
ap-920	32	35	�	�	PROPN
ap-920	32	36	(	(	PUNCT
ap-920	32	37	)	)	PUNCT
ap-920	32	38	a	a	DET
ap-920	32	39	aw	aw	INTJ
ap-920	32	40	�	�	PROPN
ap-920	32	41	for	for	ADP
ap-920	32	42	some	some	DET
ap-920	32	43	non	non	ADJ
ap-920	32	44	-	-	ADJ
ap-920	32	45	empty	empty	ADJ
ap-920	32	46	word	word	NOUN
ap-920	32	47	w	w	PROPN
ap-920	32	48	�	�	PROPN
ap-920	32	49	�	�	PROPN
ap-920	32	50	*	*	PUNCT
ap-920	32	51	,	,	PUNCT
ap-920	32	52	is	be	AUX
ap-920	32	53	called	call	VERB
ap-920	32	54	a	a	DET
ap-920	32	55	substitution	substitution	NOUN
ap-920	32	56	.	.	PUNCT
ap-920	33	1	an	an	DET
ap-920	33	2	infinite	infinite	ADJ
ap-920	33	3	word	word	NOUN
ap-920	33	4	u	u	NOUN
ap-920	33	5	such	such	ADJ
ap-920	33	6	that	that	DET
ap-920	33	7	�	�	PROPN
ap-920	33	8	(	(	PUNCT
ap-920	33	9	)	)	PUNCT
ap-920	33	10	u	u	PROPN
ap-920	33	11	u	u	NOUN
ap-920	33	12	�	�	PROPN
ap-920	33	13	is	be	AUX
ap-920	33	14	called	call	VERB
ap-920	33	15	a	a	DET
ap-920	33	16	fixed	fix	VERB
ap-920	33	17	point	point	NOUN
ap-920	33	18	of	of	ADP
ap-920	33	19	the	the	DET
ap-920	33	20	substitution	substitution	NOUN
ap-920	33	21	�	�	PROPN
ap-920	33	22	.	.	PUNCT
ap-920	34	1	obviously	obviously	ADV
ap-920	34	2	,	,	PUNCT
ap-920	34	3	every	every	DET
ap-920	34	4	substitution	substitution	NOUN
ap-920	34	5	has	have	VERB
ap-920	34	6	at	at	ADV
ap-920	34	7	least	least	ADV
ap-920	34	8	one	one	NUM
ap-920	34	9	fixed	fix	VERB
ap-920	34	10	point	point	NOUN
ap-920	34	11	,	,	PUNCT
ap-920	34	12	namely	namely	ADV
ap-920	34	13	lim	lim	NOUN
ap-920	34	14	(	(	PUNCT
ap-920	34	15	)	)	PUNCT
ap-920	34	16	n	n	CCONJ
ap-920	34	17	n	n	PRON
ap-920	34	18	a	a	DET
ap-920	34	19	�	�	PROPN
ap-920	34	20	�	�	PROPN
ap-920	34	21	�	�	PROPN
ap-920	34	22	.	.	PUNCT
ap-920	35	1	in	in	ADP
ap-920	35	2	everything	everything	PRON
ap-920	35	3	that	that	PRON
ap-920	35	4	follows	follow	VERB
ap-920	35	5	,	,	PUNCT
ap-920	35	6	we	we	PRON
ap-920	35	7	will	will	AUX
ap-920	35	8	focus	focus	VERB
ap-920	35	9	on	on	ADP
ap-920	35	10	the	the	DET
ap-920	35	11	infinite	infinite	ADJ
ap-920	35	12	word	word	NOUN
ap-920	35	13	u	u	NOUN
ap-920	35	14	�	�	PROPN
ap-920	35	15	being	be	AUX
ap-920	35	16	the	the	DET
ap-920	35	17	only	only	ADJ
ap-920	35	18	fixed	fix	VERB
ap-920	35	19	point	point	NOUN
ap-920	35	20	of	of	ADP
ap-920	35	21	the	the	DET
ap-920	35	22	substitution	substitution	NOUN
ap-920	35	23	�	�	NOUN
ap-920	35	24	given	give	VERB
ap-920	35	25	by	by	ADP
ap-920	35	26	�	�	PROPN
ap-920	35	27	�	�	PROPN
ap-920	35	28	(	(	PUNCT
ap-920	35	29	)	)	PUNCT
ap-920	35	30	,	,	PUNCT
ap-920	35	31	(	(	PUNCT
ap-920	35	32	)	)	PUNCT
ap-920	35	33	,	,	PUNCT
ap-920	35	34	,	,	PUNCT
ap-920	35	35	0	0	NUM
ap-920	35	36	0	0	NUM
ap-920	35	37	1	1	NUM
ap-920	35	38	1	1	NUM
ap-920	35	39	0	0	NUM
ap-920	35	40	1	1	NUM
ap-920	35	41	1	1	NUM
ap-920	35	42	�	�	PROPN
ap-920	35	43	�	�	PROPN
ap-920	35	44	�	�	PROPN
ap-920	35	45	�	�	PROPN
ap-920	35	46	�	�	PROPN
ap-920	35	47	a	a	DET
ap-920	35	48	b	b	NOUN
ap-920	35	49	a	a	DET
ap-920	35	50	b	b	NOUN
ap-920	35	51	a	a	DET
ap-920	35	52	�	�	PROPN
ap-920	35	53	.	.	PUNCT
ap-920	36	1	(	(	PUNCT
ap-920	36	2	1	1	X
ap-920	36	3	)	)	PUNCT
ap-920	36	4	let	let	VERB
ap-920	36	5	us	we	PRON
ap-920	36	6	only	only	ADV
ap-920	36	7	briefly	briefly	ADV
ap-920	36	8	mention	mention	VERB
ap-920	36	9	that	that	SCONJ
ap-920	36	10	this	this	DET
ap-920	36	11	infinite	infinite	ADJ
ap-920	36	12	word	word	NOUN
ap-920	36	13	codes	code	VERB
ap-920	36	14	the	the	DET
ap-920	36	15	set	set	NOUN
ap-920	36	16	of	of	ADP
ap-920	36	17	�	�	PROPN
ap-920	36	18	-integers	-integer	NOUN
ap-920	36	19	�	�	PROPN
ap-920	36	20	�	�	PROPN
ap-920	36	21	,	,	PUNCT
ap-920	36	22	where	where	SCONJ
ap-920	36	23	�	�	PROPN
ap-920	36	24	is	be	AUX
ap-920	36	25	a	a	DET
ap-920	36	26	quadratic	quadratic	ADJ
ap-920	36	27	non	non	ADJ
ap-920	36	28	-	-	ADJ
ap-920	36	29	simple	simple	ADJ
ap-920	36	30	parry	parry	NOUN
ap-920	36	31	number	number	NOUN
ap-920	36	32	.	.	PUNCT
ap-920	37	1	all	all	DET
ap-920	37	2	details	detail	NOUN
ap-920	37	3	can	can	AUX
ap-920	37	4	be	be	AUX
ap-920	37	5	found	find	VERB
ap-920	37	6	,	,	PUNCT
ap-920	37	7	for	for	ADP
ap-920	37	8	example	example	NOUN
ap-920	37	9	,	,	PUNCT
ap-920	37	10	in	in	ADP
ap-920	37	11	[	[	X
ap-920	37	12	8	8	NUM
ap-920	37	13	]	]	PUNCT
ap-920	37	14	.	.	PUNCT
ap-920	38	1	since	since	SCONJ
ap-920	38	2	our	our	PRON
ap-920	38	3	main	main	ADJ
ap-920	38	4	interest	interest	NOUN
ap-920	38	5	is	be	AUX
ap-920	38	6	in	in	ADP
ap-920	38	7	studying	study	VERB
ap-920	38	8	return	return	NOUN
ap-920	38	9	words	word	NOUN
ap-920	38	10	and	and	CCONJ
ap-920	38	11	the	the	DET
ap-920	38	12	recurrence	recurrence	NOUN
ap-920	38	13	function	function	NOUN
ap-920	38	14	,	,	PUNCT
ap-920	38	15	let	let	VERB
ap-920	38	16	us	we	PRON
ap-920	38	17	give	give	VERB
ap-920	38	18	the	the	DET
ap-920	38	19	corresponding	corresponding	ADJ
ap-920	38	20	definitions	definition	NOUN
ap-920	38	21	.	.	PUNCT
ap-920	39	1	definition	definition	NOUN
ap-920	39	2	1	1	NUM
ap-920	39	3	let	let	VERB
ap-920	39	4	w	w	NOUN
ap-920	39	5	be	be	AUX
ap-920	39	6	a	a	DET
ap-920	39	7	factor	factor	NOUN
ap-920	39	8	of	of	ADP
ap-920	39	9	an	an	DET
ap-920	39	10	infinite	infinite	ADJ
ap-920	39	11	word	word	NOUN
ap-920	39	12	u	u	PROPN
ap-920	39	13	u	u	PROPN
ap-920	39	14	u	u	NOUN
ap-920	39	15	�	�	PROPN
ap-920	39	16	0	0	NUM
ap-920	39	17	1	1	NUM
ap-920	39	18	�	�	PROPN
ap-920	39	19	(	(	PUNCT
ap-920	39	20	with	with	ADP
ap-920	39	21	u	u	PROPN
ap-920	39	22	j	j	PROPN
ap-920	39	23	�	�	PROPN
ap-920	39	24	�	�	PROPN
ap-920	39	25	)	)	PUNCT
ap-920	39	26	,	,	PUNCT
ap-920	39	27	w	w	PROPN
ap-920	39	28	�	�	PROPN
ap-920	39	29	�	�	PROPN
ap-920	39	30	.	.	PUNCT
ap-920	40	1	an	an	DET
ap-920	40	2	integer	integer	NOUN
ap-920	40	3	�	�	PROPN
ap-920	40	4	is	be	AUX
ap-920	40	5	an	an	DET
ap-920	40	6	occurrence	occurrence	NOUN
ap-920	40	7	of	of	ADP
ap-920	40	8	w	w	NOUN
ap-920	40	9	in	in	ADP
ap-920	40	10	u	u	NOUN
ap-920	40	11	if	if	SCONJ
ap-920	40	12	u	u	PRON
ap-920	40	13	u	u	VERB
ap-920	40	14	u	u	NOUN
ap-920	40	15	wj	wj	PROPN
ap-920	40	16	j	j	PROPN
ap-920	40	17	j	j	PROPN
ap-920	40	18	�	�	PROPN
ap-920	40	19	�	�	PROPN
ap-920	40	20	�	�	PROPN
ap-920	40	21	�	�	PROPN
ap-920	40	22	1	1	NUM
ap-920	40	23	1	1	NUM
ap-920	40	24	�	�	PROPN
ap-920	40	25	�	�	PROPN
ap-920	40	26	.	.	PUNCT
ap-920	41	1	let	let	VERB
ap-920	41	2	j	j	PROPN
ap-920	41	3	,	,	PUNCT
ap-920	41	4	k	k	PROPN
ap-920	41	5	,	,	PUNCT
ap-920	41	6	j	j	PROPN
ap-920	41	7	<	<	X
ap-920	41	8	k	k	PROPN
ap-920	41	9	,	,	PUNCT
ap-920	41	10	be	be	AUX
ap-920	41	11	successive	successive	ADJ
ap-920	41	12	occurrences	occurrence	NOUN
ap-920	41	13	of	of	ADP
ap-920	41	14	w.	w.	NOUN
ap-920	41	15	then	then	ADV
ap-920	41	16	u	u	X
ap-920	41	17	u	u	PROPN
ap-920	41	18	uj	uj	PROPN
ap-920	41	19	j	j	PROPN
ap-920	41	20	k	k	PROPN
ap-920	41	21	�	�	PROPN
ap-920	41	22	�	�	PROPN
ap-920	41	23	1	1	NUM
ap-920	41	24	1	1	NUM
ap-920	41	25	�	�	NOUN
ap-920	41	26	is	be	AUX
ap-920	41	27	a	a	DET
ap-920	41	28	return	return	NOUN
ap-920	41	29	word	word	NOUN
ap-920	41	30	of	of	ADP
ap-920	41	31	w.	w.	NOUN
ap-920	41	32	the	the	DET
ap-920	41	33	set	set	NOUN
ap-920	41	34	of	of	ADP
ap-920	41	35	all	all	DET
ap-920	41	36	return	return	VERB
ap-920	41	37	words	word	NOUN
ap-920	41	38	of	of	ADP
ap-920	41	39	w	w	PROPN
ap-920	41	40	is	be	AUX
ap-920	41	41	denoted	denote	VERB
ap-920	41	42	by	by	ADP
ap-920	41	43	ret(w	ret(w	NOUN
ap-920	41	44	)	)	PUNCT
ap-920	41	45	,	,	PUNCT
ap-920	41	46	i.e.	i.e.	X
ap-920	41	47	,	,	PUNCT
ap-920	41	48	ret	ret	PROPN
ap-920	41	49	(	(	PUNCT
ap-920	41	50	)	)	PUNCT
ap-920	41	51	,	,	PUNCT
ap-920	41	52	w	w	PROPN
ap-920	41	53	u	u	NOUN
ap-920	41	54	u	u	X
ap-920	41	55	u	u	NOUN
ap-920	41	56	j	j	PROPN
ap-920	41	57	k	k	X
ap-920	41	58	being	be	AUX
ap-920	41	59	succesive	succesive	ADJ
ap-920	41	60	occurences	occurence	NOUN
ap-920	41	61	of	of	ADP
ap-920	41	62	wj	wj	PROPN
ap-920	41	63	j	j	PROPN
ap-920	41	64	k	k	PROPN
ap-920	41	65	�	�	PROPN
ap-920	41	66	�	�	PROPN
ap-920	41	67	�	�	PROPN
ap-920	41	68	1	1	NUM
ap-920	41	69	1	1	NUM
ap-920	41	70	�	�	PROPN
ap-920	41	71	.	.	PUNCT
ap-920	42	1	©	©	PROPN
ap-920	42	2	czech	czech	PROPN
ap-920	42	3	technical	technical	PROPN
ap-920	42	4	university	university	PROPN
ap-920	42	5	publishing	publishing	NOUN
ap-920	42	6	house	house	NOUN
ap-920	42	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-920	42	8	15	15	NUM
ap-920	42	9	acta	acta	PROPN
ap-920	42	10	polytechnica	polytechnica	PROPN
ap-920	42	11	vol	vol	NOUN
ap-920	42	12	.	.	PUNCT
ap-920	43	1	47	47	NUM
ap-920	43	2	no	no	INTJ
ap-920	43	3	.	.	PUNCT
ap-920	44	1	2–3/2007	2–3/2007	NUM
ap-920	44	2	return	return	NOUN
ap-920	44	3	words	word	NOUN
ap-920	44	4	and	and	CCONJ
ap-920	44	5	recurrence	recurrence	NOUN
ap-920	44	6	function	function	NOUN
ap-920	44	7	of	of	ADP
ap-920	44	8	a	a	DET
ap-920	44	9	class	class	NOUN
ap-920	44	10	of	of	ADP
ap-920	44	11	infinite	infinite	ADJ
ap-920	44	12	words	word	NOUN
ap-920	44	13	l	l	NOUN
ap-920	44	14	’	'	PUNCT
ap-920	44	15	.	.	PUNCT
ap-920	45	1	balková	balková	VERB
ap-920	45	2	many	many	ADJ
ap-920	45	3	combinatorial	combinatorial	ADJ
ap-920	45	4	and	and	CCONJ
ap-920	45	5	arithmetical	arithmetical	ADJ
ap-920	45	6	properties	property	NOUN
ap-920	45	7	have	have	AUX
ap-920	45	8	been	be	AUX
ap-920	45	9	studied	study	VERB
ap-920	45	10	for	for	ADP
ap-920	45	11	infinite	infinite	ADJ
ap-920	45	12	words	word	NOUN
ap-920	45	13	u	u	NOUN
ap-920	45	14	�	�	PROPN
ap-920	45	15	associated	associate	VERB
ap-920	45	16	with	with	ADP
ap-920	45	17	�	�	NOUN
ap-920	45	18	-integers	-integer	NOUN
ap-920	45	19	.	.	PUNCT
ap-920	46	1	here	here	ADV
ap-920	46	2	,	,	PUNCT
ap-920	46	3	new	new	ADJ
ap-920	46	4	results	result	NOUN
ap-920	46	5	describing	describe	VERB
ap-920	46	6	return	return	NOUN
ap-920	46	7	words	word	NOUN
ap-920	46	8	and	and	CCONJ
ap-920	46	9	recurrence	recurrence	NOUN
ap-920	46	10	function	function	NOUN
ap-920	46	11	for	for	ADP
ap-920	46	12	a	a	DET
ap-920	46	13	special	special	ADJ
ap-920	46	14	case	case	NOUN
ap-920	46	15	of	of	ADP
ap-920	46	16	u	u	NOUN
ap-920	46	17	�	�	PROPN
ap-920	46	18	will	will	AUX
ap-920	46	19	be	be	AUX
ap-920	46	20	presented	present	VERB
ap-920	46	21	.	.	PUNCT
ap-920	47	1	the	the	DET
ap-920	47	2	methods	method	NOUN
ap-920	47	3	used	use	VERB
ap-920	47	4	here	here	ADV
ap-920	47	5	can	can	AUX
ap-920	47	6	be	be	AUX
ap-920	47	7	applied	apply	VERB
ap-920	47	8	to	to	ADP
ap-920	47	9	more	more	ADV
ap-920	47	10	general	general	ADJ
ap-920	47	11	infinite	infinite	ADJ
ap-920	47	12	words	word	NOUN
ap-920	47	13	,	,	PUNCT
ap-920	47	14	but	but	CCONJ
ap-920	47	15	the	the	DET
ap-920	47	16	description	description	NOUN
ap-920	47	17	then	then	ADV
ap-920	47	18	becomes	become	VERB
ap-920	47	19	rather	rather	ADV
ap-920	47	20	technical	technical	ADJ
ap-920	47	21	.	.	PUNCT
ap-920	48	1	keywords	keyword	NOUN
ap-920	48	2	:	:	PUNCT
ap-920	48	3	return	return	VERB
ap-920	48	4	words	word	NOUN
ap-920	48	5	,	,	PUNCT
ap-920	48	6	recurrence	recurrence	NOUN
ap-920	48	7	function	function	NOUN
ap-920	48	8	,	,	PUNCT
ap-920	48	9	parry	parry	PROPN
ap-920	48	10	numbers	number	NOUN
ap-920	48	11	.	.	PUNCT
ap-920	49	1	an	an	DET
ap-920	49	2	infinite	infinite	ADJ
ap-920	49	3	word	word	NOUN
ap-920	49	4	u	u	NOUN
ap-920	49	5	is	be	AUX
ap-920	49	6	said	say	VERB
ap-920	49	7	to	to	PART
ap-920	49	8	be	be	AUX
ap-920	49	9	recurrent	recurrent	ADJ
ap-920	49	10	if	if	SCONJ
ap-920	49	11	each	each	PRON
ap-920	49	12	of	of	ADP
ap-920	49	13	its	its	PRON
ap-920	49	14	factors	factor	NOUN
ap-920	49	15	appears	appear	VERB
ap-920	49	16	infinitely	infinitely	ADV
ap-920	49	17	many	many	ADJ
ap-920	49	18	times	time	NOUN
ap-920	49	19	in	in	ADP
ap-920	49	20	u.	u.	NOUN
ap-920	49	21	it	it	PRON
ap-920	49	22	is	be	AUX
ap-920	49	23	said	say	VERB
ap-920	49	24	to	to	PART
ap-920	49	25	be	be	AUX
ap-920	49	26	uniformly	uniformly	ADV
ap-920	49	27	recurrent	recurrent	ADJ
ap-920	49	28	if	if	SCONJ
ap-920	49	29	for	for	ADP
ap-920	49	30	every	every	DET
ap-920	49	31	n	n	PRON
ap-920	49	32	�	�	PROPN
ap-920	49	33	�	�	PROPN
ap-920	49	34	there	there	PRON
ap-920	49	35	exists	exist	VERB
ap-920	49	36	r(n)>0	r(n)>0	NUM
ap-920	49	37	such	such	ADJ
ap-920	49	38	that	that	SCONJ
ap-920	49	39	any	any	DET
ap-920	49	40	segment	segment	NOUN
ap-920	49	41	of	of	ADP
ap-920	49	42	u	u	NOUN
ap-920	49	43	of	of	ADP
ap-920	49	44	length	length	NOUN
ap-920	49	45	�	�	PROPN
ap-920	49	46	r	r	NOUN
ap-920	49	47	n	n	CCONJ
ap-920	49	48	(	(	PUNCT
ap-920	49	49	)	)	PUNCT
ap-920	49	50	contains	contain	VERB
ap-920	49	51	all	all	DET
ap-920	49	52	words	word	NOUN
ap-920	49	53	in	in	ADP
ap-920	49	54	�	�	PROPN
ap-920	49	55	n(u	n(u	PROPN
ap-920	49	56	)	)	PUNCT
ap-920	49	57	.	.	PUNCT
ap-920	50	1	as	as	SCONJ
ap-920	50	2	we	we	PRON
ap-920	50	3	deal	deal	VERB
ap-920	50	4	with	with	ADP
ap-920	50	5	the	the	DET
ap-920	50	6	infinite	infinite	ADJ
ap-920	50	7	word	word	NOUN
ap-920	50	8	u	u	PROPN
ap-920	50	9	n	n	CCONJ
ap-920	50	10	�	�	PROPN
ap-920	50	11	�	�	PROPN
ap-920	50	12	�	�	PROPN
ap-920	50	13	�	�	PROPN
ap-920	50	14	�	�	PROPN
ap-920	50	15	lim	lim	PROPN
ap-920	50	16	(	(	PUNCT
ap-920	50	17	)	)	PUNCT
ap-920	50	18	0	0	NUM
ap-920	50	19	,	,	PUNCT
ap-920	50	20	where	where	SCONJ
ap-920	50	21	�	�	PROPN
ap-920	50	22	(	(	PUNCT
ap-920	50	23	)	)	PUNCT
ap-920	50	24	0	0	SYM
ap-920	50	25	0	0	NUM
ap-920	50	26	1	1	NUM
ap-920	50	27	�	�	PROPN
ap-920	50	28	a	a	PRON
ap-920	50	29	,	,	PUNCT
ap-920	50	30	�	�	PROPN
ap-920	50	31	(	(	PUNCT
ap-920	50	32	)	)	PUNCT
ap-920	50	33	1	1	NUM
ap-920	50	34	0	0	NUM
ap-920	50	35	1	1	NUM
ap-920	50	36	�	�	PROPN
ap-920	50	37	b	b	PROPN
ap-920	50	38	,	,	PUNCT
ap-920	50	39	a	a	DET
ap-920	50	40	b	b	PROPN
ap-920	50	41	�	�	PROPN
ap-920	50	42	�	�	PROPN
ap-920	50	43	1	1	NUM
ap-920	50	44	,	,	PUNCT
ap-920	50	45	let	let	VERB
ap-920	50	46	us	we	PRON
ap-920	50	47	also	also	ADV
ap-920	50	48	recall	recall	VERB
ap-920	50	49	what	what	PRON
ap-920	50	50	is	be	AUX
ap-920	50	51	known	know	VERB
ap-920	50	52	about	about	ADP
ap-920	50	53	the	the	DET
ap-920	50	54	uniform	uniform	ADJ
ap-920	50	55	recurrence	recurrence	NOUN
ap-920	50	56	of	of	ADP
ap-920	50	57	words	word	NOUN
ap-920	50	58	being	be	AUX
ap-920	50	59	fixed	fix	VERB
ap-920	50	60	points	point	NOUN
ap-920	50	61	of	of	ADP
ap-920	50	62	a	a	DET
ap-920	50	63	substitution	substitution	NOUN
ap-920	50	64	.	.	PUNCT
ap-920	51	1	definition	definition	NOUN
ap-920	51	2	2	2	NUM
ap-920	51	3	a	a	DET
ap-920	51	4	substitution	substitution	NOUN
ap-920	51	5	�	�	NOUN
ap-920	51	6	over	over	ADP
ap-920	51	7	an	an	DET
ap-920	51	8	alphabet	alphabet	PROPN
ap-920	51	9	�	�	PROPN
ap-920	51	10	�	�	PROPN
ap-920	51	11	a	a	DET
ap-920	51	12	a	a	DET
ap-920	51	13	ak1	ak1	NOUN
ap-920	51	14	2	2	NUM
ap-920	51	15	,	,	PUNCT
ap-920	51	16	,	,	PUNCT
ap-920	51	17	,	,	PUNCT
ap-920	51	18	,	,	PUNCT
ap-920	51	19	�	�	PROPN
ap-920	51	20	is	be	AUX
ap-920	51	21	called	call	VERB
ap-920	51	22	primitive	primitive	ADJ
ap-920	51	23	if	if	SCONJ
ap-920	51	24	there	there	PRON
ap-920	51	25	exists	exist	VERB
ap-920	51	26	k	k	PROPN
ap-920	51	27	�	�	PROPN
ap-920	51	28	�	�	PROPN
ap-920	51	29	such	such	ADJ
ap-920	51	30	that	that	PRON
ap-920	51	31	for	for	ADP
ap-920	51	32	any	any	DET
ap-920	51	33	letter	letter	NOUN
ap-920	51	34	ai	ai	VERB
ap-920	51	35	�	�	PROPN
ap-920	51	36	�	�	PROPN
ap-920	51	37	,	,	PUNCT
ap-920	51	38	the	the	DET
ap-920	51	39	word	word	NOUN
ap-920	51	40	�	�	NOUN
ap-920	51	41	k(ai	k(ai	NOUN
ap-920	51	42	)	)	PUNCT
ap-920	51	43	contains	contain	VERB
ap-920	51	44	all	all	DET
ap-920	51	45	letters	letter	NOUN
ap-920	51	46	of	of	ADP
ap-920	51	47	�	�	PROPN
ap-920	51	48	.	.	PUNCT
ap-920	52	1	queffélec	queffélec	NOUN
ap-920	52	2	in	in	ADP
ap-920	52	3	[	[	X
ap-920	52	4	10	10	NUM
ap-920	52	5	]	]	PUNCT
ap-920	52	6	has	have	AUX
ap-920	52	7	shown	show	VERB
ap-920	52	8	that	that	SCONJ
ap-920	52	9	any	any	DET
ap-920	52	10	fixed	fixed	ADJ
ap-920	52	11	point	point	NOUN
ap-920	52	12	of	of	ADP
ap-920	52	13	a	a	DET
ap-920	52	14	primitive	primitive	ADJ
ap-920	52	15	substitution	substitution	NOUN
ap-920	52	16	�	�	NOUN
ap-920	52	17	is	be	AUX
ap-920	52	18	a	a	DET
ap-920	52	19	uniformly	uniformly	ADV
ap-920	52	20	recurrent	recurrent	ADJ
ap-920	52	21	word	word	NOUN
ap-920	52	22	.	.	PUNCT
ap-920	53	1	thus	thus	ADV
ap-920	53	2	,	,	PUNCT
ap-920	53	3	since	since	SCONJ
ap-920	53	4	the	the	DET
ap-920	53	5	infinite	infinite	ADJ
ap-920	53	6	word	word	NOUN
ap-920	53	7	ub	ub	ADV
ap-920	53	8	is	be	AUX
ap-920	53	9	a	a	DET
ap-920	53	10	fixed	fix	VERB
ap-920	53	11	point	point	NOUN
ap-920	53	12	of	of	ADP
ap-920	53	13	a	a	DET
ap-920	53	14	primitive	primitive	ADJ
ap-920	53	15	substitution	substitution	NOUN
ap-920	53	16	,	,	PUNCT
ap-920	53	17	u	u	NOUN
ap-920	53	18	�	�	PROPN
ap-920	53	19	is	be	AUX
ap-920	53	20	uniformly	uniformly	ADV
ap-920	53	21	recurrent	recurrent	ADJ
ap-920	53	22	.	.	PUNCT
ap-920	54	1	it	it	PRON
ap-920	54	2	is	be	AUX
ap-920	54	3	not	not	PART
ap-920	54	4	difficult	difficult	ADJ
ap-920	54	5	to	to	PART
ap-920	54	6	see	see	VERB
ap-920	54	7	that	that	SCONJ
ap-920	54	8	the	the	DET
ap-920	54	9	set	set	NOUN
ap-920	54	10	of	of	ADP
ap-920	54	11	return	return	NOUN
ap-920	54	12	words	word	NOUN
ap-920	54	13	of	of	ADP
ap-920	54	14	w	w	PROPN
ap-920	54	15	is	be	AUX
ap-920	54	16	finite	finite	ADJ
ap-920	54	17	for	for	ADP
ap-920	54	18	any	any	DET
ap-920	54	19	factor	factor	NOUN
ap-920	54	20	w	w	PROPN
ap-920	54	21	u	u	PROPN
ap-920	54	22	�	�	PROPN
ap-920	54	23	�	�	PROPN
ap-920	54	24	(	(	PUNCT
ap-920	54	25	)	)	PUNCT
ap-920	54	26	if	if	SCONJ
ap-920	54	27	u	u	NOUN
ap-920	54	28	is	be	AUX
ap-920	54	29	a	a	DET
ap-920	54	30	uniformly	uniformly	ADV
ap-920	54	31	recurrent	recurrent	ADJ
ap-920	54	32	word	word	NOUN
ap-920	54	33	.	.	PUNCT
ap-920	55	1	definition	definition	NOUN
ap-920	55	2	3	3	NUM
ap-920	55	3	the	the	DET
ap-920	55	4	recurrence	recurrence	NOUN
ap-920	55	5	function	function	NOUN
ap-920	55	6	of	of	ADP
ap-920	55	7	an	an	DET
ap-920	55	8	infinite	infinite	ADJ
ap-920	55	9	word	word	NOUN
ap-920	55	10	u	u	NOUN
ap-920	55	11	is	be	AUX
ap-920	55	12	the	the	DET
ap-920	55	13	function	function	NOUN
ap-920	55	14	ru	ru	NOUN
ap-920	55	15	:	:	PUNCT
ap-920	55	16	�	�	PROPN
ap-920	55	17	�	�	PROPN
ap-920	55	18	�	�	PROPN
ap-920	55	19	�	�	PROPN
ap-920	55	20	�	�	PROPN
ap-920	55	21	�	�	PROPN
ap-920	55	22	defined	define	VERB
ap-920	55	23	by	by	ADP
ap-920	55	24	�	�	PROPN
ap-920	55	25	r	r	NOUN
ap-920	55	26	n	n	NOUN
ap-920	55	27	n	n	NOUN
ap-920	55	28	v	v	PART
ap-920	55	29	u	u	PRON
ap-920	55	30	v	v	NOUN
ap-920	55	31	uu	uu	ADP
ap-920	55	32	n	n	CCONJ
ap-920	55	33	n	n	CCONJ
ap-920	55	34	n	n	CCONJ
ap-920	55	35	(	(	PUNCT
ap-920	55	36	)	)	PUNCT
ap-920	55	37	inf	inf	NOUN
ap-920	55	38	(	(	PUNCT
ap-920	55	39	)	)	PUNCT
ap-920	55	40	,	,	PUNCT
ap-920	55	41	(	(	PUNCT
ap-920	55	42	)	)	PUNCT
ap-920	55	43	(	(	PUNCT
ap-920	55	44	)	)	PUNCT
ap-920	55	45	�	�	PROPN
ap-920	55	46	�	�	PROPN
ap-920	55	47	�	�	PROPN
ap-920	55	48	�	�	PROPN
ap-920	55	49	�	�	PROPN
ap-920	55	50	�	�	PROPN
ap-920	55	51	�	�	PROPN
ap-920	55	52	�	�	PROPN
ap-920	55	53	�	�	PROPN
ap-920	55	54	�	�	PROPN
ap-920	55	55	�	�	PROPN
ap-920	55	56	�	�	PROPN
ap-920	55	57	in	in	ADP
ap-920	55	58	other	other	ADJ
ap-920	55	59	words	word	NOUN
ap-920	55	60	,	,	PUNCT
ap-920	55	61	ru(n	ru(n	NOUN
ap-920	55	62	)	)	PUNCT
ap-920	55	63	is	be	AUX
ap-920	55	64	the	the	DET
ap-920	55	65	smallest	small	ADJ
ap-920	55	66	length	length	NOUN
ap-920	55	67	such	such	ADJ
ap-920	55	68	that	that	SCONJ
ap-920	55	69	if	if	SCONJ
ap-920	55	70	we	we	PRON
ap-920	55	71	take	take	VERB
ap-920	55	72	any	any	DET
ap-920	55	73	segment	segment	NOUN
ap-920	55	74	of	of	ADP
ap-920	55	75	u	u	NOUN
ap-920	55	76	of	of	ADP
ap-920	55	77	length	length	NOUN
ap-920	55	78	ru(n	ru(n	PROPN
ap-920	55	79	)	)	PUNCT
ap-920	55	80	,	,	PUNCT
ap-920	55	81	we	we	PRON
ap-920	55	82	will	will	AUX
ap-920	55	83	find	find	VERB
ap-920	55	84	there	there	ADV
ap-920	55	85	all	all	DET
ap-920	55	86	the	the	DET
ap-920	55	87	factors	factor	NOUN
ap-920	55	88	of	of	ADP
ap-920	55	89	u	u	NOUN
ap-920	55	90	of	of	ADP
ap-920	55	91	length	length	NOUN
ap-920	55	92	n.	n.	PROPN
ap-920	55	93	clearly	clearly	ADV
ap-920	55	94	,	,	PUNCT
ap-920	55	95	u	u	NOUN
ap-920	55	96	is	be	AUX
ap-920	55	97	uniformly	uniformly	ADV
ap-920	55	98	recurrent	recurrent	ADJ
ap-920	55	99	if	if	SCONJ
ap-920	55	100	and	and	CCONJ
ap-920	55	101	only	only	ADV
ap-920	55	102	if	if	SCONJ
ap-920	55	103	ru(n	ru(n	NOUN
ap-920	55	104	)	)	PUNCT
ap-920	55	105	is	be	AUX
ap-920	55	106	finite	finite	ADJ
ap-920	55	107	for	for	ADP
ap-920	55	108	every	every	DET
ap-920	55	109	n	n	PRON
ap-920	55	110	�	�	PROPN
ap-920	55	111	�	�	PROPN
ap-920	55	112	.	.	PUNCT
ap-920	55	113	to	to	PART
ap-920	55	114	get	get	VERB
ap-920	55	115	another	another	DET
ap-920	55	116	expression	expression	NOUN
ap-920	55	117	for	for	ADP
ap-920	55	118	ru(n	ru(n	NOUN
ap-920	55	119	)	)	PUNCT
ap-920	55	120	that	that	PRON
ap-920	55	121	is	be	AUX
ap-920	55	122	convenient	convenient	ADJ
ap-920	55	123	to	to	PART
ap-920	55	124	work	work	VERB
ap-920	55	125	with	with	ADP
ap-920	55	126	,	,	PUNCT
ap-920	55	127	let	let	VERB
ap-920	55	128	us	we	PRON
ap-920	55	129	introduce	introduce	VERB
ap-920	55	130	some	some	PRON
ap-920	55	131	more	more	ADJ
ap-920	55	132	terms	term	NOUN
ap-920	55	133	.	.	PUNCT
ap-920	56	1	definition	definition	NOUN
ap-920	56	2	4	4	NUM
ap-920	56	3	let	let	VERB
ap-920	56	4	u	u	PRON
ap-920	56	5	be	be	AUX
ap-920	56	6	an	an	DET
ap-920	56	7	infinite	infinite	ADJ
ap-920	56	8	uniformly	uniformly	ADV
ap-920	56	9	recurrent	recurrent	ADJ
ap-920	56	10	word	word	NOUN
ap-920	56	11	.	.	PUNCT
ap-920	57	1	�	�	PROPN
ap-920	57	2	let	let	VERB
ap-920	57	3	w	w	PART
ap-920	57	4	u	u	PROPN
ap-920	57	5	�	�	PROPN
ap-920	57	6	�	�	PROPN
ap-920	57	7	(	(	PUNCT
ap-920	57	8	)	)	PUNCT
ap-920	57	9	,	,	PUNCT
ap-920	57	10	then	then	ADV
ap-920	57	11	l	l	PROPN
ap-920	57	12	w	w	PROPN
ap-920	57	13	v	v	X
ap-920	57	14	v	v	NUM
ap-920	57	15	wu	wu	PROPN
ap-920	57	16	(	(	PUNCT
ap-920	57	17	)	)	PUNCT
ap-920	57	18	max	max	PROPN
ap-920	57	19	(	(	PUNCT
ap-920	57	20	)	)	PUNCT
ap-920	57	21	�	�	PROPN
ap-920	57	22	�	�	PROPN
ap-920	57	23	ret	ret	PROPN
ap-920	57	24	is	be	AUX
ap-920	57	25	the	the	DET
ap-920	57	26	maximal	maximal	ADJ
ap-920	57	27	return	return	NOUN
ap-920	57	28	time	time	NOUN
ap-920	57	29	of	of	ADP
ap-920	57	30	w	w	NOUN
ap-920	57	31	in	in	ADP
ap-920	57	32	u.	u.	PROPN
ap-920	57	33	�	�	PROPN
ap-920	57	34	for	for	ADP
ap-920	57	35	all	all	DET
ap-920	57	36	n	n	PRON
ap-920	57	37	�	�	PROPN
ap-920	57	38	�	�	PROPN
ap-920	57	39	,	,	PUNCT
ap-920	57	40	we	we	PRON
ap-920	57	41	define	define	VERB
ap-920	57	42	l	l	NOUN
ap-920	57	43	n	n	NUM
ap-920	57	44	l	l	NOUN
ap-920	57	45	w	w	PROPN
ap-920	57	46	w	w	PROPN
ap-920	57	47	uu	uu	PRON
ap-920	57	48	u	u	NOUN
ap-920	57	49	n	n	CCONJ
ap-920	57	50	(	(	PUNCT
ap-920	57	51	)	)	PUNCT
ap-920	57	52	max	max	PROPN
ap-920	57	53	(	(	PUNCT
ap-920	57	54	)	)	PUNCT
ap-920	57	55	(	(	PUNCT
ap-920	57	56	)	)	PUNCT
ap-920	57	57	�	�	PROPN
ap-920	57	58	�	�	PROPN
ap-920	57	59	�	�	PROPN
ap-920	57	60	.	.	PUNCT
ap-920	58	1	once	once	SCONJ
ap-920	58	2	we	we	PRON
ap-920	58	3	have	have	AUX
ap-920	58	4	determined	determine	VERB
ap-920	58	5	the	the	DET
ap-920	58	6	lengths	length	NOUN
ap-920	58	7	of	of	ADP
ap-920	58	8	the	the	DET
ap-920	58	9	return	return	NOUN
ap-920	58	10	words	word	NOUN
ap-920	58	11	,	,	PUNCT
ap-920	58	12	the	the	DET
ap-920	58	13	following	follow	VERB
ap-920	58	14	proposition	proposition	NOUN
ap-920	58	15	from	from	ADP
ap-920	58	16	[	[	X
ap-920	58	17	5	5	NUM
ap-920	58	18	]	]	PUNCT
ap-920	58	19	will	will	AUX
ap-920	58	20	allow	allow	VERB
ap-920	58	21	us	we	PRON
ap-920	58	22	to	to	PART
ap-920	58	23	calculate	calculate	VERB
ap-920	58	24	the	the	DET
ap-920	58	25	recurrence	recurrence	NOUN
ap-920	58	26	function	function	NOUN
ap-920	58	27	ru(n	ru(n	NOUN
ap-920	58	28	)	)	PUNCT
ap-920	58	29	.	.	PUNCT
ap-920	59	1	proposition	proposition	NOUN
ap-920	59	2	5	5	NUM
ap-920	59	3	for	for	ADP
ap-920	59	4	any	any	DET
ap-920	59	5	infinite	infinite	ADJ
ap-920	59	6	uniformly	uniformly	ADV
ap-920	59	7	recurrent	recurrent	ADJ
ap-920	59	8	word	word	NOUN
ap-920	59	9	u	u	NOUN
ap-920	59	10	and	and	CCONJ
ap-920	59	11	for	for	ADP
ap-920	59	12	any	any	DET
ap-920	59	13	n	n	DET
ap-920	59	14	�	�	PROPN
ap-920	59	15	�	�	PROPN
ap-920	59	16	,	,	PUNCT
ap-920	59	17	one	one	NUM
ap-920	59	18	has	have	VERB
ap-920	59	19	r	r	NOUN
ap-920	59	20	n	n	ADP
ap-920	59	21	l	l	NOUN
ap-920	59	22	n	n	CCONJ
ap-920	59	23	nu	nu	INTJ
ap-920	59	24	u	u	NOUN
ap-920	59	25	(	(	PUNCT
ap-920	59	26	)	)	PUNCT
ap-920	59	27	(	(	PUNCT
ap-920	59	28	)	)	PUNCT
ap-920	59	29	�	�	PROPN
ap-920	59	30	�	�	PROPN
ap-920	59	31	�	�	PROPN
ap-920	59	32	1	1	NUM
ap-920	59	33	3	3	NUM
ap-920	59	34	return	return	NOUN
ap-920	59	35	words	word	NOUN
ap-920	59	36	the	the	DET
ap-920	59	37	aim	aim	NOUN
ap-920	59	38	of	of	ADP
ap-920	59	39	this	this	DET
ap-920	59	40	section	section	NOUN
ap-920	59	41	is	be	AUX
ap-920	59	42	to	to	PART
ap-920	59	43	determine	determine	VERB
ap-920	59	44	return	return	NOUN
ap-920	59	45	words	word	NOUN
ap-920	59	46	of	of	ADP
ap-920	59	47	the	the	DET
ap-920	59	48	infinite	infinite	ADJ
ap-920	59	49	word	word	NOUN
ap-920	59	50	u	u	NOUN
ap-920	59	51	�	�	PROPN
ap-920	59	52	being	be	AUX
ap-920	59	53	the	the	DET
ap-920	59	54	fixed	fix	VERB
ap-920	59	55	point	point	NOUN
ap-920	59	56	of	of	ADP
ap-920	59	57	the	the	DET
ap-920	59	58	substitution	substitution	NOUN
ap-920	59	59	�	�	PROPN
ap-920	59	60	introduced	introduce	VERB
ap-920	59	61	in	in	ADP
ap-920	59	62	(	(	PUNCT
ap-920	59	63	1	1	NUM
ap-920	59	64	)	)	PUNCT
ap-920	59	65	.	.	PUNCT
ap-920	60	1	vuillon	vuillon	NOUN
ap-920	60	2	in	in	ADP
ap-920	60	3	[	[	X
ap-920	60	4	1	1	NUM
ap-920	60	5	]	]	PUNCT
ap-920	60	6	has	have	AUX
ap-920	60	7	shown	show	VERB
ap-920	60	8	the	the	DET
ap-920	60	9	following	following	ADJ
ap-920	60	10	result	result	NOUN
ap-920	60	11	for	for	ADP
ap-920	60	12	sturmian	sturmian	NOUN
ap-920	60	13	words	word	NOUN
ap-920	60	14	.	.	PUNCT
ap-920	61	1	proposition	proposition	NOUN
ap-920	61	2	6	6	NUM
ap-920	61	3	let	let	VERB
ap-920	61	4	u	u	PRON
ap-920	61	5	be	be	AUX
ap-920	61	6	an	an	DET
ap-920	61	7	infinite	infinite	ADJ
ap-920	61	8	word	word	NOUN
ap-920	61	9	over	over	ADP
ap-920	61	10	a	a	DET
ap-920	61	11	two	two	NUM
ap-920	61	12	letter	letter	NOUN
ap-920	61	13	alphabet	alphabet	PROPN
ap-920	61	14	.	.	PUNCT
ap-920	62	1	then	then	ADV
ap-920	62	2	u	u	NOUN
ap-920	62	3	is	be	AUX
ap-920	62	4	sturmian	sturmian	ADJ
ap-920	62	5	if	if	SCONJ
ap-920	63	1	and	and	CCONJ
ap-920	63	2	only	only	ADV
ap-920	63	3	if	if	SCONJ
ap-920	63	4	#	#	NOUN
ap-920	63	5	(	(	PUNCT
ap-920	63	6	)	)	PUNCT
ap-920	63	7	ret	ret	PROPN
ap-920	63	8	w	w	PROPN
ap-920	63	9	�	�	PROPN
ap-920	63	10	2	2	NUM
ap-920	63	11	for	for	ADP
ap-920	63	12	every	every	DET
ap-920	63	13	factor	factor	NOUN
ap-920	63	14	w	w	PROPN
ap-920	63	15	of	of	ADP
ap-920	63	16	u.	u.	NOUN
ap-920	63	17	let	let	VERB
ap-920	63	18	us	we	PRON
ap-920	63	19	mention	mention	VERB
ap-920	63	20	that	that	SCONJ
ap-920	63	21	u	u	PROPN
ap-920	63	22	�	�	PROPN
ap-920	63	23	is	be	AUX
ap-920	63	24	sturmian	sturmian	NOUN
ap-920	63	25	for	for	ADP
ap-920	63	26	a	a	DET
ap-920	63	27	b	b	PROPN
ap-920	63	28	�	�	PROPN
ap-920	63	29	�	�	PROPN
ap-920	63	30	1	1	NUM
ap-920	63	31	,	,	PUNCT
ap-920	63	32	as	as	SCONJ
ap-920	63	33	follows	follow	VERB
ap-920	63	34	from	from	ADP
ap-920	63	35	[	[	X
ap-920	63	36	7	7	NUM
ap-920	63	37	]	]	PUNCT
ap-920	63	38	.	.	PUNCT
ap-920	64	1	example	example	NOUN
ap-920	64	2	7	7	NUM
ap-920	64	3	let	let	VERB
ap-920	64	4	u	u	PRON
ap-920	64	5	�	�	PROPN
ap-920	64	6	�	�	PROPN
ap-920	64	7	001001010010010100101	001001010010010100101	NUM
ap-920	64	8	�	�	PROPN
ap-920	64	9	be	be	AUX
ap-920	64	10	the	the	DET
ap-920	64	11	fixed	fix	VERB
ap-920	64	12	point	point	NOUN
ap-920	64	13	of	of	ADP
ap-920	64	14	the	the	DET
ap-920	64	15	substitution	substitution	NOUN
ap-920	64	16	�	�	PROPN
ap-920	64	17	�	�	PROPN
ap-920	64	18	(	(	PUNCT
ap-920	64	19	)	)	PUNCT
ap-920	64	20	,	,	PUNCT
ap-920	64	21	(	(	PUNCT
ap-920	64	22	)	)	PUNCT
ap-920	64	23	0	0	NUM
ap-920	64	24	001	001	NUM
ap-920	64	25	1	1	NUM
ap-920	64	26	01	01	NUM
ap-920	64	27	�	�	PROPN
ap-920	64	28	�	�	PROPN
ap-920	64	29	(	(	PUNCT
ap-920	64	30	sturmian	sturmian	NOUN
ap-920	64	31	case	case	NOUN
ap-920	64	32	)	)	PUNCT
ap-920	64	33	.	.	PUNCT
ap-920	65	1	let	let	VERB
ap-920	65	2	us	we	PRON
ap-920	65	3	show	show	VERB
ap-920	65	4	examples	example	NOUN
ap-920	65	5	of	of	ADP
ap-920	65	6	return	return	NOUN
ap-920	65	7	words	word	NOUN
ap-920	65	8	:	:	PUNCT
ap-920	65	9	ret	ret	NOUN
ap-920	65	10	(	(	PUNCT
ap-920	65	11	)	)	PUNCT
ap-920	65	12	{	{	PUNCT
ap-920	65	13	,	,	PUNCT
ap-920	65	14	}	}	PUNCT
ap-920	65	15	0	0	NUM
ap-920	65	16	0	0	NUM
ap-920	65	17	01	01	NUM
ap-920	65	18	�	�	PROPN
ap-920	65	19	ret	ret	PROPN
ap-920	65	20	(	(	PUNCT
ap-920	65	21	)	)	PUNCT
ap-920	65	22	{	{	PUNCT
ap-920	65	23	,	,	PUNCT
ap-920	65	24	}	}	PUNCT
ap-920	65	25	00	00	NUM
ap-920	65	26	001	001	NUM
ap-920	65	27	00101	00101	NUM
ap-920	65	28	�	�	PROPN
ap-920	65	29	ret	ret	PROPN
ap-920	65	30	(	(	PUNCT
ap-920	65	31	)	)	PUNCT
ap-920	65	32	{	{	PUNCT
ap-920	65	33	,	,	PUNCT
ap-920	65	34	}	}	PUNCT
ap-920	65	35	001	001	NUM
ap-920	65	36	001	001	NUM
ap-920	65	37	00101	00101	NUM
ap-920	65	38	�	�	PROPN
ap-920	65	39	ret	ret	PROPN
ap-920	65	40	(	(	PUNCT
ap-920	65	41	)	)	PUNCT
ap-920	65	42	{	{	PUNCT
ap-920	65	43	,	,	PUNCT
ap-920	65	44	}	}	PUNCT
ap-920	65	45	0010	0010	NUM
ap-920	65	46	001	001	NUM
ap-920	65	47	00101	00101	NUM
ap-920	65	48	�	�	PROPN
ap-920	65	49	throughout	throughout	ADP
ap-920	65	50	this	this	DET
ap-920	65	51	section	section	NOUN
ap-920	65	52	,	,	PUNCT
ap-920	65	53	we	we	PRON
ap-920	65	54	will	will	AUX
ap-920	65	55	use	use	VERB
ap-920	65	56	methods	method	NOUN
ap-920	65	57	analogous	analogous	ADJ
ap-920	65	58	to	to	ADP
ap-920	65	59	those	those	DET
ap-920	65	60	ones	one	NOUN
ap-920	65	61	introduced	introduce	VERB
ap-920	65	62	in	in	ADP
ap-920	65	63	[	[	X
ap-920	65	64	4	4	NUM
ap-920	65	65	]	]	PUNCT
ap-920	65	66	.	.	PUNCT
ap-920	66	1	in	in	ADP
ap-920	66	2	order	order	NOUN
ap-920	66	3	to	to	PART
ap-920	66	4	study	study	VERB
ap-920	66	5	return	return	NOUN
ap-920	66	6	words	word	NOUN
ap-920	66	7	ret(w	ret(w	NOUN
ap-920	66	8	)	)	PUNCT
ap-920	66	9	of	of	ADP
ap-920	66	10	factors	factor	NOUN
ap-920	66	11	w	w	ADP
ap-920	66	12	of	of	ADP
ap-920	66	13	an	an	DET
ap-920	66	14	infinite	infinite	ADJ
ap-920	66	15	uniformly	uniformly	ADV
ap-920	66	16	recurrent	recurrent	ADJ
ap-920	66	17	word	word	NOUN
ap-920	66	18	u	u	NOUN
ap-920	66	19	,	,	PUNCT
ap-920	66	20	it	it	PRON
ap-920	66	21	is	be	AUX
ap-920	66	22	possible	possible	ADJ
ap-920	66	23	to	to	PART
ap-920	66	24	limit	limit	VERB
ap-920	66	25	our	our	PRON
ap-920	66	26	considerations	consideration	NOUN
ap-920	66	27	to	to	ADP
ap-920	66	28	bispecial	bispecial	ADJ
ap-920	66	29	factors	factor	NOUN
ap-920	66	30	.	.	PUNCT
ap-920	67	1	namely	namely	ADV
ap-920	67	2	,	,	PUNCT
ap-920	67	3	if	if	SCONJ
ap-920	67	4	a	a	DET
ap-920	67	5	factor	factor	NOUN
ap-920	67	6	w	w	NOUN
ap-920	67	7	is	be	AUX
ap-920	67	8	not	not	PART
ap-920	67	9	right	right	ADJ
ap-920	67	10	special	special	ADJ
ap-920	67	11	,	,	PUNCT
ap-920	67	12	i.e.	i.e.	X
ap-920	67	13	,	,	PUNCT
ap-920	67	14	if	if	SCONJ
ap-920	67	15	it	it	PRON
ap-920	67	16	has	have	VERB
ap-920	67	17	a	a	DET
ap-920	67	18	unique	unique	ADJ
ap-920	67	19	right	right	ADJ
ap-920	67	20	extension	extension	NOUN
ap-920	67	21	a	a	DET
ap-920	67	22	�	�	PROPN
ap-920	67	23	�	�	PROPN
ap-920	67	24	,	,	PUNCT
ap-920	67	25	then	then	ADV
ap-920	67	26	the	the	DET
ap-920	67	27	sets	set	NOUN
ap-920	67	28	of	of	ADP
ap-920	67	29	occurrences	occurrence	NOUN
ap-920	67	30	of	of	ADP
ap-920	67	31	w	w	NOUN
ap-920	67	32	and	and	CCONJ
ap-920	67	33	wa	wa	ADJ
ap-920	67	34	coincide	coincide	NOUN
ap-920	67	35	,	,	PUNCT
ap-920	67	36	and	and	CCONJ
ap-920	67	37	ret	ret	PROPN
ap-920	67	38	ret	ret	PROPN
ap-920	67	39	(	(	PUNCT
ap-920	67	40	)	)	PUNCT
ap-920	67	41	(	(	PUNCT
ap-920	67	42	)	)	PUNCT
ap-920	67	43	w	w	PROPN
ap-920	67	44	wa	wa	PROPN
ap-920	67	45	�	�	PROPN
ap-920	67	46	(	(	PUNCT
ap-920	67	47	2	2	NUM
ap-920	67	48	)	)	PUNCT
ap-920	68	1	if	if	SCONJ
ap-920	68	2	a	a	DET
ap-920	68	3	factor	factor	NOUN
ap-920	68	4	w	w	NOUN
ap-920	68	5	has	have	VERB
ap-920	68	6	a	a	DET
ap-920	68	7	unique	unique	ADJ
ap-920	68	8	left	left	ADJ
ap-920	68	9	extension	extension	NOUN
ap-920	68	10	b	b	PROPN
ap-920	68	11	�	�	PROPN
ap-920	68	12	�	�	PROPN
ap-920	68	13	,	,	PUNCT
ap-920	68	14	then	then	ADV
ap-920	68	15	j	j	PROPN
ap-920	68	16	�	�	PROPN
ap-920	68	17	1is	1is	PROPN
ap-920	68	18	an	an	DET
ap-920	68	19	occurrence	occurrence	NOUN
ap-920	68	20	of	of	ADP
ap-920	68	21	w	w	NOUN
ap-920	68	22	in	in	ADP
ap-920	68	23	the	the	DET
ap-920	68	24	infinite	infinite	ADJ
ap-920	68	25	word	word	NOUN
ap-920	68	26	u	u	NOUN
ap-920	68	27	if	if	SCONJ
ap-920	68	28	and	and	CCONJ
ap-920	68	29	only	only	ADV
ap-920	68	30	if	if	SCONJ
ap-920	68	31	j	j	PROPN
ap-920	68	32	�	�	PROPN
ap-920	68	33	1	1	NUM
ap-920	68	34	is	be	AUX
ap-920	68	35	an	an	DET
ap-920	68	36	occurrence	occurrence	NOUN
ap-920	68	37	of	of	ADP
ap-920	68	38	bw	bw	NOUN
ap-920	68	39	.	.	PUNCT
ap-920	69	1	this	this	DET
ap-920	69	2	statement	statement	NOUN
ap-920	69	3	does	do	AUX
ap-920	69	4	not	not	PART
ap-920	69	5	hold	hold	VERB
ap-920	69	6	for	for	ADP
ap-920	69	7	j	j	PROPN
ap-920	69	8	�	�	PROPN
ap-920	69	9	0	0	NUM
ap-920	69	10	.	.	PUNCT
ap-920	70	1	nevertheless	nevertheless	ADV
ap-920	70	2	,	,	PUNCT
ap-920	70	3	if	if	SCONJ
ap-920	70	4	u	u	NOUN
ap-920	70	5	is	be	AUX
ap-920	70	6	a	a	DET
ap-920	70	7	uniformly	uniformly	ADV
ap-920	70	8	recurrent	recurrent	ADJ
ap-920	70	9	infinite	infinite	ADJ
ap-920	70	10	word	word	NOUN
ap-920	70	11	,	,	PUNCT
ap-920	70	12	then	then	ADV
ap-920	70	13	the	the	DET
ap-920	70	14	set	set	NOUN
ap-920	70	15	ret(w	ret(w	PROPN
ap-920	70	16	)	)	PUNCT
ap-920	70	17	of	of	ADP
ap-920	70	18	return	return	NOUN
ap-920	70	19	words	word	NOUN
ap-920	70	20	of	of	ADP
ap-920	70	21	w	w	NOUN
ap-920	70	22	stays	stay	VERB
ap-920	70	23	the	the	DET
ap-920	70	24	same	same	ADJ
ap-920	70	25	no	no	ADV
ap-920	70	26	matter	matter	ADV
ap-920	70	27	whether	whether	SCONJ
ap-920	70	28	we	we	PRON
ap-920	70	29	include	include	VERB
ap-920	70	30	the	the	DET
ap-920	70	31	return	return	NOUN
ap-920	70	32	word	word	NOUN
ap-920	70	33	corresponding	correspond	VERB
ap-920	70	34	to	to	ADP
ap-920	70	35	the	the	DET
ap-920	70	36	prefix	prefix	NOUN
ap-920	70	37	w	w	NOUN
ap-920	70	38	of	of	ADP
ap-920	70	39	u	u	NOUN
ap-920	70	40	or	or	CCONJ
ap-920	70	41	not	not	PART
ap-920	70	42	.	.	PUNCT
ap-920	71	1	consequently	consequently	ADV
ap-920	71	2	,	,	PUNCT
ap-920	71	3	we	we	PRON
ap-920	71	4	have	have	VERB
ap-920	71	5	ret	ret	PROPN
ap-920	71	6	ret	ret	PROPN
ap-920	71	7	ret	ret	PROPN
ap-920	71	8	(	(	PUNCT
ap-920	71	9	)	)	PUNCT
ap-920	71	10	(	(	PUNCT
ap-920	71	11	)	)	PUNCT
ap-920	71	12	(	(	PUNCT
ap-920	71	13	)	)	PUNCT
ap-920	71	14	bw	bw	PROPN
ap-920	71	15	b	b	PROPN
ap-920	71	16	w	w	PROPN
ap-920	71	17	b	b	PROPN
ap-920	71	18	bvb	bvb	NOUN
ap-920	71	19	v	v	PROPN
ap-920	71	20	w	w	PROPN
ap-920	71	21	�	�	PROPN
ap-920	71	22	�	�	PROPN
ap-920	71	23	�	�	PROPN
ap-920	71	24	�	�	PROPN
ap-920	71	25	�	�	PROPN
ap-920	71	26	1	1	NUM
ap-920	71	27	1	1	NUM
ap-920	71	28	,	,	PUNCT
ap-920	71	29	(	(	PUNCT
ap-920	71	30	3	3	X
ap-920	71	31	)	)	PUNCT
ap-920	71	32	where	where	SCONJ
ap-920	71	33	bvb	bvb	NOUN
ap-920	71	34	�	�	PROPN
ap-920	71	35	1	1	NUM
ap-920	71	36	means	mean	VERB
ap-920	71	37	that	that	SCONJ
ap-920	71	38	the	the	DET
ap-920	71	39	word	word	NOUN
ap-920	71	40	v	v	NOUN
ap-920	71	41	is	be	AUX
ap-920	71	42	extended	extend	VERB
ap-920	71	43	to	to	ADP
ap-920	71	44	the	the	DET
ap-920	71	45	left	leave	VERB
ap-920	71	46	by	by	ADP
ap-920	71	47	the	the	DET
ap-920	71	48	letter	letter	NOUN
ap-920	71	49	b	b	PROPN
ap-920	71	50	and	and	CCONJ
ap-920	71	51	the	the	DET
ap-920	71	52	letter	letter	NOUN
ap-920	71	53	b	b	PROPN
ap-920	71	54	on	on	ADP
ap-920	71	55	the	the	DET
ap-920	71	56	right	right	ADJ
ap-920	71	57	end	end	NOUN
ap-920	71	58	is	be	AUX
ap-920	71	59	erased	erase	VERB
ap-920	71	60	(	(	PUNCT
ap-920	71	61	note	note	VERB
ap-920	71	62	that	that	SCONJ
ap-920	71	63	b	b	NOUN
ap-920	71	64	is	be	AUX
ap-920	71	65	always	always	ADV
ap-920	71	66	the	the	DET
ap-920	71	67	suffix	suffix	NOUN
ap-920	71	68	of	of	ADP
ap-920	71	69	v	v	NOUN
ap-920	71	70	for	for	ADP
ap-920	71	71	v	v	PRON
ap-920	71	72	w	w	PROPN
ap-920	71	73	�	�	PROPN
ap-920	71	74	ret	ret	PROPN
ap-920	71	75	(	(	PUNCT
ap-920	71	76	)	)	PUNCT
ap-920	71	77	)	)	PUNCT
ap-920	71	78	.	.	PUNCT
ap-920	72	1	observation	observation	NOUN
ap-920	72	2	8	8	NUM
ap-920	72	3	note	note	VERB
ap-920	72	4	that	that	SCONJ
ap-920	72	5	relation	relation	NOUN
ap-920	72	6	(	(	PUNCT
ap-920	72	7	2	2	NUM
ap-920	72	8	)	)	PUNCT
ap-920	72	9	implies	imply	VERB
ap-920	72	10	that	that	SCONJ
ap-920	72	11	if	if	SCONJ
ap-920	72	12	w	w	PROPN
ap-920	72	13	u	u	PROPN
ap-920	72	14	�	�	PROPN
ap-920	72	15	�	�	PROPN
ap-920	72	16	(	(	PUNCT
ap-920	72	17	)	)	PUNCT
ap-920	72	18	is	be	AUX
ap-920	72	19	not	not	PART
ap-920	72	20	right	right	ADJ
ap-920	72	21	special	special	ADJ
ap-920	72	22	,	,	PUNCT
ap-920	72	23	then	then	ADV
ap-920	72	24	the	the	DET
ap-920	72	25	maximal	maximal	ADJ
ap-920	72	26	return	return	NOUN
ap-920	72	27	times	time	NOUN
ap-920	72	28	from	from	ADP
ap-920	72	29	definition	definition	NOUN
ap-920	72	30	4	4	NUM
ap-920	72	31	satisfy	satisfy	NOUN
ap-920	72	32	l	l	PROPN
ap-920	72	33	w	w	PROPN
ap-920	72	34	l	l	PROPN
ap-920	72	35	wau	wau	PROPN
ap-920	72	36	u	u	PROPN
ap-920	72	37	(	(	PUNCT
ap-920	72	38	)	)	PUNCT
ap-920	72	39	(	(	PUNCT
ap-920	72	40	)	)	PUNCT
ap-920	72	41	�	�	PROPN
ap-920	72	42	,	,	PUNCT
ap-920	72	43	where	where	SCONJ
ap-920	72	44	a	a	DET
ap-920	72	45	�	�	PROPN
ap-920	72	46	�	�	PROPN
ap-920	72	47	is	be	AUX
ap-920	72	48	the	the	DET
ap-920	72	49	only	only	ADJ
ap-920	72	50	right	right	ADJ
ap-920	72	51	extension	extension	NOUN
ap-920	72	52	of	of	ADP
ap-920	72	53	w.	w.	NOUN
ap-920	72	54	similarly	similarly	ADV
ap-920	72	55	,	,	PUNCT
ap-920	72	56	relation	relation	NOUN
ap-920	72	57	(	(	PUNCT
ap-920	72	58	3	3	NUM
ap-920	72	59	)	)	PUNCT
ap-920	72	60	implies	imply	VERB
ap-920	72	61	that	that	SCONJ
ap-920	72	62	if	if	SCONJ
ap-920	72	63	w	w	NOUN
ap-920	72	64	is	be	AUX
ap-920	72	65	not	not	PART
ap-920	72	66	left	leave	VERB
ap-920	72	67	special	special	ADJ
ap-920	72	68	,	,	PUNCT
ap-920	72	69	then	then	ADV
ap-920	72	70	l	l	PROPN
ap-920	72	71	w	w	PROPN
ap-920	72	72	l	l	PROPN
ap-920	72	73	bwu	bwu	NOUN
ap-920	72	74	u	u	PROPN
ap-920	72	75	(	(	PUNCT
ap-920	72	76	)	)	PUNCT
ap-920	72	77	(	(	PUNCT
ap-920	72	78	)	)	PUNCT
ap-920	72	79	�	�	PROPN
ap-920	72	80	,	,	PUNCT
ap-920	72	81	where	where	SCONJ
ap-920	72	82	b	b	X
ap-920	72	83	�	�	PROPN
ap-920	72	84	�	�	PROPN
ap-920	72	85	is	be	AUX
ap-920	72	86	the	the	DET
ap-920	72	87	only	only	ADJ
ap-920	72	88	left	left	ADJ
ap-920	72	89	extension	extension	NOUN
ap-920	72	90	of	of	ADP
ap-920	72	91	w.	w.	NOUN
ap-920	72	92	for	for	ADP
ap-920	72	93	an	an	DET
ap-920	72	94	aperiodic	aperiodic	ADJ
ap-920	72	95	uniformly	uniformly	ADJ
ap-920	72	96	recurrent	recurrent	ADJ
ap-920	72	97	infinite	infinite	ADJ
ap-920	72	98	word	word	NOUN
ap-920	72	99	u	u	NOUN
ap-920	72	100	,	,	PUNCT
ap-920	72	101	each	each	DET
ap-920	72	102	factor	factor	NOUN
ap-920	72	103	w	w	PROPN
ap-920	72	104	can	can	AUX
ap-920	72	105	be	be	AUX
ap-920	72	106	extended	extend	VERB
ap-920	72	107	to	to	ADP
ap-920	72	108	the	the	DET
ap-920	72	109	left	left	NOUN
ap-920	72	110	and	and	CCONJ
ap-920	72	111	to	to	ADP
ap-920	72	112	the	the	DET
ap-920	72	113	right	right	NOUN
ap-920	72	114	to	to	ADP
ap-920	72	115	a	a	DET
ap-920	72	116	bispecial	bispecial	ADJ
ap-920	72	117	factor	factor	NOUN
ap-920	72	118	.	.	PUNCT
ap-920	73	1	to	to	PART
ap-920	73	2	describe	describe	VERB
ap-920	73	3	the	the	DET
ap-920	73	4	cardinality	cardinality	NOUN
ap-920	73	5	of	of	ADP
ap-920	73	6	ret	ret	PROPN
ap-920	73	7	(	(	PUNCT
ap-920	73	8	)	)	PUNCT
ap-920	73	9	w	w	NOUN
ap-920	73	10	,	,	PUNCT
ap-920	73	11	it	it	PRON
ap-920	73	12	suffices	suffice	VERB
ap-920	73	13	therefore	therefore	ADV
ap-920	73	14	to	to	PART
ap-920	73	15	consider	consider	VERB
ap-920	73	16	bispecial	bispecial	ADJ
ap-920	73	17	factors	factor	NOUN
ap-920	73	18	w.	w.	NOUN
ap-920	73	19	observation	observation	NOUN
ap-920	73	20	9	9	NUM
ap-920	73	21	the	the	DET
ap-920	73	22	only	only	ADJ
ap-920	73	23	bispecial	bispecial	ADJ
ap-920	73	24	factors	factor	NOUN
ap-920	73	25	of	of	ADP
ap-920	73	26	u	u	NOUN
ap-920	73	27	�	�	PROPN
ap-920	73	28	that	that	PRON
ap-920	73	29	do	do	AUX
ap-920	73	30	not	not	PART
ap-920	73	31	contain	contain	VERB
ap-920	73	32	the	the	DET
ap-920	73	33	letter	letter	NOUN
ap-920	73	34	1	1	NUM
ap-920	73	35	are	be	AUX
ap-920	73	36	0r	0r	NUM
ap-920	73	37	,	,	PUNCT
ap-920	73	38	r	r	PROPN
ap-920	73	39	a	a	DET
ap-920	73	40	�	�	PROPN
ap-920	73	41	�	�	PROPN
ap-920	73	42	1	1	NUM
ap-920	73	43	.	.	PUNCT
ap-920	74	1	observation	observation	NOUN
ap-920	74	2	10	10	NUM
ap-920	74	3	every	every	DET
ap-920	74	4	bispecial	bispecial	ADJ
ap-920	74	5	factor	factor	NOUN
ap-920	74	6	w	w	PROPN
ap-920	74	7	of	of	ADP
ap-920	74	8	u	u	PROPN
ap-920	74	9	�	�	PROPN
ap-920	74	10	containing	contain	VERB
ap-920	74	11	at	at	ADV
ap-920	74	12	least	least	ADV
ap-920	74	13	one	one	NUM
ap-920	74	14	letter	letter	NOUN
ap-920	74	15	1	1	NUM
ap-920	74	16	has	have	VERB
ap-920	74	17	the	the	DET
ap-920	74	18	prefix	prefix	NOUN
ap-920	74	19	0b1	0b1	NOUN
ap-920	74	20	and	and	CCONJ
ap-920	74	21	the	the	DET
ap-920	74	22	suffix	suffix	PROPN
ap-920	74	23	10b	10b	NOUN
ap-920	74	24	.	.	PUNCT
ap-920	75	1	consequently	consequently	ADV
ap-920	75	2	,	,	PUNCT
ap-920	75	3	there	there	PRON
ap-920	75	4	exists	exist	VERB
ap-920	75	5	a	a	DET
ap-920	75	6	bispecial	bispecial	ADJ
ap-920	75	7	factor	factor	NOUN
ap-920	75	8	v	v	ADP
ap-920	75	9	such	such	DET
ap-920	75	10	that	that	SCONJ
ap-920	75	11	w	w	PROPN
ap-920	75	12	vb	vb	PROPN
ap-920	75	13	b	b	PROPN
ap-920	75	14	�	�	PROPN
ap-920	75	15	0	0	NUM
ap-920	75	16	1	1	NUM
ap-920	75	17	0	0	NUM
ap-920	75	18	�	�	PROPN
ap-920	75	19	(	(	PUNCT
ap-920	75	20	)	)	PUNCT
ap-920	75	21	.	.	PUNCT
ap-920	76	1	(	(	PUNCT
ap-920	76	2	the	the	DET
ap-920	76	3	empty	empty	ADJ
ap-920	76	4	word	word	NOUN
ap-920	76	5	�	�	PROPN
ap-920	76	6	is	be	AUX
ap-920	76	7	bispecial	bispecial	ADJ
ap-920	76	8	,	,	PUNCT
ap-920	76	9	too	too	ADV
ap-920	76	10	.	.	PUNCT
ap-920	76	11	)	)	PUNCT
ap-920	77	1	let	let	VERB
ap-920	77	2	us	we	PRON
ap-920	77	3	summarize	summarize	VERB
ap-920	77	4	the	the	DET
ap-920	77	5	previous	previous	ADJ
ap-920	77	6	observations	observation	NOUN
ap-920	77	7	to	to	PART
ap-920	77	8	get	get	VERB
ap-920	77	9	the	the	DET
ap-920	77	10	description	description	NOUN
ap-920	77	11	of	of	ADP
ap-920	77	12	all	all	DET
ap-920	77	13	bispecial	bispecial	ADJ
ap-920	77	14	factors	factor	NOUN
ap-920	77	15	.	.	PUNCT
ap-920	78	1	corollary	corollary	ADJ
ap-920	78	2	11	11	NUM
ap-920	78	3	the	the	DET
ap-920	78	4	set	set	NOUN
ap-920	78	5	of	of	ADP
ap-920	78	6	all	all	DET
ap-920	78	7	the	the	DET
ap-920	78	8	bispecial	bispecial	ADJ
ap-920	78	9	factors	factor	NOUN
ap-920	78	10	of	of	ADP
ap-920	78	11	u	u	NOUN
ap-920	78	12	�	�	PROPN
ap-920	78	13	is	be	AUX
ap-920	78	14	given	give	VERB
ap-920	78	15	by	by	ADP
ap-920	78	16	b	b	PROPN
ap-920	78	17	r	r	NOUN
ap-920	78	18	a	a	DET
ap-920	78	19	nr	nr	NOUN
ap-920	78	20	n	n	CCONJ
ap-920	78	21	(	(	PUNCT
ap-920	78	22	)	)	PUNCT
ap-920	78	23	,	,	PUNCT
ap-920	78	24	,	,	PUNCT
ap-920	78	25	,	,	PUNCT
ap-920	78	26	�	�	PROPN
ap-920	78	27	�	�	PROPN
ap-920	78	28	�	�	PROPN
ap-920	78	29	0	0	NUM
ap-920	78	30	1	1	NUM
ap-920	78	31	�	�	PROPN
ap-920	78	32	�	�	PROPN
ap-920	78	33	,	,	PUNCT
ap-920	78	34	where	where	SCONJ
ap-920	78	35	b	b	X
ap-920	78	36	br	br	NOUN
ap-920	78	37	n	n	NOUN
ap-920	78	38	b	b	NOUN
ap-920	78	39	r	r	NOUN
ap-920	78	40	n	n	SYM
ap-920	78	41	b	b	NOUN
ap-920	78	42	(	(	PUNCT
ap-920	78	43	)	)	PUNCT
ap-920	78	44	(	(	PUNCT
ap-920	78	45	)	)	PUNCT
ap-920	78	46	(	(	PUNCT
ap-920	78	47	)	)	PUNCT
ap-920	78	48	�	�	PROPN
ap-920	78	49	�	�	PROPN
ap-920	78	50	1	1	NUM
ap-920	78	51	0	0	NUM
ap-920	78	52	1	1	NUM
ap-920	78	53	0	0	NUM
ap-920	78	54	�	�	PROPN
ap-920	78	55	for	for	ADP
ap-920	78	56	all	all	DET
ap-920	78	57	n	n	PRON
ap-920	78	58	�	�	PROPN
ap-920	78	59	�	�	PROPN
ap-920	78	60	,	,	PUNCT
ap-920	78	61	b0	b0	PROPN
ap-920	78	62	1	1	NUM
ap-920	78	63	(	(	PUNCT
ap-920	78	64	)	)	PUNCT
ap-920	78	65	�	�	PROPN
ap-920	78	66	�	�	PROPN
ap-920	78	67	,	,	PUNCT
ap-920	78	68	and	and	CCONJ
ap-920	78	69	br	br	NOUN
ap-920	78	70	r	r	NOUN
ap-920	78	71	(	(	PUNCT
ap-920	78	72	)	)	PUNCT
ap-920	78	73	1	1	NUM
ap-920	78	74	0	0	NUM
ap-920	78	75	�	�	PROPN
ap-920	78	76	for	for	ADP
ap-920	78	77	r	r	PROPN
ap-920	78	78	a	a	DET
ap-920	78	79	�	�	PROPN
ap-920	78	80	�	�	PROPN
ap-920	78	81	0	0	NUM
ap-920	78	82	1	1	NUM
ap-920	78	83	,	,	PUNCT
ap-920	78	84	,	,	PUNCT
ap-920	78	85	�	�	PROPN
ap-920	78	86	.	.	PUNCT
ap-920	79	1	in	in	ADP
ap-920	79	2	order	order	NOUN
ap-920	79	3	to	to	PART
ap-920	79	4	find	find	VERB
ap-920	79	5	return	return	NOUN
ap-920	79	6	words	word	NOUN
ap-920	79	7	of	of	ADP
ap-920	79	8	bispecial	bispecial	ADJ
ap-920	79	9	factors	factor	NOUN
ap-920	79	10	,	,	PUNCT
ap-920	79	11	let	let	VERB
ap-920	79	12	us	we	PRON
ap-920	79	13	recall	recall	VERB
ap-920	79	14	a	a	DET
ap-920	79	15	lemma	lemma	PROPN
ap-920	79	16	from	from	ADP
ap-920	79	17	[	[	X
ap-920	79	18	4	4	NUM
ap-920	79	19	]	]	PUNCT
ap-920	79	20	.	.	PUNCT
ap-920	80	1	to	to	PART
ap-920	80	2	formulate	formulate	VERB
ap-920	80	3	it	it	PRON
ap-920	80	4	,	,	PUNCT
ap-920	80	5	we	we	PRON
ap-920	80	6	also	also	ADV
ap-920	80	7	need	need	VERB
ap-920	80	8	to	to	PART
ap-920	80	9	recall	recall	VERB
ap-920	80	10	a	a	DET
ap-920	80	11	definition	definition	NOUN
ap-920	80	12	.	.	PUNCT
ap-920	81	1	definition	definition	NOUN
ap-920	81	2	12	12	NUM
ap-920	81	3	let	let	VERB
ap-920	81	4	w	w	NOUN
ap-920	81	5	be	be	AUX
ap-920	81	6	a	a	DET
ap-920	81	7	factor	factor	NOUN
ap-920	81	8	of	of	ADP
ap-920	81	9	a	a	DET
ap-920	81	10	fixed	fix	VERB
ap-920	81	11	point	point	NOUN
ap-920	81	12	u	u	NOUN
ap-920	81	13	of	of	ADP
ap-920	81	14	a	a	DET
ap-920	81	15	substitution	substitution	NOUN
ap-920	81	16	�	�	NOUN
ap-920	81	17	.	.	PUNCT
ap-920	82	1	we	we	PRON
ap-920	82	2	say	say	VERB
ap-920	82	3	that	that	SCONJ
ap-920	82	4	a	a	DET
ap-920	82	5	word	word	NOUN
ap-920	82	6	v	v	ADP
ap-920	82	7	v	v	NUM
ap-920	82	8	v	v	NUM
ap-920	82	9	v	v	NOUN
ap-920	82	10	un	un	PROPN
ap-920	82	11	n	n	PROPN
ap-920	82	12	n0	n0	NUM
ap-920	82	13	1	1	NUM
ap-920	82	14	1	1	NUM
ap-920	82	15	1	1	NUM
ap-920	82	16	�	�	PROPN
ap-920	82	17	�	�	PROPN
ap-920	82	18	�	�	PROPN
ap-920	82	19	�	�	PROPN
ap-920	82	20	�	�	PROPN
ap-920	82	21	(	(	PUNCT
ap-920	82	22	)	)	PUNCT
ap-920	82	23	is	be	AUX
ap-920	82	24	an	an	DET
ap-920	82	25	ancestor	ancestor	NOUN
ap-920	82	26	of	of	ADP
ap-920	82	27	w	w	PROPN
ap-920	82	28	if	if	SCONJ
ap-920	82	29	�	�	PROPN
ap-920	82	30	w	w	PROPN
ap-920	82	31	is	be	AUX
ap-920	82	32	a	a	DET
ap-920	82	33	factor	factor	NOUN
ap-920	82	34	of	of	ADP
ap-920	82	35	�	�	PROPN
ap-920	82	36	�	�	PROPN
ap-920	82	37	v	v	NOUN
ap-920	82	38	v	v	NOUN
ap-920	82	39	v	v	PROPN
ap-920	82	40	vn	vn	PROPN
ap-920	82	41	n0	n0	NUM
ap-920	82	42	1	1	NUM
ap-920	82	43	1	1	NUM
ap-920	82	44	�	�	PROPN
ap-920	82	45	�	�	PROPN
ap-920	82	46	)	)	PUNCT
ap-920	82	47	,	,	PUNCT
ap-920	82	48	16	16	NUM
ap-920	82	49	©	©	PROPN
ap-920	82	50	czech	czech	PROPN
ap-920	82	51	technical	technical	PROPN
ap-920	82	52	university	university	PROPN
ap-920	82	53	publishing	publishing	NOUN
ap-920	82	54	house	house	NOUN
ap-920	82	55	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-920	82	56	acta	acta	PROPN
ap-920	82	57	polytechnica	polytechnica	PROPN
ap-920	82	58	vol	vol	NOUN
ap-920	82	59	.	.	PUNCT
ap-920	83	1	47	47	NUM
ap-920	83	2	no	no	NOUN
ap-920	83	3	.	.	PUNCT
ap-920	84	1	2–3/2007	2–3/2007	NUM
ap-920	84	2	�	�	PROPN
ap-920	84	3	w	w	PROPN
ap-920	84	4	is	be	AUX
ap-920	84	5	neither	neither	CCONJ
ap-920	84	6	a	a	DET
ap-920	84	7	factor	factor	NOUN
ap-920	84	8	of	of	ADP
ap-920	84	9	�	�	PROPN
ap-920	84	10	�	�	PROPN
ap-920	84	11	v	v	NOUN
ap-920	84	12	v	v	NOUN
ap-920	84	13	vn	vn	ADP
ap-920	84	14	n1	n1	PROPN
ap-920	84	15	1	1	NUM
ap-920	84	16	�	�	PROPN
ap-920	84	17	�	�	PROPN
ap-920	84	18	)	)	PUNCT
ap-920	84	19	nor	nor	CCONJ
ap-920	84	20	of	of	ADP
ap-920	84	21	�	�	PROPN
ap-920	84	22	�	�	PROPN
ap-920	84	23	v	v	NOUN
ap-920	84	24	v	v	NOUN
ap-920	84	25	v	v	PROPN
ap-920	84	26	vn	vn	PROPN
ap-920	84	27	n0	n0	NUM
ap-920	84	28	1	1	NUM
ap-920	84	29	1	1	NUM
ap-920	84	30	�	�	PROPN
ap-920	84	31	�	�	PROPN
ap-920	84	32	)	)	PUNCT
ap-920	84	33	.	.	PUNCT
ap-920	85	1	clearly	clearly	ADV
ap-920	85	2	,	,	PUNCT
ap-920	85	3	any	any	DET
ap-920	85	4	factor	factor	NOUN
ap-920	85	5	of	of	ADP
ap-920	85	6	the	the	DET
ap-920	85	7	form	form	NOUN
ap-920	85	8	�	�	PROPN
ap-920	85	9	(	(	PUNCT
ap-920	85	10	)	)	PUNCT
ap-920	85	11	w	w	NOUN
ap-920	85	12	has	have	AUX
ap-920	85	13	at	at	ADV
ap-920	85	14	least	least	ADV
ap-920	85	15	one	one	NUM
ap-920	85	16	ancestor	ancestor	NOUN
ap-920	85	17	,	,	PUNCT
ap-920	85	18	namely	namely	ADV
ap-920	85	19	the	the	DET
ap-920	85	20	factor	factor	NOUN
ap-920	85	21	w.	w.	PROPN
ap-920	85	22	lemma	lemma	PROPN
ap-920	85	23	13	13	NUM
ap-920	85	24	let	let	VERB
ap-920	85	25	an	an	DET
ap-920	85	26	infinite	infinite	ADJ
ap-920	85	27	word	word	NOUN
ap-920	85	28	u	u	NOUN
ap-920	85	29	be	be	AUX
ap-920	85	30	a	a	DET
ap-920	85	31	fixed	fixed	ADJ
ap-920	85	32	point	point	NOUN
ap-920	85	33	of	of	ADP
ap-920	85	34	a	a	DET
ap-920	85	35	substitution	substitution	NOUN
ap-920	85	36	�	�	NOUN
ap-920	85	37	and	and	CCONJ
ap-920	85	38	let	let	VERB
ap-920	85	39	be	be	AUX
ap-920	85	40	a	a	DET
ap-920	85	41	factor	factor	NOUN
ap-920	85	42	of	of	ADP
ap-920	85	43	u.	u.	NOUN
ap-920	85	44	if	if	SCONJ
ap-920	85	45	the	the	DET
ap-920	85	46	only	only	ADJ
ap-920	85	47	ancestor	ancestor	NOUN
ap-920	85	48	of	of	ADP
ap-920	85	49	�	�	PROPN
ap-920	85	50	(	(	PUNCT
ap-920	85	51	w	w	NOUN
ap-920	85	52	)	)	PUNCT
ap-920	85	53	is	be	AUX
ap-920	85	54	the	the	DET
ap-920	85	55	factor	factor	NOUN
ap-920	85	56	w	w	NOUN
ap-920	85	57	,	,	PUNCT
ap-920	85	58	then	then	ADV
ap-920	85	59	ret	ret	PROPN
ap-920	85	60	ret	ret	PROPN
ap-920	85	61	(	(	PUNCT
ap-920	85	62	(	(	PUNCT
ap-920	85	63	)	)	PUNCT
ap-920	85	64	)	)	PUNCT
ap-920	85	65	(	(	PUNCT
ap-920	85	66	(	(	PUNCT
ap-920	85	67	)	)	PUNCT
ap-920	85	68	)	)	PUNCT
ap-920	85	69	�	�	PROPN
ap-920	85	70	�	�	PROPN
ap-920	85	71	w	w	PROPN
ap-920	85	72	w	w	PROPN
ap-920	85	73	�	�	PROPN
ap-920	85	74	.	.	PUNCT
ap-920	86	1	proposition	proposition	NOUN
ap-920	86	2	14	14	NUM
ap-920	86	3	let	let	VERB
ap-920	86	4	w	w	NOUN
ap-920	86	5	be	be	AUX
ap-920	86	6	a	a	DET
ap-920	86	7	non	non	ADJ
ap-920	86	8	-	-	ADJ
ap-920	86	9	empty	empty	ADJ
ap-920	86	10	factor	factor	NOUN
ap-920	86	11	of	of	ADP
ap-920	86	12	u	u	PROPN
ap-920	86	13	�	�	PROPN
ap-920	86	14	,	,	PUNCT
ap-920	86	15	then	then	ADV
ap-920	86	16	�	�	PROPN
ap-920	86	17	(	(	PUNCT
ap-920	86	18	w	w	NOUN
ap-920	86	19	)	)	PUNCT
ap-920	86	20	has	have	VERB
ap-920	86	21	a	a	DET
ap-920	86	22	unique	unique	ADJ
ap-920	86	23	ancestor	ancestor	NOUN
ap-920	86	24	,	,	PUNCT
ap-920	86	25	namely	namely	ADV
ap-920	86	26	w.	w.	NOUN
ap-920	86	27	proof	proof	NOUN
ap-920	86	28	.	.	PUNCT
ap-920	87	1	it	it	PRON
ap-920	87	2	is	be	AUX
ap-920	87	3	a	a	DET
ap-920	87	4	direct	direct	ADJ
ap-920	87	5	consequence	consequence	NOUN
ap-920	87	6	of	of	ADP
ap-920	87	7	the	the	DET
ap-920	87	8	form	form	NOUN
ap-920	87	9	of	of	ADP
ap-920	87	10	the	the	DET
ap-920	87	11	substitution	substitution	NOUN
ap-920	87	12	defined	define	VERB
ap-920	87	13	by	by	ADP
ap-920	87	14	(	(	PUNCT
ap-920	87	15	1	1	NUM
ap-920	87	16	)	)	PUNCT
ap-920	87	17	that	that	SCONJ
ap-920	87	18	any	any	DET
ap-920	87	19	factor	factor	NOUN
ap-920	87	20	v	v	VERB
ap-920	87	21	having	have	VERB
ap-920	87	22	suffix	suffix	PROPN
ap-920	87	23	1	1	NUM
ap-920	87	24	occurs	occur	VERB
ap-920	87	25	only	only	ADV
ap-920	87	26	as	as	ADP
ap-920	87	27	suffix	suffix	NOUN
ap-920	87	28	of	of	ADP
ap-920	87	29	�	�	PROPN
ap-920	87	30	(	(	PUNCT
ap-920	87	31	w	w	NOUN
ap-920	87	32	)	)	PUNCT
ap-920	87	33	for	for	ADP
ap-920	87	34	some	some	DET
ap-920	87	35	factor	factor	NOUN
ap-920	87	36	w	w	PROPN
ap-920	87	37	u	u	PROPN
ap-920	87	38	�	�	PROPN
ap-920	87	39	�	�	PROPN
ap-920	87	40	(	(	PUNCT
ap-920	87	41	)	)	PUNCT
ap-920	87	42	�	�	PROPN
ap-920	87	43	.	.	PUNCT
ap-920	88	1	moreover	moreover	ADV
ap-920	88	2	,	,	PUNCT
ap-920	88	3	any	any	DET
ap-920	88	4	factor	factor	NOUN
ap-920	88	5	�	�	PROPN
ap-920	88	6	v	v	NOUN
ap-920	88	7	which	which	PRON
ap-920	88	8	has	have	VERB
ap-920	88	9	only	only	ADV
ap-920	88	10	1	1	NUM
ap-920	88	11	as	as	ADP
ap-920	88	12	its	its	PRON
ap-920	88	13	left	left	ADJ
ap-920	88	14	extension	extension	NOUN
ap-920	88	15	,	,	PUNCT
ap-920	88	16	occurs	occur	VERB
ap-920	88	17	only	only	ADV
ap-920	88	18	as	as	ADP
ap-920	88	19	prefix	prefix	NOUN
ap-920	88	20	of	of	ADP
ap-920	88	21	�	�	PROPN
ap-920	88	22	(	(	PUNCT
ap-920	88	23	�	�	PROPN
ap-920	88	24	)	)	PUNCT
ap-920	88	25	w	w	NOUN
ap-920	88	26	for	for	ADP
ap-920	88	27	some	some	DET
ap-920	88	28	�	�	PROPN
ap-920	88	29	(	(	PUNCT
ap-920	88	30	)	)	PUNCT
ap-920	88	31	w	w	PROPN
ap-920	88	32	u	u	PROPN
ap-920	88	33	�	�	PROPN
ap-920	88	34	�	�	PROPN
ap-920	88	35	�	�	PROPN
ap-920	88	36	.	.	PUNCT
ap-920	89	1	the	the	DET
ap-920	89	2	statement	statement	NOUN
ap-920	89	3	follows	follow	VERB
ap-920	89	4	by	by	ADP
ap-920	89	5	injectivity	injectivity	NOUN
ap-920	89	6	of	of	ADP
ap-920	89	7	�	�	PROPN
ap-920	89	8	.	.	PUNCT
ap-920	90	1	now	now	ADV
ap-920	90	2	we	we	PRON
ap-920	90	3	are	be	AUX
ap-920	90	4	able	able	ADJ
ap-920	90	5	to	to	PART
ap-920	90	6	explain	explain	VERB
ap-920	90	7	how	how	SCONJ
ap-920	90	8	to	to	PART
ap-920	90	9	get	get	VERB
ap-920	90	10	return	return	NOUN
ap-920	90	11	words	word	NOUN
ap-920	90	12	of	of	ADP
ap-920	90	13	all	all	DET
ap-920	90	14	bispecial	bispecial	ADJ
ap-920	90	15	factors	factor	NOUN
ap-920	90	16	.	.	PUNCT
ap-920	91	1	corollary	corollary	ADJ
ap-920	91	2	15	15	NUM
ap-920	91	3	let	let	VERB
ap-920	91	4	br	br	PROPN
ap-920	91	5	n	n	CCONJ
ap-920	91	6	(	(	PUNCT
ap-920	91	7	)	)	PUNCT
ap-920	91	8	be	be	AUX
ap-920	91	9	a	a	DET
ap-920	91	10	bispecial	bispecial	ADJ
ap-920	91	11	factor	factor	NOUN
ap-920	91	12	of	of	ADP
ap-920	91	13	u	u	PROPN
ap-920	91	14	�	�	PROPN
ap-920	91	15	.	.	PUNCT
ap-920	92	1	then	then	ADV
ap-920	92	2	#	#	NOUN
ap-920	92	3	(	(	PUNCT
ap-920	92	4	)	)	PUNCT
ap-920	92	5	#	#	NOUN
ap-920	92	6	(	(	PUNCT
ap-920	92	7	)	)	PUNCT
ap-920	92	8	(	(	PUNCT
ap-920	92	9	)	)	PUNCT
ap-920	92	10	(	(	PUNCT
ap-920	92	11	)	)	PUNCT
ap-920	92	12	ret	ret	VERB
ap-920	92	13	retb	retb	ADJ
ap-920	92	14	br	br	NOUN
ap-920	93	1	n	n	CCONJ
ap-920	93	2	r	r	NOUN
ap-920	93	3	n	n	CCONJ
ap-920	93	4	�	�	PROPN
ap-920	93	5	�	�	PROPN
ap-920	93	6	1	1	NUM
ap-920	93	7	for	for	ADP
ap-920	93	8	every	every	DET
ap-920	93	9	n	n	PRON
ap-920	93	10	�	�	PROPN
ap-920	93	11	2	2	NUM
ap-920	93	12	and	and	CCONJ
ap-920	93	13	r	r	PROPN
ap-920	93	14	a	a	DET
ap-920	93	15	�	�	PROPN
ap-920	93	16	�	�	PROPN
ap-920	93	17	0	0	NUM
ap-920	93	18	1	1	NUM
ap-920	93	19	,	,	PUNCT
ap-920	93	20	,	,	PUNCT
ap-920	93	21	�	�	PROPN
ap-920	93	22	.	.	PUNCT
ap-920	94	1	proof	proof	NOUN
ap-920	94	2	.	.	PUNCT
ap-920	95	1	it	it	PRON
ap-920	95	2	follows	follow	VERB
ap-920	95	3	from	from	ADP
ap-920	95	4	proposition	proposition	NOUN
ap-920	95	5	14	14	NUM
ap-920	95	6	that	that	SCONJ
ap-920	95	7	#	#	NOUN
ap-920	95	8	(	(	PUNCT
ap-920	95	9	)	)	PUNCT
ap-920	95	10	#	#	NOUN
ap-920	95	11	(	(	PUNCT
ap-920	95	12	(	(	PUNCT
ap-920	95	13	)	)	PUNCT
ap-920	95	14	)	)	PUNCT
ap-920	95	15	(	(	PUNCT
ap-920	95	16	)	)	PUNCT
ap-920	95	17	(	(	PUNCT
ap-920	95	18	)	)	PUNCT
ap-920	95	19	ret	ret	VERB
ap-920	95	20	retb	retb	ADJ
ap-920	95	21	br	br	NOUN
ap-920	95	22	n	n	CCONJ
ap-920	95	23	r	r	NOUN
ap-920	95	24	n	n	CCONJ
ap-920	95	25	�	�	PROPN
ap-920	95	26	�	�	PROPN
ap-920	95	27	�	�	PROPN
ap-920	95	28	1	1	NUM
ap-920	95	29	1	1	NUM
ap-920	95	30	�	�	PROPN
ap-920	95	31	.	.	PUNCT
ap-920	96	1	then	then	ADV
ap-920	96	2	,	,	PUNCT
ap-920	96	3	relations	relation	NOUN
ap-920	96	4	(	(	PUNCT
ap-920	96	5	2	2	NUM
ap-920	96	6	)	)	PUNCT
ap-920	96	7	and	and	CCONJ
ap-920	96	8	(	(	PUNCT
ap-920	96	9	3	3	X
ap-920	96	10	)	)	PUNCT
ap-920	96	11	say	say	VERB
ap-920	96	12	that	that	SCONJ
ap-920	96	13	#	#	NOUN
ap-920	96	14	(	(	PUNCT
ap-920	96	15	(	(	PUNCT
ap-920	96	16	)	)	PUNCT
ap-920	96	17	)	)	PUNCT
ap-920	96	18	#	#	NOUN
ap-920	96	19	(	(	PUNCT
ap-920	96	20	(	(	PUNCT
ap-920	96	21	)	)	PUNCT
ap-920	96	22	)	)	PUNCT
ap-920	96	23	#	#	NOUN
ap-920	96	24	(	(	PUNCT
ap-920	96	25	)	)	PUNCT
ap-920	96	26	(	(	PUNCT
ap-920	96	27	)	)	PUNCT
ap-920	96	28	(	(	PUNCT
ap-920	96	29	)	)	PUNCT
ap-920	96	30	(	(	PUNCT
ap-920	96	31	)	)	PUNCT
ap-920	96	32	ret	ret	PROPN
ap-920	96	33	ret	ret	PROPN
ap-920	96	34	ret	ret	PROPN
ap-920	96	35	�	�	PROPN
ap-920	96	36	�	�	PROPN
ap-920	96	37	b	b	PROPN
ap-920	96	38	b	b	PROPN
ap-920	96	39	br	br	NOUN
ap-920	96	40	n	n	PROPN
ap-920	96	41	b	b	NOUN
ap-920	96	42	r	r	NOUN
ap-920	96	43	n	n	PROPN
ap-920	96	44	b	b	NOUN
ap-920	96	45	r	r	NOUN
ap-920	96	46	n	n	CCONJ
ap-920	96	47	�	�	PROPN
ap-920	96	48	�	�	PROPN
ap-920	96	49	�	�	PROPN
ap-920	96	50	�	�	PROPN
ap-920	96	51	1	1	NUM
ap-920	96	52	10	10	NUM
ap-920	96	53	1	1	NUM
ap-920	96	54	0	0	NUM
ap-920	96	55	.	.	PUNCT
ap-920	97	1	let	let	VERB
ap-920	97	2	us	we	PRON
ap-920	97	3	sum	sum	VERB
ap-920	97	4	up	up	ADP
ap-920	97	5	the	the	DET
ap-920	97	6	results	result	NOUN
ap-920	97	7	to	to	PART
ap-920	97	8	get	get	VERB
ap-920	97	9	the	the	DET
ap-920	97	10	main	main	ADJ
ap-920	97	11	theorem	theorem	NOUN
ap-920	97	12	about	about	ADP
ap-920	97	13	the	the	DET
ap-920	97	14	cardinality	cardinality	NOUN
ap-920	97	15	of	of	ADP
ap-920	97	16	the	the	DET
ap-920	97	17	set	set	NOUN
ap-920	97	18	of	of	ADP
ap-920	97	19	return	return	NOUN
ap-920	97	20	words	word	NOUN
ap-920	97	21	of	of	ADP
ap-920	97	22	any	any	DET
ap-920	97	23	factor	factor	NOUN
ap-920	97	24	of	of	ADP
ap-920	97	25	u	u	PROPN
ap-920	97	26	�	�	PROPN
ap-920	97	27	.	.	PUNCT
ap-920	97	28	theorem	theorem	PROPN
ap-920	97	29	16	16	NUM
ap-920	97	30	let	let	VERB
ap-920	97	31	w	w	NOUN
ap-920	97	32	be	be	AUX
ap-920	97	33	a	a	DET
ap-920	97	34	factor	factor	NOUN
ap-920	97	35	of	of	ADP
ap-920	97	36	u	u	PROPN
ap-920	97	37	�	�	PROPN
ap-920	97	38	.	.	PUNCT
ap-920	98	1	then	then	ADV
ap-920	98	2	2	2	NUM
ap-920	98	3	3	3	NUM
ap-920	98	4	�	�	PROPN
ap-920	98	5	�	�	NOUN
ap-920	98	6	#	#	NOUN
ap-920	98	7	(	(	PUNCT
ap-920	98	8	)	)	PUNCT
ap-920	98	9	ret	ret	PROPN
ap-920	98	10	w	w	PROPN
ap-920	98	11	.	.	PUNCT
ap-920	99	1	proof	proof	NOUN
ap-920	99	2	.	.	PUNCT
ap-920	100	1	using	use	VERB
ap-920	100	2	corollary	corollary	ADJ
ap-920	100	3	15	15	NUM
ap-920	100	4	,	,	PUNCT
ap-920	100	5	it	it	PRON
ap-920	100	6	suffices	suffice	VERB
ap-920	100	7	to	to	PART
ap-920	100	8	consider	consider	VERB
ap-920	100	9	only	only	ADJ
ap-920	100	10	bispecial	bispecial	ADJ
ap-920	100	11	factors	factor	NOUN
ap-920	100	12	of	of	ADP
ap-920	100	13	the	the	DET
ap-920	100	14	form	form	NOUN
ap-920	100	15	0r	0r	NUM
ap-920	100	16	,	,	PUNCT
ap-920	100	17	r	r	PROPN
ap-920	100	18	a	a	DET
ap-920	100	19	�	�	PROPN
ap-920	100	20	�	�	PROPN
ap-920	100	21	1	1	NUM
ap-920	100	22	,	,	PUNCT
ap-920	100	23	and	and	CCONJ
ap-920	100	24	�	�	PROPN
ap-920	100	25	to	to	PART
ap-920	100	26	obtain	obtain	VERB
ap-920	100	27	all	all	DET
ap-920	100	28	possible	possible	ADJ
ap-920	100	29	cardinalities	cardinality	NOUN
ap-920	100	30	of	of	ADP
ap-920	100	31	the	the	DET
ap-920	100	32	sets	set	NOUN
ap-920	100	33	of	of	ADP
ap-920	100	34	return	return	NOUN
ap-920	100	35	words	word	NOUN
ap-920	100	36	of	of	ADP
ap-920	100	37	factors	factor	NOUN
ap-920	100	38	of	of	ADP
ap-920	100	39	u	u	NOUN
ap-920	100	40	�	�	PROPN
ap-920	100	41	.	.	PUNCT
ap-920	101	1	it	it	PRON
ap-920	101	2	is	be	AUX
ap-920	101	3	not	not	PART
ap-920	101	4	difficult	difficult	ADJ
ap-920	101	5	to	to	PART
ap-920	101	6	see	see	VERB
ap-920	101	7	that	that	SCONJ
ap-920	101	8	the	the	DET
ap-920	101	9	return	return	NOUN
ap-920	101	10	words	word	NOUN
ap-920	101	11	of	of	ADP
ap-920	101	12	the	the	DET
ap-920	101	13	simplest	simple	ADJ
ap-920	101	14	bispecial	bispecial	ADJ
ap-920	101	15	factors	factor	NOUN
ap-920	101	16	are	be	AUX
ap-920	101	17	the	the	DET
ap-920	101	18	following	follow	VERB
ap-920	101	19	:	:	PUNCT
ap-920	101	20	�	�	PROPN
ap-920	101	21	let	let	VERB
ap-920	101	22	r	r	NOUN
ap-920	101	23	b	b	PROPN
ap-920	101	24	�	�	PROPN
ap-920	101	25	then	then	ADV
ap-920	101	26	#	#	NOUN
ap-920	101	27	(	(	PUNCT
ap-920	101	28	)	)	PUNCT
ap-920	101	29	,	,	PUNCT
ap-920	101	30	ret	ret	NOUN
ap-920	101	31	0	0	NUM
ap-920	101	32	0	0	NUM
ap-920	101	33	0	0	NUM
ap-920	101	34	1r	1r	NUM
ap-920	101	35	r	r	PROPN
ap-920	101	36	�	�	PROPN
ap-920	101	37	.	.	PUNCT
ap-920	102	1	�	�	PROPN
ap-920	102	2	let	let	VERB
ap-920	102	3	b	b	NOUN
ap-920	102	4	r	r	NOUN
ap-920	102	5	a	a	DET
ap-920	102	6	�	�	PROPN
ap-920	102	7	�	�	PROPN
ap-920	102	8	�	�	PROPN
ap-920	102	9	1then	1then	ADJ
ap-920	102	10	#	#	NOUN
ap-920	102	11	(	(	PUNCT
ap-920	102	12	)	)	PUNCT
ap-920	102	13	,	,	PUNCT
ap-920	102	14	,	,	PUNCT
ap-920	102	15	ret	ret	PROPN
ap-920	102	16	0	0	NUM
ap-920	102	17	0	0	NUM
ap-920	102	18	0	0	NUM
ap-920	102	19	1	1	NUM
ap-920	102	20	0	0	NUM
ap-920	102	21	10r	10r	NOUN
ap-920	102	22	r	r	NOUN
ap-920	102	23	r	r	NOUN
ap-920	102	24	b	b	PROPN
ap-920	102	25	�	�	PROPN
ap-920	102	26	.	.	PUNCT
ap-920	103	1	�	�	PROPN
ap-920	103	2	since	since	SCONJ
ap-920	103	3	#	#	NOUN
ap-920	103	4	(	(	PUNCT
ap-920	103	5	(	(	PUNCT
ap-920	103	6	)	)	PUNCT
ap-920	103	7	)	)	PUNCT
ap-920	103	8	(	(	PUNCT
ap-920	103	9	)	)	PUNCT
ap-920	103	10	(	(	PUNCT
ap-920	103	11	)	)	PUNCT
ap-920	103	12	,	,	PUNCT
ap-920	103	13	(	(	PUNCT
ap-920	103	14	)	)	PUNCT
ap-920	103	15	(	(	PUNCT
ap-920	103	16	)	)	PUNCT
ap-920	103	17	ret	ret	NOUN
ap-920	103	18	0	0	NUM
ap-920	104	1	1	1	NUM
ap-920	104	2	0	0	NUM
ap-920	104	3	0	0	NUM
ap-920	104	4	1	1	NUM
ap-920	104	5	0	0	NUM
ap-920	104	6	0	0	NUM
ap-920	104	7	1	1	NUM
ap-920	104	8	0	0	NUM
ap-920	104	9	1	1	NUM
ap-920	104	10	1	1	NUM
ap-920	104	11	0	0	NUM
ap-920	104	12	1	1	NUM
ap-920	104	13	0	0	NUM
ap-920	104	14	10	10	NUM
ap-920	104	15	1	1	NUM
ap-920	104	16	1b	1b	NUM
ap-920	104	17	b	b	PROPN
ap-920	104	18	b	b	X
ap-920	104	19	b	b	PROPN
ap-920	104	20	b	b	PROPN
ap-920	104	21	b	b	PROPN
ap-920	104	22	b	b	PROPN
ap-920	104	23	�	�	PROPN
ap-920	104	24	�	�	PROPN
ap-920	104	25	�	�	PROPN
ap-920	104	26	�	�	PROPN
ap-920	104	27	�	�	PROPN
ap-920	104	28	�	�	PROPN
ap-920	104	29	�	�	PROPN
ap-920	104	30	�	�	PROPN
ap-920	104	31	a	a	DET
ap-920	104	32	b	b	PROPN
ap-920	104	33	b	b	PROPN
ap-920	104	34	�	�	PROPN
ap-920	104	35	,	,	PUNCT
ap-920	104	36	,	,	PUNCT
ap-920	104	37	0	0	NUM
ap-920	104	38	1	1	NUM
ap-920	104	39	it	it	PRON
ap-920	104	40	is	be	AUX
ap-920	104	41	useful	useful	ADJ
ap-920	104	42	to	to	PART
ap-920	104	43	put	put	VERB
ap-920	104	44	ret	ret	NOUN
ap-920	104	45	(	(	PUNCT
ap-920	104	46	)	)	PUNCT
ap-920	104	47	,	,	PUNCT
ap-920	104	48	�	�	PROPN
ap-920	104	49	�	�	PROPN
ap-920	104	50	0	0	NUM
ap-920	104	51	1	1	NUM
ap-920	104	52	.	.	PUNCT
ap-920	105	1	observation	observation	NOUN
ap-920	105	2	17	17	NUM
ap-920	105	3	from	from	ADP
ap-920	105	4	the	the	DET
ap-920	105	5	proof	proof	NOUN
ap-920	105	6	of	of	ADP
ap-920	105	7	theorem	theorem	NOUN
ap-920	105	8	16	16	NUM
ap-920	105	9	,	,	PUNCT
ap-920	105	10	we	we	PRON
ap-920	105	11	can	can	AUX
ap-920	105	12	observe	observe	VERB
ap-920	105	13	that	that	SCONJ
ap-920	105	14	in	in	ADP
ap-920	105	15	the	the	DET
ap-920	105	16	case	case	NOUN
ap-920	105	17	b	b	PROPN
ap-920	105	18	a	a	DET
ap-920	105	19	�	�	PROPN
ap-920	105	20	�	�	PROPN
ap-920	105	21	1	1	NUM
ap-920	105	22	,	,	PUNCT
ap-920	105	23	#	#	NOUN
ap-920	105	24	(	(	PUNCT
ap-920	105	25	)	)	PUNCT
ap-920	105	26	ret	ret	PROPN
ap-920	105	27	w	w	PROPN
ap-920	105	28	�	�	PROPN
ap-920	105	29	2	2	NUM
ap-920	105	30	for	for	ADP
ap-920	105	31	all	all	DET
ap-920	105	32	the	the	DET
ap-920	105	33	factors	factor	NOUN
ap-920	105	34	of	of	ADP
ap-920	105	35	u	u	PROPN
ap-920	105	36	�	�	PROPN
ap-920	105	37	.	.	PUNCT
ap-920	106	1	thanks	thank	NOUN
ap-920	106	2	to	to	ADP
ap-920	106	3	proposition	proposition	NOUN
ap-920	106	4	6	6	NUM
ap-920	106	5	,	,	PUNCT
ap-920	106	6	we	we	PRON
ap-920	106	7	have	have	VERB
ap-920	106	8	another	another	DET
ap-920	106	9	confirmation	confirmation	NOUN
ap-920	106	10	of	of	ADP
ap-920	106	11	the	the	DET
ap-920	106	12	fact	fact	NOUN
ap-920	106	13	that	that	SCONJ
ap-920	106	14	u	u	PROPN
ap-920	106	15	�	�	PROPN
ap-920	106	16	for	for	ADP
ap-920	106	17	b	b	PROPN
ap-920	106	18	a	a	DET
ap-920	106	19	�	�	PROPN
ap-920	106	20	�	�	PROPN
ap-920	106	21	1	1	NUM
ap-920	106	22	is	be	AUX
ap-920	106	23	a	a	DET
ap-920	106	24	sturmian	sturmian	ADJ
ap-920	106	25	word	word	NOUN
ap-920	106	26	.	.	PUNCT
ap-920	107	1	4	4	NUM
ap-920	107	2	how	how	SCONJ
ap-920	107	3	to	to	PART
ap-920	107	4	compute	compute	VERB
ap-920	107	5	the	the	DET
ap-920	107	6	recurrence	recurrence	NOUN
ap-920	107	7	function	function	NOUN
ap-920	107	8	let	let	VERB
ap-920	107	9	us	we	PRON
ap-920	107	10	show	show	VERB
ap-920	107	11	how	how	SCONJ
ap-920	107	12	to	to	PART
ap-920	107	13	apply	apply	VERB
ap-920	107	14	the	the	DET
ap-920	107	15	knowledge	knowledge	NOUN
ap-920	107	16	of	of	ADP
ap-920	107	17	return	return	NOUN
ap-920	107	18	words	word	NOUN
ap-920	107	19	to	to	PART
ap-920	107	20	describe	describe	VERB
ap-920	107	21	the	the	DET
ap-920	107	22	recurrence	recurrence	NOUN
ap-920	107	23	function	function	NOUN
ap-920	107	24	(	(	PUNCT
ap-920	107	25	definition	definition	NOUN
ap-920	107	26	3	3	NUM
ap-920	107	27	)	)	PUNCT
ap-920	107	28	of	of	ADP
ap-920	107	29	the	the	DET
ap-920	107	30	infinite	infinite	ADJ
ap-920	107	31	word	word	NOUN
ap-920	107	32	u	u	NOUN
ap-920	107	33	�	�	PROPN
ap-920	107	34	.	.	PUNCT
ap-920	108	1	the	the	DET
ap-920	108	2	methods	method	NOUN
ap-920	108	3	used	use	VERB
ap-920	108	4	here	here	ADV
ap-920	108	5	follow	follow	VERB
ap-920	108	6	the	the	DET
ap-920	108	7	ideas	idea	NOUN
ap-920	108	8	from	from	ADP
ap-920	108	9	[	[	X
ap-920	108	10	6	6	NUM
ap-920	108	11	]	]	PUNCT
ap-920	108	12	.	.	PUNCT
ap-920	109	1	as	as	SCONJ
ap-920	109	2	the	the	DET
ap-920	109	3	reader	reader	NOUN
ap-920	109	4	will	will	AUX
ap-920	109	5	have	have	AUX
ap-920	109	6	anticipated	anticipate	VERB
ap-920	109	7	,	,	PUNCT
ap-920	109	8	we	we	PRON
ap-920	109	9	want	want	VERB
ap-920	109	10	to	to	PART
ap-920	109	11	compute	compute	VERB
ap-920	109	12	lu(n	lu(n	NOUN
ap-920	109	13	)	)	PUNCT
ap-920	109	14	in	in	ADP
ap-920	109	15	order	order	NOUN
ap-920	109	16	to	to	PART
ap-920	109	17	get	get	VERB
ap-920	109	18	the	the	DET
ap-920	109	19	recurrence	recurrence	NOUN
ap-920	109	20	function	function	NOUN
ap-920	109	21	ru(n	ru(n	NOUN
ap-920	109	22	)	)	PUNCT
ap-920	109	23	for	for	ADP
ap-920	109	24	every	every	DET
ap-920	109	25	n	n	PRON
ap-920	109	26	�	�	PROPN
ap-920	109	27	�	�	PROPN
ap-920	109	28	.	.	PUNCT
ap-920	110	1	this	this	DET
ap-920	110	2	task	task	NOUN
ap-920	110	3	can	can	AUX
ap-920	110	4	be	be	AUX
ap-920	110	5	simplified	simplify	VERB
ap-920	110	6	using	use	VERB
ap-920	110	7	the	the	DET
ap-920	110	8	notion	notion	NOUN
ap-920	110	9	of	of	ADP
ap-920	110	10	singular	singular	ADJ
ap-920	110	11	factors	factor	NOUN
ap-920	110	12	.	.	PUNCT
ap-920	111	1	a	a	DET
ap-920	111	2	factor	factor	NOUN
ap-920	111	3	w	w	NOUN
ap-920	111	4	u	u	PROPN
ap-920	111	5	�	�	PROPN
ap-920	111	6	�	�	PROPN
ap-920	111	7	(	(	PUNCT
ap-920	111	8	)	)	PUNCT
ap-920	111	9	is	be	AUX
ap-920	111	10	called	call	VERB
ap-920	111	11	singular	singular	ADJ
ap-920	111	12	if	if	SCONJ
ap-920	111	13	w	w	PROPN
ap-920	111	14	�	�	PROPN
ap-920	111	15	1	1	NUM
ap-920	111	16	or	or	CCONJ
ap-920	111	17	if	if	SCONJ
ap-920	111	18	there	there	PRON
ap-920	111	19	exist	exist	VERB
ap-920	111	20	a	a	DET
ap-920	111	21	word	word	NOUN
ap-920	111	22	v	v	ADP
ap-920	111	23	u	u	PROPN
ap-920	111	24	�	�	PROPN
ap-920	111	25	�	�	PROPN
ap-920	111	26	(	(	PUNCT
ap-920	111	27	)	)	PUNCT
ap-920	111	28	and	and	CCONJ
ap-920	111	29	letters	letter	NOUN
ap-920	111	30	x	x	PUNCT
ap-920	111	31	x	x	PUNCT
ap-920	111	32	y	y	PROPN
ap-920	111	33	y	y	PROPN
ap-920	111	34	,	,	PUNCT
ap-920	111	35	,	,	PUNCT
ap-920	111	36	,	,	PUNCT
ap-920	111	37	�	�	PROPN
ap-920	111	38	�	�	PROPN
ap-920	111	39	�	�	PROPN
ap-920	111	40	�	�	PROPN
ap-920	111	41	such	such	ADJ
ap-920	111	42	that	that	SCONJ
ap-920	111	43	w	w	PROPN
ap-920	111	44	xvy	xvy	PROPN
ap-920	111	45	�	�	PROPN
ap-920	111	46	,	,	PUNCT
ap-920	111	47	x	x	SYM
ap-920	111	48	x	x	SYM
ap-920	111	49	�	�	PROPN
ap-920	111	50	�	�	PROPN
ap-920	111	51	,	,	PUNCT
ap-920	111	52	y	y	PROPN
ap-920	111	53	y	y	PROPN
ap-920	111	54	�	�	PROPN
ap-920	111	55	�	�	PROPN
ap-920	111	56	,	,	PUNCT
ap-920	111	57	and	and	CCONJ
ap-920	111	58	�	�	PROPN
ap-920	111	59	�	�	PROPN
ap-920	111	60	�	�	PROPN
ap-920	111	61	x	x	PROPN
ap-920	111	62	vy	vy	NOUN
ap-920	111	63	xvy	xvy	PROPN
ap-920	111	64	u	u	PROPN
ap-920	111	65	,	,	PUNCT
ap-920	111	66	(	(	PUNCT
ap-920	111	67	)	)	PUNCT
ap-920	111	68	�	�	PROPN
ap-920	111	69	.	.	PUNCT
ap-920	112	1	obviously	obviously	ADV
ap-920	112	2	,	,	PUNCT
ap-920	112	3	v	v	NOUN
ap-920	112	4	is	be	AUX
ap-920	112	5	a	a	DET
ap-920	112	6	bispecial	bispecial	ADJ
ap-920	112	7	factor	factor	NOUN
ap-920	112	8	.	.	PUNCT
ap-920	113	1	proposition	proposition	NOUN
ap-920	113	2	18	18	NUM
ap-920	113	3	let	let	VERB
ap-920	113	4	u	u	PRON
ap-920	113	5	be	be	AUX
ap-920	113	6	a	a	DET
ap-920	113	7	uniformly	uniformly	ADV
ap-920	113	8	recurrent	recurrent	ADJ
ap-920	113	9	word	word	NOUN
ap-920	113	10	and	and	CCONJ
ap-920	113	11	n	n	PRON
ap-920	113	12	�	�	PROPN
ap-920	113	13	1	1	NUM
ap-920	113	14	.	.	PUNCT
ap-920	114	1	if	if	SCONJ
ap-920	114	2	l	l	PROPN
ap-920	114	3	n	n	ADP
ap-920	114	4	l	l	X
ap-920	114	5	nu	nu	INTJ
ap-920	114	6	u	u	NOUN
ap-920	114	7	(	(	PUNCT
ap-920	114	8	)	)	PUNCT
ap-920	114	9	(	(	PUNCT
ap-920	114	10	)	)	PUNCT
ap-920	114	11	�	�	PROPN
ap-920	114	12	�	�	PROPN
ap-920	114	13	1	1	NUM
ap-920	114	14	,	,	PUNCT
ap-920	114	15	then	then	ADV
ap-920	114	16	there	there	PRON
ap-920	114	17	exists	exist	VERB
ap-920	114	18	a	a	DET
ap-920	114	19	singular	singular	ADJ
ap-920	114	20	factor	factor	NOUN
ap-920	114	21	w	w	PROPN
ap-920	114	22	of	of	ADP
ap-920	114	23	length	length	NOUN
ap-920	114	24	n	n	PRON
ap-920	114	25	such	such	ADJ
ap-920	114	26	that	that	SCONJ
ap-920	114	27	l	l	PROPN
ap-920	114	28	w	w	PROPN
ap-920	114	29	l	l	PROPN
ap-920	114	30	nu	nu	INTJ
ap-920	114	31	u	u	NOUN
ap-920	114	32	(	(	PUNCT
ap-920	114	33	)	)	PUNCT
ap-920	114	34	(	(	PUNCT
ap-920	114	35	)	)	PUNCT
ap-920	114	36	�	�	PROPN
ap-920	114	37	.	.	PUNCT
ap-920	115	1	a	a	DET
ap-920	115	2	singular	singular	ADJ
ap-920	115	3	factor	factor	NOUN
ap-920	115	4	w	w	NOUN
ap-920	115	5	is	be	AUX
ap-920	115	6	said	say	VERB
ap-920	115	7	to	to	PART
ap-920	115	8	be	be	AUX
ap-920	115	9	essential	essential	ADJ
ap-920	115	10	if	if	SCONJ
ap-920	115	11	l	l	PROPN
ap-920	115	12	w	w	PROPN
ap-920	115	13	l	l	PROPN
ap-920	115	14	w	w	PROPN
ap-920	115	15	l	l	PROPN
ap-920	115	16	wu	wu	PROPN
ap-920	116	1	u	u	NOUN
ap-920	116	2	u	u	PROPN
ap-920	116	3	(	(	PUNCT
ap-920	116	4	)	)	PUNCT
ap-920	116	5	(	(	PUNCT
ap-920	116	6	)	)	PUNCT
ap-920	116	7	(	(	PUNCT
ap-920	116	8	)	)	PUNCT
ap-920	116	9	�	�	PROPN
ap-920	116	10	�	�	PROPN
ap-920	116	11	�	�	PROPN
ap-920	116	12	1	1	NUM
ap-920	116	13	.	.	PUNCT
ap-920	117	1	it	it	PRON
ap-920	117	2	follows	follow	VERB
ap-920	117	3	that	that	PRON
ap-920	117	4	to	to	PART
ap-920	117	5	calculate	calculate	VERB
ap-920	117	6	l	l	PROPN
ap-920	117	7	nu	nu	PROPN
ap-920	117	8	(	(	PUNCT
ap-920	117	9	)	)	PUNCT
ap-920	117	10	,	,	PUNCT
ap-920	117	11	it	it	PRON
ap-920	117	12	is	be	AUX
ap-920	117	13	sufficient	sufficient	ADJ
ap-920	117	14	to	to	PART
ap-920	117	15	consider	consider	VERB
ap-920	117	16	singular	singular	NOUN
ap-920	117	17	,	,	PUNCT
ap-920	117	18	or	or	CCONJ
ap-920	117	19	,	,	PUNCT
ap-920	117	20	even	even	ADV
ap-920	117	21	,	,	PUNCT
ap-920	117	22	only	only	ADV
ap-920	117	23	essential	essential	ADJ
ap-920	117	24	singular	singular	ADJ
ap-920	117	25	factors	factor	NOUN
ap-920	117	26	.	.	PUNCT
ap-920	118	1	theorem	theorem	VERB
ap-920	118	2	19	19	NUM
ap-920	118	3	let	let	VERB
ap-920	118	4	u	u	PRON
ap-920	118	5	be	be	AUX
ap-920	118	6	a	a	DET
ap-920	118	7	uniformly	uniformly	ADV
ap-920	118	8	recurrent	recurrent	ADJ
ap-920	118	9	word	word	NOUN
ap-920	118	10	and	and	CCONJ
ap-920	118	11	n	n	PRON
ap-920	118	12	�	�	PROPN
ap-920	118	13	1	1	NUM
ap-920	118	14	.	.	PUNCT
ap-920	119	1	l	l	NOUN
ap-920	119	2	n	n	NUM
ap-920	119	3	l	l	NOUN
ap-920	119	4	w	w	PROPN
ap-920	119	5	w	w	PROPN
ap-920	119	6	n	n	PROPN
ap-920	119	7	and	and	CCONJ
ap-920	119	8	w	w	ADP
ap-920	119	9	l	l	PROPN
ap-920	119	10	w	w	PROPN
ap-920	119	11	w	w	PROPN
ap-920	119	12	n	n	PROPN
ap-920	119	13	and	and	CCONJ
ap-920	119	14	w	w	PROPN
ap-920	119	15	essen	essen	PROPN
ap-920	119	16	u	u	PROPN
ap-920	119	17	u	u	PROPN
ap-920	119	18	u	u	NOUN
ap-920	119	19	(	(	PUNCT
ap-920	119	20	)	)	PUNCT
ap-920	119	21	max	max	PROPN
ap-920	119	22	(	(	PUNCT
ap-920	119	23	)	)	PUNCT
ap-920	119	24	max	max	PROPN
ap-920	119	25	(	(	PUNCT
ap-920	119	26	)	)	PUNCT
ap-920	119	27	�	�	PROPN
ap-920	119	28	�	�	PROPN
ap-920	119	29	�	�	PROPN
ap-920	119	30	�	�	PROPN
ap-920	119	31	singular	singular	PROPN
ap-920	119	32	tial	tial	ADJ
ap-920	119	33	singular	singular	NOUN
ap-920	119	34	.	.	PUNCT
ap-920	120	1	now	now	ADV
ap-920	120	2	we	we	PRON
ap-920	120	3	are	be	AUX
ap-920	120	4	able	able	ADJ
ap-920	120	5	to	to	PART
ap-920	120	6	give	give	VERB
ap-920	120	7	an	an	DET
ap-920	120	8	algorithm	algorithm	NOUN
ap-920	120	9	for	for	ADP
ap-920	120	10	computing	compute	VERB
ap-920	120	11	the	the	DET
ap-920	120	12	recurrence	recurrence	NOUN
ap-920	120	13	function	function	NOUN
ap-920	120	14	of	of	ADP
ap-920	120	15	an	an	DET
ap-920	120	16	infinite	infinite	ADJ
ap-920	120	17	uniformly	uniformly	ADV
ap-920	120	18	recurrent	recurrent	ADJ
ap-920	120	19	word	word	NOUN
ap-920	120	20	u	u	NOUN
ap-920	120	21	:	:	PUNCT
ap-920	120	22	1	1	NUM
ap-920	120	23	.	.	X
ap-920	120	24	determine	determine	VERB
ap-920	120	25	bispecial	bispecial	ADJ
ap-920	120	26	factors	factor	NOUN
ap-920	120	27	.	.	PUNCT
ap-920	121	1	2	2	X
ap-920	121	2	.	.	X
ap-920	121	3	deduce	deduce	VERB
ap-920	121	4	the	the	DET
ap-920	121	5	form	form	NOUN
ap-920	121	6	of	of	ADP
ap-920	121	7	singular	singular	ADJ
ap-920	121	8	factors	factor	NOUN
ap-920	121	9	and	and	CCONJ
ap-920	121	10	compute	compute	VERB
ap-920	121	11	their	their	PRON
ap-920	121	12	lengths	length	NOUN
ap-920	121	13	.	.	PUNCT
ap-920	122	1	3	3	X
ap-920	122	2	.	.	X
ap-920	122	3	for	for	ADP
ap-920	122	4	every	every	DET
ap-920	122	5	singular	singular	ADJ
ap-920	122	6	factor	factor	NOUN
ap-920	122	7	,	,	PUNCT
ap-920	122	8	determine	determine	VERB
ap-920	122	9	the	the	DET
ap-920	122	10	associated	associated	ADJ
ap-920	122	11	return	return	NOUN
ap-920	122	12	words	word	NOUN
ap-920	122	13	and	and	CCONJ
ap-920	122	14	compute	compute	VERB
ap-920	122	15	their	their	PRON
ap-920	122	16	lengths	length	NOUN
ap-920	122	17	.	.	PUNCT
ap-920	123	1	4	4	X
ap-920	123	2	.	.	X
ap-920	123	3	compute	compute	VERB
ap-920	123	4	the	the	DET
ap-920	123	5	function	function	NOUN
ap-920	123	6	lu(n	lu(n	NOUN
ap-920	123	7	)	)	PUNCT
ap-920	123	8	to	to	PART
ap-920	123	9	get	get	VERB
ap-920	123	10	the	the	DET
ap-920	123	11	recurrence	recurrence	NOUN
ap-920	123	12	function	function	NOUN
ap-920	123	13	ru(n	ru(n	NOUN
ap-920	123	14	)	)	PUNCT
ap-920	123	15	for	for	ADP
ap-920	123	16	every	every	DET
ap-920	123	17	n	n	PRON
ap-920	123	18	�	�	PROPN
ap-920	123	19	�	�	PROPN
ap-920	123	20	using	use	VERB
ap-920	123	21	proposition	proposition	NOUN
ap-920	123	22	5	5	NUM
ap-920	123	23	.	.	SYM
ap-920	123	24	5	5	NUM
ap-920	123	25	computation	computation	NOUN
ap-920	123	26	of	of	ADP
ap-920	123	27	the	the	DET
ap-920	123	28	recurrence	recurrence	NOUN
ap-920	123	29	function	function	NOUN
ap-920	123	30	of	of	ADP
ap-920	123	31	u	u	NOUN
ap-920	123	32	�	�	PROPN
ap-920	123	33	let	let	VERB
ap-920	123	34	us	we	PRON
ap-920	123	35	apply	apply	VERB
ap-920	123	36	the	the	DET
ap-920	123	37	above	above	ADJ
ap-920	123	38	described	describe	VERB
ap-920	123	39	algorithm	algorithm	NOUN
ap-920	123	40	for	for	ADP
ap-920	123	41	computing	compute	VERB
ap-920	123	42	the	the	DET
ap-920	123	43	recurrence	recurrence	NOUN
ap-920	123	44	function	function	NOUN
ap-920	123	45	of	of	ADP
ap-920	123	46	the	the	DET
ap-920	123	47	infinite	infinite	ADJ
ap-920	123	48	word	word	NOUN
ap-920	123	49	u	u	NOUN
ap-920	123	50	�	�	PROPN
ap-920	123	51	being	be	AUX
ap-920	123	52	the	the	DET
ap-920	123	53	only	only	ADJ
ap-920	123	54	fixed	fix	VERB
ap-920	123	55	point	point	NOUN
ap-920	123	56	of	of	ADP
ap-920	123	57	the	the	DET
ap-920	123	58	substitution	substitution	NOUN
ap-920	123	59	�	�	PROPN
ap-920	123	60	(	(	PUNCT
ap-920	123	61	)	)	PUNCT
ap-920	123	62	0	0	SYM
ap-920	123	63	0	0	NUM
ap-920	123	64	1	1	NUM
ap-920	123	65	�	�	PROPN
ap-920	123	66	a	a	PRON
ap-920	123	67	,	,	PUNCT
ap-920	123	68	�	�	PROPN
ap-920	123	69	(	(	PUNCT
ap-920	123	70	)	)	PUNCT
ap-920	123	71	1	1	NUM
ap-920	123	72	0	0	NUM
ap-920	123	73	1	1	NUM
ap-920	123	74	�	�	PROPN
ap-920	123	75	b	b	PROPN
ap-920	123	76	,	,	PUNCT
ap-920	123	77	a	a	DET
ap-920	123	78	b	b	PROPN
ap-920	123	79	�	�	PROPN
ap-920	123	80	�	�	PROPN
ap-920	123	81	1	1	NUM
ap-920	123	82	.	.	PUNCT
ap-920	124	1	1	1	X
ap-920	124	2	.	.	X
ap-920	124	3	the	the	DET
ap-920	124	4	bispecial	bispecial	ADJ
ap-920	124	5	factors	factor	NOUN
ap-920	124	6	of	of	ADP
ap-920	124	7	u	u	NOUN
ap-920	124	8	�	�	PROPN
ap-920	124	9	are	be	AUX
ap-920	124	10	described	describe	VERB
ap-920	124	11	in	in	ADP
ap-920	124	12	corollary	corollary	ADJ
ap-920	124	13	11	11	NUM
ap-920	124	14	.	.	NOUN
ap-920	125	1	2	2	X
ap-920	125	2	.	.	X
ap-920	125	3	let	let	VERB
ap-920	125	4	us	we	PRON
ap-920	125	5	show	show	VERB
ap-920	125	6	how	how	SCONJ
ap-920	125	7	the	the	DET
ap-920	125	8	task	task	NOUN
ap-920	125	9	of	of	ADP
ap-920	125	10	describing	describe	VERB
ap-920	125	11	the	the	DET
ap-920	125	12	singular	singular	ADJ
ap-920	125	13	factors	factor	NOUN
ap-920	125	14	can	can	AUX
ap-920	125	15	be	be	AUX
ap-920	125	16	simplified	simplify	VERB
ap-920	125	17	using	use	VERB
ap-920	125	18	the	the	DET
ap-920	125	19	relation	relation	NOUN
ap-920	125	20	between	between	ADP
ap-920	125	21	a	a	DET
ap-920	125	22	factor	factor	NOUN
ap-920	125	23	and	and	CCONJ
ap-920	125	24	its	its	PRON
ap-920	125	25	image	image	NOUN
ap-920	125	26	under	under	ADP
ap-920	125	27	the	the	DET
ap-920	125	28	substitution	substitution	NOUN
ap-920	125	29	�	�	PROPN
ap-920	125	30	.	.	PUNCT
ap-920	126	1	observation	observation	NOUN
ap-920	126	2	20	20	NUM
ap-920	126	3	let	let	VERB
ap-920	126	4	n	n	PRON
ap-920	126	5	�	�	PROPN
ap-920	126	6	2	2	NUM
ap-920	126	7	and	and	CCONJ
ap-920	126	8	r	r	PROPN
ap-920	126	9	a	a	DET
ap-920	126	10	�	�	PROPN
ap-920	126	11	�	�	PROPN
ap-920	126	12	0	0	NUM
ap-920	126	13	1	1	NUM
ap-920	126	14	,	,	PUNCT
ap-920	126	15	,	,	PUNCT
ap-920	126	16	�	�	PROPN
ap-920	126	17	.	.	PUNCT
ap-920	127	1	then	then	ADV
ap-920	127	2	,	,	PUNCT
ap-920	127	3	s	s	NOUN
ap-920	127	4	x	x	X
ap-920	127	5	y	y	PROPN
ap-920	127	6	x	x	SYM
ap-920	127	7	b	b	PROPN
ap-920	128	1	yr	yr	NOUN
ap-920	128	2	n	n	ADP
ap-920	128	3	r	r	NOUN
ap-920	128	4	n	n	CCONJ
ap-920	128	5	(	(	PUNCT
ap-920	128	6	)	)	PUNCT
ap-920	128	7	(	(	PUNCT
ap-920	128	8	)	)	PUNCT
ap-920	128	9	(	(	PUNCT
ap-920	128	10	,	,	PUNCT
ap-920	128	11	)	)	PUNCT
ap-920	128	12	�	�	PROPN
ap-920	128	13	is	be	AUX
ap-920	128	14	a	a	DET
ap-920	128	15	singular	singular	ADJ
ap-920	128	16	factor	factor	NOUN
ap-920	128	17	if	if	SCONJ
ap-920	128	18	and	and	CCONJ
ap-920	128	19	only	only	ADV
ap-920	128	20	ifs	ifs	PROPN
ap-920	128	21	x	x	PUNCT
ap-920	128	22	y	y	PROPN
ap-920	128	23	x	x	SYM
ap-920	128	24	b	b	PROPN
ap-920	128	25	yr	yr	NOUN
ap-920	128	26	n	n	ADP
ap-920	128	27	r	r	NOUN
ap-920	128	28	n	n	CCONJ
ap-920	128	29	(	(	PUNCT
ap-920	128	30	)	)	PUNCT
ap-920	128	31	(	(	PUNCT
ap-920	128	32	)	)	PUNCT
ap-920	128	33	(	(	PUNCT
ap-920	128	34	,	,	PUNCT
ap-920	128	35	)	)	PUNCT
ap-920	128	36	�	�	PROPN
ap-920	128	37	�	�	PROPN
ap-920	128	38	�	�	PROPN
ap-920	128	39	1	1	NUM
ap-920	128	40	1	1	NUM
ap-920	128	41	is	be	AUX
ap-920	128	42	a	a	DET
ap-920	128	43	singular	singular	ADJ
ap-920	128	44	factor	factor	NOUN
ap-920	128	45	.	.	PUNCT
ap-920	129	1	if	if	SCONJ
ap-920	129	2	we	we	PRON
ap-920	129	3	describe	describe	VERB
ap-920	129	4	all	all	DET
ap-920	129	5	the	the	DET
ap-920	129	6	simplest	simple	ADJ
ap-920	129	7	non	non	ADJ
ap-920	129	8	-	-	ADJ
ap-920	129	9	trivial	trivial	ADJ
ap-920	129	10	singular	singular	ADJ
ap-920	129	11	factors	factor	NOUN
ap-920	129	12	,	,	PUNCT
ap-920	129	13	i.e.	i.e.	X
ap-920	129	14	,	,	PUNCT
ap-920	129	15	those	those	DET
ap-920	129	16	factors	factor	NOUN
ap-920	129	17	of	of	ADP
ap-920	129	18	the	the	DET
ap-920	129	19	form	form	NOUN
ap-920	129	20	s	s	PART
ap-920	129	21	x	x	X
ap-920	129	22	y	y	PROPN
ap-920	129	23	x	x	SYM
ap-920	129	24	b	b	NOUN
ap-920	129	25	yr	yr	NOUN
ap-920	129	26	r	r	NOUN
ap-920	129	27	(	(	PUNCT
ap-920	129	28	)	)	PUNCT
ap-920	129	29	(	(	PUNCT
ap-920	129	30	)	)	PUNCT
ap-920	129	31	(	(	PUNCT
ap-920	129	32	,	,	PUNCT
ap-920	129	33	)	)	PUNCT
ap-920	129	34	1	1	NUM
ap-920	129	35	1	1	NUM
ap-920	129	36	�	�	PROPN
ap-920	129	37	,	,	PUNCT
ap-920	129	38	x	x	PROPN
ap-920	129	39	y	y	PROPN
ap-920	129	40	,	,	PUNCT
ap-920	129	41	,	,	PUNCT
ap-920	129	42	�	�	PROPN
ap-920	129	43	0	0	NUM
ap-920	129	44	1	1	NUM
ap-920	129	45	,	,	PUNCT
ap-920	129	46	observation	observation	NOUN
ap-920	129	47	20	20	NUM
ap-920	129	48	will	will	AUX
ap-920	129	49	allow	allow	VERB
ap-920	129	50	us	we	PRON
ap-920	129	51	to	to	PART
ap-920	129	52	get	get	VERB
ap-920	129	53	the	the	DET
ap-920	129	54	set	set	NOUN
ap-920	129	55	of	of	ADP
ap-920	129	56	all	all	DET
ap-920	129	57	singular	singular	ADJ
ap-920	129	58	factors	factor	NOUN
ap-920	129	59	of	of	ADP
ap-920	129	60	u	u	PROPN
ap-920	129	61	�	�	PROPN
ap-920	129	62	.	.	PUNCT
ap-920	130	1	©	©	PROPN
ap-920	130	2	czech	czech	PROPN
ap-920	130	3	technical	technical	PROPN
ap-920	130	4	university	university	PROPN
ap-920	130	5	publishing	publishing	NOUN
ap-920	130	6	house	house	NOUN
ap-920	130	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-920	130	8	17	17	NUM
ap-920	130	9	acta	acta	PROPN
ap-920	130	10	polytechnica	polytechnica	PROPN
ap-920	130	11	vol	vol	NOUN
ap-920	130	12	.	.	PUNCT
ap-920	131	1	47	47	NUM
ap-920	131	2	no	no	NOUN
ap-920	131	3	.	.	PUNCT
ap-920	132	1	2–3/2007	2–3/2007	NUM
ap-920	132	2	proposition	proposition	NOUN
ap-920	132	3	21	21	NUM
ap-920	132	4	the	the	DET
ap-920	132	5	set	set	NOUN
ap-920	132	6	of	of	ADP
ap-920	132	7	all	all	DET
ap-920	132	8	singular	singular	ADJ
ap-920	132	9	factors	factor	NOUN
ap-920	132	10	of	of	ADP
ap-920	132	11	u	u	NOUN
ap-920	132	12	�	�	PROPN
ap-920	132	13	is	be	AUX
ap-920	132	14	given	give	VERB
ap-920	132	15	by	by	ADP
ap-920	132	16	0	0	NUM
ap-920	132	17	1	1	NUM
ap-920	132	18	0	0	NUM
ap-920	132	19	1	1	NUM
ap-920	132	20	,	,	PUNCT
ap-920	132	21	(	(	PUNCT
ap-920	132	22	,	,	PUNCT
ap-920	132	23	)	)	PUNCT
ap-920	132	24	,	,	PUNCT
ap-920	132	25	,	,	PUNCT
ap-920	132	26	,	,	PUNCT
ap-920	132	27	(	(	PUNCT
ap-920	132	28	)	)	PUNCT
ap-920	132	29	�	�	PROPN
ap-920	132	30	�	�	PROPN
ap-920	132	31	�	�	PROPN
ap-920	132	32	�	�	PROPN
ap-920	132	33	s	s	PART
ap-920	132	34	x	x	SYM
ap-920	132	35	y	y	NOUN
ap-920	132	36	r	r	PROPN
ap-920	132	37	a	a	DET
ap-920	132	38	nr	nr	PROPN
ap-920	132	39	n	n	PRON
ap-920	132	40	�	�	PROPN
ap-920	132	41	�	�	PROPN
ap-920	132	42	where	where	SCONJ
ap-920	132	43	s	s	VERB
ap-920	132	44	x	x	X
ap-920	132	45	y	y	PROPN
ap-920	132	46	x	x	SYM
ap-920	132	47	b	b	PROPN
ap-920	132	48	yr	yr	NOUN
ap-920	132	49	n	n	ADP
ap-920	132	50	r	r	NOUN
ap-920	132	51	n	n	CCONJ
ap-920	132	52	(	(	PUNCT
ap-920	132	53	)	)	PUNCT
ap-920	132	54	(	(	PUNCT
ap-920	132	55	)	)	PUNCT
ap-920	132	56	(	(	PUNCT
ap-920	132	57	,	,	PUNCT
ap-920	132	58	)	)	PUNCT
ap-920	132	59	�	�	PROPN
ap-920	132	60	for	for	ADP
ap-920	132	61	all	all	DET
ap-920	132	62	n	n	PRON
ap-920	132	63	�	�	PROPN
ap-920	132	64	�	�	PROPN
ap-920	132	65	and	and	CCONJ
ap-920	132	66	x	x	NOUN
ap-920	132	67	,	,	PUNCT
ap-920	132	68	y	y	PROPN
ap-920	132	69	come	come	VERB
ap-920	132	70	from	from	ADP
ap-920	132	71	the	the	DET
ap-920	132	72	form	form	NOUN
ap-920	132	73	of	of	ADP
ap-920	132	74	the	the	DET
ap-920	132	75	simplest	simple	ADJ
ap-920	132	76	non	non	ADJ
ap-920	132	77	-	-	ADJ
ap-920	132	78	trivial	trivial	ADJ
ap-920	132	79	singular	singular	ADJ
ap-920	132	80	factors	factor	NOUN
ap-920	132	81	:	:	PUNCT
ap-920	133	1	s	s	X
ap-920	133	2	r	r	NOUN
ap-920	133	3	ar	ar	NOUN
ap-920	133	4	r	r	NOUN
ap-920	133	5	(	(	PUNCT
ap-920	133	6	)	)	PUNCT
ap-920	133	7	(	(	PUNCT
ap-920	133	8	,	,	PUNCT
ap-920	133	9	)	)	PUNCT
ap-920	133	10	,	,	PUNCT
ap-920	133	11	1	1	NUM
ap-920	133	12	0	0	NUM
ap-920	133	13	0	0	NUM
ap-920	133	14	00	00	NUM
ap-920	133	15	0	0	NUM
ap-920	133	16	2	2	NUM
ap-920	133	17	�	�	PROPN
ap-920	133	18	�	�	PROPN
ap-920	133	19	�	�	PROPN
ap-920	133	20	sb	sb	PROPN
ap-920	133	21	b	b	PROPN
ap-920	133	22	(	(	PUNCT
ap-920	133	23	)	)	PUNCT
ap-920	133	24	(	(	PUNCT
ap-920	133	25	,	,	PUNCT
ap-920	133	26	)	)	PUNCT
ap-920	133	27	1	1	NUM
ap-920	133	28	1	1	NUM
ap-920	133	29	0	0	NUM
ap-920	133	30	10	10	NUM
ap-920	133	31	0	0	NUM
ap-920	133	32	�	�	PROPN
ap-920	133	33	,	,	PUNCT
ap-920	133	34	sb	sb	PROPN
ap-920	133	35	b	b	PROPN
ap-920	133	36	(	(	PUNCT
ap-920	133	37	)	)	PUNCT
ap-920	133	38	(	(	PUNCT
ap-920	133	39	,	,	PUNCT
ap-920	133	40	)	)	PUNCT
ap-920	133	41	1	1	NUM
ap-920	133	42	0	0	NUM
ap-920	133	43	1	1	NUM
ap-920	133	44	00	00	NUM
ap-920	133	45	1	1	NUM
ap-920	133	46	�	�	PROPN
ap-920	133	47	,	,	PUNCT
ap-920	133	48	sb	sb	PROPN
ap-920	133	49	b	b	PROPN
ap-920	133	50	(	(	PUNCT
ap-920	133	51	)	)	PUNCT
ap-920	133	52	(	(	PUNCT
ap-920	133	53	,	,	PUNCT
ap-920	133	54	)	)	PUNCT
ap-920	133	55	1	1	NUM
ap-920	133	56	1	1	NUM
ap-920	133	57	1	1	NUM
ap-920	133	58	10	10	NUM
ap-920	133	59	1	1	NUM
ap-920	133	60	�	�	PROPN
ap-920	133	61	,	,	PUNCT
ap-920	133	62	s0	s0	PROPN
ap-920	133	63	1	1	NUM
ap-920	133	64	0	0	NUM
ap-920	133	65	0	0	NUM
ap-920	133	66	00	00	NUM
ap-920	133	67	(	(	PUNCT
ap-920	133	68	)	)	PUNCT
ap-920	133	69	(	(	PUNCT
ap-920	133	70	,	,	PUNCT
ap-920	133	71	)	)	PUNCT
ap-920	133	72	�	�	PROPN
ap-920	133	73	.	.	PUNCT
ap-920	134	1	to	to	PART
ap-920	134	2	compute	compute	VERB
ap-920	134	3	the	the	DET
ap-920	134	4	length	length	NOUN
ap-920	134	5	of	of	ADP
ap-920	134	6	singular	singular	ADJ
ap-920	134	7	factors	factor	NOUN
ap-920	134	8	,	,	PUNCT
ap-920	134	9	it	it	PRON
ap-920	134	10	is	be	AUX
ap-920	134	11	,	,	PUNCT
ap-920	134	12	of	of	ADP
ap-920	134	13	course	course	NOUN
ap-920	134	14	,	,	PUNCT
ap-920	134	15	enough	enough	ADJ
ap-920	134	16	to	to	PART
ap-920	134	17	compute	compute	VERB
ap-920	134	18	the	the	DET
ap-920	134	19	length	length	NOUN
ap-920	134	20	of	of	ADP
ap-920	134	21	bispecial	bispecial	ADJ
ap-920	134	22	factors	factor	NOUN
ap-920	134	23	since	since	SCONJ
ap-920	134	24	s	s	NOUN
ap-920	134	25	x	x	SYM
ap-920	134	26	y	y	VERB
ap-920	134	27	br	br	NOUN
ap-920	134	28	n	n	CCONJ
ap-920	134	29	r	r	NOUN
ap-920	134	30	n	n	CCONJ
ap-920	134	31	(	(	PUNCT
ap-920	134	32	)	)	PUNCT
ap-920	134	33	(	(	PUNCT
ap-920	134	34	)	)	PUNCT
ap-920	134	35	(	(	PUNCT
ap-920	134	36	,	,	PUNCT
ap-920	134	37	)	)	PUNCT
ap-920	134	38	�	�	PROPN
ap-920	134	39	�	�	PROPN
ap-920	134	40	2	2	NUM
ap-920	134	41	.	.	PUNCT
ap-920	135	1	for	for	ADP
ap-920	135	2	the	the	DET
ap-920	135	3	lengths	length	NOUN
ap-920	135	4	of	of	ADP
ap-920	135	5	bispecial	bispecial	ADJ
ap-920	135	6	factors	factor	NOUN
ap-920	135	7	,	,	PUNCT
ap-920	135	8	we	we	PRON
ap-920	135	9	have	have	VERB
ap-920	135	10	b	b	PROPN
ap-920	135	11	b	b	NOUN
ap-920	135	12	br	br	NOUN
ap-920	135	13	n	n	NOUN
ap-920	135	14	r	r	NOUN
ap-920	135	15	n	n	CCONJ
ap-920	135	16	r	r	NOUN
ap-920	135	17	n	n	CCONJ
ap-920	135	18	(	(	PUNCT
ap-920	135	19	)	)	PUNCT
ap-920	135	20	(	(	PUNCT
ap-920	135	21	)	)	PUNCT
ap-920	135	22	(	(	PUNCT
ap-920	135	23	)	)	PUNCT
ap-920	135	24	�	�	PROPN
ap-920	135	25	�	�	PROPN
ap-920	135	26	0	0	NUM
ap-920	135	27	1	1	NUM
ap-920	135	28	where	where	SCONJ
ap-920	135	29	denotes	denote	VERB
ap-920	135	30	the	the	DET
ap-920	135	31	number	number	NOUN
ap-920	135	32	of	of	ADP
ap-920	135	33	0	0	NUM
ap-920	135	34	’s	’s	NOUN
ap-920	135	35	in	in	ADP
ap-920	135	36	br	br	PROPN
ap-920	135	37	n	n	CCONJ
ap-920	135	38	(	(	PUNCT
ap-920	135	39	)	)	PUNCT
ap-920	135	40	and	and	CCONJ
ap-920	135	41	br	br	PROPN
ap-920	135	42	n	n	CCONJ
ap-920	135	43	(	(	PUNCT
ap-920	135	44	)	)	PUNCT
ap-920	135	45	1	1	NUM
ap-920	135	46	denotes	denote	VERB
ap-920	135	47	the	the	DET
ap-920	135	48	number	number	NOUN
ap-920	135	49	of	of	ADP
ap-920	135	50	1	1	NUM
ap-920	135	51	’s	’s	NOUN
ap-920	135	52	in	in	ADP
ap-920	135	53	br	br	PROPN
ap-920	135	54	n	n	CCONJ
ap-920	135	55	(	(	PUNCT
ap-920	135	56	)	)	PUNCT
ap-920	135	57	.	.	PUNCT
ap-920	136	1	then	then	ADV
ap-920	136	2	b	b	X
ap-920	136	3	b	b	PROPN
ap-920	136	4	a	a	DET
ap-920	136	5	b	b	PROPN
ap-920	136	6	b	b	PROPN
ap-920	136	7	b	b	NOUN
ap-920	136	8	r	r	NOUN
ap-920	136	9	n	n	ADP
ap-920	136	10	r	r	NOUN
ap-920	136	11	n	n	ADP
ap-920	136	12	r	r	NOUN
ap-920	136	13	n	n	ADP
ap-920	136	14	r	r	NOUN
ap-920	136	15	n	n	NOUN
ap-920	136	16	(	(	PUNCT
ap-920	136	17	)	)	PUNCT
ap-920	136	18	(	(	PUNCT
ap-920	136	19	)	)	PUNCT
ap-920	136	20	(	(	PUNCT
ap-920	136	21	)	)	PUNCT
ap-920	136	22	(	(	PUNCT
ap-920	136	23	)	)	PUNCT
ap-920	136	24	0	0	NUM
ap-920	136	25	1	1	NUM
ap-920	136	26	1	1	NUM
ap-920	136	27	0	0	NUM
ap-920	136	28	11	11	NUM
ap-920	136	29	1	1	NUM
ap-920	136	30	�	�	PROPN
ap-920	136	31	�	�	PROPN
ap-920	136	32	�	�	PROPN
ap-920	136	33	�	�	PROPN
ap-920	136	34	�	�	PROPN
ap-920	136	35	�	�	PROPN
ap-920	136	36	�	�	PROPN
ap-920	136	37	�	�	PROPN
ap-920	136	38	�	�	PROPN
ap-920	136	39	�	�	PROPN
ap-920	136	40	�	�	PROPN
ap-920	136	41	�	�	PROPN
ap-920	136	42	�	�	PROPN
ap-920	136	43	�	�	PROPN
ap-920	136	44	�	�	PROPN
ap-920	136	45	�	�	PROPN
ap-920	136	46	�	�	PROPN
ap-920	136	47	�	�	PROPN
ap-920	136	48	�	�	PROPN
ap-920	136	49	�	�	PROPN
ap-920	136	50	�	�	PROPN
ap-920	136	51	1	1	NUM
ap-920	136	52	�	�	PROPN
ap-920	136	53	�	�	PROPN
ap-920	136	54	�	�	PROPN
ap-920	136	55	�	�	PROPN
ap-920	136	56	�	�	PROPN
ap-920	136	57	�	�	PROPN
ap-920	136	58	�	�	PROPN
ap-920	136	59	�	�	PROPN
ap-920	136	60	�	�	PROPN
ap-920	136	61	�	�	PROPN
ap-920	136	62	for	for	ADP
ap-920	136	63	all	all	DET
ap-920	136	64	n	n	PRON
ap-920	136	65	�	�	PROPN
ap-920	136	66	2	2	NUM
ap-920	136	67	.	.	PUNCT
ap-920	137	1	3	3	X
ap-920	137	2	.	.	X
ap-920	137	3	to	to	PART
ap-920	137	4	describe	describe	VERB
ap-920	137	5	the	the	DET
ap-920	137	6	return	return	NOUN
ap-920	137	7	words	word	NOUN
ap-920	137	8	of	of	ADP
ap-920	137	9	singular	singular	ADJ
ap-920	137	10	factors	factor	NOUN
ap-920	137	11	,	,	PUNCT
ap-920	137	12	we	we	PRON
ap-920	137	13	can	can	AUX
ap-920	137	14	again	again	ADV
ap-920	137	15	make	make	VERB
ap-920	137	16	use	use	NOUN
ap-920	137	17	of	of	ADP
ap-920	137	18	a	a	DET
ap-920	137	19	relation	relation	NOUN
ap-920	137	20	between	between	ADP
ap-920	137	21	return	return	NOUN
ap-920	137	22	words	word	NOUN
ap-920	137	23	of	of	ADP
ap-920	137	24	a	a	DET
ap-920	137	25	singular	singular	ADJ
ap-920	137	26	factor	factor	NOUN
ap-920	137	27	and	and	CCONJ
ap-920	137	28	return	return	VERB
ap-920	137	29	words	word	NOUN
ap-920	137	30	of	of	ADP
ap-920	137	31	its	its	PRON
ap-920	137	32	image	image	NOUN
ap-920	137	33	under	under	ADP
ap-920	137	34	�	�	PROPN
ap-920	137	35	.	.	PUNCT
ap-920	138	1	proposition	proposition	NOUN
ap-920	138	2	22	22	NUM
ap-920	138	3	let	let	VERB
ap-920	138	4	n	n	PRON
ap-920	138	5	�	�	PROPN
ap-920	138	6	2	2	NUM
ap-920	138	7	,	,	PUNCT
ap-920	138	8	r	r	PROPN
ap-920	138	9	a	a	DET
ap-920	138	10	�	�	PROPN
ap-920	138	11	�	�	PROPN
ap-920	138	12	0	0	NUM
ap-920	138	13	1	1	NUM
ap-920	138	14	,	,	PUNCT
ap-920	138	15	,	,	PUNCT
ap-920	138	16	�	�	PROPN
ap-920	138	17	.	.	PUNCT
ap-920	139	1	the	the	DET
ap-920	139	2	following	follow	VERB
ap-920	139	3	sets	set	NOUN
ap-920	139	4	are	be	AUX
ap-920	139	5	equal	equal	ADJ
ap-920	139	6	w	w	ADP
ap-920	139	7	w	w	PROPN
ap-920	139	8	s	s	PROPN
ap-920	139	9	x	x	SYM
ap-920	139	10	y	y	PROPN
ap-920	139	11	v	v	NUM
ap-920	139	12	v	v	NOUN
ap-920	139	13	s	s	NOUN
ap-920	139	14	x	x	NOUN
ap-920	139	15	yr	yr	NOUN
ap-920	139	16	n	n	ADP
ap-920	139	17	r	r	NOUN
ap-920	139	18	n	n	CCONJ
ap-920	139	19	�	�	PROPN
ap-920	139	20	�	�	PROPN
ap-920	139	21	�	�	PROPN
ap-920	139	22	�	�	PROPN
ap-920	139	23	ret	ret	PROPN
ap-920	139	24	ret	ret	PROPN
ap-920	139	25	(	(	PUNCT
ap-920	139	26	(	(	PUNCT
ap-920	139	27	,	,	PUNCT
ap-920	139	28	)	)	PUNCT
ap-920	139	29	)	)	PUNCT
ap-920	139	30	(	(	PUNCT
ap-920	139	31	)	)	PUNCT
ap-920	139	32	(	(	PUNCT
ap-920	139	33	(	(	PUNCT
ap-920	139	34	,	,	PUNCT
ap-920	139	35	)	)	PUNCT
ap-920	139	36	)	)	PUNCT
ap-920	139	37	�	�	PROPN
ap-920	139	38	1	1	NUM
ap-920	139	39	.	.	PUNCT
ap-920	140	1	proof	proof	NOUN
ap-920	140	2	.	.	PUNCT
ap-920	141	1	we	we	PRON
ap-920	141	2	will	will	AUX
ap-920	141	3	distinguish	distinguish	VERB
ap-920	141	4	two	two	NUM
ap-920	141	5	situations	situation	NOUN
ap-920	141	6	.	.	PUNCT
ap-920	142	1	a	a	X
ap-920	142	2	)	)	PUNCT
ap-920	142	3	for	for	ADP
ap-920	142	4	x	x	X
ap-920	142	5	�	�	PROPN
ap-920	142	6	0	0	NUM
ap-920	142	7	and	and	CCONJ
ap-920	142	8	y	y	PROPN
ap-920	142	9	�	�	PROPN
ap-920	142	10	0	0	NUM
ap-920	142	11	1	1	NUM
ap-920	142	12	,	,	PUNCT
ap-920	142	13	,	,	PUNCT
ap-920	142	14	applying	apply	VERB
ap-920	142	15	observation	observation	NOUN
ap-920	142	16	8	8	NUM
ap-920	142	17	on	on	ADP
ap-920	142	18	return	return	NOUN
ap-920	142	19	words	word	NOUN
ap-920	142	20	of	of	ADP
ap-920	142	21	factors	factor	NOUN
ap-920	142	22	which	which	PRON
ap-920	142	23	are	be	AUX
ap-920	142	24	not	not	PART
ap-920	142	25	right	right	ADJ
ap-920	142	26	or	or	CCONJ
ap-920	142	27	left	leave	VERB
ap-920	142	28	special	special	ADJ
ap-920	142	29	,	,	PUNCT
ap-920	142	30	it	it	PRON
ap-920	142	31	follows	follow	VERB
ap-920	142	32	that	that	SCONJ
ap-920	142	33	the	the	DET
ap-920	142	34	set	set	NOUN
ap-920	142	35	of	of	ADP
ap-920	142	36	lengths	length	NOUN
ap-920	142	37	of	of	ADP
ap-920	142	38	return	return	NOUN
ap-920	142	39	words	word	NOUN
ap-920	142	40	of	of	ADP
ap-920	142	41	s	s	NOUN
ap-920	142	42	x	x	X
ap-920	142	43	y	y	PROPN
ap-920	142	44	x	x	SYM
ap-920	142	45	b	b	PROPN
ap-920	142	46	yr	yr	NOUN
ap-920	142	47	n	n	ADP
ap-920	142	48	b	b	PROPN
ap-920	142	49	r	r	NOUN
ap-920	142	50	n	n	SYM
ap-920	142	51	b	b	NOUN
ap-920	142	52	(	(	PUNCT
ap-920	142	53	)	)	PUNCT
ap-920	142	54	(	(	PUNCT
ap-920	142	55	)	)	PUNCT
ap-920	142	56	(	(	PUNCT
ap-920	142	57	,	,	PUNCT
ap-920	142	58	)	)	PUNCT
ap-920	142	59	(	(	PUNCT
ap-920	142	60	)	)	PUNCT
ap-920	142	61	�	�	PROPN
ap-920	142	62	�	�	PROPN
ap-920	142	63	0	0	NUM
ap-920	142	64	1	1	NUM
ap-920	142	65	01	01	NUM
ap-920	142	66	�	�	PROPN
ap-920	142	67	is	be	AUX
ap-920	142	68	the	the	DET
ap-920	142	69	same	same	ADJ
ap-920	142	70	as	as	ADP
ap-920	142	71	that	that	PRON
ap-920	142	72	of	of	ADP
ap-920	142	73	�	�	PROPN
ap-920	142	74	�	�	PROPN
ap-920	142	75	�	�	PROPN
ap-920	142	76	�	�	PROPN
ap-920	142	77	�	�	PROPN
ap-920	142	78	�	�	PROPN
ap-920	142	79	�	�	PROPN
ap-920	142	80	x	x	SYM
ap-920	142	81	b	b	PROPN
ap-920	142	82	yr	yr	NOUN
ap-920	142	83	n	n	CCONJ
ap-920	142	84	(	(	PUNCT
ap-920	142	85	)	)	PUNCT
ap-920	142	86	(	(	PUNCT
ap-920	142	87	)	)	PUNCT
ap-920	142	88	�	�	PROPN
ap-920	142	89	1	1	NUM
ap-920	142	90	.	.	PUNCT
ap-920	143	1	thus	thus	ADV
ap-920	143	2	,	,	PUNCT
ap-920	143	3	we	we	PRON
ap-920	143	4	get	get	VERB
ap-920	143	5	w	w	PROPN
ap-920	143	6	w	w	PROPN
ap-920	143	7	s	s	PROPN
ap-920	143	8	x	x	X
ap-920	143	9	y	y	PROPN
ap-920	143	10	w	w	PROPN
ap-920	143	11	w	w	PROPN
ap-920	143	12	s	s	PROPN
ap-920	143	13	x	x	SYM
ap-920	143	14	yr	yr	NOUN
ap-920	143	15	n	n	ADP
ap-920	143	16	r	r	NOUN
ap-920	143	17	n	n	CCONJ
ap-920	143	18	�	�	PROPN
ap-920	143	19	�	�	PROPN
ap-920	143	20	�	�	PROPN
ap-920	143	21	�	�	PROPN
ap-920	143	22	ret	ret	PROPN
ap-920	143	23	ret	ret	PROPN
ap-920	143	24	(	(	PUNCT
ap-920	143	25	(	(	PUNCT
ap-920	143	26	,	,	PUNCT
ap-920	143	27	)	)	PUNCT
ap-920	143	28	)	)	PUNCT
ap-920	144	1	(	(	PUNCT
ap-920	144	2	(	(	PUNCT
ap-920	144	3	(	(	PUNCT
ap-920	144	4	,	,	PUNCT
ap-920	144	5	)	)	PUNCT
ap-920	144	6	)	)	PUNCT
ap-920	144	7	)	)	PUNCT
ap-920	144	8	�	�	PROPN
ap-920	144	9	1	1	NUM
ap-920	144	10	.	.	PUNCT
ap-920	145	1	b	b	X
ap-920	145	2	)	)	PUNCT
ap-920	145	3	the	the	DET
ap-920	145	4	singular	singular	ADJ
ap-920	145	5	factor	factor	NOUN
ap-920	145	6	s	s	PART
ap-920	145	7	br	br	NOUN
ap-920	145	8	n	n	ADV
ap-920	145	9	b	b	NOUN
ap-920	145	10	r	r	NOUN
ap-920	145	11	n	n	SYM
ap-920	145	12	b	b	NOUN
ap-920	145	13	(	(	PUNCT
ap-920	145	14	)	)	PUNCT
ap-920	145	15	(	(	PUNCT
ap-920	145	16	)	)	PUNCT
ap-920	145	17	(	(	PUNCT
ap-920	145	18	,	,	PUNCT
ap-920	145	19	)	)	PUNCT
ap-920	145	20	(	(	PUNCT
ap-920	145	21	)	)	PUNCT
ap-920	145	22	11	11	NUM
ap-920	145	23	10	10	NUM
ap-920	145	24	1	1	NUM
ap-920	145	25	0	0	NUM
ap-920	145	26	11	11	NUM
ap-920	145	27	�	�	PROPN
ap-920	145	28	�	�	PROPN
ap-920	145	29	�	�	PROPN
ap-920	145	30	can	can	AUX
ap-920	145	31	be	be	AUX
ap-920	145	32	extended	extend	VERB
ap-920	145	33	to	to	ADP
ap-920	145	34	the	the	DET
ap-920	145	35	left	left	NOUN
ap-920	145	36	without	without	ADP
ap-920	145	37	changing	change	VERB
ap-920	145	38	the	the	DET
ap-920	145	39	set	set	NOUN
ap-920	145	40	of	of	ADP
ap-920	145	41	lengths	length	NOUN
ap-920	145	42	of	of	ADP
ap-920	145	43	return	return	NOUN
ap-920	145	44	words	word	NOUN
ap-920	145	45	to	to	ADP
ap-920	145	46	0	0	NUM
ap-920	145	47	10	10	NUM
ap-920	145	48	1	1	NUM
ap-920	145	49	0	0	NUM
ap-920	145	50	1	1	NUM
ap-920	145	51	01	01	NUM
ap-920	145	52	11	11	NUM
ap-920	145	53	1a	1a	NOUN
ap-920	145	54	b	b	SYM
ap-920	145	55	r	r	NOUN
ap-920	145	56	n	n	NOUN
ap-920	145	57	b	b	NOUN
ap-920	145	58	r	r	NOUN
ap-920	145	59	nb	nb	PROPN
ap-920	145	60	b	b	PROPN
ap-920	145	61	�	�	PROPN
ap-920	145	62	�	�	PROPN
ap-920	145	63	�	�	PROPN
ap-920	145	64	�	�	PROPN
ap-920	145	65	(	(	PUNCT
ap-920	145	66	)	)	PUNCT
ap-920	145	67	(	(	PUNCT
ap-920	145	68	)	)	PUNCT
ap-920	145	69	(	(	PUNCT
ap-920	145	70	)	)	PUNCT
ap-920	145	71	(	(	PUNCT
ap-920	145	72	)	)	PUNCT
ap-920	145	73	(	(	PUNCT
ap-920	145	74	)	)	PUNCT
ap-920	145	75	(	(	PUNCT
ap-920	145	76	)	)	PUNCT
ap-920	145	77	�	�	PROPN
ap-920	145	78	�	�	PROPN
ap-920	145	79	�	�	PROPN
ap-920	145	80	.	.	PUNCT
ap-920	146	1	thus	thus	ADV
ap-920	146	2	,	,	PUNCT
ap-920	146	3	we	we	PRON
ap-920	146	4	get	get	VERB
ap-920	146	5	w	w	PROPN
ap-920	146	6	w	w	PROPN
ap-920	146	7	s	s	PROPN
ap-920	146	8	x	x	X
ap-920	146	9	y	y	PROPN
ap-920	146	10	w	w	PROPN
ap-920	146	11	w	w	PROPN
ap-920	146	12	sr	sr	PROPN
ap-920	146	13	n	n	CCONJ
ap-920	146	14	r	r	NOUN
ap-920	146	15	n	n	CCONJ
ap-920	146	16	�	�	PROPN
ap-920	146	17	�	�	PROPN
ap-920	146	18	�	�	PROPN
ap-920	146	19	�	�	PROPN
ap-920	146	20	ret	ret	PROPN
ap-920	146	21	ret	ret	PROPN
ap-920	146	22	(	(	PUNCT
ap-920	146	23	(	(	PUNCT
ap-920	146	24	,	,	PUNCT
ap-920	146	25	)	)	PUNCT
ap-920	146	26	)	)	PUNCT
ap-920	147	1	(	(	PUNCT
ap-920	147	2	(	(	PUNCT
ap-920	147	3	(	(	PUNCT
ap-920	147	4	,	,	PUNCT
ap-920	147	5	)	)	PUNCT
ap-920	147	6	)	)	PUNCT
ap-920	147	7	)	)	PUNCT
ap-920	147	8	�	�	PROPN
ap-920	147	9	0	0	NUM
ap-920	147	10	1	1	NUM
ap-920	147	11	11	11	NUM
ap-920	147	12	.	.	PUNCT
ap-920	148	1	the	the	DET
ap-920	148	2	statement	statement	NOUN
ap-920	148	3	then	then	ADV
ap-920	148	4	follows	follow	VERB
ap-920	148	5	using	use	VERB
ap-920	148	6	lemma	lemma	PROPN
ap-920	148	7	12	12	NUM
ap-920	148	8	and	and	CCONJ
ap-920	148	9	proposition	proposition	NOUN
ap-920	148	10	14	14	NUM
ap-920	148	11	,	,	PUNCT
ap-920	148	12	and	and	CCONJ
ap-920	148	13	,	,	PUNCT
ap-920	148	14	in	in	ADP
ap-920	148	15	the	the	DET
ap-920	148	16	case	case	NOUN
ap-920	148	17	of	of	ADP
ap-920	148	18	(	(	PUNCT
ap-920	148	19	b	b	NOUN
ap-920	148	20	)	)	PUNCT
ap-920	148	21	,	,	PUNCT
ap-920	148	22	also	also	ADV
ap-920	148	23	using	use	VERB
ap-920	148	24	relation	relation	NOUN
ap-920	148	25	(	(	PUNCT
ap-920	148	26	3	3	NUM
ap-920	148	27	)	)	PUNCT
ap-920	148	28	for	for	ADP
ap-920	148	29	return	return	NOUN
ap-920	148	30	words	word	NOUN
ap-920	148	31	of	of	ADP
ap-920	148	32	0	0	NUM
ap-920	148	33	1	1	NUM
ap-920	148	34	11sr	11sr	NOUN
ap-920	148	35	n	n	DET
ap-920	148	36	�	�	PROPN
ap-920	148	37	(	(	PUNCT
ap-920	148	38	,	,	PUNCT
ap-920	148	39	)	)	PUNCT
ap-920	148	40	and	and	CCONJ
ap-920	148	41	sr	sr	PROPN
ap-920	148	42	n	n	PROPN
ap-920	148	43	�	�	PROPN
ap-920	148	44	1	1	NUM
ap-920	148	45	1	1	NUM
ap-920	148	46	1	1	NUM
ap-920	148	47	(	(	PUNCT
ap-920	148	48	,	,	PUNCT
ap-920	148	49	)	)	PUNCT
ap-920	148	50	.	.	PUNCT
ap-920	149	1	now	now	ADV
ap-920	149	2	it	it	PRON
ap-920	149	3	suffices	suffice	VERB
ap-920	149	4	to	to	PART
ap-920	149	5	determine	determine	VERB
ap-920	149	6	return	return	NOUN
ap-920	149	7	words	word	NOUN
ap-920	149	8	and	and	CCONJ
ap-920	149	9	their	their	PRON
ap-920	149	10	lengths	length	NOUN
ap-920	149	11	for	for	ADP
ap-920	149	12	the	the	DET
ap-920	149	13	simplest	simple	ADJ
ap-920	149	14	singular	singular	NOUN
ap-920	149	15	factorss	factorss	ADJ
ap-920	149	16	x	x	SYM
ap-920	149	17	yr	yr	PROPN
ap-920	149	18	(	(	PUNCT
ap-920	149	19	)	)	PUNCT
ap-920	149	20	(	(	PUNCT
ap-920	149	21	,	,	PUNCT
ap-920	149	22	)	)	PUNCT
ap-920	149	23	1	1	X
ap-920	149	24	.	.	PUNCT
ap-920	150	1	proposition	proposition	NOUN
ap-920	150	2	22	22	NUM
ap-920	150	3	implies	imply	VERB
ap-920	150	4	that	that	SCONJ
ap-920	150	5	the	the	DET
ap-920	150	6	lengths	length	NOUN
ap-920	150	7	of	of	ADP
ap-920	150	8	return	return	NOUN
ap-920	150	9	words	word	NOUN
ap-920	150	10	of	of	ADP
ap-920	150	11	all	all	DET
ap-920	150	12	the	the	DET
ap-920	150	13	other	other	ADJ
ap-920	150	14	singular	singular	ADJ
ap-920	150	15	factors	factor	NOUN
ap-920	150	16	will	will	AUX
ap-920	150	17	be	be	AUX
ap-920	150	18	obtained	obtain	VERB
ap-920	150	19	by	by	ADP
ap-920	150	20	calculating	calculate	VERB
ap-920	150	21	the	the	DET
ap-920	150	22	lengths	length	NOUN
ap-920	150	23	of	of	ADP
ap-920	150	24	images	image	NOUN
ap-920	150	25	of	of	ADP
ap-920	150	26	the	the	DET
ap-920	150	27	simplest	simple	ADJ
ap-920	150	28	return	return	NOUN
ap-920	150	29	words	word	NOUN
ap-920	150	30	.	.	PUNCT
ap-920	151	1	here	here	ADV
ap-920	151	2	are	be	AUX
ap-920	151	3	the	the	DET
ap-920	151	4	return	return	NOUN
ap-920	151	5	words	word	NOUN
ap-920	151	6	of	of	ADP
ap-920	151	7	the	the	DET
ap-920	151	8	simplest	simple	ADJ
ap-920	151	9	singular	singular	ADJ
ap-920	151	10	factors	factor	NOUN
ap-920	151	11	.	.	PUNCT
ap-920	152	1	a	a	X
ap-920	152	2	)	)	PUNCT
ap-920	152	3	for	for	ADP
ap-920	152	4	the	the	DET
ap-920	152	5	trivial	trivial	ADJ
ap-920	152	6	singular	singular	ADJ
ap-920	152	7	factors	factor	NOUN
ap-920	152	8	0	0	NUM
ap-920	152	9	,	,	PUNCT
ap-920	152	10	1	1	NUM
ap-920	152	11	,	,	PUNCT
ap-920	152	12	one	one	PRON
ap-920	152	13	gets	get	VERB
ap-920	152	14	ret	ret	NOUN
ap-920	152	15	(	(	PUNCT
ap-920	152	16	)	)	PUNCT
ap-920	152	17	,	,	PUNCT
ap-920	152	18	0	0	NUM
ap-920	152	19	0	0	NUM
ap-920	152	20	01	01	NUM
ap-920	152	21	�	�	PROPN
ap-920	152	22	and	and	CCONJ
ap-920	152	23	ret	ret	PROPN
ap-920	152	24	(	(	PUNCT
ap-920	152	25	)	)	PUNCT
ap-920	152	26	,	,	PUNCT
ap-920	152	27	1	1	NUM
ap-920	152	28	10	10	NUM
ap-920	152	29	10	10	NUM
ap-920	152	30	�	�	PROPN
ap-920	152	31	a	a	DET
ap-920	152	32	b	b	NOUN
ap-920	152	33	.	.	PUNCT
ap-920	153	1	(	(	PUNCT
ap-920	153	2	4	4	NUM
ap-920	153	3	)	)	SYM
ap-920	153	4	b	b	NOUN
ap-920	153	5	)	)	PUNCT
ap-920	153	6	forsr	forsr	VERB
ap-920	153	7	r	r	NOUN
ap-920	153	8	(	(	PUNCT
ap-920	153	9	)	)	PUNCT
ap-920	153	10	(	(	PUNCT
ap-920	153	11	,	,	PUNCT
ap-920	153	12	)	)	PUNCT
ap-920	153	13	1	1	NUM
ap-920	153	14	0	0	NUM
ap-920	153	15	0	0	NUM
ap-920	153	16	00	00	NUM
ap-920	153	17	0	0	NUM
ap-920	153	18	�	�	PROPN
ap-920	153	19	,	,	PUNCT
ap-920	153	20	using	use	VERB
ap-920	153	21	the	the	DET
ap-920	153	22	proof	proof	NOUN
ap-920	153	23	of	of	ADP
ap-920	153	24	theorem	theorem	NOUN
ap-920	153	25	16	16	NUM
ap-920	153	26	,	,	PUNCT
ap-920	153	27	we	we	PRON
ap-920	153	28	have	have	VERB
ap-920	153	29	ret	ret	NOUN
ap-920	153	30	(	(	PUNCT
ap-920	153	31	)	)	PUNCT
ap-920	153	32	,	,	PUNCT
ap-920	153	33	,	,	PUNCT
ap-920	153	34	,	,	PUNCT
ap-920	153	35	00	00	NUM
ap-920	153	36	0	0	SYM
ap-920	153	37	0	0	NUM
ap-920	154	1	1	1	NUM
ap-920	154	2	0	0	NUM
ap-920	154	3	10	10	NUM
ap-920	154	4	1	1	NUM
ap-920	154	5	2	2	NUM
ap-920	154	6	0	0	NUM
ap-920	154	7	0	0	NUM
ap-920	154	8	1	1	NUM
ap-920	154	9	0	0	NUM
ap-920	154	10	10	10	NUM
ap-920	154	11	1	1	NUM
ap-920	154	12	22	22	NUM
ap-920	154	13	2r	2r	NUM
ap-920	154	14	a	a	DET
ap-920	154	15	a	a	DET
ap-920	154	16	b	b	NOUN
ap-920	154	17	r	r	NOUN
ap-920	154	18	r	r	NOUN
ap-920	154	19	b	b	NOUN
ap-920	154	20	r	r	NOUN
ap-920	154	21	a	a	DET
ap-920	154	22	b	b	NOUN
ap-920	154	23	r	r	NOUN
ap-920	154	24	�	�	PROPN
ap-920	154	25	�	�	PROPN
ap-920	154	26	�	�	PROPN
ap-920	154	27	�	�	PROPN
ap-920	154	28	�	�	PROPN
ap-920	154	29	�	�	PROPN
ap-920	154	30	�	�	PROPN
ap-920	154	31	if	if	SCONJ
ap-920	154	32	if	if	SCONJ
ap-920	154	33	�	�	PROPN
ap-920	154	34	�	�	PROPN
ap-920	154	35	�	�	PROPN
ap-920	154	36	�	�	PROPN
ap-920	154	37	�	�	PROPN
ap-920	154	38	�	�	PROPN
ap-920	154	39	�	�	PROPN
ap-920	154	40	�	�	PROPN
ap-920	154	41	�	�	PROPN
ap-920	154	42	�	�	PROPN
ap-920	154	43	�	�	PROPN
ap-920	154	44	�	�	PROPN
ap-920	154	45	�	�	PROPN
ap-920	154	46	a	a	DET
ap-920	154	47	r	r	NOUN
ap-920	154	48	br	br	NOUN
ap-920	154	49	2	2	NUM
ap-920	154	50	0	0	NUM
ap-920	154	51	0	0	NUM
ap-920	154	52	1	1	NUM
ap-920	154	53	1	1	NUM
ap-920	154	54	22	22	NUM
ap-920	154	55	,	,	PUNCT
ap-920	154	56	if	if	SCONJ
ap-920	154	57	(	(	PUNCT
ap-920	154	58	5	5	NUM
ap-920	154	59	)	)	PUNCT
ap-920	154	60	c	c	NOUN
ap-920	154	61	)	)	PUNCT
ap-920	154	62	for	for	ADP
ap-920	154	63	sb	sb	PROPN
ap-920	154	64	b	b	PROPN
ap-920	154	65	(	(	PUNCT
ap-920	154	66	)	)	PUNCT
ap-920	154	67	(	(	PUNCT
ap-920	154	68	,	,	PUNCT
ap-920	154	69	)	)	PUNCT
ap-920	154	70	1	1	NUM
ap-920	155	1	1	1	NUM
ap-920	155	2	0	0	NUM
ap-920	155	3	10	10	NUM
ap-920	155	4	0	0	NUM
ap-920	155	5	�	�	PROPN
ap-920	155	6	,	,	PUNCT
ap-920	155	7	one	one	PRON
ap-920	155	8	can	can	AUX
ap-920	155	9	easily	easily	ADV
ap-920	155	10	find	find	VERB
ap-920	155	11	ret	ret	NOUN
ap-920	155	12	(	(	PUNCT
ap-920	155	13	)	)	PUNCT
ap-920	155	14	,	,	PUNCT
ap-920	155	15	10	10	NUM
ap-920	155	16	0	0	NUM
ap-920	155	17	10	10	NUM
ap-920	155	18	10	10	NUM
ap-920	155	19	10b	10b	NOUN
ap-920	155	20	a	a	DET
ap-920	155	21	a	a	DET
ap-920	155	22	b	b	PROPN
ap-920	155	23	�	�	PROPN
ap-920	155	24	.	.	PUNCT
ap-920	156	1	(	(	PUNCT
ap-920	156	2	6	6	NUM
ap-920	156	3	)	)	PUNCT
ap-920	156	4	d	d	NOUN
ap-920	156	5	)	)	PUNCT
ap-920	156	6	for	for	ADP
ap-920	156	7	sb	sb	PROPN
ap-920	156	8	b	b	PROPN
ap-920	156	9	(	(	PUNCT
ap-920	156	10	)	)	PUNCT
ap-920	156	11	(	(	PUNCT
ap-920	156	12	,	,	PUNCT
ap-920	156	13	)	)	PUNCT
ap-920	156	14	1	1	NUM
ap-920	156	15	0	0	NUM
ap-920	156	16	1	1	NUM
ap-920	156	17	00	00	NUM
ap-920	156	18	1	1	NUM
ap-920	156	19	�	�	PROPN
ap-920	156	20	,	,	PUNCT
ap-920	156	21	one	one	PRON
ap-920	156	22	has	have	VERB
ap-920	156	23	ret	ret	NOUN
ap-920	156	24	(	(	PUNCT
ap-920	156	25	)	)	PUNCT
ap-920	156	26	,	,	PUNCT
ap-920	156	27	(	(	PUNCT
ap-920	156	28	)	)	PUNCT
ap-920	156	29	(	(	PUNCT
ap-920	156	30	)	)	PUNCT
ap-920	156	31	00	00	NUM
ap-920	157	1	1	1	NUM
ap-920	157	2	0	0	NUM
ap-920	157	3	10	10	NUM
ap-920	157	4	0	0	NUM
ap-920	157	5	10	10	NUM
ap-920	157	6	101	101	NUM
ap-920	157	7	1	1	NUM
ap-920	157	8	1	1	NUM
ap-920	157	9	1b	1b	NUM
ap-920	157	10	b	b	NOUN
ap-920	157	11	a	a	DET
ap-920	157	12	b	b	PROPN
ap-920	157	13	b	b	PROPN
ap-920	157	14	b	b	PROPN
ap-920	157	15	a	a	DET
ap-920	157	16	b	b	PROPN
ap-920	157	17	�	�	PROPN
ap-920	157	18	�	�	PROPN
ap-920	157	19	�	�	PROPN
ap-920	157	20	�	�	PROPN
ap-920	157	21	�	�	PROPN
ap-920	157	22	�	�	PROPN
ap-920	157	23	�	�	PROPN
ap-920	157	24	.	.	PUNCT
ap-920	158	1	(	(	PUNCT
ap-920	158	2	7	7	X
ap-920	158	3	)	)	PUNCT
ap-920	158	4	e	e	NOUN
ap-920	158	5	)	)	PUNCT
ap-920	158	6	sincesb	sincesb	PROPN
ap-920	158	7	b	b	PROPN
ap-920	158	8	(	(	PUNCT
ap-920	158	9	)	)	PUNCT
ap-920	158	10	(	(	PUNCT
ap-920	158	11	,	,	PUNCT
ap-920	158	12	)	)	PUNCT
ap-920	158	13	(	(	PUNCT
ap-920	158	14	)	)	SYM
ap-920	158	15	1	1	NUM
ap-920	158	16	1	1	NUM
ap-920	158	17	1	1	NUM
ap-920	158	18	10	10	NUM
ap-920	158	19	1	1	NUM
ap-920	158	20	1	1	NUM
ap-920	158	21	1	1	NUM
ap-920	158	22	�	�	PROPN
ap-920	158	23	�	�	PROPN
ap-920	158	24	�	�	PROPN
ap-920	158	25	,	,	PUNCT
ap-920	158	26	using	use	VERB
ap-920	158	27	relation	relation	NOUN
ap-920	158	28	(	(	PUNCT
ap-920	158	29	3	3	NUM
ap-920	158	30	)	)	PUNCT
ap-920	158	31	,	,	PUNCT
ap-920	158	32	we	we	PRON
ap-920	158	33	have	have	VERB
ap-920	158	34	ret	ret	PROPN
ap-920	158	35	ret	ret	PROPN
ap-920	158	36	(	(	PUNCT
ap-920	158	37	)	)	PUNCT
ap-920	158	38	(	(	PUNCT
ap-920	158	39	(	(	PUNCT
ap-920	158	40	)	)	PUNCT
ap-920	158	41	)	)	PUNCT
ap-920	158	42	(	(	PUNCT
ap-920	158	43	)	)	PUNCT
ap-920	158	44	,	,	PUNCT
ap-920	158	45	(	(	PUNCT
ap-920	158	46	)	)	PUNCT
ap-920	158	47	.	.	PUNCT
ap-920	159	1	10	10	NUM
ap-920	159	2	1	1	NUM
ap-920	159	3	1	1	NUM
ap-920	159	4	1	1	NUM
ap-920	159	5	1	1	NUM
ap-920	159	6	1	1	NUM
ap-920	159	7	10	10	NUM
ap-920	159	8	1	1	NUM
ap-920	159	9	1	1	NUM
ap-920	159	10	10	10	NUM
ap-920	159	11	1	1	NUM
ap-920	159	12	1	1	NUM
ap-920	159	13	1	1	NUM
ap-920	159	14	1	1	NUM
ap-920	159	15	b	b	PROPN
ap-920	159	16	a	a	DET
ap-920	159	17	b	b	PROPN
ap-920	159	18	v	v	NUM
ap-920	159	19	v	v	PRON
ap-920	159	20	�	�	PROPN
ap-920	159	21	�	�	PROPN
ap-920	159	22	�	�	PROPN
ap-920	159	23	�	�	PROPN
ap-920	159	24	�	�	PROPN
ap-920	159	25	�	�	PROPN
ap-920	159	26	�	�	PROPN
ap-920	159	27	�	�	PROPN
ap-920	159	28	�	�	PROPN
ap-920	159	29	(	(	PUNCT
ap-920	159	30	8)	8)	NUM
ap-920	159	31	f	f	NOUN
ap-920	159	32	)	)	PUNCT
ap-920	159	33	for	for	ADP
ap-920	159	34	s0	s0	PROPN
ap-920	159	35	1	1	NUM
ap-920	159	36	0	0	NUM
ap-920	159	37	0	0	NUM
ap-920	159	38	00	00	NUM
ap-920	159	39	(	(	PUNCT
ap-920	159	40	)	)	PUNCT
ap-920	159	41	(	(	PUNCT
ap-920	159	42	,	,	PUNCT
ap-920	159	43	)	)	PUNCT
ap-920	159	44	�	�	PROPN
ap-920	159	45	,	,	PUNCT
ap-920	159	46	one	one	PRON
ap-920	159	47	has	have	VERB
ap-920	159	48	to	to	PART
ap-920	159	49	consider	consider	VERB
ap-920	159	50	more	more	ADJ
ap-920	159	51	cases	case	NOUN
ap-920	159	52	:	:	PUNCT
ap-920	159	53	�	�	PROPN
ap-920	159	54	let	let	VERB
ap-920	159	55	b	b	PROPN
ap-920	159	56	�	�	PROPN
ap-920	159	57	1and	1and	PROPN
ap-920	159	58	a	a	DET
ap-920	159	59	�	�	PROPN
ap-920	159	60	2	2	NUM
ap-920	159	61	(	(	PUNCT
ap-920	159	62	a	a	DET
ap-920	159	63	sturmian	sturmian	NOUN
ap-920	159	64	case	case	NOUN
ap-920	159	65	)	)	PUNCT
ap-920	159	66	,	,	PUNCT
ap-920	159	67	it	it	PRON
ap-920	159	68	holds	hold	VERB
ap-920	159	69	ret	ret	PROPN
ap-920	159	70	(	(	PUNCT
ap-920	159	71	)	)	PUNCT
ap-920	159	72	,	,	PUNCT
ap-920	159	73	00	00	NUM
ap-920	159	74	001	001	NUM
ap-920	159	75	00101	00101	NUM
ap-920	159	76	�	�	PROPN
ap-920	159	77	.	.	PUNCT
ap-920	160	1	�	�	PROPN
ap-920	160	2	let	let	VERB
ap-920	160	3	b	b	PROPN
ap-920	160	4	�	�	PROPN
ap-920	160	5	1and	1and	PROPN
ap-920	160	6	a	a	DET
ap-920	160	7	�	�	PROPN
ap-920	160	8	2	2	NUM
ap-920	160	9	,	,	PUNCT
ap-920	160	10	then	then	ADV
ap-920	160	11	ret	ret	PROPN
ap-920	160	12	(	(	PUNCT
ap-920	160	13	)	)	PUNCT
ap-920	160	14	,	,	PUNCT
ap-920	160	15	00	00	NUM
ap-920	160	16	0	0	NUM
ap-920	160	17	00101	00101	NUM
ap-920	160	18	�	�	PROPN
ap-920	160	19	.	.	PUNCT
ap-920	161	1	�	�	PROPN
ap-920	161	2	let	let	VERB
ap-920	161	3	b	b	PROPN
ap-920	161	4	�	�	PROPN
ap-920	161	5	2	2	NUM
ap-920	161	6	,	,	PUNCT
ap-920	161	7	then	then	ADV
ap-920	161	8	ret	ret	PROPN
ap-920	161	9	(	(	PUNCT
ap-920	161	10	)	)	PUNCT
ap-920	161	11	,	,	PUNCT
ap-920	161	12	00	00	NUM
ap-920	161	13	0	0	NUM
ap-920	161	14	001	001	NUM
ap-920	161	15	�	�	PROPN
ap-920	161	16	.	.	PUNCT
ap-920	162	1	4	4	X
ap-920	162	2	.	.	X
ap-920	162	3	the	the	DET
ap-920	162	4	last	last	ADJ
ap-920	162	5	step	step	NOUN
ap-920	162	6	is	be	AUX
ap-920	162	7	to	to	PART
ap-920	162	8	compute	compute	VERB
ap-920	162	9	l	l	PROPN
ap-920	162	10	k	k	PROPN
ap-920	162	11	ku	ku	PROPN
ap-920	162	12	�	�	PROPN
ap-920	162	13	(	(	PUNCT
ap-920	162	14	)	)	PUNCT
ap-920	162	15	,	,	PUNCT
ap-920	162	16	�	�	PROPN
ap-920	162	17	�	�	PROPN
ap-920	162	18	.	.	PUNCT
ap-920	163	1	for	for	ADP
ap-920	163	2	simplicity	simplicity	NOUN
ap-920	163	3	,	,	PUNCT
ap-920	163	4	let	let	VERB
ap-920	163	5	us	we	PRON
ap-920	163	6	write	write	VERB
ap-920	163	7	l(k	l(k	PROPN
ap-920	163	8	)	)	PUNCT
ap-920	163	9	instead	instead	ADV
ap-920	163	10	of	of	ADP
ap-920	163	11	l	l	PROPN
ap-920	163	12	ku	ku	PROPN
ap-920	163	13	�	�	PROPN
ap-920	163	14	(	(	PUNCT
ap-920	163	15	)	)	PUNCT
ap-920	163	16	in	in	ADP
ap-920	163	17	the	the	DET
ap-920	163	18	sequel	sequel	NOUN
ap-920	163	19	.	.	PUNCT
ap-920	164	1	before	before	ADP
ap-920	164	2	starting	start	VERB
ap-920	164	3	,	,	PUNCT
ap-920	164	4	let	let	VERB
ap-920	164	5	us	we	PRON
ap-920	164	6	exclude	exclude	VERB
ap-920	164	7	singular	singular	ADJ
ap-920	164	8	factors	factor	NOUN
ap-920	164	9	which	which	PRON
ap-920	164	10	are	be	AUX
ap-920	164	11	not	not	PART
ap-920	164	12	essential	essential	ADJ
ap-920	164	13	.	.	PUNCT
ap-920	165	1	(	(	PUNCT
ap-920	165	2	let	let	VERB
ap-920	165	3	us	we	PRON
ap-920	165	4	recall	recall	VERB
ap-920	165	5	that	that	SCONJ
ap-920	165	6	a	a	DET
ap-920	165	7	singular	singular	ADJ
ap-920	165	8	factor	factor	NOUN
ap-920	165	9	w	w	NOUN
ap-920	165	10	is	be	AUX
ap-920	165	11	essential	essential	ADJ
ap-920	165	12	if	if	SCONJ
ap-920	165	13	l	l	PROPN
ap-920	165	14	w	w	PROPN
ap-920	165	15	l	l	PROPN
ap-920	165	16	w	w	PROPN
ap-920	165	17	l	l	PROPN
ap-920	165	18	w	w	PROPN
ap-920	165	19	(	(	PUNCT
ap-920	165	20	)	)	PUNCT
ap-920	165	21	(	(	PUNCT
ap-920	165	22	)	)	PUNCT
ap-920	165	23	(	(	PUNCT
ap-920	165	24	)	)	PUNCT
ap-920	165	25	�	�	PROPN
ap-920	165	26	�	�	PROPN
ap-920	165	27	�	�	PROPN
ap-920	165	28	1	1	NUM
ap-920	165	29	.	.	PUNCT
ap-920	165	30	)	)	PUNCT
ap-920	165	31	naturally	naturally	ADV
ap-920	165	32	,	,	PUNCT
ap-920	165	33	we	we	PRON
ap-920	165	34	will	will	AUX
ap-920	165	35	apply	apply	VERB
ap-920	165	36	proposition	proposition	NOUN
ap-920	165	37	22	22	NUM
ap-920	165	38	to	to	PART
ap-920	165	39	determine	determine	VERB
ap-920	165	40	the	the	DET
ap-920	165	41	maximal	maximal	ADJ
ap-920	165	42	return	return	NOUN
ap-920	165	43	times	time	NOUN
ap-920	165	44	l(w	l(w	NOUN
ap-920	165	45	)	)	PUNCT
ap-920	165	46	of	of	ADP
ap-920	165	47	singular	singular	PROPN
ap-920	165	48	factor	factor	NOUN
ap-920	165	49	w.	w.	PROPN
ap-920	165	50	a	a	DET
ap-920	165	51	)	)	PUNCT
ap-920	165	52	note	note	NOUN
ap-920	165	53	that	that	SCONJ
ap-920	165	54	s	s	VERB
ap-920	165	55	s	s	PROPN
ap-920	165	56	sb	sb	PROPN
ap-920	165	57	n	n	PROPN
ap-920	165	58	b	b	PROPN
ap-920	165	59	n	n	ADP
ap-920	165	60	b	b	PROPN
ap-920	165	61	n	n	CCONJ
ap-920	165	62	(	(	PUNCT
ap-920	165	63	)	)	PUNCT
ap-920	165	64	(	(	PUNCT
ap-920	165	65	)	)	PUNCT
ap-920	165	66	(	(	PUNCT
ap-920	165	67	)	)	PUNCT
ap-920	165	68	(	(	PUNCT
ap-920	165	69	,	,	PUNCT
ap-920	165	70	)	)	PUNCT
ap-920	165	71	(	(	PUNCT
ap-920	165	72	,	,	PUNCT
ap-920	165	73	)	)	PUNCT
ap-920	165	74	(	(	PUNCT
ap-920	165	75	,	,	PUNCT
ap-920	165	76	)	)	PUNCT
ap-920	165	77	1	1	NUM
ap-920	165	78	0	0	NUM
ap-920	165	79	0	0	NUM
ap-920	165	80	1	1	NUM
ap-920	165	81	1	1	NUM
ap-920	165	82	1	1	NUM
ap-920	165	83	�	�	PROPN
ap-920	165	84	�	�	PROPN
ap-920	165	85	,	,	PUNCT
ap-920	165	86	but	but	CCONJ
ap-920	165	87	from	from	ADP
ap-920	165	88	relations	relation	NOUN
ap-920	165	89	(	(	PUNCT
ap-920	165	90	6	6	NUM
ap-920	165	91	)	)	PUNCT
ap-920	165	92	,	,	PUNCT
ap-920	165	93	(	(	PUNCT
ap-920	165	94	7	7	NUM
ap-920	165	95	)	)	PUNCT
ap-920	165	96	,	,	PUNCT
ap-920	165	97	and	and	CCONJ
ap-920	165	98	(	(	PUNCT
ap-920	165	99	8)	8)	NUM
ap-920	165	100	,	,	PUNCT
ap-920	165	101	it	it	PRON
ap-920	165	102	is	be	AUX
ap-920	165	103	clear	clear	ADJ
ap-920	165	104	that	that	SCONJ
ap-920	165	105	for	for	ADP
ap-920	165	106	all	all	DET
ap-920	165	107	n	n	PRON
ap-920	165	108	�	�	PROPN
ap-920	165	109	�	�	PROPN
ap-920	165	110	,	,	PUNCT
ap-920	165	111	one	one	NUM
ap-920	165	112	gets	get	VERB
ap-920	165	113	l	l	NOUN
ap-920	165	114	s	s	PART
ap-920	165	115	l	l	NOUN
ap-920	165	116	s	s	PART
ap-920	165	117	l	l	NOUN
ap-920	165	118	sb	sb	PROPN
ap-920	166	1	n	n	PROPN
ap-920	166	2	b	b	PROPN
ap-920	166	3	n	n	ADP
ap-920	166	4	b	b	PROPN
ap-920	166	5	n	n	CCONJ
ap-920	166	6	(	(	PUNCT
ap-920	166	7	(	(	PUNCT
ap-920	166	8	,	,	PUNCT
ap-920	166	9	)	)	PUNCT
ap-920	166	10	)	)	PUNCT
ap-920	166	11	(	(	PUNCT
ap-920	166	12	(	(	PUNCT
ap-920	166	13	,	,	PUNCT
ap-920	166	14	)	)	PUNCT
ap-920	166	15	)	)	PUNCT
ap-920	166	16	(	(	PUNCT
ap-920	166	17	(	(	PUNCT
ap-920	166	18	,	,	PUNCT
ap-920	166	19	)	)	PUNCT
ap-920	166	20	)	)	PUNCT
ap-920	166	21	(	(	PUNCT
ap-920	166	22	)	)	PUNCT
ap-920	166	23	(	(	PUNCT
ap-920	166	24	)	)	PUNCT
ap-920	166	25	(	(	PUNCT
ap-920	166	26	)	)	PUNCT
ap-920	166	27	1	1	NUM
ap-920	166	28	0	0	NUM
ap-920	166	29	0	0	NUM
ap-920	166	30	1	1	NUM
ap-920	166	31	1	1	NUM
ap-920	166	32	1	1	NUM
ap-920	166	33	�	�	PROPN
ap-920	166	34	�	�	PROPN
ap-920	166	35	.	.	PUNCT
ap-920	167	1	thus	thus	ADV
ap-920	167	2	,	,	PUNCT
ap-920	167	3	sb	sb	PROPN
ap-920	167	4	n	n	CCONJ
ap-920	167	5	(	(	PUNCT
ap-920	167	6	)	)	PUNCT
ap-920	167	7	(	(	PUNCT
ap-920	167	8	,	,	PUNCT
ap-920	167	9	)	)	PUNCT
ap-920	167	10	1	1	NUM
ap-920	167	11	0	0	NUM
ap-920	167	12	and	and	CCONJ
ap-920	167	13	sb	sb	PROPN
ap-920	167	14	n	n	CCONJ
ap-920	167	15	(	(	PUNCT
ap-920	167	16	)	)	PUNCT
ap-920	167	17	(	(	PUNCT
ap-920	167	18	,	,	PUNCT
ap-920	167	19	)	)	PUNCT
ap-920	167	20	0	0	NUM
ap-920	167	21	1	1	NUM
ap-920	167	22	are	be	AUX
ap-920	167	23	not	not	PART
ap-920	167	24	essential	essential	ADJ
ap-920	167	25	singular	singular	ADJ
ap-920	167	26	factors	factor	NOUN
ap-920	167	27	and	and	CCONJ
ap-920	167	28	one	one	PRON
ap-920	167	29	does	do	AUX
ap-920	167	30	not	not	PART
ap-920	167	31	have	have	VERB
ap-920	167	32	to	to	PART
ap-920	167	33	consider	consider	VERB
ap-920	167	34	them	they	PRON
ap-920	167	35	in	in	ADP
ap-920	167	36	calculation	calculation	NOUN
ap-920	167	37	of	of	ADP
ap-920	167	38	l(k	l(k	PROPN
ap-920	167	39	)	)	PUNCT
ap-920	167	40	,	,	PUNCT
ap-920	167	41	k	k	PROPN
ap-920	167	42	�	�	PROPN
ap-920	167	43	�	�	PROPN
ap-920	167	44	.	.	PUNCT
ap-920	168	1	b	b	X
ap-920	168	2	)	)	PUNCT
ap-920	169	1	by	by	ADP
ap-920	169	2	analogy	analogy	NOUN
ap-920	169	3	,	,	PUNCT
ap-920	169	4	if	if	SCONJ
ap-920	169	5	b	b	PROPN
ap-920	169	6	�	�	PROPN
ap-920	169	7	2	2	NUM
ap-920	169	8	,	,	PUNCT
ap-920	169	9	we	we	PRON
ap-920	169	10	have	have	VERB
ap-920	169	11	s	s	PROPN
ap-920	169	12	sn	sn	PROPN
ap-920	169	13	b	b	PROPN
ap-920	169	14	n	n	CCONJ
ap-920	169	15	0	0	NUM
ap-920	169	16	1	1	NUM
ap-920	169	17	0	0	NUM
ap-920	169	18	0	0	NUM
ap-920	169	19	1	1	NUM
ap-920	169	20	1	1	NUM
ap-920	169	21	(	(	PUNCT
ap-920	169	22	)	)	PUNCT
ap-920	169	23	(	(	PUNCT
ap-920	169	24	)	)	PUNCT
ap-920	169	25	(	(	PUNCT
ap-920	169	26	,	,	PUNCT
ap-920	169	27	)	)	PUNCT
ap-920	169	28	(	(	PUNCT
ap-920	169	29	,	,	PUNCT
ap-920	169	30	)	)	PUNCT
ap-920	169	31	�	�	PROPN
ap-920	169	32	�	�	PROPN
ap-920	169	33	,	,	PUNCT
ap-920	169	34	while	while	SCONJ
ap-920	169	35	l	l	PROPN
ap-920	169	36	s	s	PROPN
ap-920	169	37	l	l	X
ap-920	169	38	sn	sn	PROPN
ap-920	169	39	b	b	PROPN
ap-920	169	40	n	n	CCONJ
ap-920	169	41	(	(	PUNCT
ap-920	169	42	(	(	PUNCT
ap-920	169	43	,	,	PUNCT
ap-920	169	44	)	)	PUNCT
ap-920	169	45	)	)	PUNCT
ap-920	170	1	(	(	PUNCT
ap-920	170	2	(	(	PUNCT
ap-920	170	3	,	,	PUNCT
ap-920	170	4	)	)	PUNCT
ap-920	170	5	)	)	PUNCT
ap-920	170	6	(	(	PUNCT
ap-920	170	7	)	)	PUNCT
ap-920	170	8	(	(	PUNCT
ap-920	170	9	)	)	PUNCT
ap-920	170	10	0	0	NUM
ap-920	170	11	1	1	NUM
ap-920	170	12	0	0	NUM
ap-920	170	13	0	0	NUM
ap-920	170	14	1	1	NUM
ap-920	170	15	1	1	NUM
ap-920	170	16	�	�	PROPN
ap-920	170	17	�	�	PROPN
ap-920	170	18	for	for	ADP
ap-920	170	19	all	all	PRON
ap-920	170	20	n	n	DET
ap-920	170	21	�	�	PROPN
ap-920	170	22	�	�	PROPN
ap-920	170	23	.	.	PUNCT
ap-920	171	1	hence	hence	ADV
ap-920	171	2	,	,	PUNCT
ap-920	171	3	the	the	DET
ap-920	171	4	singular	singular	ADJ
ap-920	171	5	factors	factor	NOUN
ap-920	171	6	s	s	PART
ap-920	171	7	n	n	NOUN
ap-920	171	8	0	0	NUM
ap-920	171	9	1	1	NUM
ap-920	171	10	0	0	NUM
ap-920	171	11	0	0	NUM
ap-920	171	12	(	(	PUNCT
ap-920	171	13	)	)	PUNCT
ap-920	171	14	(	(	PUNCT
ap-920	171	15	,	,	PUNCT
ap-920	171	16	)	)	PUNCT
ap-920	171	17	�	�	PROPN
ap-920	171	18	are	be	AUX
ap-920	171	19	not	not	PART
ap-920	171	20	essential	essential	ADJ
ap-920	171	21	.	.	PUNCT
ap-920	172	1	c	c	X
ap-920	172	2	)	)	PUNCT
ap-920	172	3	next	next	ADV
ap-920	172	4	,	,	PUNCT
ap-920	172	5	if	if	SCONJ
ap-920	172	6	a	a	DET
ap-920	172	7	r	r	NOUN
ap-920	172	8	b	b	PROPN
ap-920	172	9	�	�	PROPN
ap-920	172	10	�	�	PROPN
ap-920	172	11	�	�	PROPN
ap-920	172	12	2	2	NUM
ap-920	172	13	,	,	PUNCT
ap-920	172	14	we	we	PRON
ap-920	172	15	have	have	VERB
ap-920	172	16	s	s	PROPN
ap-920	172	17	sr	sr	PROPN
ap-920	172	18	n	n	PROPN
ap-920	172	19	b	b	PROPN
ap-920	172	20	n	n	CCONJ
ap-920	172	21	(	(	PUNCT
ap-920	172	22	)	)	PUNCT
ap-920	172	23	(	(	PUNCT
ap-920	172	24	)	)	PUNCT
ap-920	172	25	(	(	PUNCT
ap-920	172	26	,	,	PUNCT
ap-920	172	27	)	)	PUNCT
ap-920	172	28	(	(	PUNCT
ap-920	172	29	,	,	PUNCT
ap-920	172	30	)	)	PUNCT
ap-920	172	31	0	0	SYM
ap-920	172	32	0	0	NUM
ap-920	172	33	1	1	NUM
ap-920	172	34	1	1	NUM
ap-920	172	35	�	�	PROPN
ap-920	172	36	,	,	PUNCT
ap-920	172	37	nevertheless	nevertheless	ADV
ap-920	172	38	,	,	PUNCT
ap-920	172	39	l	l	PROPN
ap-920	172	40	s	s	PART
ap-920	172	41	l	l	X
ap-920	172	42	sr	sr	PROPN
ap-920	172	43	n	n	PROPN
ap-920	172	44	b	b	PROPN
ap-920	172	45	n	n	CCONJ
ap-920	172	46	(	(	PUNCT
ap-920	172	47	(	(	PUNCT
ap-920	172	48	,	,	PUNCT
ap-920	172	49	)	)	PUNCT
ap-920	172	50	)	)	PUNCT
ap-920	173	1	(	(	PUNCT
ap-920	173	2	(	(	PUNCT
ap-920	173	3	,	,	PUNCT
ap-920	173	4	)	)	PUNCT
ap-920	173	5	)	)	PUNCT
ap-920	173	6	(	(	PUNCT
ap-920	173	7	)	)	PUNCT
ap-920	173	8	(	(	PUNCT
ap-920	173	9	)	)	PUNCT
ap-920	173	10	0	0	SYM
ap-920	173	11	0	0	NUM
ap-920	173	12	1	1	NUM
ap-920	173	13	1	1	NUM
ap-920	173	14	�	�	NOUN
ap-920	173	15	for	for	ADP
ap-920	173	16	all	all	DET
ap-920	173	17	n	n	PRON
ap-920	173	18	�	�	PROPN
ap-920	173	19	�	�	PROPN
ap-920	173	20	.	.	PUNCT
ap-920	174	1	therefore	therefore	ADV
ap-920	174	2	,	,	PUNCT
ap-920	174	3	sr	sr	PROPN
ap-920	174	4	n	n	CCONJ
ap-920	174	5	(	(	PUNCT
ap-920	174	6	)	)	PUNCT
ap-920	174	7	(	(	PUNCT
ap-920	174	8	,	,	PUNCT
ap-920	174	9	)	)	PUNCT
ap-920	174	10	0	0	NUM
ap-920	174	11	0	0	NUM
ap-920	174	12	,	,	PUNCT
ap-920	174	13	r	r	PROPN
ap-920	174	14	b	b	PROPN
ap-920	174	15	�	�	PROPN
ap-920	174	16	,	,	PUNCT
ap-920	174	17	are	be	AUX
ap-920	174	18	not	not	PART
ap-920	174	19	essential	essential	ADJ
ap-920	174	20	.	.	PUNCT
ap-920	175	1	18	18	NUM
ap-920	175	2	©	©	PROPN
ap-920	175	3	czech	czech	PROPN
ap-920	175	4	technical	technical	PROPN
ap-920	175	5	university	university	PROPN
ap-920	175	6	publishing	publishing	NOUN
ap-920	175	7	house	house	NOUN
ap-920	175	8	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-920	175	9	acta	acta	PROPN
ap-920	175	10	polytechnica	polytechnica	PROPN
ap-920	175	11	vol	vol	NOUN
ap-920	175	12	.	.	PUNCT
ap-920	176	1	47	47	NUM
ap-920	176	2	no	no	INTJ
ap-920	176	3	.	.	PUNCT
ap-920	177	1	2–3/2007	2–3/2007	NUM
ap-920	177	2	d	d	NOUN
ap-920	177	3	)	)	PUNCT
ap-920	177	4	if	if	SCONJ
ap-920	177	5	1	1	NUM
ap-920	177	6	2	2	NUM
ap-920	177	7	�	�	PROPN
ap-920	177	8	�	�	PROPN
ap-920	177	9	�	�	PROPN
ap-920	177	10	r	r	NOUN
ap-920	177	11	b	b	PROPN
ap-920	177	12	,	,	PUNCT
ap-920	177	13	then	then	ADV
ap-920	177	14	we	we	PRON
ap-920	177	15	obtain	obtain	VERB
ap-920	177	16	s	s	VERB
ap-920	177	17	sr	sr	PROPN
ap-920	177	18	n	n	PROPN
ap-920	177	19	b	b	PROPN
ap-920	177	20	n	n	CCONJ
ap-920	177	21	(	(	PUNCT
ap-920	177	22	)	)	PUNCT
ap-920	177	23	(	(	PUNCT
ap-920	177	24	)	)	PUNCT
ap-920	177	25	(	(	PUNCT
ap-920	177	26	,	,	PUNCT
ap-920	177	27	)	)	PUNCT
ap-920	177	28	(	(	PUNCT
ap-920	177	29	,	,	PUNCT
ap-920	177	30	)	)	PUNCT
ap-920	177	31	�	�	PROPN
ap-920	177	32	�	�	PROPN
ap-920	177	33	1	1	NUM
ap-920	177	34	0	0	NUM
ap-920	177	35	0	0	NUM
ap-920	177	36	1	1	NUM
ap-920	177	37	1	1	NUM
ap-920	177	38	,	,	PUNCT
ap-920	177	39	but	but	CCONJ
ap-920	177	40	l	l	NOUN
ap-920	177	41	s	s	PROPN
ap-920	177	42	l	l	X
ap-920	177	43	sr	sr	PROPN
ap-920	177	44	n	n	PROPN
ap-920	177	45	b	b	PROPN
ap-920	177	46	n	n	CCONJ
ap-920	177	47	(	(	PUNCT
ap-920	177	48	(	(	PUNCT
ap-920	177	49	,	,	PUNCT
ap-920	177	50	)	)	PUNCT
ap-920	177	51	)	)	PUNCT
ap-920	178	1	(	(	PUNCT
ap-920	178	2	(	(	PUNCT
ap-920	178	3	,	,	PUNCT
ap-920	178	4	)	)	PUNCT
ap-920	178	5	)	)	PUNCT
ap-920	178	6	(	(	PUNCT
ap-920	178	7	)	)	PUNCT
ap-920	178	8	(	(	PUNCT
ap-920	178	9	)	)	PUNCT
ap-920	178	10	�	�	PROPN
ap-920	178	11	�	�	PROPN
ap-920	178	12	1	1	NUM
ap-920	178	13	0	0	NUM
ap-920	178	14	0	0	NUM
ap-920	178	15	1	1	NUM
ap-920	178	16	1	1	NUM
ap-920	178	17	for	for	ADP
ap-920	178	18	all	all	DET
ap-920	178	19	n	n	PRON
ap-920	178	20	�	�	PROPN
ap-920	178	21	�	�	PROPN
ap-920	178	22	,	,	PUNCT
ap-920	178	23	thus	thus	ADV
ap-920	178	24	,	,	PUNCT
ap-920	178	25	the	the	DET
ap-920	178	26	singular	singular	PROPN
ap-920	178	27	factors	factor	VERB
ap-920	178	28	sr	sr	PROPN
ap-920	178	29	n	n	CCONJ
ap-920	178	30	(	(	PUNCT
ap-920	178	31	)	)	PUNCT
ap-920	178	32	(	(	PUNCT
ap-920	178	33	,	,	PUNCT
ap-920	178	34	)	)	PUNCT
ap-920	178	35	�	�	PROPN
ap-920	178	36	1	1	NUM
ap-920	178	37	0	0	NUM
ap-920	178	38	0	0	NUM
ap-920	178	39	,	,	PUNCT
ap-920	178	40	1	1	NUM
ap-920	178	41	2	2	NUM
ap-920	178	42	�	�	PROPN
ap-920	178	43	�	�	PROPN
ap-920	178	44	�	�	PROPN
ap-920	178	45	r	r	NOUN
ap-920	178	46	b	b	PROPN
ap-920	178	47	,	,	PUNCT
ap-920	178	48	are	be	AUX
ap-920	178	49	not	not	PART
ap-920	178	50	essential	essential	ADJ
ap-920	178	51	.	.	PUNCT
ap-920	179	1	e	e	X
ap-920	179	2	)	)	PUNCT
ap-920	179	3	the	the	DET
ap-920	179	4	last	last	ADJ
ap-920	179	5	remark	remark	NOUN
ap-920	179	6	is	be	AUX
ap-920	179	7	that	that	SCONJ
ap-920	179	8	for	for	ADP
ap-920	179	9	the	the	DET
ap-920	179	10	trivial	trivial	ADJ
ap-920	179	11	singular	singular	ADJ
ap-920	179	12	factor	factor	NOUN
ap-920	179	13	w	w	PROPN
ap-920	179	14	�	�	PROPN
ap-920	179	15	1	1	NUM
ap-920	179	16	,	,	PUNCT
ap-920	179	17	we	we	PRON
ap-920	179	18	have	have	VERB
ap-920	179	19	w	w	PROPN
ap-920	179	20	sr	sr	PROPN
ap-920	179	21	�	�	PROPN
ap-920	179	22	(	(	PUNCT
ap-920	179	23	)	)	PUNCT
ap-920	179	24	(	(	PUNCT
ap-920	179	25	,	,	PUNCT
ap-920	179	26	)	)	PUNCT
ap-920	180	1	1	1	NUM
ap-920	180	2	0	0	NUM
ap-920	180	3	0	0	NUM
ap-920	180	4	,	,	PUNCT
ap-920	180	5	1	1	NUM
ap-920	180	6	2	2	NUM
ap-920	180	7	�	�	PROPN
ap-920	180	8	�	�	PROPN
ap-920	180	9	�	�	PROPN
ap-920	180	10	r	r	NOUN
ap-920	180	11	b	b	PROPN
ap-920	180	12	,	,	PUNCT
ap-920	180	13	but	but	CCONJ
ap-920	180	14	l	l	NOUN
ap-920	180	15	s	s	PROPN
ap-920	180	16	l	l	X
ap-920	180	17	wr	wr	X
ap-920	180	18	(	(	PUNCT
ap-920	180	19	(	(	PUNCT
ap-920	180	20	,	,	PUNCT
ap-920	180	21	)	)	PUNCT
ap-920	180	22	)	)	PUNCT
ap-920	180	23	(	(	PUNCT
ap-920	180	24	)	)	PUNCT
ap-920	180	25	(	(	PUNCT
ap-920	180	26	)	)	PUNCT
ap-920	180	27	1	1	NUM
ap-920	180	28	0	0	NUM
ap-920	180	29	0	0	NUM
ap-920	180	30	�	�	PROPN
ap-920	180	31	,	,	PUNCT
ap-920	180	32	hence	hence	ADV
ap-920	180	33	,	,	PUNCT
ap-920	180	34	sr	sr	PROPN
ap-920	180	35	(	(	PUNCT
ap-920	180	36	)	)	PUNCT
ap-920	180	37	(	(	PUNCT
ap-920	180	38	,	,	PUNCT
ap-920	180	39	)	)	PUNCT
ap-920	180	40	1	1	NUM
ap-920	180	41	0	0	NUM
ap-920	180	42	0	0	NUM
ap-920	180	43	,	,	PUNCT
ap-920	180	44	1	1	NUM
ap-920	180	45	2	2	NUM
ap-920	180	46	�	�	PROPN
ap-920	180	47	�	�	PROPN
ap-920	180	48	�	�	PROPN
ap-920	180	49	r	r	NOUN
ap-920	180	50	b	b	PROPN
ap-920	180	51	,	,	PUNCT
ap-920	180	52	are	be	AUX
ap-920	180	53	not	not	PART
ap-920	180	54	essential	essential	ADJ
ap-920	180	55	.	.	PUNCT
ap-920	181	1	the	the	DET
ap-920	181	2	previous	previous	ADJ
ap-920	181	3	facts	fact	NOUN
ap-920	181	4	imply	imply	VERB
ap-920	181	5	that	that	SCONJ
ap-920	181	6	in	in	ADP
ap-920	181	7	order	order	NOUN
ap-920	181	8	to	to	PART
ap-920	181	9	calculate	calculate	VERB
ap-920	181	10	l(k	l(k	PROPN
ap-920	181	11	)	)	PUNCT
ap-920	181	12	we	we	PRON
ap-920	181	13	have	have	VERB
ap-920	181	14	to	to	PART
ap-920	181	15	take	take	VERB
ap-920	181	16	into	into	ADP
ap-920	181	17	account	account	NOUN
ap-920	181	18	only	only	ADV
ap-920	181	19	the	the	DET
ap-920	181	20	trivial	trivial	ADJ
ap-920	181	21	singular	singular	ADJ
ap-920	181	22	factors	factor	NOUN
ap-920	181	23	,	,	PUNCT
ap-920	181	24	the	the	DET
ap-920	181	25	non	non	ADJ
ap-920	181	26	-	-	ADJ
ap-920	181	27	trivial	trivial	ADJ
ap-920	181	28	singular	singular	ADJ
ap-920	181	29	factors	factor	NOUN
ap-920	181	30	of	of	ADP
ap-920	181	31	the	the	DET
ap-920	181	32	form	form	NOUN
ap-920	181	33	sb	sb	PROPN
ap-920	181	34	n	n	PROPN
ap-920	181	35	(	(	PUNCT
ap-920	181	36	)	)	PUNCT
ap-920	181	37	(	(	PUNCT
ap-920	181	38	,	,	PUNCT
ap-920	181	39	)	)	PUNCT
ap-920	181	40	1	1	NUM
ap-920	181	41	1	1	NUM
ap-920	181	42	,	,	PUNCT
ap-920	181	43	and	and	CCONJ
ap-920	181	44	,	,	PUNCT
ap-920	181	45	eventually	eventually	ADV
ap-920	181	46	,	,	PUNCT
ap-920	181	47	s	s	VERB
ap-920	181	48	n	n	PRON
ap-920	181	49	0	0	NUM
ap-920	181	50	0	0	NUM
ap-920	181	51	0	0	NUM
ap-920	181	52	(	(	PUNCT
ap-920	181	53	)	)	PUNCT
ap-920	181	54	(	(	PUNCT
ap-920	181	55	,	,	PUNCT
ap-920	181	56	)	)	PUNCT
ap-920	181	57	and	and	CCONJ
ap-920	181	58	sb	sb	PROPN
ap-920	181	59	n	n	PROPN
ap-920	181	60	�	�	PROPN
ap-920	181	61	1	1	NUM
ap-920	181	62	0	0	NUM
ap-920	181	63	0	0	NUM
ap-920	181	64	(	(	PUNCT
ap-920	181	65	)	)	PUNCT
ap-920	181	66	(	(	PUNCT
ap-920	181	67	,	,	PUNCT
ap-920	181	68	)	)	PUNCT
ap-920	181	69	.	.	PUNCT
ap-920	182	1	the	the	DET
ap-920	182	2	formulae	formulae	NOUN
ap-920	182	3	for	for	ADP
ap-920	182	4	l(k	l(k	PROPN
ap-920	182	5	)	)	PUNCT
ap-920	182	6	,	,	PUNCT
ap-920	182	7	k	k	PROPN
ap-920	182	8	�	�	PROPN
ap-920	182	9	�	�	PROPN
ap-920	182	10	,	,	PUNCT
ap-920	182	11	will	will	AUX
ap-920	182	12	split	split	VERB
ap-920	182	13	into	into	ADP
ap-920	182	14	more	more	ADJ
ap-920	182	15	cases	case	NOUN
ap-920	182	16	,	,	PUNCT
ap-920	182	17	according	accord	VERB
ap-920	182	18	to	to	ADP
ap-920	182	19	the	the	DET
ap-920	182	20	values	value	NOUN
ap-920	182	21	of	of	ADP
ap-920	182	22	a	a	PRON
ap-920	182	23	and	and	CCONJ
ap-920	182	24	b	b	NOUN
ap-920	182	25	in	in	ADP
ap-920	182	26	the	the	DET
ap-920	182	27	substitution	substitution	NOUN
ap-920	182	28	(	(	PUNCT
ap-920	182	29	1	1	NUM
ap-920	182	30	)	)	PUNCT
ap-920	182	31	.	.	PUNCT
ap-920	183	1	a	a	X
ap-920	183	2	)	)	PUNCT
ap-920	183	3	for	for	ADP
ap-920	183	4	b	b	PROPN
ap-920	183	5	�	�	PROPN
ap-920	183	6	2	2	NUM
ap-920	183	7	,	,	PUNCT
ap-920	183	8	combining	combine	VERB
ap-920	183	9	the	the	DET
ap-920	183	10	previous	previous	ADJ
ap-920	183	11	facts	fact	NOUN
ap-920	183	12	and	and	CCONJ
ap-920	183	13	the	the	DET
ap-920	183	14	description	description	NOUN
ap-920	183	15	of	of	ADP
ap-920	183	16	the	the	DET
ap-920	183	17	simplest	simple	ADJ
ap-920	183	18	singular	singular	ADJ
ap-920	183	19	factors	factor	NOUN
ap-920	183	20	,	,	PUNCT
ap-920	183	21	we	we	PRON
ap-920	183	22	obtain	obtain	VERB
ap-920	183	23	the	the	DET
ap-920	183	24	following	follow	VERB
ap-920	183	25	formula	formula	NOUN
ap-920	183	26	for	for	ADP
ap-920	183	27	l(k	l(k	PROPN
ap-920	183	28	)	)	PUNCT
ap-920	183	29	,	,	PUNCT
ap-920	183	30	k	k	PROPN
ap-920	183	31	�	�	PROPN
ap-920	183	32	�	�	PROPN
ap-920	183	33	,	,	PUNCT
ap-920	183	34	�	�	PROPN
ap-920	183	35	if	if	SCONJ
ap-920	183	36	2	2	NUM
ap-920	183	37	1b	1b	NUM
ap-920	183	38	a	a	DET
ap-920	183	39	�	�	PROPN
ap-920	183	40	�	�	PROPN
ap-920	183	41	,	,	PUNCT
ap-920	183	42	then	then	ADV
ap-920	183	43	l	l	NOUN
ap-920	183	44	l	l	PROPN
ap-920	183	45	b	b	X
ap-920	183	46	a	a	PRON
ap-920	183	47	(	(	PUNCT
ap-920	183	48	)	)	PUNCT
ap-920	183	49	(	(	PUNCT
ap-920	183	50	)	)	SYM
ap-920	183	51	1	1	NUM
ap-920	183	52	1	1	NUM
ap-920	183	53	�	�	PROPN
ap-920	183	54	�	�	PROPN
ap-920	183	55	�	�	PROPN
ap-920	183	56	�	�	PROPN
ap-920	183	57	�	�	PROPN
ap-920	183	58	,	,	PUNCT
ap-920	183	59	l	l	PROPN
ap-920	183	60	b	b	PROPN
ap-920	183	61	b	b	X
ap-920	183	62	(	(	PUNCT
ap-920	183	63	)	)	PUNCT
ap-920	183	64	�	�	PROPN
ap-920	183	65	�	�	PROPN
ap-920	183	66	�	�	PROPN
ap-920	183	67	1	1	NUM
ap-920	183	68	2	2	NUM
ap-920	183	69	3	3	NUM
ap-920	183	70	,	,	PUNCT
ap-920	183	71	l	l	PROPN
ap-920	183	72	k	k	PROPN
ap-920	183	73	n	n	CCONJ
ap-920	183	74	a	a	PRON
ap-920	183	75	(	(	PUNCT
ap-920	183	76	)	)	PUNCT
ap-920	183	77	(	(	PUNCT
ap-920	183	78	)	)	PUNCT
ap-920	183	79	�	�	PROPN
ap-920	183	80	�	�	PROPN
ap-920	183	81	10	10	NUM
ap-920	183	82	,	,	PUNCT
ap-920	183	83	for	for	ADP
ap-920	183	84	s	s	PROPN
ap-920	183	85	k	k	PROPN
ap-920	183	86	sb	sb	PROPN
ap-920	183	87	n	n	PROPN
ap-920	183	88	b	b	PROPN
ap-920	183	89	n	n	CCONJ
ap-920	183	90	(	(	PUNCT
ap-920	183	91	)	)	PUNCT
ap-920	183	92	(	(	PUNCT
ap-920	183	93	)	)	PUNCT
ap-920	183	94	(	(	PUNCT
ap-920	183	95	,	,	PUNCT
ap-920	183	96	)	)	PUNCT
ap-920	183	97	(	(	PUNCT
ap-920	183	98	,	,	PUNCT
ap-920	183	99	)	)	PUNCT
ap-920	183	100	1	1	NUM
ap-920	183	101	1	1	NUM
ap-920	183	102	0	0	NUM
ap-920	183	103	01	01	NUM
ap-920	183	104	1	1	NUM
ap-920	183	105	�	�	PROPN
ap-920	183	106	�	�	PROPN
ap-920	183	107	�	�	PROPN
ap-920	183	108	�	�	PROPN
ap-920	183	109	,	,	PUNCT
ap-920	183	110	n	n	PROPN
ap-920	183	111	�	�	PROPN
ap-920	183	112	�	�	PROPN
ap-920	183	113	,	,	PUNCT
ap-920	183	114	l	l	PROPN
ap-920	183	115	k	k	PROPN
ap-920	183	116	n	n	PROPN
ap-920	183	117	b	b	PROPN
ap-920	183	118	b	b	PROPN
ap-920	183	119	(	(	PUNCT
ap-920	183	120	)	)	PUNCT
ap-920	183	121	(	(	PUNCT
ap-920	183	122	)	)	PUNCT
ap-920	183	123	�	�	PROPN
ap-920	183	124	�	�	PROPN
ap-920	183	125	�	�	PROPN
ap-920	183	126	0	0	NUM
ap-920	183	127	10	10	NUM
ap-920	183	128	11	11	NUM
ap-920	183	129	,	,	PUNCT
ap-920	183	130	for	for	ADP
ap-920	183	131	s	s	PROPN
ap-920	183	132	k	k	PROPN
ap-920	183	133	sb	sb	PROPN
ap-920	183	134	n	n	PROPN
ap-920	183	135	b	b	PROPN
ap-920	183	136	n	n	CCONJ
ap-920	183	137	�	�	PROPN
ap-920	183	138	�	�	PROPN
ap-920	183	139	�	�	PROPN
ap-920	183	140	�	�	PROPN
ap-920	183	141	�	�	PROPN
ap-920	183	142	1	1	NUM
ap-920	183	143	1	1	NUM
ap-920	183	144	10	10	NUM
ap-920	183	145	0	0	NUM
ap-920	183	146	1	1	NUM
ap-920	183	147	1	1	NUM
ap-920	183	148	(	(	PUNCT
ap-920	183	149	)	)	PUNCT
ap-920	183	150	(	(	PUNCT
ap-920	183	151	)	)	PUNCT
ap-920	183	152	(	(	PUNCT
ap-920	183	153	,	,	PUNCT
ap-920	183	154	)	)	PUNCT
ap-920	183	155	(	(	PUNCT
ap-920	183	156	,	,	PUNCT
ap-920	183	157	)	)	PUNCT
ap-920	183	158	,	,	PUNCT
ap-920	183	159	n	n	PROPN
ap-920	183	160	�	�	PROPN
ap-920	183	161	�	�	PROPN
ap-920	183	162	.	.	PUNCT
ap-920	183	163	�	�	PROPN
ap-920	184	1	if	if	SCONJ
ap-920	184	2	2b+1	2b+1	PROPN
ap-920	184	3	<	<	X
ap-920	184	4	a	a	X
ap-920	184	5	,	,	PUNCT
ap-920	184	6	then	then	ADV
ap-920	184	7	l	l	NOUN
ap-920	184	8	l	l	PROPN
ap-920	184	9	b	b	X
ap-920	184	10	a	a	PRON
ap-920	184	11	(	(	PUNCT
ap-920	184	12	)	)	PUNCT
ap-920	184	13	(	(	PUNCT
ap-920	184	14	)	)	SYM
ap-920	184	15	1	1	NUM
ap-920	184	16	1	1	NUM
ap-920	184	17	1	1	NUM
ap-920	184	18	�	�	PROPN
ap-920	184	19	�	�	PROPN
ap-920	184	20	�	�	PROPN
ap-920	184	21	�	�	PROPN
ap-920	184	22	�	�	PROPN
ap-920	184	23	�	�	PROPN
ap-920	184	24	,	,	PUNCT
ap-920	184	25	l	l	PROPN
ap-920	184	26	k	k	PROPN
ap-920	184	27	n	n	CCONJ
ap-920	184	28	a	a	PRON
ap-920	184	29	(	(	PUNCT
ap-920	184	30	)	)	PUNCT
ap-920	184	31	(	(	PUNCT
ap-920	184	32	)	)	PUNCT
ap-920	184	33	�	�	PROPN
ap-920	184	34	�	�	PROPN
ap-920	184	35	10	10	NUM
ap-920	184	36	,	,	PUNCT
ap-920	184	37	for	for	ADP
ap-920	184	38	s	s	PROPN
ap-920	184	39	k	k	PROPN
ap-920	184	40	sb	sb	PROPN
ap-920	184	41	n	n	PROPN
ap-920	184	42	b	b	PROPN
ap-920	184	43	n	n	CCONJ
ap-920	184	44	(	(	PUNCT
ap-920	184	45	)	)	PUNCT
ap-920	184	46	(	(	PUNCT
ap-920	184	47	)	)	PUNCT
ap-920	184	48	(	(	PUNCT
ap-920	184	49	,	,	PUNCT
ap-920	184	50	)	)	PUNCT
ap-920	184	51	(	(	PUNCT
ap-920	184	52	,	,	PUNCT
ap-920	184	53	)	)	PUNCT
ap-920	184	54	1	1	NUM
ap-920	184	55	1	1	NUM
ap-920	184	56	1	1	NUM
ap-920	184	57	11	11	NUM
ap-920	184	58	�	�	PROPN
ap-920	184	59	�	�	PROPN
ap-920	184	60	�	�	PROPN
ap-920	184	61	,	,	PUNCT
ap-920	184	62	n	n	PROPN
ap-920	184	63	�	�	PROPN
ap-920	184	64	�	�	PROPN
ap-920	184	65	.	.	PUNCT
ap-920	185	1	b	b	X
ap-920	185	2	)	)	PUNCT
ap-920	186	1	for	for	ADP
ap-920	186	2	b	b	PROPN
ap-920	186	3	�	�	PROPN
ap-920	186	4	1and	1and	NUM
ap-920	186	5	2	2	NUM
ap-920	186	6	3	3	NUM
ap-920	186	7	�	�	PROPN
ap-920	186	8	�	�	PROPN
ap-920	186	9	a	a	PRON
ap-920	186	10	,	,	PUNCT
ap-920	186	11	then	then	ADV
ap-920	186	12	it	it	PRON
ap-920	186	13	holds	hold	VERB
ap-920	186	14	for	for	ADP
ap-920	186	15	l(k	l(k	PROPN
ap-920	186	16	)	)	PUNCT
ap-920	186	17	,	,	PUNCT
ap-920	186	18	k	k	PROPN
ap-920	186	19	�	�	PROPN
ap-920	186	20	�	�	PROPN
ap-920	186	21	,	,	PUNCT
ap-920	186	22	l	l	PROPN
ap-920	186	23	a	a	X
ap-920	186	24	(	(	PUNCT
ap-920	186	25	)	)	SYM
ap-920	186	26	1	1	NUM
ap-920	186	27	1	1	NUM
ap-920	186	28	�	�	PROPN
ap-920	186	29	�	�	PROPN
ap-920	186	30	,	,	PUNCT
ap-920	186	31	l	l	PROPN
ap-920	186	32	(	(	PUNCT
ap-920	186	33	)	)	PUNCT
ap-920	186	34	2	2	NUM
ap-920	186	35	5	5	NUM
ap-920	186	36	�	�	PROPN
ap-920	186	37	,	,	PUNCT
ap-920	186	38	l	l	PROPN
ap-920	186	39	k	k	PROPN
ap-920	186	40	n	n	CCONJ
ap-920	186	41	a	a	PRON
ap-920	186	42	(	(	PUNCT
ap-920	186	43	)	)	PUNCT
ap-920	186	44	(	(	PUNCT
ap-920	186	45	)	)	PUNCT
ap-920	186	46	�	�	PROPN
ap-920	186	47	�	�	PROPN
ap-920	186	48	10	10	NUM
ap-920	186	49	,	,	PUNCT
ap-920	186	50	for	for	ADP
ap-920	186	51	s	s	PROPN
ap-920	186	52	k	k	PROPN
ap-920	186	53	sn	sn	PROPN
ap-920	186	54	n	n	PROPN
ap-920	186	55	1	1	NUM
ap-920	186	56	0	0	NUM
ap-920	186	57	11	11	NUM
ap-920	186	58	1	1	NUM
ap-920	186	59	0	0	NUM
ap-920	186	60	0	0	NUM
ap-920	186	61	(	(	PUNCT
ap-920	186	62	)	)	PUNCT
ap-920	186	63	(	(	PUNCT
ap-920	186	64	)	)	PUNCT
ap-920	186	65	(	(	PUNCT
ap-920	186	66	,	,	PUNCT
ap-920	186	67	)	)	PUNCT
ap-920	186	68	(	(	PUNCT
ap-920	186	69	,	,	PUNCT
ap-920	186	70	)	)	PUNCT
ap-920	186	71	�	�	PROPN
ap-920	186	72	�	�	PROPN
ap-920	186	73	�	�	PROPN
ap-920	186	74	,	,	PUNCT
ap-920	186	75	n	n	PROPN
ap-920	186	76	�	�	PROPN
ap-920	186	77	�	�	PROPN
ap-920	186	78	,	,	PUNCT
ap-920	186	79	l	l	PROPN
ap-920	186	80	k	k	PROPN
ap-920	186	81	n	n	CCONJ
ap-920	186	82	(	(	PUNCT
ap-920	186	83	)	)	PUNCT
ap-920	186	84	(	(	PUNCT
ap-920	186	85	)	)	PUNCT
ap-920	186	86	�	�	PROPN
ap-920	186	87	�	�	PROPN
ap-920	186	88	00101	00101	PROPN
ap-920	186	89	for	for	ADP
ap-920	186	90	s	s	PROPN
ap-920	186	91	k	k	PROPN
ap-920	186	92	sn	sn	PROPN
ap-920	186	93	n	n	PROPN
ap-920	186	94	0	0	NUM
ap-920	186	95	1	1	NUM
ap-920	186	96	1	1	NUM
ap-920	186	97	10	10	NUM
ap-920	186	98	0	0	NUM
ap-920	186	99	1	1	NUM
ap-920	186	100	1	1	NUM
ap-920	186	101	(	(	PUNCT
ap-920	186	102	)	)	PUNCT
ap-920	186	103	(	(	PUNCT
ap-920	186	104	)	)	PUNCT
ap-920	186	105	(	(	PUNCT
ap-920	186	106	,	,	PUNCT
ap-920	186	107	)	)	PUNCT
ap-920	186	108	(	(	PUNCT
ap-920	186	109	,	,	PUNCT
ap-920	186	110	)	)	PUNCT
ap-920	186	111	�	�	PROPN
ap-920	186	112	�	�	PROPN
ap-920	186	113	�	�	PROPN
ap-920	186	114	�	�	PROPN
ap-920	186	115	,	,	PUNCT
ap-920	186	116	n	n	X
ap-920	186	117	�	�	PROPN
ap-920	186	118	�	�	PROPN
ap-920	186	119	.	.	PUNCT
ap-920	187	1	c	c	X
ap-920	187	2	)	)	PUNCT
ap-920	187	3	for	for	ADP
ap-920	187	4	b	b	PROPN
ap-920	187	5	�	�	PROPN
ap-920	187	6	1and	1and	PROPN
ap-920	187	7	a	a	DET
ap-920	187	8	�	�	PROPN
ap-920	187	9	3	3	NUM
ap-920	187	10	,	,	PUNCT
ap-920	187	11	we	we	PRON
ap-920	187	12	get	get	VERB
ap-920	187	13	l	l	NOUN
ap-920	187	14	l	l	NOUN
ap-920	187	15	a	a	X
ap-920	187	16	(	(	PUNCT
ap-920	187	17	)	)	PUNCT
ap-920	187	18	(	(	PUNCT
ap-920	187	19	)	)	SYM
ap-920	187	20	1	1	NUM
ap-920	187	21	2	2	NUM
ap-920	187	22	1	1	NUM
ap-920	187	23	�	�	PROPN
ap-920	187	24	�	�	PROPN
ap-920	187	25	�	�	PROPN
ap-920	187	26	,	,	PUNCT
ap-920	188	1	l	l	PROPN
ap-920	188	2	k	k	PROPN
ap-920	189	1	n	n	CCONJ
ap-920	189	2	a	a	PRON
ap-920	189	3	(	(	PUNCT
ap-920	189	4	)	)	PUNCT
ap-920	189	5	(	(	PUNCT
ap-920	189	6	)	)	PUNCT
ap-920	189	7	�	�	PROPN
ap-920	189	8	�	�	PROPN
ap-920	189	9	10	10	NUM
ap-920	189	10	,	,	PUNCT
ap-920	189	11	for	for	ADP
ap-920	189	12	s	s	PROPN
ap-920	189	13	k	k	PROPN
ap-920	189	14	sn	sn	PROPN
ap-920	189	15	n	n	PROPN
ap-920	189	16	1	1	NUM
ap-920	189	17	1	1	NUM
ap-920	189	18	11	11	NUM
ap-920	189	19	1	1	NUM
ap-920	189	20	1	1	NUM
ap-920	189	21	1	1	NUM
ap-920	189	22	(	(	PUNCT
ap-920	189	23	)	)	PUNCT
ap-920	189	24	(	(	PUNCT
ap-920	189	25	)	)	PUNCT
ap-920	189	26	(	(	PUNCT
ap-920	189	27	,	,	PUNCT
ap-920	189	28	)	)	PUNCT
ap-920	189	29	(	(	PUNCT
ap-920	189	30	,	,	PUNCT
ap-920	189	31	)	)	PUNCT
ap-920	189	32	�	�	PROPN
ap-920	189	33	�	�	PROPN
ap-920	189	34	�	�	PROPN
ap-920	189	35	,	,	PUNCT
ap-920	189	36	n	n	PROPN
ap-920	189	37	�	�	PROPN
ap-920	189	38	�	�	PROPN
ap-920	189	39	.	.	PUNCT
ap-920	190	1	having	having	AUX
ap-920	190	2	calculated	calculate	VERB
ap-920	190	3	the	the	DET
ap-920	190	4	formula	formula	NOUN
ap-920	190	5	for	for	ADP
ap-920	190	6	l(k	l(k	PROPN
ap-920	190	7	)	)	PUNCT
ap-920	190	8	,	,	PUNCT
ap-920	190	9	k	k	PROPN
ap-920	190	10	�	�	PROPN
ap-920	190	11	�	�	PROPN
ap-920	190	12	,	,	PUNCT
ap-920	190	13	we	we	PRON
ap-920	190	14	have	have	AUX
ap-920	190	15	also	also	ADV
ap-920	190	16	computed	compute	VERB
ap-920	190	17	the	the	DET
ap-920	190	18	recurrence	recurrence	NOUN
ap-920	190	19	function	function	NOUN
ap-920	190	20	,	,	PUNCT
ap-920	190	21	since	since	SCONJ
ap-920	190	22	r	r	PROPN
ap-920	190	23	k	k	PROPN
ap-920	190	24	l	l	PROPN
ap-920	190	25	k	k	PROPN
ap-920	191	1	k	k	X
ap-920	191	2	(	(	PUNCT
ap-920	191	3	)	)	PUNCT
ap-920	191	4	(	(	PUNCT
ap-920	191	5	)	)	PUNCT
ap-920	191	6	�	�	PROPN
ap-920	191	7	�	�	PROPN
ap-920	191	8	�	�	PROPN
ap-920	191	9	1	1	NUM
ap-920	191	10	.	.	PUNCT
ap-920	192	1	references	reference	NOUN
ap-920	192	2	[	[	X
ap-920	192	3	1	1	NUM
ap-920	192	4	]	]	PUNCT
ap-920	192	5	vuillon	vuillon	NOUN
ap-920	192	6	,	,	PUNCT
ap-920	192	7	l.	l.	PROPN
ap-920	192	8	:	:	PUNCT
ap-920	192	9	a	a	DET
ap-920	192	10	characterization	characterization	NOUN
ap-920	192	11	of	of	ADP
ap-920	192	12	sturmian	sturmian	ADJ
ap-920	192	13	words	word	NOUN
ap-920	192	14	by	by	ADP
ap-920	192	15	return	return	NOUN
ap-920	192	16	words	word	NOUN
ap-920	192	17	.	.	PUNCT
ap-920	193	1	eur	eur	PROPN
ap-920	193	2	.	.	PUNCT
ap-920	194	1	j.	j.	PROPN
ap-920	194	2	comb	comb	PROPN
ap-920	194	3	.	.	PUNCT
ap-920	194	4	,	,	PUNCT
ap-920	194	5	vol	vol	NOUN
ap-920	194	6	.	.	PROPN
ap-920	194	7	22	22	NUM
ap-920	194	8	(	(	PUNCT
ap-920	194	9	2001	2001	NUM
ap-920	194	10	)	)	PUNCT
ap-920	194	11	,	,	PUNCT
ap-920	194	12	no	no	INTJ
ap-920	194	13	.	.	NOUN
ap-920	194	14	2	2	NUM
ap-920	194	15	,	,	PUNCT
ap-920	194	16	p.	p.	NOUN
ap-920	194	17	263–275	263–275	NUM
ap-920	194	18	.	.	PUNCT
ap-920	195	1	[	[	X
ap-920	195	2	2	2	NUM
ap-920	195	3	]	]	X
ap-920	195	4	justin	justin	PROPN
ap-920	195	5	,	,	PUNCT
ap-920	195	6	j.	j.	PROPN
ap-920	195	7	,	,	PUNCT
ap-920	195	8	vuillon	vuillon	PROPN
ap-920	195	9	,	,	PUNCT
ap-920	195	10	l.	l.	PROPN
ap-920	195	11	:	:	PUNCT
ap-920	195	12	return	return	VERB
ap-920	195	13	words	word	NOUN
ap-920	195	14	in	in	ADP
ap-920	195	15	sturmian	sturmian	NOUN
ap-920	195	16	and	and	CCONJ
ap-920	195	17	episturmian	episturmian	ADJ
ap-920	195	18	words	word	NOUN
ap-920	195	19	.	.	PUNCT
ap-920	196	1	theor	theor	PROPN
ap-920	196	2	.	.	PUNCT
ap-920	197	1	inform	inform	NOUN
ap-920	197	2	.	.	PUNCT
ap-920	198	1	appl	appl	PROPN
ap-920	198	2	.	.	PROPN
ap-920	198	3	,	,	PUNCT
ap-920	198	4	vol	vol	NOUN
ap-920	198	5	.	.	PUNCT
ap-920	199	1	34	34	NUM
ap-920	199	2	(	(	PUNCT
ap-920	199	3	2000	2000	NUM
ap-920	199	4	)	)	PUNCT
ap-920	199	5	,	,	PUNCT
ap-920	200	1	p.	p.	NOUN
ap-920	200	2	343–356	343–356	NUM
ap-920	200	3	.	.	PUNCT
ap-920	201	1	[	[	X
ap-920	201	2	3	3	NUM
ap-920	201	3	]	]	X
ap-920	201	4	vuillon	vuillon	NOUN
ap-920	201	5	,	,	PUNCT
ap-920	201	6	l.	l.	PROPN
ap-920	201	7	:	:	PUNCT
ap-920	201	8	on	on	ADP
ap-920	201	9	the	the	DET
ap-920	201	10	number	number	NOUN
ap-920	201	11	of	of	ADP
ap-920	201	12	return	return	NOUN
ap-920	201	13	words	word	NOUN
ap-920	201	14	in	in	ADP
ap-920	201	15	infinite	infinite	ADJ
ap-920	201	16	words	word	NOUN
ap-920	201	17	with	with	ADP
ap-920	201	18	complexity	complexity	NOUN
ap-920	201	19	.	.	PUNCT
ap-920	202	1	liafa	liafa	PROPN
ap-920	202	2	research	research	PROPN
ap-920	202	3	report	report	PROPN
ap-920	202	4	2000/15	2000/15	NUM
ap-920	202	5	.	.	PUNCT
ap-920	203	1	[	[	X
ap-920	203	2	4	4	X
ap-920	203	3	]	]	PUNCT
ap-920	203	4	balková	balková	X
ap-920	203	5	,	,	PUNCT
ap-920	203	6	l	l	NOUN
ap-920	203	7	’	'	PUNCT
ap-920	203	8	.	.	PUNCT
ap-920	203	9	,	,	PUNCT
ap-920	203	10	pelantová	pelantová	PROPN
ap-920	203	11	,	,	PUNCT
ap-920	203	12	e.	e.	PROPN
ap-920	203	13	,	,	PUNCT
ap-920	203	14	steiner	steiner	PROPN
ap-920	203	15	,	,	PUNCT
ap-920	203	16	w.	w.	PROPN
ap-920	203	17	:	:	PUNCT
ap-920	203	18	return	return	VERB
ap-920	203	19	words	word	NOUN
ap-920	203	20	in	in	ADP
ap-920	203	21	the	the	DET
ap-920	203	22	thue	thue	NOUN
ap-920	203	23	-	-	PUNCT
ap-920	203	24	morse	morse	PROPN
ap-920	203	25	and	and	CCONJ
ap-920	203	26	other	other	ADJ
ap-920	203	27	sequences	sequence	NOUN
ap-920	203	28	.	.	PUNCT
ap-920	204	1	arxiv	arxiv	PROPN
ap-920	204	2	:	:	PUNCT
ap-920	204	3	math/0608	math/0608	PROPN
ap-920	204	4	603	603	NUM
ap-920	204	5	sci	sci	PROPN
ap-920	204	6	.	.	PROPN
ap-920	204	7	,	,	PUNCT
ap-920	204	8	2006	2006	NUM
ap-920	204	9	.	.	PUNCT
ap-920	205	1	[	[	X
ap-920	205	2	5	5	NUM
ap-920	205	3	]	]	X
ap-920	205	4	cassaigne	cassaigne	PROPN
ap-920	205	5	,	,	PUNCT
ap-920	205	6	j.	j.	PROPN
ap-920	205	7	:	:	PUNCT
ap-920	205	8	limit	limit	VERB
ap-920	205	9	values	value	NOUN
ap-920	205	10	of	of	ADP
ap-920	205	11	the	the	DET
ap-920	205	12	recurrence	recurrence	NOUN
ap-920	205	13	quotient	quotient	NOUN
ap-920	205	14	of	of	ADP
ap-920	205	15	sturmian	sturmian	ADJ
ap-920	205	16	sequences	sequence	NOUN
ap-920	205	17	.	.	PUNCT
ap-920	206	1	theor	theor	PROPN
ap-920	206	2	.	.	PUNCT
ap-920	207	1	comput	comput	PROPN
ap-920	207	2	.	.	PUNCT
ap-920	208	1	sci	sci	PROPN
ap-920	208	2	.	.	PROPN
ap-920	208	3	,	,	PUNCT
ap-920	208	4	vol	vol	NOUN
ap-920	208	5	.	.	PROPN
ap-920	208	6	218	218	NUM
ap-920	208	7	(	(	PUNCT
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ap-920	208	9	)	)	PUNCT
ap-920	208	10	,	,	PUNCT
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ap-920	208	12	.	.	NOUN
ap-920	208	13	1	1	NUM
ap-920	208	14	,	,	PUNCT
ap-920	208	15	p.	p.	NOUN
ap-920	208	16	3–12	3–12	PROPN
ap-920	208	17	.	.	PUNCT
ap-920	209	1	[	[	X
ap-920	209	2	6	6	NUM
ap-920	209	3	]	]	X
ap-920	209	4	cassaigne	cassaigne	PROPN
ap-920	209	5	,	,	PUNCT
ap-920	209	6	j.	j.	PROPN
ap-920	209	7	:	:	PUNCT
ap-920	209	8	recurrence	recurrence	NOUN
ap-920	209	9	in	in	ADP
ap-920	209	10	infinite	infinite	ADJ
ap-920	209	11	words	word	NOUN
ap-920	209	12	.	.	PUNCT
ap-920	210	1	lecture	lecture	NOUN
ap-920	210	2	notes	note	NOUN
ap-920	210	3	in	in	ADP
ap-920	210	4	computer	computer	NOUN
ap-920	210	5	science	science	NOUN
ap-920	210	6	,	,	PUNCT
ap-920	210	7	springer	springer	NOUN
ap-920	210	8	verlag	verlag	PROPN
ap-920	210	9	,	,	PUNCT
ap-920	210	10	vol	vol	NOUN
ap-920	210	11	.	.	PROPN
ap-920	210	12	2010	2010	NUM
ap-920	210	13	,	,	PUNCT
ap-920	210	14	2001	2001	NUM
ap-920	210	15	,	,	PUNCT
ap-920	210	16	p.	p.	PROPN
ap-920	210	17	1–11	1–11	PROPN
ap-920	210	18	.	.	PUNCT
ap-920	211	1	[	[	X
ap-920	211	2	7	7	X
ap-920	211	3	]	]	PUNCT
ap-920	211	4	balková	balková	NOUN
ap-920	211	5	,	,	PUNCT
ap-920	211	6	l	l	NOUN
ap-920	211	7	’	'	PUNCT
ap-920	211	8	.	.	PUNCT
ap-920	212	1	:	:	PUNCT
ap-920	213	1	complexity	complexity	NOUN
ap-920	213	2	for	for	ADP
ap-920	213	3	infinite	infinite	ADJ
ap-920	213	4	words	word	NOUN
ap-920	213	5	associated	associate	VERB
ap-920	213	6	with	with	ADP
ap-920	213	7	quadratic	quadratic	ADJ
ap-920	213	8	non	non	ADJ
ap-920	213	9	-	-	ADJ
ap-920	213	10	simple	simple	ADJ
ap-920	213	11	parry	parry	NOUN
ap-920	213	12	numbers	number	NOUN
ap-920	213	13	.	.	PUNCT
ap-920	214	1	journal	journal	NOUN
ap-920	214	2	of	of	ADP
ap-920	214	3	geometry	geometry	NOUN
ap-920	214	4	and	and	CCONJ
ap-920	214	5	symmetry	symmetry	NOUN
ap-920	214	6	in	in	ADP
ap-920	214	7	physics	physics	NOUN
ap-920	214	8	(	(	PUNCT
ap-920	214	9	wgmp	wgmp	NOUN
ap-920	214	10	2005	2005	NUM
ap-920	214	11	proceedings	proceeding	NOUN
ap-920	214	12	)	)	PUNCT
ap-920	214	13	vol	vol	NOUN
ap-920	214	14	.	.	PROPN
ap-920	214	15	7	7	NUM
ap-920	214	16	(	(	PUNCT
ap-920	214	17	2006	2006	NUM
ap-920	214	18	)	)	PUNCT
ap-920	214	19	,	,	PUNCT
ap-920	214	20	p.	p.	PROPN
ap-920	214	21	1–11	1–11	PROPN
ap-920	214	22	.	.	PUNCT
ap-920	215	1	[	[	X
ap-920	215	2	8	8	NUM
ap-920	215	3	]	]	PUNCT
ap-920	215	4	balková	balková	NOUN
ap-920	215	5	,	,	PUNCT
ap-920	215	6	l	l	NOUN
ap-920	215	7	’	'	PUNCT
ap-920	215	8	.	.	PUNCT
ap-920	215	9	,	,	PUNCT
ap-920	215	10	masáková	masáková	PROPN
ap-920	215	11	,	,	PUNCT
ap-920	215	12	z.	z.	PROPN
ap-920	215	13	:	:	PUNCT
ap-920	215	14	palindromic	palindromic	ADJ
ap-920	215	15	complexity	complexity	NOUN
ap-920	215	16	of	of	ADP
ap-920	215	17	infinite	infinite	ADJ
ap-920	215	18	words	word	NOUN
ap-920	215	19	associated	associate	VERB
ap-920	215	20	with	with	ADP
ap-920	215	21	non	non	ADJ
ap-920	215	22	-	-	ADJ
ap-920	215	23	simple	simple	ADJ
ap-920	215	24	parry	parry	NOUN
ap-920	215	25	numbers	number	NOUN
ap-920	215	26	.	.	PUNCT
ap-920	215	27	submitted	submit	VERB
ap-920	215	28	to	to	ADP
ap-920	215	29	rairo	rairo	PROPN
ap-920	215	30	theor	theor	PROPN
ap-920	215	31	.	.	PUNCT
ap-920	216	1	inform	inform	NOUN
ap-920	216	2	.	.	PUNCT
ap-920	217	1	appl	appl	PROPN
ap-920	217	2	.	.	PROPN
ap-920	217	3	,	,	PUNCT
ap-920	217	4	2006	2006	NUM
ap-920	217	5	,	,	PUNCT
ap-920	218	1	16	16	NUM
ap-920	218	2	p.	p.	NOUN
ap-920	219	1	[	[	X
ap-920	219	2	9	9	X
ap-920	219	3	]	]	PUNCT
ap-920	219	4	balková	balková	NOUN
ap-920	219	5	,	,	PUNCT
ap-920	219	6	l	l	NOUN
ap-920	219	7	’	'	PUNCT
ap-920	219	8	.	.	PUNCT
ap-920	219	9	,	,	PUNCT
ap-920	219	10	pelantová	pelantová	PROPN
ap-920	219	11	,	,	PUNCT
ap-920	219	12	e.	e.	PROPN
ap-920	219	13	,	,	PUNCT
ap-920	219	14	turek	turek	NOUN
ap-920	219	15	,	,	PUNCT
ap-920	219	16	o.	o.	NOUN
ap-920	219	17	:	:	PUNCT
ap-920	219	18	combinatorial	combinatorial	ADJ
ap-920	219	19	and	and	CCONJ
ap-920	219	20	arithmetical	arithmetical	ADJ
ap-920	219	21	properties	property	NOUN
ap-920	219	22	of	of	ADP
ap-920	219	23	infinite	infinite	ADJ
ap-920	219	24	words	word	NOUN
ap-920	219	25	associated	associate	VERB
ap-920	219	26	with	with	ADP
ap-920	219	27	non	non	ADJ
ap-920	219	28	-	-	ADJ
ap-920	219	29	simple	simple	ADJ
ap-920	219	30	quadratic	quadratic	ADJ
ap-920	219	31	parry	parry	NOUN
ap-920	219	32	numbers	number	NOUN
ap-920	219	33	.	.	PUNCT
ap-920	220	1	to	to	PART
ap-920	220	2	appear	appear	VERB
ap-920	220	3	in	in	ADP
ap-920	220	4	rairo	rairo	PROPN
ap-920	220	5	theor	theor	PROPN
ap-920	220	6	.	.	PUNCT
ap-920	221	1	inform	inform	NOUN
ap-920	221	2	.	.	PUNCT
ap-920	222	1	appl	appl	PROPN
ap-920	222	2	.	.	PROPN
ap-920	222	3	,	,	PUNCT
ap-920	222	4	2006	2006	NUM
ap-920	222	5	,	,	PUNCT
ap-920	223	1	17	17	NUM
ap-920	223	2	p.	p.	NOUN
ap-920	224	1	[	[	X
ap-920	224	2	10	10	NUM
ap-920	224	3	]	]	X
ap-920	224	4	queffélec	queffélec	NOUN
ap-920	224	5	,	,	PUNCT
ap-920	224	6	m.	m.	NOUN
ap-920	224	7	:	:	PUNCT
ap-920	224	8	substitution	substitution	NOUN
ap-920	224	9	dynamical	dynamical	ADJ
ap-920	224	10	systems	system	NOUN
ap-920	224	11	–	–	PUNCT
ap-920	224	12	spectral	spectral	ADJ
ap-920	224	13	analysis	analysis	NOUN
ap-920	224	14	.	.	PUNCT
ap-920	225	1	lecture	lecture	NOUN
ap-920	225	2	notes	note	NOUN
ap-920	225	3	in	in	ADP
ap-920	225	4	math	math	NOUN
ap-920	225	5	.	.	PUNCT
ap-920	225	6	,	,	PUNCT
ap-920	225	7	springer	springer	NOUN
ap-920	225	8	berlin	berlin	PROPN
ap-920	225	9	vol	vol	NOUN
ap-920	225	10	.	.	PUNCT
ap-920	226	1	1294	1294	NUM
ap-920	226	2	,	,	PUNCT
ap-920	226	3	1987	1987	NUM
ap-920	226	4	.	.	PUNCT
ap-920	227	1	ing.l’ubomíra	ing.l’ubomíra	PROPN
ap-920	228	1	balková	balková	X
ap-920	228	2	phone	phone	NOUN
ap-920	228	3	:	:	PUNCT
ap-920	228	4	+420	+420	PROPN
ap-920	228	5	224	224	NUM
ap-920	228	6	358	358	NUM
ap-920	228	7	560	560	NUM
ap-920	228	8	e	e	NOUN
ap-920	228	9	-	-	NOUN
ap-920	228	10	mail	mail	NOUN
ap-920	228	11	:	:	PUNCT
ap-920	228	12	l.balkova@centrum.cz	l.balkova@centrum.cz	VERB
ap-920	228	13	doppler	doppler	NOUN
ap-920	228	14	institute	institute	NOUN
ap-920	228	15	for	for	ADP
ap-920	228	16	mathematical	mathematical	ADJ
ap-920	228	17	physics	physics	NOUN
ap-920	228	18	and	and	CCONJ
ap-920	228	19	applied	apply	VERB
ap-920	228	20	mathematics	mathematics	PROPN
ap-920	228	21	&	&	CCONJ
ap-920	228	22	department	department	PROPN
ap-920	228	23	of	of	ADP
ap-920	228	24	mathematics	mathematics	PROPN
ap-920	228	25	czech	czech	PROPN
ap-920	228	26	technical	technical	PROPN
ap-920	228	27	university	university	PROPN
ap-920	228	28	in	in	ADP
ap-920	228	29	prague	prague	PROPN
ap-920	228	30	faculty	faculty	NOUN
ap-920	228	31	of	of	ADP
ap-920	228	32	nuclear	nuclear	ADJ
ap-920	228	33	sciences	science	NOUN
ap-920	228	34	and	and	CCONJ
ap-920	228	35	physical	physical	ADJ
ap-920	228	36	engineering	engineering	NOUN
ap-920	228	37	trojanova	trojanova	ADP
ap-920	228	38	13	13	NUM
ap-920	228	39	120	120	NUM
ap-920	228	40	00	00	NUM
ap-920	228	41	praha	praha	PROPN
ap-920	228	42	2	2	NUM
ap-920	228	43	,	,	PUNCT
ap-920	228	44	czech	czech	PROPN
ap-920	228	45	republic	republic	NOUN
ap-920	228	46	©	©	PROPN
ap-920	228	47	czech	czech	PROPN
ap-920	228	48	technical	technical	PROPN
ap-920	228	49	university	university	PROPN
ap-920	228	50	publishing	publishing	NOUN
ap-920	228	51	house	house	NOUN
ap-920	228	52	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-920	228	53	19	19	NUM
ap-920	228	54	acta	acta	PROPN
ap-920	228	55	polytechnica	polytechnica	PROPN
ap-920	228	56	vol	vol	NOUN
ap-920	228	57	.	.	PUNCT
ap-920	229	1	47	47	NUM
ap-920	229	2	no	no	INTJ
ap-920	229	3	.	.	PUNCT
ap-920	230	1	2–3/2007	2–3/2007	NUM
ap-920	230	2	k	k	NOUN
ap-920	230	3	1	1	NUM
ap-920	230	4	2	2	NUM
ap-920	230	5	3	3	NUM
ap-920	230	6	4	4	NUM
ap-920	230	7	5	5	NUM
ap-920	230	8	6	6	NUM
ap-920	230	9	7	7	NUM
ap-920	230	10	8	8	NUM
ap-920	230	11	9	9	NUM
ap-920	230	12	10	10	NUM
ap-920	230	13	11	11	NUM
ap-920	230	14	12	12	NUM
ap-920	230	15	13	13	NUM
ap-920	230	16	14	14	NUM
ap-920	230	17	15	15	NUM
ap-920	230	18	16	16	NUM
ap-920	230	19	17	17	NUM
ap-920	230	20	18	18	NUM
ap-920	230	21	19	19	NUM
ap-920	230	22	20	20	NUM
ap-920	230	23	l(k	l(k	NOUN
ap-920	230	24	)	)	PUNCT
ap-920	230	25	3	3	NUM
ap-920	230	26	5	5	NUM
ap-920	230	27	8	8	NUM
ap-920	230	28	8	8	NUM
ap-920	230	29	13	13	NUM
ap-920	230	30	13	13	NUM
ap-920	230	31	13	13	NUM
ap-920	230	32	21	21	NUM
ap-920	230	33	21	21	NUM
ap-920	230	34	21	21	NUM
ap-920	230	35	21	21	NUM
ap-920	230	36	21	21	NUM
ap-920	230	37	34	34	NUM
ap-920	230	38	34	34	NUM
ap-920	230	39	34	34	NUM
ap-920	230	40	34	34	NUM
ap-920	230	41	34	34	NUM
ap-920	230	42	34	34	NUM
ap-920	230	43	34	34	NUM
ap-920	230	44	34	34	NUM
ap-920	230	45	r(k	r(k	NOUN
ap-920	230	46	)	)	PUNCT
ap-920	230	47	3	3	NUM
ap-920	230	48	6	6	NUM
ap-920	230	49	10	10	NUM
ap-920	230	50	11	11	NUM
ap-920	230	51	17	17	NUM
ap-920	230	52	18	18	NUM
ap-920	230	53	19	19	NUM
ap-920	230	54	28	28	NUM
ap-920	230	55	29	29	NUM
ap-920	230	56	30	30	NUM
ap-920	230	57	31	31	NUM
ap-920	230	58	32	32	NUM
ap-920	230	59	46	46	NUM
ap-920	230	60	47	47	NUM
ap-920	230	61	48	48	NUM
ap-920	230	62	49	49	NUM
ap-920	230	63	50	50	NUM
ap-920	230	64	51	51	NUM
ap-920	230	65	52	52	NUM
ap-920	230	66	53	53	NUM
ap-920	230	67	the	the	DET
ap-920	230	68	table	table	NOUN
ap-920	230	69	of	of	ADP
ap-920	230	70	the	the	DET
ap-920	230	71	first	first	ADJ
ap-920	230	72	20	20	NUM
ap-920	230	73	values	value	NOUN
ap-920	230	74	of	of	ADP
ap-920	230	75	l(k	l(k	PROPN
ap-920	230	76	)	)	PUNCT
ap-920	230	77	and	and	CCONJ
ap-920	230	78	r(k	r(k	PROPN
ap-920	230	79	)	)	PUNCT
ap-920	230	80	for	for	ADP
ap-920	230	81	the	the	DET
ap-920	230	82	simplest	simple	ADJ
ap-920	230	83	case	case	NOUN
ap-920	230	84	a	a	DET
ap-920	230	85	�	�	PROPN
ap-920	230	86	2	2	NUM
ap-920	230	87	and	and	CCONJ
ap-920	230	88	b	b	PROPN
ap-920	230	89	�	�	PROPN
ap-920	230	90	1	1	NUM