id	sid	tid	token	lemma	pos
ap-3794	1	1	acta	acta	PROPN
ap-3794	1	2	polytechnica	polytechnica	PROPN
ap-3794	1	3	doi:10.14311	doi:10.14311	PROPN
ap-3794	1	4	/	/	SYM
ap-3794	1	5	ap.2016.56.0462	ap.2016.56.0462	PROPN
ap-3794	1	6	acta	acta	PROPN
ap-3794	1	7	polytechnica	polytechnica	PROPN
ap-3794	1	8	56(6):462–471	56(6):462–471	PROPN
ap-3794	1	9	,	,	PUNCT
ap-3794	1	10	2016	2016	NUM
ap-3794	1	11	©	©	PROPN
ap-3794	1	12	czech	czech	PROPN
ap-3794	1	13	technical	technical	PROPN
ap-3794	1	14	university	university	PROPN
ap-3794	1	15	in	in	ADP
ap-3794	1	16	prague	prague	PROPN
ap-3794	1	17	,	,	PUNCT
ap-3794	1	18	2016	2016	NUM
ap-3794	1	19	available	available	ADJ
ap-3794	1	20	online	online	ADV
ap-3794	1	21	at	at	ADP
ap-3794	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3794	1	23	itineraries	itinerary	NOUN
ap-3794	1	24	induced	induce	VERB
ap-3794	1	25	by	by	ADP
ap-3794	1	26	exchange	exchange	NOUN
ap-3794	1	27	of	of	ADP
ap-3794	1	28	three	three	NUM
ap-3794	1	29	intervals	interval	NOUN
ap-3794	1	30	zuzana	zuzana	PROPN
ap-3794	1	31	masákováa	masákováa	PROPN
ap-3794	1	32	,	,	PUNCT
ap-3794	1	33	edita	edita	PROPN
ap-3794	1	34	pelantováa	pelantováa	NOUN
ap-3794	1	35	,	,	PUNCT
ap-3794	1	36	štěpán	štěpán	X
ap-3794	1	37	starostab,∗	starostab,∗	PUNCT
ap-3794	2	1	a	a	DET
ap-3794	2	2	faculty	faculty	NOUN
ap-3794	2	3	of	of	ADP
ap-3794	2	4	nuclear	nuclear	ADJ
ap-3794	2	5	sciences	science	NOUN
ap-3794	2	6	and	and	CCONJ
ap-3794	2	7	physical	physical	ADJ
ap-3794	2	8	engineering	engineering	NOUN
ap-3794	2	9	,	,	PUNCT
ap-3794	2	10	czech	czech	PROPN
ap-3794	2	11	technical	technical	PROPN
ap-3794	2	12	university	university	PROPN
ap-3794	2	13	in	in	ADP
ap-3794	2	14	prague	prague	PROPN
ap-3794	2	15	,	,	PUNCT
ap-3794	2	16	prague	prague	PROPN
ap-3794	2	17	,	,	PUNCT
ap-3794	2	18	czech	czech	PROPN
ap-3794	2	19	republic	republic	PROPN
ap-3794	2	20	b	b	PROPN
ap-3794	2	21	faculty	faculty	NOUN
ap-3794	2	22	of	of	ADP
ap-3794	2	23	information	information	NOUN
ap-3794	2	24	technology	technology	NOUN
ap-3794	2	25	,	,	PUNCT
ap-3794	2	26	czech	czech	PROPN
ap-3794	2	27	technical	technical	PROPN
ap-3794	2	28	university	university	PROPN
ap-3794	2	29	in	in	ADP
ap-3794	2	30	prague	prague	PROPN
ap-3794	2	31	,	,	PUNCT
ap-3794	2	32	prague	prague	PROPN
ap-3794	2	33	,	,	PUNCT
ap-3794	2	34	czech	czech	PROPN
ap-3794	2	35	republic	republic	NOUN
ap-3794	2	36	∗	∗	NOUN
ap-3794	2	37	corresponding	correspond	VERB
ap-3794	2	38	author	author	NOUN
ap-3794	2	39	:	:	PUNCT
ap-3794	2	40	stepan.starosta@fit.cvut.cz	stepan.starosta@fit.cvut.cz	NOUN
ap-3794	2	41	abstract	abstract	NOUN
ap-3794	2	42	.	.	PUNCT
ap-3794	3	1	we	we	PRON
ap-3794	3	2	focus	focus	VERB
ap-3794	3	3	on	on	ADP
ap-3794	3	4	a	a	DET
ap-3794	3	5	generalization	generalization	NOUN
ap-3794	3	6	of	of	ADP
ap-3794	3	7	the	the	DET
ap-3794	3	8	three	three	NUM
ap-3794	3	9	gap	gap	NOUN
ap-3794	3	10	theorem	theorem	VERB
ap-3794	3	11	well	well	ADV
ap-3794	3	12	known	know	VERB
ap-3794	3	13	in	in	ADP
ap-3794	3	14	the	the	DET
ap-3794	3	15	framework	framework	NOUN
ap-3794	3	16	of	of	ADP
ap-3794	3	17	exchange	exchange	NOUN
ap-3794	3	18	of	of	ADP
ap-3794	3	19	two	two	NUM
ap-3794	3	20	intervals	interval	NOUN
ap-3794	3	21	.	.	PUNCT
ap-3794	4	1	for	for	ADP
ap-3794	4	2	the	the	DET
ap-3794	4	3	case	case	NOUN
ap-3794	4	4	of	of	ADP
ap-3794	4	5	three	three	NUM
ap-3794	4	6	intervals	interval	NOUN
ap-3794	4	7	,	,	PUNCT
ap-3794	4	8	our	our	PRON
ap-3794	4	9	main	main	ADJ
ap-3794	4	10	result	result	NOUN
ap-3794	4	11	provides	provide	VERB
ap-3794	4	12	an	an	DET
ap-3794	4	13	analogue	analogue	NOUN
ap-3794	4	14	of	of	ADP
ap-3794	4	15	this	this	DET
ap-3794	4	16	result	result	NOUN
ap-3794	4	17	implying	imply	VERB
ap-3794	4	18	that	that	SCONJ
ap-3794	4	19	there	there	PRON
ap-3794	4	20	are	be	VERB
ap-3794	4	21	at	at	ADP
ap-3794	4	22	most	most	ADJ
ap-3794	4	23	5	5	NUM
ap-3794	4	24	gaps	gap	NOUN
ap-3794	4	25	.	.	PUNCT
ap-3794	5	1	to	to	PART
ap-3794	5	2	derive	derive	VERB
ap-3794	5	3	this	this	DET
ap-3794	5	4	result	result	NOUN
ap-3794	5	5	,	,	PUNCT
ap-3794	5	6	we	we	PRON
ap-3794	5	7	give	give	VERB
ap-3794	5	8	a	a	DET
ap-3794	5	9	detailed	detailed	ADJ
ap-3794	5	10	description	description	NOUN
ap-3794	5	11	of	of	ADP
ap-3794	5	12	the	the	DET
ap-3794	5	13	return	return	NOUN
ap-3794	5	14	times	time	NOUN
ap-3794	5	15	to	to	ADP
ap-3794	5	16	a	a	DET
ap-3794	5	17	subinterval	subinterval	NOUN
ap-3794	5	18	and	and	CCONJ
ap-3794	5	19	the	the	DET
ap-3794	5	20	corresponding	corresponding	ADJ
ap-3794	5	21	itineraries	itinerary	NOUN
ap-3794	5	22	.	.	PUNCT
ap-3794	6	1	keywords	keyword	NOUN
ap-3794	6	2	:	:	PUNCT
ap-3794	6	3	interval	interval	NOUN
ap-3794	6	4	exchange	exchange	NOUN
ap-3794	6	5	transformation	transformation	NOUN
ap-3794	6	6	;	;	PUNCT
ap-3794	6	7	three	three	NUM
ap-3794	6	8	gap	gap	NOUN
ap-3794	6	9	theorem	theorem	VERB
ap-3794	6	10	;	;	PUNCT
ap-3794	6	11	return	return	NOUN
ap-3794	6	12	time	time	NOUN
ap-3794	6	13	;	;	PUNCT
ap-3794	6	14	first	first	ADJ
ap-3794	6	15	return	return	NOUN
ap-3794	6	16	map	map	NOUN
ap-3794	6	17	.	.	PUNCT
ap-3794	7	1	1	1	X
ap-3794	7	2	.	.	X
ap-3794	7	3	introduction	introduction	NOUN
ap-3794	7	4	the	the	DET
ap-3794	7	5	well	well	ADV
ap-3794	7	6	-	-	PUNCT
ap-3794	7	7	known	know	VERB
ap-3794	7	8	three	three	NUM
ap-3794	7	9	gap	gap	NOUN
ap-3794	7	10	theorem	theorem	NOUN
ap-3794	7	11	provides	provide	VERB
ap-3794	7	12	information	information	NOUN
ap-3794	7	13	about	about	ADP
ap-3794	7	14	gaps	gap	NOUN
ap-3794	7	15	between	between	ADP
ap-3794	7	16	consecutive	consecutive	ADJ
ap-3794	7	17	integers	integer	NOUN
ap-3794	7	18	n	n	X
ap-3794	7	19	for	for	ADP
ap-3794	7	20	which	which	PRON
ap-3794	7	21	{	{	PUNCT
ap-3794	7	22	αn	αn	NOUN
ap-3794	7	23	}	}	PUNCT
ap-3794	7	24	<	<	X
ap-3794	7	25	β	β	NOUN
ap-3794	7	26	with	with	ADP
ap-3794	7	27	α	α	PROPN
ap-3794	7	28	,	,	PUNCT
ap-3794	7	29	β	β	X
ap-3794	7	30	∈	∈	PROPN
ap-3794	7	31	(	(	PUNCT
ap-3794	7	32	0	0	NUM
ap-3794	7	33	,	,	PUNCT
ap-3794	7	34	1	1	NUM
ap-3794	7	35	)	)	PUNCT
ap-3794	7	36	,	,	PUNCT
ap-3794	7	37	where	where	SCONJ
ap-3794	7	38	the	the	DET
ap-3794	7	39	notation	notation	NOUN
ap-3794	7	40	{	{	PUNCT
ap-3794	7	41	x	x	NOUN
ap-3794	7	42	}	}	PUNCT
ap-3794	7	43	=	=	SYM
ap-3794	7	44	x−	x−	PROPN
ap-3794	7	45	bxc	bxc	PROPN
ap-3794	7	46	stands	stand	VERB
ap-3794	7	47	for	for	ADP
ap-3794	7	48	the	the	DET
ap-3794	7	49	fractional	fractional	ADJ
ap-3794	7	50	part	part	NOUN
ap-3794	7	51	of	of	ADP
ap-3794	7	52	x.	x.	NOUN
ap-3794	7	53	in	in	ADP
ap-3794	7	54	particular	particular	ADJ
ap-3794	7	55	,	,	PUNCT
ap-3794	7	56	the	the	DET
ap-3794	7	57	gaps	gap	NOUN
ap-3794	7	58	take	take	VERB
ap-3794	7	59	at	at	ADV
ap-3794	7	60	most	most	ADV
ap-3794	7	61	three	three	NUM
ap-3794	7	62	values	value	NOUN
ap-3794	7	63	,	,	PUNCT
ap-3794	7	64	the	the	DET
ap-3794	7	65	longest	long	ADJ
ap-3794	7	66	one	one	NOUN
ap-3794	7	67	being	be	AUX
ap-3794	7	68	the	the	DET
ap-3794	7	69	sum	sum	NOUN
ap-3794	7	70	of	of	ADP
ap-3794	7	71	the	the	DET
ap-3794	7	72	other	other	ADJ
ap-3794	7	73	two	two	NUM
ap-3794	7	74	.	.	PUNCT
ap-3794	8	1	this	this	DET
ap-3794	8	2	result	result	NOUN
ap-3794	8	3	was	be	AUX
ap-3794	8	4	first	first	ADV
ap-3794	8	5	proved	prove	VERB
ap-3794	8	6	by	by	ADP
ap-3794	8	7	slater	slater	NOUN
ap-3794	8	8	[	[	X
ap-3794	8	9	14	14	NUM
ap-3794	8	10	]	]	PUNCT
ap-3794	8	11	,	,	PUNCT
ap-3794	8	12	but	but	CCONJ
ap-3794	8	13	it	it	PRON
ap-3794	8	14	appeared	appear	VERB
ap-3794	8	15	in	in	ADP
ap-3794	8	16	different	different	ADJ
ap-3794	8	17	versions	version	NOUN
ap-3794	8	18	and	and	CCONJ
ap-3794	8	19	generalizations	generalization	NOUN
ap-3794	8	20	multiple	multiple	ADJ
ap-3794	8	21	times	time	NOUN
ap-3794	8	22	since	since	ADV
ap-3794	8	23	.	.	PUNCT
ap-3794	9	1	for	for	ADP
ap-3794	9	2	a	a	DET
ap-3794	9	3	nice	nice	ADJ
ap-3794	9	4	overview	overview	NOUN
ap-3794	9	5	of	of	ADP
ap-3794	9	6	this	this	DET
ap-3794	9	7	problem	problem	NOUN
ap-3794	9	8	we	we	PRON
ap-3794	9	9	refer	refer	VERB
ap-3794	9	10	to	to	ADP
ap-3794	9	11	[	[	X
ap-3794	9	12	1	1	NUM
ap-3794	9	13	]	]	PUNCT
ap-3794	9	14	.	.	PUNCT
ap-3794	10	1	the	the	DET
ap-3794	10	2	reason	reason	NOUN
ap-3794	10	3	is	be	AUX
ap-3794	10	4	that	that	SCONJ
ap-3794	10	5	the	the	DET
ap-3794	10	6	theorem	theorem	NOUN
ap-3794	10	7	can	can	AUX
ap-3794	10	8	be	be	AUX
ap-3794	10	9	interpreted	interpret	VERB
ap-3794	10	10	in	in	ADP
ap-3794	10	11	the	the	DET
ap-3794	10	12	framework	framework	NOUN
ap-3794	10	13	of	of	ADP
ap-3794	10	14	coding	code	VERB
ap-3794	10	15	with	with	ADP
ap-3794	10	16	respect	respect	NOUN
ap-3794	10	17	to	to	ADP
ap-3794	10	18	intervals	interval	NOUN
ap-3794	10	19	[	[	X
ap-3794	10	20	0	0	NUM
ap-3794	10	21	,	,	PUNCT
ap-3794	10	22	β	β	NOUN
ap-3794	10	23	)	)	PUNCT
ap-3794	10	24	,	,	PUNCT
ap-3794	10	25	[	[	X
ap-3794	10	26	β	β	X
ap-3794	10	27	,	,	PUNCT
ap-3794	10	28	1	1	NUM
ap-3794	10	29	)	)	PUNCT
ap-3794	10	30	of	of	ADP
ap-3794	10	31	rotation	rotation	NOUN
ap-3794	10	32	by	by	ADP
ap-3794	10	33	the	the	DET
ap-3794	10	34	angle	angle	NOUN
ap-3794	10	35	α	α	NOUN
ap-3794	10	36	on	on	ADP
ap-3794	10	37	the	the	DET
ap-3794	10	38	unit	unit	NOUN
ap-3794	10	39	circle	circle	NOUN
ap-3794	10	40	.	.	PUNCT
ap-3794	11	1	for	for	ADP
ap-3794	11	2	irrational	irrational	ADJ
ap-3794	11	3	α	α	NOUN
ap-3794	11	4	and	and	CCONJ
ap-3794	11	5	β	β	X
ap-3794	11	6	=	=	SYM
ap-3794	11	7	1−	1−	NUM
ap-3794	11	8	α	α	NOUN
ap-3794	11	9	,	,	PUNCT
ap-3794	11	10	such	such	ADJ
ap-3794	11	11	coding	code	VERB
ap-3794	11	12	gives	give	VERB
ap-3794	11	13	rise	rise	NOUN
ap-3794	11	14	to	to	ADP
ap-3794	11	15	famous	famous	ADJ
ap-3794	11	16	sturmian	sturmian	NOUN
ap-3794	11	17	words	word	NOUN
ap-3794	11	18	.	.	PUNCT
ap-3794	12	1	the	the	DET
ap-3794	12	2	three	three	NUM
ap-3794	12	3	gap	gap	NOUN
ap-3794	12	4	theorem	theorem	NOUN
ap-3794	12	5	is	be	AUX
ap-3794	12	6	then	then	ADV
ap-3794	12	7	intimately	intimately	ADV
ap-3794	12	8	connected	connect	VERB
ap-3794	12	9	with	with	ADP
ap-3794	12	10	the	the	DET
ap-3794	12	11	dynamical	dynamical	ADJ
ap-3794	12	12	system	system	NOUN
ap-3794	12	13	associated	associate	VERB
ap-3794	12	14	with	with	ADP
ap-3794	12	15	codings	coding	NOUN
ap-3794	12	16	of	of	ADP
ap-3794	12	17	rotations	rotation	NOUN
ap-3794	12	18	,	,	PUNCT
ap-3794	12	19	induced	induced	ADJ
ap-3794	12	20	transformations	transformation	NOUN
ap-3794	12	21	,	,	PUNCT
ap-3794	12	22	return	return	NOUN
ap-3794	12	23	times	time	NOUN
ap-3794	12	24	and	and	CCONJ
ap-3794	12	25	return	return	VERB
ap-3794	12	26	itineraries	itinerary	NOUN
ap-3794	12	27	.	.	PUNCT
ap-3794	13	1	see	see	VERB
ap-3794	13	2	also	also	ADV
ap-3794	13	3	[	[	X
ap-3794	13	4	8	8	NUM
ap-3794	13	5	]	]	PUNCT
ap-3794	13	6	for	for	ADP
ap-3794	13	7	a	a	DET
ap-3794	13	8	distinct	distinct	ADJ
ap-3794	13	9	setting	setting	NOUN
ap-3794	13	10	of	of	ADP
ap-3794	13	11	exchange	exchange	NOUN
ap-3794	13	12	of	of	ADP
ap-3794	13	13	two	two	NUM
ap-3794	13	14	intervals	interval	NOUN
ap-3794	13	15	related	relate	VERB
ap-3794	13	16	to	to	ADP
ap-3794	13	17	the	the	DET
ap-3794	13	18	three	three	NUM
ap-3794	13	19	gap	gap	NOUN
ap-3794	13	20	theorem	theorem	VERB
ap-3794	13	21	.	.	PUNCT
ap-3794	14	1	codings	coding	NOUN
ap-3794	14	2	of	of	ADP
ap-3794	14	3	rotations	rotation	NOUN
ap-3794	14	4	are	be	AUX
ap-3794	14	5	advantageously	advantageously	ADV
ap-3794	14	6	interpreted	interpret	VERB
ap-3794	14	7	in	in	ADP
ap-3794	14	8	the	the	DET
ap-3794	14	9	language	language	NOUN
ap-3794	14	10	of	of	ADP
ap-3794	14	11	interval	interval	NOUN
ap-3794	14	12	exchange	exchange	NOUN
ap-3794	14	13	.	.	PUNCT
ap-3794	15	1	the	the	DET
ap-3794	15	2	simplest	simple	ADJ
ap-3794	15	3	case	case	NOUN
ap-3794	15	4	provides	provide	VERB
ap-3794	15	5	sturmian	sturmian	ADJ
ap-3794	15	6	words	word	NOUN
ap-3794	15	7	as	as	ADP
ap-3794	15	8	codings	coding	NOUN
ap-3794	15	9	of	of	ADP
ap-3794	15	10	exchange	exchange	NOUN
ap-3794	15	11	of	of	ADP
ap-3794	15	12	two	two	NUM
ap-3794	15	13	intervals	interval	NOUN
ap-3794	15	14	.	.	PUNCT
ap-3794	16	1	we	we	PRON
ap-3794	16	2	follow	follow	VERB
ap-3794	16	3	the	the	DET
ap-3794	16	4	study	study	NOUN
ap-3794	16	5	on	on	ADP
ap-3794	16	6	itineraries	itinerary	NOUN
ap-3794	16	7	induced	induce	VERB
ap-3794	16	8	by	by	ADP
ap-3794	16	9	exchange	exchange	NOUN
ap-3794	16	10	of	of	ADP
ap-3794	16	11	two	two	NUM
ap-3794	16	12	intervals	interval	NOUN
ap-3794	16	13	,	,	PUNCT
ap-3794	16	14	presented	present	VERB
ap-3794	16	15	in	in	ADP
ap-3794	16	16	[	[	X
ap-3794	16	17	13	13	NUM
ap-3794	16	18	]	]	PUNCT
ap-3794	16	19	,	,	PUNCT
ap-3794	16	20	to	to	PART
ap-3794	16	21	study	study	VERB
ap-3794	16	22	the	the	DET
ap-3794	16	23	exchange	exchange	NOUN
ap-3794	16	24	of	of	ADP
ap-3794	16	25	three	three	NUM
ap-3794	16	26	intervals	interval	NOUN
ap-3794	16	27	.	.	PUNCT
ap-3794	17	1	in	in	ADP
ap-3794	17	2	this	this	DET
ap-3794	17	3	article	article	NOUN
ap-3794	17	4	we	we	PRON
ap-3794	17	5	focus	focus	VERB
ap-3794	17	6	on	on	ADP
ap-3794	17	7	codings	coding	NOUN
ap-3794	17	8	of	of	ADP
ap-3794	17	9	a	a	DET
ap-3794	17	10	nondegenerate	nondegenerate	ADJ
ap-3794	17	11	symmetric	symmetric	ADJ
ap-3794	17	12	exchange	exchange	PROPN
ap-3794	17	13	t	t	PROPN
ap-3794	17	14	:	:	PUNCT
ap-3794	17	15	j	j	PROPN
ap-3794	17	16	→	→	SYM
ap-3794	17	17	j	j	PROPN
ap-3794	17	18	of	of	ADP
ap-3794	17	19	three	three	NUM
ap-3794	17	20	intervals	interval	NOUN
ap-3794	17	21	.	.	PUNCT
ap-3794	18	1	the	the	DET
ap-3794	18	2	main	main	ADJ
ap-3794	18	3	result	result	NOUN
ap-3794	18	4	is	be	AUX
ap-3794	18	5	the	the	DET
ap-3794	18	6	description	description	NOUN
ap-3794	18	7	of	of	ADP
ap-3794	18	8	the	the	DET
ap-3794	18	9	return	return	NOUN
ap-3794	18	10	times	time	NOUN
ap-3794	18	11	to	to	ADP
ap-3794	18	12	a	a	DET
ap-3794	18	13	general	general	ADJ
ap-3794	18	14	interval	interval	NOUN
ap-3794	19	1	i	i	PRON
ap-3794	19	2	⊂	⊂	PROPN
ap-3794	19	3	j	j	PROPN
ap-3794	19	4	and	and	CCONJ
ap-3794	19	5	an	an	DET
ap-3794	19	6	insight	insight	NOUN
ap-3794	19	7	into	into	ADP
ap-3794	19	8	the	the	DET
ap-3794	19	9	structure	structure	NOUN
ap-3794	19	10	of	of	ADP
ap-3794	19	11	the	the	DET
ap-3794	19	12	set	set	NOUN
ap-3794	19	13	of	of	ADP
ap-3794	19	14	i	i	PROPN
ap-3794	19	15	-	-	PUNCT
ap-3794	19	16	itineraries	itinerary	NOUN
ap-3794	19	17	,	,	PUNCT
ap-3794	19	18	i.e.	i.e.	X
ap-3794	19	19	,	,	PUNCT
ap-3794	19	20	the	the	DET
ap-3794	19	21	finite	finite	ADJ
ap-3794	19	22	words	word	NOUN
ap-3794	19	23	that	that	PRON
ap-3794	19	24	are	be	AUX
ap-3794	19	25	codings	coding	NOUN
ap-3794	19	26	of	of	ADP
ap-3794	19	27	the	the	DET
ap-3794	19	28	return	return	NOUN
ap-3794	19	29	trajectories	trajectory	NOUN
ap-3794	19	30	to	to	ADP
ap-3794	19	31	i	i	PRON
ap-3794	19	32	(	(	PUNCT
ap-3794	19	33	see	see	VERB
ap-3794	19	34	the	the	DET
ap-3794	19	35	definition	definition	NOUN
ap-3794	19	36	below	below	ADP
ap-3794	19	37	)	)	PUNCT
ap-3794	19	38	.	.	PUNCT
ap-3794	20	1	these	these	DET
ap-3794	20	2	results	result	NOUN
ap-3794	20	3	are	be	AUX
ap-3794	20	4	given	give	VERB
ap-3794	20	5	in	in	ADP
ap-3794	20	6	theorem	theorem	ADJ
ap-3794	20	7	4.1	4.1	NUM
ap-3794	20	8	and	and	CCONJ
ap-3794	20	9	then	then	ADV
ap-3794	20	10	interpreted	interpret	VERB
ap-3794	20	11	as	as	ADP
ap-3794	20	12	analogues	analogue	NOUN
ap-3794	20	13	of	of	ADP
ap-3794	20	14	the	the	DET
ap-3794	20	15	well	well	ADV
ap-3794	20	16	-	-	PUNCT
ap-3794	20	17	known	know	VERB
ap-3794	20	18	three	three	NUM
ap-3794	20	19	gap	gap	NOUN
ap-3794	20	20	and	and	CCONJ
ap-3794	20	21	three	three	NUM
ap-3794	20	22	distance	distance	NOUN
ap-3794	20	23	theorems	theorem	NOUN
ap-3794	20	24	(	(	PUNCT
ap-3794	20	25	see	see	VERB
ap-3794	20	26	section	section	NOUN
ap-3794	20	27	6	6	NUM
ap-3794	20	28	)	)	PUNCT
ap-3794	20	29	.	.	PUNCT
ap-3794	21	1	particular	particular	ADJ
ap-3794	21	2	attention	attention	NOUN
ap-3794	21	3	is	be	AUX
ap-3794	21	4	paid	pay	VERB
ap-3794	21	5	to	to	ADP
ap-3794	21	6	the	the	DET
ap-3794	21	7	special	special	ADJ
ap-3794	21	8	cases	case	NOUN
ap-3794	21	9	when	when	SCONJ
ap-3794	21	10	the	the	DET
ap-3794	21	11	set	set	NOUN
ap-3794	21	12	of	of	ADP
ap-3794	21	13	i	i	PROPN
ap-3794	21	14	-	-	PUNCT
ap-3794	21	15	itineraries	itinerary	NOUN
ap-3794	21	16	has	have	VERB
ap-3794	21	17	only	only	ADV
ap-3794	21	18	three	three	NUM
ap-3794	21	19	elements	element	NOUN
ap-3794	21	20	.	.	PUNCT
ap-3794	22	1	these	these	DET
ap-3794	22	2	cases	case	NOUN
ap-3794	22	3	belong	belong	VERB
ap-3794	22	4	to	to	ADP
ap-3794	22	5	the	the	DET
ap-3794	22	6	most	most	ADV
ap-3794	22	7	interesting	interesting	ADJ
ap-3794	22	8	from	from	ADP
ap-3794	22	9	the	the	DET
ap-3794	22	10	combinatorial	combinatorial	ADJ
ap-3794	22	11	point	point	NOUN
ap-3794	22	12	of	of	ADP
ap-3794	22	13	view	view	NOUN
ap-3794	22	14	,	,	PUNCT
ap-3794	22	15	since	since	SCONJ
ap-3794	22	16	they	they	PRON
ap-3794	22	17	provide	provide	VERB
ap-3794	22	18	information	information	NOUN
ap-3794	22	19	about	about	ADP
ap-3794	22	20	return	return	VERB
ap-3794	22	21	words	word	NOUN
ap-3794	22	22	to	to	ADP
ap-3794	22	23	factors	factor	NOUN
ap-3794	22	24	,	,	PUNCT
ap-3794	22	25	and	and	CCONJ
ap-3794	22	26	about	about	ADP
ap-3794	22	27	the	the	DET
ap-3794	22	28	morphisms	morphism	NOUN
ap-3794	22	29	preserving	preserve	VERB
ap-3794	22	30	three	three	NUM
ap-3794	22	31	interval	interval	NOUN
ap-3794	22	32	exchange	exchange	NOUN
ap-3794	22	33	words	word	NOUN
ap-3794	22	34	.	.	PUNCT
ap-3794	23	1	these	these	DET
ap-3794	23	2	specific	specific	ADJ
ap-3794	23	3	cases	case	NOUN
ap-3794	23	4	are	be	AUX
ap-3794	23	5	studied	study	VERB
ap-3794	23	6	in	in	ADP
ap-3794	23	7	section	section	NOUN
ap-3794	23	8	5	5	NUM
ap-3794	23	9	.	.	PUNCT
ap-3794	24	1	this	this	PRON
ap-3794	24	2	allows	allow	VERB
ap-3794	24	3	us	we	PRON
ap-3794	24	4	to	to	PART
ap-3794	24	5	describe	describe	VERB
ap-3794	24	6	the	the	DET
ap-3794	24	7	return	return	NOUN
ap-3794	24	8	words	word	NOUN
ap-3794	24	9	to	to	PART
ap-3794	24	10	palindromic	palindromic	VERB
ap-3794	24	11	bispecial	bispecial	ADJ
ap-3794	24	12	factors	factor	NOUN
ap-3794	24	13	,	,	PUNCT
ap-3794	24	14	which	which	PRON
ap-3794	24	15	can	can	AUX
ap-3794	24	16	be	be	AUX
ap-3794	24	17	seen	see	VERB
ap-3794	24	18	as	as	ADP
ap-3794	24	19	a	a	DET
ap-3794	24	20	complement	complement	NOUN
ap-3794	24	21	to	to	ADP
ap-3794	24	22	some	some	PRON
ap-3794	24	23	of	of	ADP
ap-3794	24	24	the	the	DET
ap-3794	24	25	results	result	NOUN
ap-3794	24	26	in	in	ADP
ap-3794	24	27	[	[	X
ap-3794	24	28	6	6	NUM
ap-3794	24	29	]	]	PUNCT
ap-3794	24	30	.	.	PUNCT
ap-3794	25	1	we	we	PRON
ap-3794	25	2	also	also	ADV
ap-3794	25	3	focus	focus	VERB
ap-3794	25	4	on	on	ADP
ap-3794	25	5	substitutions	substitution	NOUN
ap-3794	25	6	fixing	fix	VERB
ap-3794	25	7	words	word	NOUN
ap-3794	25	8	coding	code	VERB
ap-3794	25	9	interval	interval	NOUN
ap-3794	25	10	exchange	exchange	NOUN
ap-3794	25	11	transformations	transformation	NOUN
ap-3794	25	12	.	.	PUNCT
ap-3794	26	1	the	the	DET
ap-3794	26	2	latter	latter	ADJ
ap-3794	26	3	has	have	VERB
ap-3794	26	4	implications	implication	NOUN
ap-3794	26	5	[	[	X
ap-3794	26	6	12	12	NUM
ap-3794	26	7	]	]	PUNCT
ap-3794	26	8	for	for	ADP
ap-3794	26	9	the	the	DET
ap-3794	26	10	question	question	NOUN
ap-3794	26	11	of	of	ADP
ap-3794	26	12	hof	hof	NOUN
ap-3794	26	13	,	,	PUNCT
ap-3794	26	14	knill	knill	NOUN
ap-3794	26	15	and	and	CCONJ
ap-3794	26	16	simon	simon	PROPN
ap-3794	26	17	[	[	X
ap-3794	26	18	10	10	NUM
ap-3794	26	19	]	]	X
ap-3794	26	20	about	about	ADP
ap-3794	26	21	palindromic	palindromic	ADJ
ap-3794	26	22	substitution	substitution	NOUN
ap-3794	26	23	invariant	invariant	ADJ
ap-3794	26	24	words	word	NOUN
ap-3794	26	25	with	with	ADP
ap-3794	26	26	application	application	NOUN
ap-3794	26	27	to	to	ADP
ap-3794	26	28	aperiodic	aperiodic	ADJ
ap-3794	26	29	schrödinger	schrödinger	ADJ
ap-3794	26	30	operators	operator	NOUN
ap-3794	26	31	.	.	PUNCT
ap-3794	27	1	2	2	X
ap-3794	27	2	.	.	NUM
ap-3794	27	3	preliminaries	preliminary	NOUN
ap-3794	27	4	2.1	2.1	NUM
ap-3794	27	5	.	.	PUNCT
ap-3794	28	1	combinatorics	combinatoric	NOUN
ap-3794	28	2	on	on	ADP
ap-3794	28	3	words	word	NOUN
ap-3794	28	4	a	a	DET
ap-3794	28	5	finite	finite	ADJ
ap-3794	28	6	word	word	NOUN
ap-3794	28	7	w	w	PROPN
ap-3794	28	8	=	=	SYM
ap-3794	28	9	w0	w0	PROPN
ap-3794	28	10	·	·	PUNCT
ap-3794	28	11	·	·	PUNCT
ap-3794	29	1	·	·	PUNCT
ap-3794	29	2	wn−1	wn−1	PROPN
ap-3794	29	3	is	be	AUX
ap-3794	29	4	a	a	DET
ap-3794	29	5	concatenation	concatenation	NOUN
ap-3794	29	6	of	of	ADP
ap-3794	29	7	letters	letter	NOUN
ap-3794	29	8	of	of	ADP
ap-3794	29	9	a	a	DET
ap-3794	29	10	finite	finite	NOUN
ap-3794	29	11	alphabet	alphabet	NOUN
ap-3794	29	12	a.	a.	NOUN
ap-3794	29	13	the	the	DET
ap-3794	29	14	number	number	NOUN
ap-3794	29	15	n	n	ADP
ap-3794	29	16	of	of	ADP
ap-3794	29	17	letters	letter	NOUN
ap-3794	29	18	in	in	ADP
ap-3794	29	19	w	w	PROPN
ap-3794	29	20	is	be	AUX
ap-3794	29	21	the	the	DET
ap-3794	29	22	length	length	NOUN
ap-3794	29	23	of	of	ADP
ap-3794	29	24	w	w	NOUN
ap-3794	29	25	and	and	CCONJ
ap-3794	29	26	is	be	AUX
ap-3794	29	27	denoted	denote	VERB
ap-3794	29	28	by	by	ADP
ap-3794	29	29	|w|	|w|	PROPN
ap-3794	29	30	.	.	PUNCT
ap-3794	30	1	the	the	DET
ap-3794	30	2	set	set	NOUN
ap-3794	30	3	of	of	ADP
ap-3794	30	4	all	all	DET
ap-3794	30	5	finite	finite	ADJ
ap-3794	30	6	words	word	NOUN
ap-3794	30	7	over	over	ADP
ap-3794	30	8	an	an	DET
ap-3794	30	9	alphabet	alphabet	NOUN
ap-3794	30	10	a	a	NOUN
ap-3794	30	11	,	,	PUNCT
ap-3794	30	12	including	include	VERB
ap-3794	30	13	the	the	DET
ap-3794	30	14	empty	empty	ADJ
ap-3794	30	15	word	word	NOUN
ap-3794	30	16	ε	ε	PROPN
ap-3794	30	17	,	,	PUNCT
ap-3794	30	18	with	with	SCONJ
ap-3794	30	19	the	the	DET
ap-3794	30	20	operation	operation	NOUN
ap-3794	30	21	of	of	ADP
ap-3794	30	22	concatenation	concatenation	NOUN
ap-3794	30	23	forms	form	VERB
ap-3794	30	24	a	a	DET
ap-3794	30	25	monoid	monoid	NOUN
ap-3794	30	26	,	,	PUNCT
ap-3794	30	27	denoted	denote	VERB
ap-3794	30	28	by	by	ADP
ap-3794	30	29	a∗.	a∗.	NOUN
ap-3794	30	30	one	one	NUM
ap-3794	30	31	considers	consider	VERB
ap-3794	30	32	also	also	ADV
ap-3794	30	33	infinite	infinite	VERB
ap-3794	30	34	words	word	NOUN
ap-3794	30	35	u	u	NOUN
ap-3794	30	36	=	=	PROPN
ap-3794	30	37	u0u1u2	u0u1u2	X
ap-3794	30	38	·	·	PUNCT
ap-3794	30	39	·	·	PUNCT
ap-3794	30	40	·	·	PUNCT
ap-3794	30	41	∈	∈	PROPN
ap-3794	31	1	an	an	PRON
ap-3794	31	2	.	.	PUNCT
ap-3794	32	1	if	if	SCONJ
ap-3794	32	2	u	u	PROPN
ap-3794	32	3	∈	∈	PROPN
ap-3794	32	4	a∗	a∗	PROPN
ap-3794	32	5	∪	∪	VERB
ap-3794	32	6	an	an	DET
ap-3794	32	7	and	and	CCONJ
ap-3794	32	8	u	u	NOUN
ap-3794	32	9	=	=	PROPN
ap-3794	32	10	vwz	vwz	PROPN
ap-3794	32	11	,	,	PUNCT
ap-3794	32	12	for	for	ADP
ap-3794	32	13	some	some	DET
ap-3794	32	14	v	v	NOUN
ap-3794	32	15	,	,	PUNCT
ap-3794	32	16	w	w	PROPN
ap-3794	32	17	∈	∈	PROPN
ap-3794	32	18	a∗	a∗	NOUN
ap-3794	32	19	and	and	CCONJ
ap-3794	32	20	z	z	NOUN
ap-3794	32	21	∈	∈	PROPN
ap-3794	32	22	a∗	a∗	PROPN
ap-3794	32	23	∪	∪	ADP
ap-3794	32	24	an	an	PROPN
ap-3794	32	25	,	,	PUNCT
ap-3794	32	26	we	we	PRON
ap-3794	32	27	say	say	VERB
ap-3794	32	28	that	that	SCONJ
ap-3794	32	29	v	v	ADP
ap-3794	32	30	,	,	PUNCT
ap-3794	32	31	w	w	PROPN
ap-3794	32	32	,	,	PUNCT
ap-3794	32	33	z	z	NOUN
ap-3794	32	34	are	be	AUX
ap-3794	32	35	factors	factor	NOUN
ap-3794	32	36	of	of	ADP
ap-3794	32	37	u.	u.	NOUN
ap-3794	32	38	in	in	ADP
ap-3794	32	39	particular	particular	ADJ
ap-3794	32	40	,	,	PUNCT
ap-3794	32	41	v	v	NOUN
ap-3794	32	42	is	be	AUX
ap-3794	32	43	a	a	DET
ap-3794	32	44	prefix	prefix	NOUN
ap-3794	32	45	and	and	CCONJ
ap-3794	32	46	z	z	NOUN
ap-3794	32	47	is	be	AUX
ap-3794	32	48	a	a	DET
ap-3794	32	49	suffix	suffix	NOUN
ap-3794	32	50	of	of	ADP
ap-3794	32	51	u.	u.	NOUN
ap-3794	32	52	we	we	PRON
ap-3794	32	53	write	write	VERB
ap-3794	32	54	wz	wz	PROPN
ap-3794	32	55	=	=	SYM
ap-3794	32	56	v−1u	v−1u	PROPN
ap-3794	32	57	,	,	PUNCT
ap-3794	32	58	vw	vw	X
ap-3794	32	59	=	=	SYM
ap-3794	32	60	uz−1	uz−1	ADJ
ap-3794	32	61	.	.	PUNCT
ap-3794	33	1	an	an	DET
ap-3794	33	2	infinite	infinite	ADJ
ap-3794	33	3	word	word	NOUN
ap-3794	33	4	u	u	NOUN
ap-3794	33	5	is	be	AUX
ap-3794	33	6	said	say	VERB
ap-3794	33	7	to	to	PART
ap-3794	33	8	be	be	AUX
ap-3794	33	9	aperiodic	aperiodic	ADJ
ap-3794	33	10	if	if	SCONJ
ap-3794	33	11	it	it	PRON
ap-3794	33	12	does	do	AUX
ap-3794	33	13	not	not	PART
ap-3794	33	14	have	have	VERB
ap-3794	33	15	a	a	DET
ap-3794	33	16	suffix	suffix	NOUN
ap-3794	33	17	of	of	ADP
ap-3794	33	18	the	the	DET
ap-3794	33	19	form	form	NOUN
ap-3794	33	20	wwww	wwww	X
ap-3794	33	21	·	·	PUNCT
ap-3794	33	22	·	·	PUNCT
ap-3794	33	23	·	·	PUNCT
ap-3794	33	24	.	.	PUNCT
ap-3794	34	1	if	if	SCONJ
ap-3794	34	2	the	the	DET
ap-3794	34	3	infinite	infinite	ADJ
ap-3794	34	4	word	word	NOUN
ap-3794	34	5	u	u	NOUN
ap-3794	34	6	contains	contain	VERB
ap-3794	34	7	at	at	ADV
ap-3794	34	8	least	least	ADV
ap-3794	34	9	two	two	NUM
ap-3794	34	10	occurrences	occurrence	NOUN
ap-3794	34	11	of	of	ADP
ap-3794	34	12	each	each	PRON
ap-3794	34	13	of	of	ADP
ap-3794	34	14	its	its	PRON
ap-3794	34	15	finite	finite	ADJ
ap-3794	34	16	factors	factor	NOUN
ap-3794	34	17	,	,	PUNCT
ap-3794	34	18	then	then	ADV
ap-3794	34	19	it	it	PRON
ap-3794	34	20	is	be	AUX
ap-3794	34	21	said	say	VERB
ap-3794	34	22	to	to	PART
ap-3794	34	23	be	be	AUX
ap-3794	34	24	recurrent	recurrent	ADJ
ap-3794	34	25	.	.	PUNCT
ap-3794	35	1	if	if	SCONJ
ap-3794	35	2	the	the	DET
ap-3794	35	3	distances	distance	NOUN
ap-3794	35	4	between	between	ADP
ap-3794	35	5	two	two	NUM
ap-3794	35	6	consecutive	consecutive	ADJ
ap-3794	35	7	occurrences	occurrence	NOUN
ap-3794	35	8	of	of	ADP
ap-3794	35	9	every	every	DET
ap-3794	35	10	factor	factor	NOUN
ap-3794	35	11	are	be	AUX
ap-3794	35	12	bounded	bound	VERB
ap-3794	35	13	,	,	PUNCT
ap-3794	35	14	then	then	ADV
ap-3794	35	15	u	u	NOUN
ap-3794	35	16	is	be	AUX
ap-3794	35	17	uniformly	uniformly	ADV
ap-3794	35	18	recurrent	recurrent	ADJ
ap-3794	35	19	.	.	PUNCT
ap-3794	36	1	if	if	SCONJ
ap-3794	36	2	w	w	PROPN
ap-3794	36	3	,	,	PUNCT
ap-3794	36	4	v	v	NOUN
ap-3794	36	5	are	be	AUX
ap-3794	36	6	factors	factor	NOUN
ap-3794	36	7	of	of	ADP
ap-3794	36	8	u	u	PRON
ap-3794	36	9	such	such	ADJ
ap-3794	36	10	that	that	SCONJ
ap-3794	36	11	vw	vw	PROPN
ap-3794	36	12	is	be	AUX
ap-3794	36	13	also	also	ADV
ap-3794	36	14	a	a	DET
ap-3794	36	15	factor	factor	NOUN
ap-3794	36	16	of	of	ADP
ap-3794	36	17	u	u	PROPN
ap-3794	36	18	and	and	CCONJ
ap-3794	36	19	vw	vw	PROPN
ap-3794	36	20	contains	contain	VERB
ap-3794	36	21	w	w	ADP
ap-3794	36	22	as	as	ADP
ap-3794	36	23	its	its	PRON
ap-3794	36	24	prefix	prefix	NOUN
ap-3794	36	25	and	and	CCONJ
ap-3794	36	26	as	as	ADP
ap-3794	36	27	its	its	PRON
ap-3794	36	28	suffix	suffix	NOUN
ap-3794	36	29	but	but	CCONJ
ap-3794	36	30	not	not	PART
ap-3794	36	31	anywhere	anywhere	ADV
ap-3794	36	32	else	else	ADV
ap-3794	36	33	,	,	PUNCT
ap-3794	36	34	then	then	ADV
ap-3794	36	35	v	v	NOUN
ap-3794	36	36	is	be	AUX
ap-3794	36	37	a	a	DET
ap-3794	36	38	return	return	NOUN
ap-3794	36	39	word	word	NOUN
ap-3794	36	40	to	to	ADP
ap-3794	36	41	w	w	VERB
ap-3794	36	42	in	in	ADP
ap-3794	36	43	u.	u.	NOUN
ap-3794	36	44	thus	thus	ADV
ap-3794	36	45	u	u	NOUN
ap-3794	36	46	is	be	AUX
ap-3794	36	47	uniformly	uniformly	ADV
ap-3794	36	48	recurrent	recurrent	ADJ
ap-3794	36	49	if	if	SCONJ
ap-3794	36	50	and	and	CCONJ
ap-3794	36	51	only	only	ADV
ap-3794	36	52	if	if	SCONJ
ap-3794	36	53	each	each	DET
ap-3794	36	54	factor	factor	NOUN
ap-3794	36	55	w	w	PROPN
ap-3794	36	56	of	of	ADP
ap-3794	36	57	u	u	PROPN
ap-3794	36	58	has	have	VERB
ap-3794	36	59	finitely	finitely	ADV
ap-3794	36	60	many	many	ADJ
ap-3794	36	61	return	return	NOUN
ap-3794	36	62	words	word	NOUN
ap-3794	36	63	.	.	PUNCT
ap-3794	37	1	the	the	DET
ap-3794	37	2	language	language	NOUN
ap-3794	37	3	of	of	ADP
ap-3794	37	4	an	an	DET
ap-3794	37	5	infinite	infinite	ADJ
ap-3794	37	6	word	word	NOUN
ap-3794	37	7	u	u	NOUN
ap-3794	37	8	is	be	AUX
ap-3794	37	9	the	the	DET
ap-3794	37	10	set	set	NOUN
ap-3794	37	11	of	of	ADP
ap-3794	37	12	all	all	DET
ap-3794	37	13	its	its	PRON
ap-3794	37	14	finite	finite	ADJ
ap-3794	37	15	factors	factor	NOUN
ap-3794	37	16	.	.	PUNCT
ap-3794	38	1	it	it	PRON
ap-3794	38	2	is	be	AUX
ap-3794	38	3	denoted	denote	VERB
ap-3794	38	4	by	by	ADP
ap-3794	38	5	l(u	l(u	PROPN
ap-3794	38	6	)	)	PUNCT
ap-3794	38	7	.	.	PUNCT
ap-3794	39	1	the	the	DET
ap-3794	39	2	number	number	NOUN
ap-3794	39	3	of	of	ADP
ap-3794	39	4	factors	factor	NOUN
ap-3794	39	5	of	of	ADP
ap-3794	39	6	u	u	NOUN
ap-3794	39	7	of	of	ADP
ap-3794	39	8	length	length	NOUN
ap-3794	39	9	n	n	PROPN
ap-3794	39	10	defines	define	VERB
ap-3794	39	11	the	the	DET
ap-3794	39	12	factor	factor	NOUN
ap-3794	39	13	complexity	complexity	NOUN
ap-3794	39	14	function	function	NOUN
ap-3794	39	15	cu	cu	NOUN
ap-3794	39	16	:	:	PUNCT
ap-3794	39	17	n	n	PROPN
ap-3794	39	18	→	→	SYM
ap-3794	39	19	n.	n.	NOUN
ap-3794	39	20	it	it	PRON
ap-3794	39	21	is	be	AUX
ap-3794	39	22	known	know	VERB
ap-3794	39	23	that	that	SCONJ
ap-3794	39	24	aperiodic	aperiodic	ADJ
ap-3794	39	25	462	462	NUM
ap-3794	39	26	http://dx.doi.org/10.14311/ap.2016.56.0462	http://dx.doi.org/10.14311/ap.2016.56.0462	NOUN
ap-3794	39	27	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3794	39	28	vol	vol	NOUN
ap-3794	39	29	.	.	PUNCT
ap-3794	40	1	56	56	NUM
ap-3794	40	2	no	no	NOUN
ap-3794	40	3	.	.	PUNCT
ap-3794	41	1	6/2016	6/2016	NUM
ap-3794	41	2	itineraries	itinerary	NOUN
ap-3794	41	3	induced	induce	VERB
ap-3794	41	4	by	by	ADP
ap-3794	41	5	exchange	exchange	NOUN
ap-3794	41	6	of	of	ADP
ap-3794	41	7	three	three	NUM
ap-3794	41	8	intervals	interval	NOUN
ap-3794	41	9	infinite	infinite	VERB
ap-3794	41	10	words	word	NOUN
ap-3794	41	11	have	have	VERB
ap-3794	41	12	complexity	complexity	NOUN
ap-3794	41	13	cu(n	cu(n	NOUN
ap-3794	41	14	)	)	PUNCT
ap-3794	41	15	≥	≥	PROPN
ap-3794	41	16	n	n	PROPN
ap-3794	41	17	+	+	CCONJ
ap-3794	41	18	1	1	NUM
ap-3794	41	19	for	for	ADP
ap-3794	41	20	n	n	PRON
ap-3794	41	21	∈	∈	PROPN
ap-3794	41	22	n.	n.	NOUN
ap-3794	41	23	sturmian	sturmian	NOUN
ap-3794	41	24	words	word	NOUN
ap-3794	41	25	are	be	AUX
ap-3794	41	26	aperiodic	aperiodic	ADJ
ap-3794	41	27	words	word	NOUN
ap-3794	41	28	with	with	ADP
ap-3794	41	29	minimal	minimal	ADJ
ap-3794	41	30	factor	factor	NOUN
ap-3794	41	31	complexity	complexity	NOUN
ap-3794	41	32	.	.	PUNCT
ap-3794	42	1	2.2	2.2	NUM
ap-3794	42	2	.	.	PUNCT
ap-3794	42	3	exchange	exchange	NOUN
ap-3794	42	4	of	of	ADP
ap-3794	42	5	three	three	NUM
ap-3794	42	6	intervals	interval	NOUN
ap-3794	42	7	given	give	VERB
ap-3794	42	8	a	a	DET
ap-3794	42	9	partition	partition	NOUN
ap-3794	42	10	of	of	ADP
ap-3794	42	11	an	an	DET
ap-3794	42	12	interval	interval	NOUN
ap-3794	42	13	j	j	PROPN
ap-3794	42	14	into	into	ADP
ap-3794	42	15	disjoint	disjoint	PROPN
ap-3794	42	16	union	union	PROPN
ap-3794	42	17	of	of	ADP
ap-3794	42	18	intervals	interval	NOUN
ap-3794	42	19	j1	j1	PROPN
ap-3794	42	20	,	,	PUNCT
ap-3794	42	21	.	.	PUNCT
ap-3794	42	22	.	.	PUNCT
ap-3794	42	23	.	.	PUNCT
ap-3794	43	1	,	,	PUNCT
ap-3794	43	2	jk	jk	PROPN
ap-3794	43	3	,	,	PUNCT
ap-3794	43	4	the	the	DET
ap-3794	43	5	exchange	exchange	NOUN
ap-3794	43	6	of	of	ADP
ap-3794	43	7	k	k	PROPN
ap-3794	43	8	intervals	interval	NOUN
ap-3794	43	9	is	be	AUX
ap-3794	43	10	a	a	DET
ap-3794	43	11	bijection	bijection	NOUN
ap-3794	43	12	determined	determine	VERB
ap-3794	43	13	by	by	ADP
ap-3794	43	14	a	a	DET
ap-3794	43	15	piecewise	piecewise	NOUN
ap-3794	43	16	translation	translation	NOUN
ap-3794	43	17	permuting	permute	VERB
ap-3794	43	18	the	the	DET
ap-3794	43	19	intervals	interval	NOUN
ap-3794	43	20	according	accord	VERB
ap-3794	43	21	to	to	ADP
ap-3794	43	22	a	a	DET
ap-3794	43	23	prescribed	prescribed	ADJ
ap-3794	43	24	permutation	permutation	NOUN
ap-3794	43	25	π	π	NOUN
ap-3794	43	26	.	.	PUNCT
ap-3794	44	1	in	in	ADP
ap-3794	44	2	the	the	DET
ap-3794	44	3	article	article	NOUN
ap-3794	44	4	,	,	PUNCT
ap-3794	44	5	we	we	PRON
ap-3794	44	6	consider	consider	VERB
ap-3794	44	7	the	the	DET
ap-3794	44	8	case	case	NOUN
ap-3794	44	9	:	:	PUNCT
ap-3794	44	10	let	let	VERB
ap-3794	44	11	k	k	NOUN
ap-3794	44	12	=	=	SYM
ap-3794	44	13	3	3	NUM
ap-3794	44	14	,	,	PUNCT
ap-3794	44	15	0	0	NUM
ap-3794	44	16	<	<	X
ap-3794	44	17	α	α	X
ap-3794	44	18	<	<	X
ap-3794	44	19	β	β	X
ap-3794	44	20	<	<	X
ap-3794	44	21	1	1	NUM
ap-3794	44	22	,	,	PUNCT
ap-3794	44	23	and	and	CCONJ
ap-3794	44	24	t	t	X
ap-3794	44	25	:	:	PUNCT
ap-3794	45	1	[	[	X
ap-3794	45	2	0	0	NUM
ap-3794	45	3	,	,	PUNCT
ap-3794	45	4	1)→	1)→	NUM
ap-3794	46	1	[	[	X
ap-3794	46	2	0	0	NUM
ap-3794	46	3	,	,	PUNCT
ap-3794	46	4	1	1	NUM
ap-3794	46	5	)	)	PUNCT
ap-3794	46	6	be	be	AUX
ap-3794	46	7	given	give	VERB
ap-3794	46	8	by	by	ADP
ap-3794	46	9	t	t	PROPN
ap-3794	46	10	(	(	PUNCT
ap-3794	46	11	x	x	NOUN
ap-3794	46	12	)	)	PUNCT
ap-3794	46	13	=	=	SYM
ap-3794	47	1			NOUN
ap-3794	47	2	x+	x+	NUM
ap-3794	47	3	1−	1−	NUM
ap-3794	47	4	α	α	NOUN
ap-3794	47	5	if	if	SCONJ
ap-3794	47	6	x	x	X
ap-3794	47	7	∈	∈	PROPN
ap-3794	48	1	[	[	X
ap-3794	48	2	0	0	NUM
ap-3794	48	3	,	,	PUNCT
ap-3794	48	4	α	α	NOUN
ap-3794	48	5	)	)	PUNCT
ap-3794	48	6	=	=	NOUN
ap-3794	48	7	:	:	PUNCT
ap-3794	48	8	ja	ja	PROPN
ap-3794	48	9	,	,	PUNCT
ap-3794	48	10	x+	x+	X
ap-3794	48	11	1−	1−	NUM
ap-3794	48	12	α−	α−	ADP
ap-3794	48	13	β	β	NOUN
ap-3794	48	14	if	if	SCONJ
ap-3794	48	15	x	x	SYM
ap-3794	48	16	∈	∈	PROPN
ap-3794	48	17	[	[	X
ap-3794	48	18	α	α	X
ap-3794	48	19	,	,	PUNCT
ap-3794	48	20	β	β	NOUN
ap-3794	48	21	)	)	PUNCT
ap-3794	49	1	=	=	NOUN
ap-3794	49	2	:	:	PUNCT
ap-3794	49	3	jb	jb	PROPN
ap-3794	49	4	,	,	PUNCT
ap-3794	49	5	x−	x−	PROPN
ap-3794	49	6	β	β	PROPN
ap-3794	50	1	if	if	SCONJ
ap-3794	50	2	x	x	SYM
ap-3794	50	3	∈	∈	PROPN
ap-3794	50	4	[	[	X
ap-3794	50	5	β	β	X
ap-3794	50	6	,	,	PUNCT
ap-3794	50	7	1	1	NUM
ap-3794	50	8	)	)	PUNCT
ap-3794	50	9	=	=	NOUN
ap-3794	50	10	:	:	PUNCT
ap-3794	50	11	jc	jc	PROPN
ap-3794	50	12	.	.	PUNCT
ap-3794	51	1	(	(	PUNCT
ap-3794	51	2	1	1	X
ap-3794	51	3	)	)	PUNCT
ap-3794	51	4	the	the	DET
ap-3794	51	5	transformation	transformation	NOUN
ap-3794	51	6	t	t	PROPN
ap-3794	51	7	is	be	AUX
ap-3794	51	8	an	an	DET
ap-3794	51	9	exchange	exchange	NOUN
ap-3794	51	10	of	of	ADP
ap-3794	51	11	three	three	NUM
ap-3794	51	12	intervals	interval	NOUN
ap-3794	51	13	with	with	ADP
ap-3794	51	14	the	the	DET
ap-3794	51	15	permutation	permutation	NOUN
ap-3794	51	16	(	(	PUNCT
ap-3794	51	17	321	321	NUM
ap-3794	51	18	)	)	PUNCT
ap-3794	51	19	.	.	PUNCT
ap-3794	52	1	it	it	PRON
ap-3794	52	2	is	be	AUX
ap-3794	52	3	often	often	ADV
ap-3794	52	4	called	call	VERB
ap-3794	52	5	a	a	DET
ap-3794	52	6	3iet	3iet	PROPN
ap-3794	52	7	for	for	ADP
ap-3794	52	8	short	short	ADJ
ap-3794	52	9	.	.	PUNCT
ap-3794	53	1	the	the	DET
ap-3794	53	2	orbit	orbit	NOUN
ap-3794	53	3	{	{	PUNCT
ap-3794	53	4	tn(ρ	tn(ρ	PROPN
ap-3794	53	5	)	)	PUNCT
ap-3794	53	6	:	:	PUNCT
ap-3794	53	7	n	n	X
ap-3794	53	8	∈	∈	PROPN
ap-3794	53	9	z	z	NOUN
ap-3794	53	10	}	}	PUNCT
ap-3794	53	11	of	of	ADP
ap-3794	53	12	a	a	DET
ap-3794	53	13	point	point	NOUN
ap-3794	53	14	ρ	ρ	X
ap-3794	53	15	∈	∈	PROPN
ap-3794	54	1	[	[	X
ap-3794	54	2	0	0	NUM
ap-3794	54	3	,	,	PUNCT
ap-3794	54	4	1	1	NUM
ap-3794	54	5	)	)	PUNCT
ap-3794	54	6	can	can	AUX
ap-3794	54	7	be	be	AUX
ap-3794	54	8	coded	code	VERB
ap-3794	54	9	by	by	ADP
ap-3794	54	10	an	an	DET
ap-3794	54	11	infinite	infinite	ADJ
ap-3794	54	12	word	word	NOUN
ap-3794	54	13	uρ	uρ	ADJ
ap-3794	54	14	=	=	SYM
ap-3794	54	15	u0u1u2	u0u1u2	NOUN
ap-3794	54	16	.	.	PUNCT
ap-3794	54	17	.	.	PUNCT
ap-3794	55	1	.	.	PUNCT
ap-3794	56	1	over	over	ADP
ap-3794	56	2	the	the	DET
ap-3794	56	3	alphabet	alphabet	NOUN
ap-3794	56	4	{	{	PUNCT
ap-3794	56	5	a	a	PROPN
ap-3794	56	6	,	,	PUNCT
ap-3794	56	7	b	b	NOUN
ap-3794	56	8	,	,	PUNCT
ap-3794	56	9	c	c	NOUN
ap-3794	56	10	}	}	PUNCT
ap-3794	56	11	given	give	VERB
ap-3794	56	12	by	by	ADP
ap-3794	56	13	un	un	PROPN
ap-3794	56	14	=	=	PROPN
ap-3794	56	15	x	x	PROPN
ap-3794	56	16	if	if	SCONJ
ap-3794	56	17	tn(ρ	tn(ρ	NUM
ap-3794	56	18	)	)	PUNCT
ap-3794	56	19	∈	∈	PROPN
ap-3794	56	20	jx	jx	PROPN
ap-3794	56	21	for	for	ADP
ap-3794	56	22	x	x	PROPN
ap-3794	56	23	∈	∈	PROPN
ap-3794	56	24	{	{	PUNCT
ap-3794	56	25	a	a	PRON
ap-3794	56	26	,	,	PUNCT
ap-3794	56	27	b	b	NOUN
ap-3794	56	28	,	,	PUNCT
ap-3794	56	29	c	c	NOUN
ap-3794	56	30	}	}	PUNCT
ap-3794	56	31	.	.	PUNCT
ap-3794	57	1	the	the	DET
ap-3794	57	2	infinite	infinite	ADJ
ap-3794	57	3	word	word	NOUN
ap-3794	57	4	uρ	uρ	INTJ
ap-3794	57	5	is	be	AUX
ap-3794	57	6	called	call	VERB
ap-3794	57	7	a	a	DET
ap-3794	57	8	3iet	3iet	NUM
ap-3794	57	9	word	word	NOUN
ap-3794	57	10	,	,	PUNCT
ap-3794	57	11	the	the	DET
ap-3794	57	12	point	point	NOUN
ap-3794	57	13	ρ	ρ	NOUN
ap-3794	57	14	is	be	AUX
ap-3794	57	15	called	call	VERB
ap-3794	57	16	the	the	DET
ap-3794	57	17	intercept	intercept	NOUN
ap-3794	57	18	of	of	ADP
ap-3794	57	19	uρ	uρ	ADP
ap-3794	57	20	.	.	PUNCT
ap-3794	58	1	an	an	DET
ap-3794	58	2	exchange	exchange	NOUN
ap-3794	58	3	of	of	ADP
ap-3794	58	4	intervals	interval	NOUN
ap-3794	58	5	satisfies	satisfy	VERB
ap-3794	58	6	the	the	DET
ap-3794	58	7	minimality	minimality	NOUN
ap-3794	58	8	condition	condition	NOUN
ap-3794	58	9	if	if	SCONJ
ap-3794	58	10	the	the	DET
ap-3794	58	11	orbit	orbit	NOUN
ap-3794	58	12	of	of	ADP
ap-3794	58	13	any	any	PRON
ap-3794	58	14	given	give	VERB
ap-3794	58	15	ρ	ρ	PROPN
ap-3794	58	16	∈	∈	PROPN
ap-3794	59	1	[	[	X
ap-3794	59	2	0	0	NUM
ap-3794	59	3	,	,	PUNCT
ap-3794	59	4	1	1	NUM
ap-3794	59	5	)	)	PUNCT
ap-3794	59	6	is	be	AUX
ap-3794	59	7	dense	dense	ADJ
ap-3794	59	8	in	in	ADP
ap-3794	59	9	[	[	X
ap-3794	59	10	0	0	NUM
ap-3794	59	11	,	,	PUNCT
ap-3794	59	12	1	1	NUM
ap-3794	59	13	)	)	PUNCT
ap-3794	59	14	,	,	PUNCT
ap-3794	59	15	which	which	PRON
ap-3794	59	16	amounts	amount	VERB
ap-3794	59	17	to	to	ADP
ap-3794	59	18	requiring	require	VERB
ap-3794	59	19	that	that	SCONJ
ap-3794	59	20	1	1	NUM
ap-3794	59	21	−	−	NOUN
ap-3794	59	22	α	α	NOUN
ap-3794	59	23	and	and	CCONJ
ap-3794	59	24	β	β	X
ap-3794	59	25	be	be	AUX
ap-3794	59	26	linearly	linearly	ADV
ap-3794	59	27	independent	independent	ADJ
ap-3794	59	28	over	over	ADP
ap-3794	59	29	q.	q.	PROPN
ap-3794	59	30	then	then	ADV
ap-3794	59	31	the	the	DET
ap-3794	59	32	word	word	NOUN
ap-3794	59	33	uρ	uρ	INTJ
ap-3794	59	34	is	be	AUX
ap-3794	59	35	aperiodic	aperiodic	ADJ
ap-3794	59	36	,	,	PUNCT
ap-3794	59	37	uniformly	uniformly	ADV
ap-3794	59	38	recurrent	recurrent	NOUN
ap-3794	59	39	,	,	PUNCT
ap-3794	59	40	and	and	CCONJ
ap-3794	59	41	the	the	DET
ap-3794	59	42	language	language	NOUN
ap-3794	59	43	of	of	ADP
ap-3794	59	44	uρ	uρ	INTJ
ap-3794	59	45	does	do	AUX
ap-3794	59	46	not	not	PART
ap-3794	59	47	depend	depend	VERB
ap-3794	59	48	on	on	ADP
ap-3794	59	49	the	the	DET
ap-3794	59	50	intercept	intercept	NOUN
ap-3794	59	51	ρ	ρ	PROPN
ap-3794	59	52	.	.	PUNCT
ap-3794	60	1	the	the	DET
ap-3794	60	2	complexity	complexity	NOUN
ap-3794	60	3	of	of	ADP
ap-3794	60	4	the	the	DET
ap-3794	60	5	infinite	infinite	ADJ
ap-3794	60	6	word	word	NOUN
ap-3794	60	7	uρ	uρ	INTJ
ap-3794	60	8	is	be	AUX
ap-3794	60	9	known	know	VERB
ap-3794	60	10	to	to	PART
ap-3794	60	11	satisfy	satisfy	VERB
ap-3794	60	12	cuρ(n	cuρ(n	PROPN
ap-3794	60	13	)	)	PUNCT
ap-3794	60	14	≤	≤	NUM
ap-3794	60	15	2n	2n	NUM
ap-3794	61	1	+	+	CCONJ
ap-3794	61	2	1	1	NUM
ap-3794	61	3	(	(	PUNCT
ap-3794	61	4	see	see	VERB
ap-3794	61	5	[	[	X
ap-3794	61	6	6	6	NUM
ap-3794	61	7	]	]	NUM
ap-3794	61	8	)	)	PUNCT
ap-3794	61	9	.	.	PUNCT
ap-3794	62	1	if	if	SCONJ
ap-3794	62	2	for	for	ADP
ap-3794	62	3	every	every	DET
ap-3794	62	4	n	n	PRON
ap-3794	62	5	∈	∈	NOUN
ap-3794	62	6	n	n	DET
ap-3794	62	7	equality	equality	NOUN
ap-3794	62	8	is	be	AUX
ap-3794	62	9	achieved	achieve	VERB
ap-3794	62	10	,	,	PUNCT
ap-3794	62	11	then	then	ADV
ap-3794	62	12	the	the	DET
ap-3794	62	13	transformation	transformation	NOUN
ap-3794	62	14	t	t	PROPN
ap-3794	62	15	and	and	CCONJ
ap-3794	62	16	the	the	DET
ap-3794	62	17	word	word	NOUN
ap-3794	62	18	uρ	uρ	INTJ
ap-3794	62	19	are	be	AUX
ap-3794	62	20	said	say	VERB
ap-3794	62	21	to	to	PART
ap-3794	62	22	be	be	AUX
ap-3794	62	23	non	non	ADJ
ap-3794	62	24	-	-	ADJ
ap-3794	62	25	degenerate	degenerate	ADJ
ap-3794	62	26	.	.	PUNCT
ap-3794	63	1	a	a	DET
ap-3794	63	2	necessary	necessary	ADJ
ap-3794	63	3	and	and	CCONJ
ap-3794	63	4	sufficient	sufficient	ADJ
ap-3794	63	5	condition	condition	NOUN
ap-3794	63	6	for	for	ADP
ap-3794	63	7	a	a	DET
ap-3794	63	8	3iet	3iet	PROPN
ap-3794	63	9	t	t	NOUN
ap-3794	63	10	to	to	PART
ap-3794	63	11	be	be	AUX
ap-3794	63	12	non	non	ADJ
ap-3794	63	13	-	-	ADJ
ap-3794	63	14	degenerate	degenerate	ADJ
ap-3794	63	15	is	be	AUX
ap-3794	63	16	that	that	SCONJ
ap-3794	63	17	t	t	PROPN
ap-3794	63	18	is	be	AUX
ap-3794	63	19	minimal	minimal	ADJ
ap-3794	63	20	and	and	CCONJ
ap-3794	63	21	1	1	NUM
ap-3794	63	22	/∈	/∈	INTJ
ap-3794	63	23	(	(	PUNCT
ap-3794	63	24	1−	1−	NUM
ap-3794	63	25	α)z	α)z	X
ap-3794	63	26	+	+	X
ap-3794	63	27	βz	βz	NUM
ap-3794	63	28	;	;	PUNCT
ap-3794	63	29	(	(	PUNCT
ap-3794	63	30	2	2	X
ap-3794	63	31	)	)	PUNCT
ap-3794	63	32	see	see	VERB
ap-3794	63	33	[	[	X
ap-3794	63	34	6	6	NUM
ap-3794	63	35	]	]	PUNCT
ap-3794	63	36	.	.	PUNCT
ap-3794	64	1	3	3	X
ap-3794	64	2	.	.	X
ap-3794	64	3	itineraries	itinerary	NOUN
ap-3794	64	4	in	in	ADP
ap-3794	64	5	exchange	exchange	NOUN
ap-3794	64	6	of	of	ADP
ap-3794	64	7	three	three	NUM
ap-3794	64	8	intervals	interval	NOUN
ap-3794	64	9	definition	definition	NOUN
ap-3794	64	10	3.1	3.1	NUM
ap-3794	64	11	.	.	PUNCT
ap-3794	65	1	given	give	VERB
ap-3794	65	2	a	a	DET
ap-3794	65	3	subinterval	subinterval	NOUN
ap-3794	66	1	i	i	PRON
ap-3794	66	2	⊂	⊂	PROPN
ap-3794	67	1	[	[	X
ap-3794	67	2	0	0	NUM
ap-3794	67	3	,	,	PUNCT
ap-3794	67	4	1	1	NUM
ap-3794	67	5	)	)	PUNCT
ap-3794	67	6	,	,	PUNCT
ap-3794	67	7	we	we	PRON
ap-3794	67	8	define	define	VERB
ap-3794	67	9	the	the	DET
ap-3794	67	10	so	so	ADV
ap-3794	67	11	-	-	PUNCT
ap-3794	67	12	called	call	VERB
ap-3794	67	13	return	return	NOUN
ap-3794	67	14	time	time	NOUN
ap-3794	67	15	to	to	ADP
ap-3794	67	16	i	i	PRON
ap-3794	67	17	as	as	ADP
ap-3794	67	18	a	a	DET
ap-3794	67	19	mapping	mapping	NOUN
ap-3794	67	20	ri	ri	NOUN
ap-3794	67	21	:	:	PUNCT
ap-3794	67	22	i	i	PROPN
ap-3794	67	23	→	→	SYM
ap-3794	67	24	z+	z+	NUM
ap-3794	67	25	=	=	SYM
ap-3794	67	26	{	{	PUNCT
ap-3794	67	27	1	1	NUM
ap-3794	67	28	,	,	PUNCT
ap-3794	67	29	2	2	NUM
ap-3794	67	30	,	,	PUNCT
ap-3794	67	31	3	3	NUM
ap-3794	67	32	,	,	PUNCT
ap-3794	67	33	.	.	PUNCT
ap-3794	67	34	.	.	PUNCT
ap-3794	67	35	.	.	PUNCT
ap-3794	68	1	}	}	PUNCT
ap-3794	68	2	such	such	ADJ
ap-3794	68	3	that	that	DET
ap-3794	68	4	ri(x	ri(x	NOUN
ap-3794	68	5	)	)	PUNCT
ap-3794	69	1	=	=	PUNCT
ap-3794	69	2	min{n	min{n	NOUN
ap-3794	69	3	∈	∈	NOUN
ap-3794	69	4	z+	z+	NUM
ap-3794	69	5	:	:	PUNCT
ap-3794	69	6	tn(x	tn(x	X
ap-3794	69	7	)	)	PUNCT
ap-3794	69	8	∈	∈	PROPN
ap-3794	69	9	i	i	PRON
ap-3794	69	10	}	}	PUNCT
ap-3794	69	11	.	.	PUNCT
ap-3794	70	1	the	the	DET
ap-3794	70	2	prefix	prefix	NOUN
ap-3794	70	3	of	of	ADP
ap-3794	70	4	the	the	DET
ap-3794	70	5	word	word	NOUN
ap-3794	70	6	ux	ux	ADP
ap-3794	70	7	of	of	ADP
ap-3794	70	8	length	length	NOUN
ap-3794	70	9	ri(x	ri(x	NOUN
ap-3794	70	10	)	)	PUNCT
ap-3794	70	11	coding	code	VERB
ap-3794	70	12	the	the	DET
ap-3794	70	13	orbit	orbit	NOUN
ap-3794	70	14	of	of	ADP
ap-3794	70	15	x	x	PUNCT
ap-3794	70	16	∈	∈	PROPN
ap-3794	70	17	i	i	PRON
ap-3794	70	18	under	under	ADP
ap-3794	70	19	a	a	DET
ap-3794	70	20	3iet	3iet	PROPN
ap-3794	70	21	t	t	NOUN
ap-3794	70	22	is	be	AUX
ap-3794	70	23	called	call	VERB
ap-3794	70	24	the	the	DET
ap-3794	70	25	i	i	NOUN
ap-3794	70	26	-	-	PUNCT
ap-3794	70	27	itinerary	itinerary	NOUN
ap-3794	70	28	of	of	ADP
ap-3794	70	29	x	x	PUNCT
ap-3794	70	30	and	and	CCONJ
ap-3794	70	31	denoted	denote	VERB
ap-3794	70	32	ri(x	ri(x	NOUN
ap-3794	70	33	)	)	PUNCT
ap-3794	70	34	.	.	PUNCT
ap-3794	71	1	the	the	DET
ap-3794	71	2	set	set	NOUN
ap-3794	71	3	of	of	ADP
ap-3794	71	4	all	all	PRON
ap-3794	71	5	i	i	PRON
ap-3794	71	6	-	-	NOUN
ap-3794	71	7	itineraries	itinerary	NOUN
ap-3794	71	8	is	be	AUX
ap-3794	71	9	denoted	denote	VERB
ap-3794	71	10	by	by	ADP
ap-3794	71	11	iti	iti	PROPN
ap-3794	71	12	=	=	PUNCT
ap-3794	71	13	{	{	PUNCT
ap-3794	71	14	ri(x	ri(x	NUM
ap-3794	71	15	)	)	PUNCT
ap-3794	71	16	:	:	PUNCT
ap-3794	72	1	x	x	X
ap-3794	72	2	∈	∈	NOUN
ap-3794	72	3	i	i	PRON
ap-3794	72	4	}	}	PUNCT
ap-3794	72	5	.	.	PUNCT
ap-3794	73	1	the	the	DET
ap-3794	73	2	map	map	NOUN
ap-3794	73	3	ti	ti	NOUN
ap-3794	73	4	:	:	PUNCT
ap-3794	73	5	i	i	PROPN
ap-3794	73	6	→	→	PUNCT
ap-3794	73	7	i	i	PRON
ap-3794	73	8	defined	define	VERB
ap-3794	73	9	by	by	ADP
ap-3794	73	10	ti(x	ti(x	NOUN
ap-3794	73	11	)	)	PUNCT
ap-3794	73	12	=	=	SYM
ap-3794	73	13	t	t	PROPN
ap-3794	73	14	ri(x)(x	ri(x)(x	PROPN
ap-3794	73	15	)	)	PUNCT
ap-3794	73	16	is	be	AUX
ap-3794	73	17	called	call	VERB
ap-3794	73	18	the	the	DET
ap-3794	73	19	first	first	ADJ
ap-3794	73	20	return	return	NOUN
ap-3794	73	21	map	map	NOUN
ap-3794	73	22	of	of	ADP
ap-3794	73	23	t	t	PROPN
ap-3794	73	24	to	to	ADP
ap-3794	73	25	i	i	PRON
ap-3794	73	26	,	,	PUNCT
ap-3794	73	27	or	or	CCONJ
ap-3794	73	28	induced	induce	VERB
ap-3794	73	29	map	map	NOUN
ap-3794	73	30	of	of	ADP
ap-3794	73	31	t	t	PROPN
ap-3794	73	32	on	on	ADP
ap-3794	73	33	i.	i.	PROPN
ap-3794	73	34	the	the	DET
ap-3794	73	35	indices	index	NOUN
ap-3794	73	36	in	in	ADP
ap-3794	73	37	ri	ri	PROPN
ap-3794	73	38	or	or	CCONJ
ap-3794	73	39	ri	ri	PROPN
ap-3794	73	40	are	be	AUX
ap-3794	73	41	usually	usually	ADV
ap-3794	73	42	omitted	omit	VERB
ap-3794	73	43	,	,	PUNCT
ap-3794	73	44	if	if	SCONJ
ap-3794	73	45	this	this	PRON
ap-3794	73	46	causes	cause	VERB
ap-3794	73	47	no	no	DET
ap-3794	73	48	confusion	confusion	NOUN
ap-3794	73	49	.	.	PUNCT
ap-3794	74	1	for	for	ADP
ap-3794	74	2	a	a	DET
ap-3794	74	3	given	give	VERB
ap-3794	74	4	subinterval	subinterval	NOUN
ap-3794	74	5	i	i	PRON
ap-3794	74	6	⊂	⊂	PROPN
ap-3794	75	1	[	[	X
ap-3794	75	2	0	0	NUM
ap-3794	75	3	,	,	PUNCT
ap-3794	75	4	1	1	NUM
ap-3794	75	5	)	)	PUNCT
ap-3794	75	6	there	there	PRON
ap-3794	75	7	exist	exist	VERB
ap-3794	75	8	at	at	ADP
ap-3794	75	9	most	most	ADV
ap-3794	75	10	five	five	NUM
ap-3794	75	11	i	i	NOUN
ap-3794	75	12	-	-	PUNCT
ap-3794	75	13	itineraries	itinerary	NOUN
ap-3794	75	14	under	under	ADP
ap-3794	75	15	a	a	DET
ap-3794	75	16	3iet	3iet	PROPN
ap-3794	75	17	t	t	NOUN
ap-3794	75	18	.	.	PUNCT
ap-3794	76	1	in	in	ADP
ap-3794	76	2	particular	particular	ADJ
ap-3794	76	3	,	,	PUNCT
ap-3794	76	4	from	from	ADP
ap-3794	76	5	the	the	DET
ap-3794	76	6	article	article	NOUN
ap-3794	76	7	of	of	ADP
ap-3794	76	8	keane	keane	PROPN
ap-3794	77	1	[	[	X
ap-3794	77	2	11	11	NUM
ap-3794	77	3	]	]	PUNCT
ap-3794	77	4	,	,	PUNCT
ap-3794	77	5	one	one	PRON
ap-3794	77	6	can	can	AUX
ap-3794	77	7	deduce	deduce	VERB
ap-3794	77	8	what	what	PRON
ap-3794	77	9	the	the	DET
ap-3794	77	10	intervals	interval	NOUN
ap-3794	77	11	of	of	ADP
ap-3794	77	12	points	point	NOUN
ap-3794	77	13	with	with	ADP
ap-3794	77	14	the	the	DET
ap-3794	77	15	same	same	ADJ
ap-3794	77	16	itinerary	itinerary	NOUN
ap-3794	77	17	are	be	AUX
ap-3794	77	18	.	.	PUNCT
ap-3794	78	1	we	we	PRON
ap-3794	78	2	summarize	summarize	VERB
ap-3794	78	3	it	it	PRON
ap-3794	78	4	as	as	ADP
ap-3794	78	5	the	the	DET
ap-3794	78	6	following	follow	VERB
ap-3794	78	7	lemma	lemma	PROPN
ap-3794	78	8	.	.	PUNCT
ap-3794	79	1	lemma	lemma	PROPN
ap-3794	79	2	3.2	3.2	NUM
ap-3794	79	3	.	.	PUNCT
ap-3794	80	1	let	let	VERB
ap-3794	80	2	t	t	PROPN
ap-3794	80	3	be	be	AUX
ap-3794	80	4	a	a	DET
ap-3794	80	5	3iet	3iet	NUM
ap-3794	80	6	defined	define	VERB
ap-3794	80	7	by	by	ADP
ap-3794	80	8	(	(	PUNCT
ap-3794	80	9	1	1	NUM
ap-3794	80	10	)	)	PUNCT
ap-3794	80	11	and	and	CCONJ
ap-3794	80	12	let	let	VERB
ap-3794	80	13	i	i	PRON
ap-3794	80	14	=	=	PUNCT
ap-3794	81	1	[	[	X
ap-3794	81	2	γ	γ	X
ap-3794	81	3	,	,	PUNCT
ap-3794	81	4	δ	δ	PROPN
ap-3794	81	5	)	)	PUNCT
ap-3794	81	6	⊂	⊂	PROPN
ap-3794	82	1	[	[	X
ap-3794	82	2	0	0	NUM
ap-3794	82	3	,	,	PUNCT
ap-3794	82	4	1	1	NUM
ap-3794	82	5	)	)	PUNCT
ap-3794	82	6	such	such	ADJ
ap-3794	82	7	that	that	SCONJ
ap-3794	82	8	δ	δ	PROPN
ap-3794	82	9	<	<	X
ap-3794	82	10	1	1	X
ap-3794	82	11	.	.	PUNCT
ap-3794	82	12	denote	denote	VERB
ap-3794	82	13	kα	kα	X
ap-3794	82	14	:	:	PUNCT
ap-3794	82	15	=	=	SYM
ap-3794	82	16	min	min	PROPN
ap-3794	82	17	{	{	PUNCT
ap-3794	82	18	k	k	PROPN
ap-3794	82	19	∈	∈	PROPN
ap-3794	82	20	z	z	PROPN
ap-3794	82	21	,	,	PUNCT
ap-3794	82	22	k	k	X
ap-3794	82	23	≥	≥	X
ap-3794	82	24	0	0	NUM
ap-3794	82	25	:	:	PUNCT
ap-3794	82	26	t−k(α	t−k(α	NOUN
ap-3794	82	27	)	)	PUNCT
ap-3794	82	28	∈	∈	PROPN
ap-3794	82	29	(	(	PUNCT
ap-3794	82	30	γ	γ	X
ap-3794	82	31	,	,	PUNCT
ap-3794	82	32	δ	δ	PROPN
ap-3794	82	33	)	)	PUNCT
ap-3794	82	34	}	}	PUNCT
ap-3794	82	35	,	,	PUNCT
ap-3794	82	36	kβ	kβ	INTJ
ap-3794	82	37	:	:	PUNCT
ap-3794	82	38	=	=	SYM
ap-3794	82	39	min	min	NOUN
ap-3794	82	40	{	{	PUNCT
ap-3794	82	41	k	k	PROPN
ap-3794	82	42	∈	∈	PROPN
ap-3794	82	43	z	z	PROPN
ap-3794	82	44	,	,	PUNCT
ap-3794	82	45	k	k	X
ap-3794	82	46	≥	≥	X
ap-3794	82	47	0	0	NUM
ap-3794	82	48	:	:	PUNCT
ap-3794	82	49	t−k(β	t−k(β	NOUN
ap-3794	82	50	)	)	PUNCT
ap-3794	82	51	∈	∈	PROPN
ap-3794	82	52	(	(	PUNCT
ap-3794	82	53	γ	γ	X
ap-3794	82	54	,	,	PUNCT
ap-3794	82	55	δ	δ	PROPN
ap-3794	82	56	)	)	PUNCT
ap-3794	82	57	}	}	PUNCT
ap-3794	82	58	,	,	PUNCT
ap-3794	82	59	kγ	kγ	INTJ
ap-3794	82	60	:	:	PUNCT
ap-3794	82	61	=	=	SYM
ap-3794	82	62	min	min	PROPN
ap-3794	82	63	{	{	PUNCT
ap-3794	82	64	k	k	PROPN
ap-3794	82	65	∈	∈	PROPN
ap-3794	82	66	z	z	PROPN
ap-3794	82	67	,	,	PUNCT
ap-3794	82	68	k	k	PROPN
ap-3794	82	69	≥	≥	NUM
ap-3794	82	70	1	1	NUM
ap-3794	82	71	:	:	PUNCT
ap-3794	82	72	t−k(γ	t−k(γ	NUM
ap-3794	82	73	)	)	PUNCT
ap-3794	82	74	∈	∈	PROPN
ap-3794	82	75	(	(	PUNCT
ap-3794	82	76	γ	γ	X
ap-3794	82	77	,	,	PUNCT
ap-3794	82	78	δ	δ	PROPN
ap-3794	82	79	)	)	PUNCT
ap-3794	82	80	}	}	PUNCT
ap-3794	82	81	,	,	PUNCT
ap-3794	82	82	kδ	kδ	NOUN
ap-3794	82	83	:	:	PUNCT
ap-3794	82	84	=	=	SYM
ap-3794	82	85	min	min	PROPN
ap-3794	82	86	{	{	PUNCT
ap-3794	82	87	k	k	PROPN
ap-3794	82	88	∈	∈	PROPN
ap-3794	82	89	z	z	PROPN
ap-3794	82	90	,	,	PUNCT
ap-3794	82	91	k	k	PROPN
ap-3794	82	92	≥	≥	NUM
ap-3794	82	93	1	1	NUM
ap-3794	82	94	:	:	PUNCT
ap-3794	82	95	t−k(δ	t−k(δ	PROPN
ap-3794	82	96	)	)	PUNCT
ap-3794	82	97	∈	∈	PROPN
ap-3794	82	98	(	(	PUNCT
ap-3794	82	99	γ	γ	X
ap-3794	82	100	,	,	PUNCT
ap-3794	82	101	δ	δ	PROPN
ap-3794	82	102	)	)	PUNCT
ap-3794	82	103	}	}	PUNCT
ap-3794	82	104	,	,	PUNCT
ap-3794	82	105	and	and	CCONJ
ap-3794	82	106	further	far	ADV
ap-3794	82	107	a	a	DET
ap-3794	82	108	:	:	PUNCT
ap-3794	82	109	=	=	SYM
ap-3794	82	110	t−kα(α	t−kα(α	NUM
ap-3794	82	111	)	)	PUNCT
ap-3794	82	112	,	,	PUNCT
ap-3794	82	113	b	b	X
ap-3794	82	114	:	:	PUNCT
ap-3794	82	115	=	=	SYM
ap-3794	82	116	t−kβ	t−kβ	X
ap-3794	82	117	(	(	PUNCT
ap-3794	82	118	β	β	NOUN
ap-3794	82	119	)	)	PUNCT
ap-3794	82	120	,	,	PUNCT
ap-3794	82	121	c	c	NOUN
ap-3794	82	122	:	:	PUNCT
ap-3794	82	123	=	=	SYM
ap-3794	82	124	t−kγ	t−kγ	PROPN
ap-3794	82	125	(	(	PUNCT
ap-3794	82	126	γ	γ	NOUN
ap-3794	82	127	)	)	PUNCT
ap-3794	82	128	,	,	PUNCT
ap-3794	82	129	d	d	X
ap-3794	82	130	:	:	PUNCT
ap-3794	82	131	=	=	SYM
ap-3794	82	132	t−kδ(δ	t−kδ(δ	NOUN
ap-3794	82	133	)	)	PUNCT
ap-3794	82	134	.	.	PUNCT
ap-3794	83	1	for	for	SCONJ
ap-3794	83	2	x	x	PROPN
ap-3794	83	3	∈	∈	PROPN
ap-3794	83	4	i	i	PRON
ap-3794	83	5	,	,	PUNCT
ap-3794	83	6	let	let	VERB
ap-3794	83	7	kx	kx	PROPN
ap-3794	83	8	be	be	AUX
ap-3794	83	9	a	a	DET
ap-3794	83	10	maximal	maximal	ADJ
ap-3794	83	11	interval	interval	NOUN
ap-3794	83	12	such	such	ADJ
ap-3794	83	13	that	that	PRON
ap-3794	83	14	for	for	ADP
ap-3794	83	15	every	every	DET
ap-3794	83	16	y	y	PROPN
ap-3794	83	17	∈	∈	PROPN
ap-3794	83	18	kx	kx	PROPN
ap-3794	83	19	,	,	PUNCT
ap-3794	83	20	we	we	PRON
ap-3794	83	21	have	have	AUX
ap-3794	83	22	r(y	r(y	VERB
ap-3794	83	23	)	)	PUNCT
ap-3794	83	24	=	=	SYM
ap-3794	83	25	r(x	r(x	PROPN
ap-3794	83	26	)	)	PUNCT
ap-3794	83	27	.	.	PUNCT
ap-3794	84	1	thenkx	thenkx	NOUN
ap-3794	84	2	is	be	AUX
ap-3794	84	3	of	of	ADP
ap-3794	84	4	the	the	DET
ap-3794	84	5	form	form	NOUN
ap-3794	84	6	[	[	X
ap-3794	84	7	c	c	X
ap-3794	84	8	,	,	PUNCT
ap-3794	84	9	d	d	NOUN
ap-3794	84	10	)	)	PUNCT
ap-3794	84	11	with	with	ADP
ap-3794	84	12	c	c	NOUN
ap-3794	84	13	,	,	PUNCT
ap-3794	84	14	d	d	PROPN
ap-3794	84	15	∈	∈	PROPN
ap-3794	84	16	{	{	PUNCT
ap-3794	84	17	γ	γ	PROPN
ap-3794	84	18	,	,	PUNCT
ap-3794	84	19	δ	δ	PROPN
ap-3794	84	20	,	,	PUNCT
ap-3794	84	21	a	a	DET
ap-3794	84	22	,	,	PUNCT
ap-3794	84	23	b	b	NOUN
ap-3794	84	24	,	,	PUNCT
ap-3794	84	25	c	c	X
ap-3794	84	26	,	,	PUNCT
ap-3794	84	27	d	d	NOUN
ap-3794	84	28	}	}	PUNCT
ap-3794	84	29	.	.	PUNCT
ap-3794	85	1	consequently	consequently	ADV
ap-3794	85	2	,	,	PUNCT
ap-3794	85	3	#	#	NOUN
ap-3794	85	4	iti	iti	NOUN
ap-3794	85	5	≤	≤	NOUN
ap-3794	85	6	5	5	NUM
ap-3794	85	7	.	.	PUNCT
ap-3794	85	8	for	for	ADP
ap-3794	85	9	a	a	DET
ap-3794	85	10	3iet	3iet	PROPN
ap-3794	85	11	t	t	NOUN
ap-3794	85	12	,	,	PUNCT
ap-3794	85	13	lemma	lemma	PROPN
ap-3794	85	14	3.2	3.2	NUM
ap-3794	85	15	implies	imply	VERB
ap-3794	85	16	that	that	SCONJ
ap-3794	85	17	ti	ti	PROPN
ap-3794	85	18	is	be	AUX
ap-3794	85	19	an	an	DET
ap-3794	85	20	exchange	exchange	NOUN
ap-3794	85	21	of	of	ADP
ap-3794	85	22	at	at	ADP
ap-3794	85	23	most	most	ADJ
ap-3794	85	24	5	5	NUM
ap-3794	85	25	intervals	interval	NOUN
ap-3794	85	26	.	.	PUNCT
ap-3794	86	1	consequently	consequently	ADV
ap-3794	86	2	,	,	PUNCT
ap-3794	86	3	the	the	DET
ap-3794	86	4	transformation	transformation	NOUN
ap-3794	86	5	ti	ti	NOUN
ap-3794	86	6	has	have	VERB
ap-3794	86	7	at	at	ADP
ap-3794	86	8	most	most	ADJ
ap-3794	86	9	four	four	NUM
ap-3794	86	10	discontinuity	discontinuity	NOUN
ap-3794	86	11	points	point	NOUN
ap-3794	86	12	.	.	PUNCT
ap-3794	87	1	in	in	ADP
ap-3794	87	2	fact	fact	NOUN
ap-3794	87	3	,	,	PUNCT
ap-3794	87	4	the	the	DET
ap-3794	87	5	following	following	ADJ
ap-3794	87	6	result	result	NOUN
ap-3794	87	7	of	of	ADP
ap-3794	87	8	[	[	X
ap-3794	87	9	9	9	NUM
ap-3794	87	10	]	]	PUNCT
ap-3794	87	11	says	say	VERB
ap-3794	87	12	that	that	SCONJ
ap-3794	87	13	independently	independently	ADV
ap-3794	87	14	of	of	ADP
ap-3794	87	15	the	the	DET
ap-3794	87	16	number	number	NOUN
ap-3794	87	17	of	of	ADP
ap-3794	87	18	i	i	PROPN
ap-3794	87	19	-	-	PUNCT
ap-3794	87	20	itineraries	itinerary	NOUN
ap-3794	87	21	,	,	PUNCT
ap-3794	87	22	the	the	DET
ap-3794	87	23	induced	induced	ADJ
ap-3794	87	24	map	map	NOUN
ap-3794	87	25	ti	ti	NOUN
ap-3794	87	26	has	have	VERB
ap-3794	87	27	always	always	ADV
ap-3794	87	28	at	at	ADP
ap-3794	87	29	most	most	ADV
ap-3794	87	30	two	two	NUM
ap-3794	87	31	discontinuity	discontinuity	NOUN
ap-3794	87	32	points	point	NOUN
ap-3794	87	33	.	.	PUNCT
ap-3794	88	1	proposition	proposition	NOUN
ap-3794	88	2	3.3	3.3	NUM
ap-3794	89	1	[	[	X
ap-3794	89	2	9	9	NUM
ap-3794	89	3	]	]	PUNCT
ap-3794	89	4	.	.	PUNCT
ap-3794	90	1	let	let	VERB
ap-3794	90	2	t	t	NOUN
ap-3794	90	3	:	:	PUNCT
ap-3794	90	4	j	j	PROPN
ap-3794	90	5	→	→	PUNCT
ap-3794	90	6	j	j	PROPN
ap-3794	90	7	be	be	AUX
ap-3794	90	8	a	a	DET
ap-3794	90	9	3iet	3iet	PROPN
ap-3794	90	10	with	with	ADP
ap-3794	90	11	the	the	DET
ap-3794	90	12	permutation	permutation	NOUN
ap-3794	90	13	(	(	PUNCT
ap-3794	90	14	321	321	NUM
ap-3794	90	15	)	)	PUNCT
ap-3794	90	16	and	and	CCONJ
ap-3794	90	17	satisfying	satisfy	VERB
ap-3794	90	18	the	the	DET
ap-3794	90	19	minimality	minimality	NOUN
ap-3794	90	20	condition	condition	NOUN
ap-3794	90	21	,	,	PUNCT
ap-3794	90	22	and	and	CCONJ
ap-3794	90	23	let	let	VERB
ap-3794	90	24	i	i	PRON
ap-3794	90	25	⊂	⊂	PROPN
ap-3794	90	26	j	j	PROPN
ap-3794	90	27	be	be	AUX
ap-3794	90	28	an	an	DET
ap-3794	90	29	interval	interval	NOUN
ap-3794	90	30	.	.	PUNCT
ap-3794	91	1	the	the	DET
ap-3794	91	2	first	first	ADJ
ap-3794	91	3	return	return	NOUN
ap-3794	91	4	map	map	NOUN
ap-3794	91	5	ti	ti	NOUN
ap-3794	91	6	is	be	AUX
ap-3794	91	7	either	either	CCONJ
ap-3794	91	8	a	a	DET
ap-3794	91	9	3iet	3iet	PROPN
ap-3794	91	10	with	with	ADP
ap-3794	91	11	permutation	permutation	NOUN
ap-3794	91	12	(	(	PUNCT
ap-3794	91	13	321	321	NUM
ap-3794	91	14	)	)	PUNCT
ap-3794	91	15	or	or	CCONJ
ap-3794	91	16	a	a	DET
ap-3794	91	17	2iet	2iet	NOUN
ap-3794	91	18	with	with	ADP
ap-3794	91	19	permutation	permutation	NOUN
ap-3794	91	20	(	(	PUNCT
ap-3794	91	21	21	21	NUM
ap-3794	91	22	)	)	PUNCT
ap-3794	91	23	.	.	PUNCT
ap-3794	92	1	in	in	ADP
ap-3794	92	2	particular	particular	ADJ
ap-3794	92	3	,	,	PUNCT
ap-3794	92	4	in	in	ADP
ap-3794	92	5	the	the	DET
ap-3794	92	6	notation	notation	NOUN
ap-3794	92	7	of	of	ADP
ap-3794	92	8	lemma	lemma	PROPN
ap-3794	92	9	3.2	3.2	NUM
ap-3794	92	10	,	,	PUNCT
ap-3794	92	11	we	we	PRON
ap-3794	92	12	have	have	VERB
ap-3794	92	13	d	d	PROPN
ap-3794	92	14	≤	≤	X
ap-3794	92	15	c.	c.	NOUN
ap-3794	92	16	we	we	PRON
ap-3794	92	17	will	will	AUX
ap-3794	92	18	use	use	VERB
ap-3794	92	19	two	two	NUM
ap-3794	92	20	other	other	ADJ
ap-3794	92	21	facts	fact	NOUN
ap-3794	92	22	about	about	ADP
ap-3794	92	23	itineraries	itinerary	NOUN
ap-3794	92	24	of	of	ADP
ap-3794	92	25	an	an	DET
ap-3794	92	26	interval	interval	NOUN
ap-3794	92	27	exchange	exchange	NOUN
ap-3794	92	28	,	,	PUNCT
ap-3794	92	29	stated	state	VERB
ap-3794	92	30	as	as	ADP
ap-3794	92	31	propositions	proposition	NOUN
ap-3794	92	32	3.4	3.4	NUM
ap-3794	92	33	and	and	CCONJ
ap-3794	92	34	3.5	3.5	NUM
ap-3794	92	35	.	.	PUNCT
ap-3794	93	1	both	both	PRON
ap-3794	93	2	of	of	ADP
ap-3794	93	3	these	these	PRON
ap-3794	93	4	were	be	AUX
ap-3794	93	5	proven	prove	VERB
ap-3794	93	6	in	in	ADP
ap-3794	93	7	[	[	X
ap-3794	93	8	12	12	NUM
ap-3794	93	9	]	]	PUNCT
ap-3794	93	10	for	for	ADP
ap-3794	93	11	general	general	ADJ
ap-3794	93	12	interval	interval	NOUN
ap-3794	93	13	exchange	exchange	NOUN
ap-3794	93	14	transformations	transformation	NOUN
ap-3794	93	15	with	with	ADP
ap-3794	93	16	symmetric	symmetric	ADJ
ap-3794	93	17	permutation	permutation	NOUN
ap-3794	93	18	and	and	CCONJ
ap-3794	93	19	thus	thus	ADV
ap-3794	93	20	hold	hold	VERB
ap-3794	93	21	also	also	ADV
ap-3794	93	22	for	for	ADP
ap-3794	93	23	3iets	3iets	NUM
ap-3794	93	24	with	with	ADP
ap-3794	93	25	permutation	permutation	NOUN
ap-3794	93	26	(	(	PUNCT
ap-3794	93	27	321	321	NUM
ap-3794	93	28	)	)	PUNCT
ap-3794	93	29	.	.	PUNCT
ap-3794	94	1	note	note	VERB
ap-3794	94	2	that	that	SCONJ
ap-3794	94	3	a	a	DET
ap-3794	94	4	3iet	3iet	PROPN
ap-3794	94	5	t	t	NOUN
ap-3794	94	6	is	be	AUX
ap-3794	94	7	right	right	ADJ
ap-3794	94	8	-	-	PUNCT
ap-3794	94	9	continuous	continuous	ADJ
ap-3794	94	10	.	.	PUNCT
ap-3794	95	1	therefore	therefore	ADV
ap-3794	95	2	,	,	PUNCT
ap-3794	95	3	if	if	SCONJ
ap-3794	95	4	i	i	PRON
ap-3794	95	5	=	=	PUNCT
ap-3794	96	1	[	[	X
ap-3794	96	2	γ	γ	X
ap-3794	96	3	,	,	PUNCT
ap-3794	96	4	δ	δ	PROPN
ap-3794	96	5	)	)	PUNCT
ap-3794	96	6	,	,	PUNCT
ap-3794	96	7	then	then	ADV
ap-3794	96	8	every	every	DET
ap-3794	96	9	word	word	NOUN
ap-3794	96	10	w	w	PROPN
ap-3794	96	11	∈	∈	PROPN
ap-3794	96	12	iti	iti	NOUN
ap-3794	96	13	=	=	PUNCT
ap-3794	96	14	{	{	PUNCT
ap-3794	96	15	r(x	r(x	PROPN
ap-3794	96	16	)	)	PUNCT
ap-3794	96	17	:	:	PUNCT
ap-3794	97	1	x	x	X
ap-3794	97	2	∈	∈	PROPN
ap-3794	97	3	i	i	PRON
ap-3794	97	4	}	}	PUNCT
ap-3794	97	5	is	be	AUX
ap-3794	97	6	an	an	DET
ap-3794	97	7	i	i	NOUN
ap-3794	97	8	-	-	PUNCT
ap-3794	97	9	itinerary	itinerary	PROPN
ap-3794	97	10	r(x	r(x	PROPN
ap-3794	97	11	)	)	PUNCT
ap-3794	97	12	for	for	ADP
ap-3794	97	13	infinitely	infinitely	ADV
ap-3794	97	14	many	many	ADJ
ap-3794	97	15	x	x	SYM
ap-3794	97	16	∈	∈	PROPN
ap-3794	97	17	i	i	PRON
ap-3794	97	18	,	,	PUNCT
ap-3794	97	19	which	which	PRON
ap-3794	97	20	form	form	VERB
ap-3794	97	21	an	an	DET
ap-3794	97	22	interval	interval	NOUN
ap-3794	97	23	,	,	PUNCT
ap-3794	97	24	again	again	ADV
ap-3794	97	25	left	left	ADJ
ap-3794	97	26	-	-	PUNCT
ap-3794	97	27	closed	close	VERB
ap-3794	97	28	right	right	ADV
ap-3794	97	29	-	-	PUNCT
ap-3794	97	30	open	open	ADJ
ap-3794	97	31	.	.	PUNCT
ap-3794	98	1	proposition	proposition	NOUN
ap-3794	98	2	3.4	3.4	NUM
ap-3794	98	3	.	.	PUNCT
ap-3794	99	1	let	let	VERB
ap-3794	99	2	t	t	PROPN
ap-3794	99	3	be	be	AUX
ap-3794	99	4	a	a	DET
ap-3794	99	5	3iet	3iet	NUM
ap-3794	99	6	satisfying	satisfy	VERB
ap-3794	99	7	the	the	DET
ap-3794	99	8	minimality	minimality	NOUN
ap-3794	99	9	condition	condition	NOUN
ap-3794	99	10	and	and	CCONJ
ap-3794	99	11	let	let	VERB
ap-3794	99	12	i	i	PRON
ap-3794	99	13	=	=	PUNCT
ap-3794	100	1	[	[	X
ap-3794	100	2	γ	γ	X
ap-3794	100	3	,	,	PUNCT
ap-3794	100	4	δ	δ	PROPN
ap-3794	100	5	)	)	PUNCT
ap-3794	100	6	⊂	⊂	PROPN
ap-3794	101	1	[	[	X
ap-3794	101	2	0	0	NUM
ap-3794	101	3	,	,	PUNCT
ap-3794	101	4	1	1	NUM
ap-3794	101	5	)	)	PUNCT
ap-3794	101	6	.	.	PUNCT
ap-3794	102	1	there	there	PRON
ap-3794	102	2	exist	exist	VERB
ap-3794	102	3	neighbourhoods	neighbourhood	NOUN
ap-3794	102	4	hγ	hγ	PRON
ap-3794	102	5	and	and	CCONJ
ap-3794	102	6	hδ	hδ	PROPN
ap-3794	102	7	of	of	ADP
ap-3794	102	8	γ	γ	PROPN
ap-3794	102	9	and	and	CCONJ
ap-3794	102	10	δ	δ	PROPN
ap-3794	102	11	,	,	PUNCT
ap-3794	102	12	respectively	respectively	ADV
ap-3794	102	13	,	,	PUNCT
ap-3794	102	14	such	such	ADJ
ap-3794	102	15	that	that	PRON
ap-3794	102	16	for	for	ADP
ap-3794	102	17	every	every	DET
ap-3794	102	18	γ̃	γ̃	PROPN
ap-3794	102	19	∈	∈	PROPN
ap-3794	102	20	hγ	hγ	NOUN
ap-3794	102	21	and	and	CCONJ
ap-3794	102	22	δ̃	δ̃	PROPN
ap-3794	102	23	∈	∈	PROPN
ap-3794	102	24	hδ	hδ	NOUN
ap-3794	102	25	with	with	ADP
ap-3794	102	26	0	0	NUM
ap-3794	102	27	≤	≤	NUM
ap-3794	103	1	γ̃	γ̃	PROPN
ap-3794	103	2	<	<	X
ap-3794	103	3	δ̃	δ̃	PROPN
ap-3794	103	4	≤	≤	ADV
ap-3794	103	5	1	1	NUM
ap-3794	103	6	one	one	NUM
ap-3794	103	7	has	have	VERB
ap-3794	103	8	itĩ	itĩ	ADP
ap-3794	103	9	⊇	⊇	PROPN
ap-3794	103	10	iti	iti	PROPN
ap-3794	103	11	,	,	PUNCT
ap-3794	103	12	where	where	SCONJ
ap-3794	103	13	ĩ	ĩ	PROPN
ap-3794	103	14	=	=	PUNCT
ap-3794	103	15	[	[	X
ap-3794	103	16	γ̃	γ̃	PROPN
ap-3794	103	17	,	,	PUNCT
ap-3794	103	18	δ̃	δ̃	PROPN
ap-3794	103	19	)	)	PUNCT
ap-3794	103	20	.	.	PUNCT
ap-3794	104	1	in	in	ADP
ap-3794	104	2	particular	particular	ADJ
ap-3794	104	3	,	,	PUNCT
ap-3794	104	4	if	if	SCONJ
ap-3794	104	5	#	#	NOUN
ap-3794	104	6	iti	iti	NOUN
ap-3794	104	7	=	=	SYM
ap-3794	104	8	5	5	NUM
ap-3794	104	9	,	,	PUNCT
ap-3794	104	10	then	then	ADV
ap-3794	104	11	itĩ	itĩ	PROPN
ap-3794	104	12	=	=	PROPN
ap-3794	104	13	iti	iti	PROPN
ap-3794	104	14	.	.	PUNCT
ap-3794	105	1	for	for	ADP
ap-3794	105	2	an	an	DET
ap-3794	105	3	interval	interval	NOUN
ap-3794	105	4	k	k	PROPN
ap-3794	106	1	=	=	PUNCT
ap-3794	107	1	[	[	X
ap-3794	107	2	c	c	X
ap-3794	107	3	,	,	PUNCT
ap-3794	107	4	d	d	NOUN
ap-3794	107	5	)	)	PUNCT
ap-3794	107	6	⊂	⊂	PROPN
ap-3794	108	1	[	[	X
ap-3794	108	2	0	0	NUM
ap-3794	108	3	,	,	PUNCT
ap-3794	108	4	1	1	NUM
ap-3794	108	5	)	)	PUNCT
ap-3794	108	6	denote	denote	NOUN
ap-3794	108	7	k	k	NOUN
ap-3794	109	1	=	=	PUNCT
ap-3794	110	1	[	[	X
ap-3794	110	2	1−	1−	NUM
ap-3794	110	3	d	d	PROPN
ap-3794	110	4	,	,	PUNCT
ap-3794	110	5	1−	1−	NUM
ap-3794	110	6	c	c	NOUN
ap-3794	110	7	)	)	PUNCT
ap-3794	110	8	.	.	PUNCT
ap-3794	111	1	then	then	ADV
ap-3794	111	2	t	t	PROPN
ap-3794	111	3	(	(	PUNCT
ap-3794	111	4	jx	jx	PROPN
ap-3794	111	5	)	)	PUNCT
ap-3794	111	6	=	=	SYM
ap-3794	111	7	jx	jx	PROPN
ap-3794	111	8	for	for	ADP
ap-3794	111	9	any	any	DET
ap-3794	111	10	letter	letter	NOUN
ap-3794	111	11	x	x	X
ap-3794	111	12	∈	∈	PROPN
ap-3794	111	13	{	{	PUNCT
ap-3794	111	14	a	a	PRON
ap-3794	111	15	,	,	PUNCT
ap-3794	111	16	b	b	NOUN
ap-3794	111	17	,	,	PUNCT
ap-3794	111	18	c	c	NOUN
ap-3794	111	19	}	}	PUNCT
ap-3794	111	20	.	.	PUNCT
ap-3794	112	1	(	(	PUNCT
ap-3794	112	2	3	3	X
ap-3794	112	3	)	)	PUNCT
ap-3794	112	4	463	463	NUM
ap-3794	112	5	z.	z.	PROPN
ap-3794	112	6	masáková	masáková	PROPN
ap-3794	112	7	,	,	PUNCT
ap-3794	112	8	e.	e.	PROPN
ap-3794	112	9	pelantová	pelantová	PROPN
ap-3794	112	10	,	,	PUNCT
ap-3794	112	11	š	š	PROPN
ap-3794	112	12	.	.	PROPN
ap-3794	112	13	starosta	starosta	PROPN
ap-3794	112	14	acta	acta	PROPN
ap-3794	112	15	polytechnica	polytechnica	PROPN
ap-3794	112	16	proposition	proposition	NOUN
ap-3794	112	17	3.5	3.5	NUM
ap-3794	112	18	.	.	PUNCT
ap-3794	113	1	let	let	VERB
ap-3794	113	2	t	t	NOUN
ap-3794	113	3	:	:	PUNCT
ap-3794	114	1	[	[	X
ap-3794	114	2	0	0	NUM
ap-3794	114	3	,	,	PUNCT
ap-3794	114	4	1	1	NUM
ap-3794	114	5	)	)	PUNCT
ap-3794	114	6	→	→	PUNCT
ap-3794	114	7	[	[	X
ap-3794	114	8	0	0	NUM
ap-3794	114	9	,	,	PUNCT
ap-3794	114	10	1	1	NUM
ap-3794	114	11	)	)	PUNCT
ap-3794	114	12	be	be	AUX
ap-3794	114	13	a	a	DET
ap-3794	114	14	3iet	3iet	PROPN
ap-3794	114	15	with	with	ADP
ap-3794	114	16	permutation	permutation	NOUN
ap-3794	114	17	(	(	PUNCT
ap-3794	114	18	321	321	NUM
ap-3794	114	19	)	)	PUNCT
ap-3794	114	20	satisfying	satisfy	VERB
ap-3794	114	21	the	the	DET
ap-3794	114	22	minimality	minimality	NOUN
ap-3794	114	23	condition	condition	NOUN
ap-3794	114	24	.	.	PUNCT
ap-3794	115	1	let	let	VERB
ap-3794	116	1	i	i	PRON
ap-3794	116	2	⊂	⊂	PROPN
ap-3794	117	1	[	[	X
ap-3794	117	2	0	0	NUM
ap-3794	117	3	,	,	PUNCT
ap-3794	117	4	1	1	NUM
ap-3794	117	5	)	)	PUNCT
ap-3794	117	6	and	and	CCONJ
ap-3794	117	7	let	let	VERB
ap-3794	117	8	r1	r1	PROPN
ap-3794	117	9	,	,	PUNCT
ap-3794	117	10	.	.	PUNCT
ap-3794	117	11	.	.	PUNCT
ap-3794	118	1	.	.	PUNCT
ap-3794	119	1	,	,	PUNCT
ap-3794	119	2	rm	rm	PROPN
ap-3794	119	3	be	be	AUX
ap-3794	119	4	the	the	DET
ap-3794	119	5	iitineraries	iitinerarie	NOUN
ap-3794	119	6	.	.	PUNCT
ap-3794	120	1	the	the	DET
ap-3794	120	2	i	i	PROPN
ap-3794	120	3	-	-	PUNCT
ap-3794	120	4	itineraries	itinerary	NOUN
ap-3794	120	5	are	be	AUX
ap-3794	120	6	the	the	DET
ap-3794	120	7	mirror	mirror	NOUN
ap-3794	120	8	images	image	NOUN
ap-3794	120	9	of	of	ADP
ap-3794	120	10	the	the	DET
ap-3794	120	11	i	i	NOUN
ap-3794	120	12	-	-	PUNCT
ap-3794	120	13	itineraries	itinerary	NOUN
ap-3794	120	14	,	,	PUNCT
ap-3794	120	15	namely	namely	ADV
ap-3794	120	16	r1	r1	NOUN
ap-3794	120	17	,	,	PUNCT
ap-3794	120	18	.	.	PUNCT
ap-3794	120	19	.	.	PUNCT
ap-3794	121	1	.	.	PUNCT
ap-3794	122	1	,	,	PUNCT
ap-3794	122	2	rm	rm	PROPN
ap-3794	122	3	.	.	PUNCT
ap-3794	123	1	moreover	moreover	ADV
ap-3794	123	2	,	,	PUNCT
ap-3794	123	3	if	if	SCONJ
ap-3794	123	4	[	[	X
ap-3794	123	5	γj	γj	NOUN
ap-3794	123	6	,	,	PUNCT
ap-3794	123	7	δj	δj	NOUN
ap-3794	123	8	)	)	PUNCT
ap-3794	123	9	:	:	PUNCT
ap-3794	124	1	=	=	SYM
ap-3794	124	2	{	{	PUNCT
ap-3794	124	3	x	x	SYM
ap-3794	124	4	∈	∈	PROPN
ap-3794	124	5	i	i	PRON
ap-3794	124	6	:	:	PUNCT
ap-3794	124	7	ri(x	ri(x	NUM
ap-3794	124	8	)	)	PUNCT
ap-3794	124	9	=	=	SYM
ap-3794	124	10	rj	rj	PROPN
ap-3794	124	11	}	}	PUNCT
ap-3794	124	12	and	and	CCONJ
ap-3794	124	13	[	[	X
ap-3794	124	14	γ′j	γ′j	PROPN
ap-3794	124	15	,	,	PUNCT
ap-3794	124	16	δ′j	δ′j	PROPN
ap-3794	124	17	)	)	PUNCT
ap-3794	124	18	:	:	PUNCT
ap-3794	124	19	=	=	SYM
ap-3794	124	20	ti	ti	X
ap-3794	124	21	(	(	PUNCT
ap-3794	124	22	[	[	X
ap-3794	124	23	γj	γj	NOUN
ap-3794	124	24	,	,	PUNCT
ap-3794	124	25	δj	δj	ADJ
ap-3794	124	26	)	)	PUNCT
ap-3794	124	27	)	)	PUNCT
ap-3794	124	28	,	,	PUNCT
ap-3794	124	29	for	for	ADP
ap-3794	124	30	j	j	PROPN
ap-3794	124	31	=	=	SYM
ap-3794	124	32	1	1	PROPN
ap-3794	124	33	,	,	PUNCT
ap-3794	124	34	.	.	PUNCT
ap-3794	124	35	.	.	PUNCT
ap-3794	124	36	.	.	PUNCT
ap-3794	125	1	,	,	PUNCT
ap-3794	125	2	m	m	PROPN
ap-3794	125	3	,	,	PUNCT
ap-3794	125	4	then	then	ADV
ap-3794	125	5	{	{	PUNCT
ap-3794	125	6	x	x	SYM
ap-3794	125	7	∈	∈	PROPN
ap-3794	125	8	i	i	PRON
ap-3794	125	9	:	:	PUNCT
ap-3794	125	10	ri(x	ri(x	NUM
ap-3794	125	11	)	)	PUNCT
ap-3794	126	1	=	=	SYM
ap-3794	126	2	rj	rj	PROPN
ap-3794	126	3	}	}	PUNCT
ap-3794	126	4	=	=	PUNCT
ap-3794	127	1	[	[	X
ap-3794	127	2	1−	1−	NUM
ap-3794	127	3	δ′j	δ′j	PROPN
ap-3794	127	4	,	,	PUNCT
ap-3794	127	5	1−	1−	NUM
ap-3794	127	6	γ′j	γ′j	NUM
ap-3794	127	7	)	)	PUNCT
ap-3794	127	8	.	.	PUNCT
ap-3794	128	1	convention	convention	NOUN
ap-3794	128	2	:	:	PUNCT
ap-3794	128	3	for	for	ADP
ap-3794	128	4	the	the	DET
ap-3794	128	5	rest	rest	NOUN
ap-3794	128	6	of	of	ADP
ap-3794	128	7	the	the	DET
ap-3794	128	8	article	article	NOUN
ap-3794	128	9	,	,	PUNCT
ap-3794	128	10	let	let	VERB
ap-3794	128	11	t	t	PROPN
ap-3794	128	12	be	be	AUX
ap-3794	128	13	a	a	DET
ap-3794	128	14	non	non	ADJ
ap-3794	128	15	-	-	ADJ
ap-3794	128	16	degenerate	degenerate	ADJ
ap-3794	128	17	exchange	exchange	NOUN
ap-3794	128	18	of	of	ADP
ap-3794	128	19	three	three	NUM
ap-3794	128	20	intervals	interval	NOUN
ap-3794	128	21	with	with	ADP
ap-3794	128	22	permutation	permutation	NOUN
ap-3794	128	23	(	(	PUNCT
ap-3794	128	24	321	321	NUM
ap-3794	128	25	)	)	PUNCT
ap-3794	128	26	given	give	VERB
ap-3794	128	27	by	by	ADP
ap-3794	128	28	(	(	PUNCT
ap-3794	128	29	1	1	NUM
ap-3794	128	30	)	)	PUNCT
ap-3794	128	31	.	.	PUNCT
ap-3794	129	1	4	4	X
ap-3794	129	2	.	.	X
ap-3794	129	3	return	return	VERB
ap-3794	129	4	time	time	NOUN
ap-3794	129	5	in	in	ADP
ap-3794	129	6	a	a	DET
ap-3794	129	7	3iet	3iet	NUM
ap-3794	129	8	the	the	DET
ap-3794	129	9	aim	aim	NOUN
ap-3794	129	10	of	of	ADP
ap-3794	129	11	this	this	DET
ap-3794	129	12	section	section	NOUN
ap-3794	129	13	is	be	AUX
ap-3794	129	14	to	to	PART
ap-3794	129	15	describe	describe	VERB
ap-3794	129	16	the	the	DET
ap-3794	129	17	possible	possible	ADJ
ap-3794	129	18	return	return	NOUN
ap-3794	129	19	times	time	NOUN
ap-3794	129	20	of	of	ADP
ap-3794	129	21	a	a	DET
ap-3794	129	22	non	non	ADJ
ap-3794	129	23	-	-	ADJ
ap-3794	129	24	degenerate	degenerate	ADJ
ap-3794	129	25	3iet	3iet	PROPN
ap-3794	129	26	t	t	NOUN
ap-3794	129	27	to	to	ADP
ap-3794	129	28	a	a	DET
ap-3794	129	29	general	general	ADJ
ap-3794	129	30	subinterval	subinterval	NOUN
ap-3794	130	1	i	i	PRON
ap-3794	130	2	⊂	⊂	PROPN
ap-3794	131	1	[	[	X
ap-3794	131	2	0	0	NUM
ap-3794	131	3	,	,	PUNCT
ap-3794	131	4	1	1	NUM
ap-3794	131	5	)	)	PUNCT
ap-3794	131	6	.	.	PUNCT
ap-3794	132	1	our	our	PRON
ap-3794	132	2	aim	aim	NOUN
ap-3794	132	3	is	be	AUX
ap-3794	132	4	to	to	PART
ap-3794	132	5	prove	prove	VERB
ap-3794	132	6	the	the	DET
ap-3794	132	7	following	follow	VERB
ap-3794	132	8	theorem	theorem	VERB
ap-3794	132	9	.	.	PUNCT
ap-3794	132	10	theorem	theorem	VERB
ap-3794	132	11	4.1	4.1	NUM
ap-3794	132	12	.	.	PUNCT
ap-3794	133	1	let	let	VERB
ap-3794	133	2	t	t	PROPN
ap-3794	133	3	be	be	AUX
ap-3794	133	4	a	a	DET
ap-3794	133	5	non	non	ADJ
ap-3794	133	6	-	-	ADJ
ap-3794	133	7	degenerate	degenerate	ADJ
ap-3794	133	8	3iet	3iet	NOUN
ap-3794	133	9	and	and	CCONJ
ap-3794	133	10	let	let	VERB
ap-3794	133	11	i	i	PRON
ap-3794	133	12	⊂	⊂	PROPN
ap-3794	134	1	[	[	X
ap-3794	134	2	0	0	NUM
ap-3794	134	3	,	,	PUNCT
ap-3794	134	4	1	1	NUM
ap-3794	134	5	)	)	PUNCT
ap-3794	134	6	.	.	PUNCT
ap-3794	135	1	there	there	PRON
ap-3794	135	2	exist	exist	VERB
ap-3794	135	3	positive	positive	ADJ
ap-3794	135	4	integers	integer	NOUN
ap-3794	135	5	r1	r1	PROPN
ap-3794	135	6	,	,	PUNCT
ap-3794	135	7	r2	r2	NOUN
ap-3794	135	8	such	such	ADJ
ap-3794	135	9	that	that	SCONJ
ap-3794	135	10	the	the	DET
ap-3794	135	11	return	return	NOUN
ap-3794	135	12	time	time	NOUN
ap-3794	135	13	of	of	ADP
ap-3794	135	14	any	any	DET
ap-3794	135	15	x	x	SYM
ap-3794	135	16	∈	∈	NOUN
ap-3794	135	17	i	i	PRON
ap-3794	135	18	takes	take	VERB
ap-3794	135	19	value	value	NOUN
ap-3794	135	20	in	in	ADP
ap-3794	135	21	the	the	DET
ap-3794	135	22	set	set	NOUN
ap-3794	135	23	{	{	PUNCT
ap-3794	135	24	r1	r1	PROPN
ap-3794	135	25	,	,	PUNCT
ap-3794	135	26	r1	r1	PROPN
ap-3794	135	27	+1	+1	PROPN
ap-3794	135	28	,	,	PUNCT
ap-3794	135	29	r2	r2	PROPN
ap-3794	135	30	,	,	PUNCT
ap-3794	135	31	r1	r1	NOUN
ap-3794	135	32	+	+	SYM
ap-3794	135	33	r2	r2	PROPN
ap-3794	135	34	,	,	PUNCT
ap-3794	135	35	r1	r1	PROPN
ap-3794	135	36	+	+	PROPN
ap-3794	135	37	r2	r2	PROPN
ap-3794	135	38	+1	+1	PROPN
ap-3794	135	39	}	}	PUNCT
ap-3794	135	40	or	or	CCONJ
ap-3794	135	41	{	{	PUNCT
ap-3794	135	42	r1	r1	PROPN
ap-3794	135	43	,	,	PUNCT
ap-3794	135	44	r1	r1	PROPN
ap-3794	135	45	+1	+1	PROPN
ap-3794	135	46	,	,	PUNCT
ap-3794	135	47	r2	r2	PROPN
ap-3794	135	48	,	,	PUNCT
ap-3794	135	49	r2	r2	PROPN
ap-3794	135	50	+	+	CCONJ
ap-3794	135	51	1	1	NUM
ap-3794	135	52	,	,	PUNCT
ap-3794	135	53	r1	r1	NOUN
ap-3794	135	54	+	+	CCONJ
ap-3794	135	55	r2	r2	PROPN
ap-3794	135	56	+	+	CCONJ
ap-3794	135	57	1	1	NUM
ap-3794	135	58	}	}	PUNCT
ap-3794	135	59	.	.	PUNCT
ap-3794	136	1	first	first	ADV
ap-3794	136	2	,	,	PUNCT
ap-3794	136	3	we	we	PRON
ap-3794	136	4	will	will	AUX
ap-3794	136	5	formulate	formulate	VERB
ap-3794	136	6	an	an	DET
ap-3794	136	7	important	important	ADJ
ap-3794	136	8	lemma	lemma	NOUN
ap-3794	136	9	,	,	PUNCT
ap-3794	136	10	which	which	PRON
ap-3794	136	11	needs	need	VERB
ap-3794	136	12	the	the	DET
ap-3794	136	13	following	follow	VERB
ap-3794	136	14	notation	notation	NOUN
ap-3794	136	15	.	.	PUNCT
ap-3794	137	1	given	give	VERB
ap-3794	137	2	letters	letter	NOUN
ap-3794	137	3	x	x	SYM
ap-3794	137	4	,	,	PUNCT
ap-3794	137	5	y	y	PROPN
ap-3794	137	6	,	,	PUNCT
ap-3794	137	7	z	z	PROPN
ap-3794	137	8	∈	∈	PROPN
ap-3794	137	9	{	{	PUNCT
ap-3794	137	10	a	a	DET
ap-3794	137	11	,	,	PUNCT
ap-3794	137	12	b	b	NOUN
ap-3794	137	13	,	,	PUNCT
ap-3794	137	14	c	c	NOUN
ap-3794	137	15	}	}	PUNCT
ap-3794	137	16	and	and	CCONJ
ap-3794	137	17	a	a	DET
ap-3794	137	18	finite	finite	ADJ
ap-3794	137	19	word	word	NOUN
ap-3794	137	20	w	w	PROPN
ap-3794	137	21	∈	∈	PROPN
ap-3794	137	22	{	{	PUNCT
ap-3794	137	23	a	a	DET
ap-3794	137	24	,	,	PUNCT
ap-3794	137	25	b	b	NOUN
ap-3794	137	26	,	,	PUNCT
ap-3794	137	27	c}∗	c}∗	NOUN
ap-3794	137	28	,	,	PUNCT
ap-3794	137	29	let	let	VERB
ap-3794	137	30	ωxy→z(w	ωxy→z(w	NOUN
ap-3794	137	31	)	)	PUNCT
ap-3794	137	32	be	be	AUX
ap-3794	137	33	the	the	DET
ap-3794	137	34	set	set	NOUN
ap-3794	137	35	of	of	ADP
ap-3794	137	36	words	word	NOUN
ap-3794	137	37	obtained	obtain	VERB
ap-3794	137	38	from	from	ADP
ap-3794	137	39	w	w	PROPN
ap-3794	137	40	replacing	replace	VERB
ap-3794	137	41	one	one	NUM
ap-3794	137	42	factor	factor	NOUN
ap-3794	137	43	xy	xy	NOUN
ap-3794	137	44	by	by	ADP
ap-3794	137	45	the	the	DET
ap-3794	137	46	letter	letter	NOUN
ap-3794	137	47	z	z	PROPN
ap-3794	137	48	,	,	PUNCT
ap-3794	137	49	i.e.	i.e.	X
ap-3794	137	50	,	,	PUNCT
ap-3794	137	51	ωxy→z(w	ωxy→z(w	NOUN
ap-3794	137	52	)	)	PUNCT
ap-3794	137	53	=	=	SYM
ap-3794	137	54	{	{	PUNCT
ap-3794	137	55	w1zw2	w1zw2	NOUN
ap-3794	137	56	:	:	PUNCT
ap-3794	137	57	w	w	X
ap-3794	137	58	=	=	SYM
ap-3794	137	59	w1xy	w1xy	NOUN
ap-3794	137	60	w2	w2	NOUN
ap-3794	137	61	}	}	PUNCT
ap-3794	137	62	.	.	PUNCT
ap-3794	138	1	(	(	PUNCT
ap-3794	138	2	4	4	X
ap-3794	138	3	)	)	PUNCT
ap-3794	138	4	similarly	similarly	ADV
ap-3794	138	5	,	,	PUNCT
ap-3794	138	6	ωz→xy	ωz→xy	PROPN
ap-3794	138	7	(	(	PUNCT
ap-3794	138	8	w	w	NOUN
ap-3794	138	9	)	)	PUNCT
ap-3794	138	10	=	=	SYM
ap-3794	138	11	{	{	PUNCT
ap-3794	138	12	w1xy	w1xy	PROPN
ap-3794	138	13	w2	w2	NOUN
ap-3794	138	14	:	:	PUNCT
ap-3794	138	15	w	w	PROPN
ap-3794	138	16	=	=	SYM
ap-3794	138	17	w1zw2	w1zw2	PROPN
ap-3794	138	18	}	}	PUNCT
ap-3794	138	19	.	.	PUNCT
ap-3794	139	1	(	(	PUNCT
ap-3794	139	2	5	5	X
ap-3794	139	3	)	)	PUNCT
ap-3794	139	4	clearly	clearly	ADV
ap-3794	139	5	,	,	PUNCT
ap-3794	139	6	v	v	PROPN
ap-3794	139	7	∈	∈	PROPN
ap-3794	139	8	ωxy→z(w	ωxy→z(w	NOUN
ap-3794	139	9	)	)	PUNCT
ap-3794	139	10	⇔	⇔	PROPN
ap-3794	139	11	w	w	PROPN
ap-3794	139	12	∈	∈	PROPN
ap-3794	139	13	ωz→xy	ωz→xy	PROPN
ap-3794	139	14	(	(	PUNCT
ap-3794	139	15	v	v	NOUN
ap-3794	139	16	)	)	PUNCT
ap-3794	139	17	.	.	PUNCT
ap-3794	140	1	(	(	PUNCT
ap-3794	140	2	6	6	NUM
ap-3794	140	3	)	)	PUNCT
ap-3794	140	4	by	by	ADP
ap-3794	140	5	abuse	abuse	NOUN
ap-3794	140	6	of	of	ADP
ap-3794	140	7	notation	notation	NOUN
ap-3794	140	8	,	,	PUNCT
ap-3794	140	9	we	we	PRON
ap-3794	140	10	write	write	VERB
ap-3794	140	11	v	v	NOUN
ap-3794	140	12	=	=	SYM
ap-3794	140	13	ωxy→z(w	ωxy→z(w	NOUN
ap-3794	140	14	)	)	PUNCT
ap-3794	140	15	instead	instead	ADV
ap-3794	140	16	of	of	ADP
ap-3794	140	17	v	v	NUM
ap-3794	140	18	∈	∈	PROPN
ap-3794	140	19	ωxy→z(w	ωxy→z(w	NOUN
ap-3794	140	20	)	)	PUNCT
ap-3794	140	21	.	.	PUNCT
ap-3794	141	1	lemma	lemma	PROPN
ap-3794	141	2	4.2	4.2	NUM
ap-3794	141	3	.	.	PUNCT
ap-3794	141	4	assume	assume	VERB
ap-3794	141	5	that	that	SCONJ
ap-3794	141	6	the	the	DET
ap-3794	141	7	orbits	orbit	NOUN
ap-3794	141	8	of	of	ADP
ap-3794	141	9	points	point	NOUN
ap-3794	141	10	α	α	PROPN
ap-3794	141	11	,	,	PUNCT
ap-3794	141	12	β	β	X
ap-3794	141	13	,	,	PUNCT
ap-3794	141	14	γ	γ	PROPN
ap-3794	141	15	and	and	CCONJ
ap-3794	141	16	δ	δ	PROPN
ap-3794	141	17	are	be	AUX
ap-3794	141	18	mutually	mutually	ADV
ap-3794	141	19	disjoint	disjoint	ADJ
ap-3794	141	20	.	.	PUNCT
ap-3794	142	1	for	for	ADP
ap-3794	142	2	sufficiently	sufficiently	ADV
ap-3794	142	3	small	small	ADJ
ap-3794	142	4	ε	ε	PROPN
ap-3794	142	5	>	>	X
ap-3794	142	6	0	0	PROPN
ap-3794	142	7	,	,	PUNCT
ap-3794	142	8	we	we	PRON
ap-3794	142	9	have	have	VERB
ap-3794	142	10	the	the	DET
ap-3794	142	11	following	follow	VERB
ap-3794	142	12	relations	relation	NOUN
ap-3794	142	13	between	between	ADP
ap-3794	142	14	iitineraries	iitinerarie	NOUN
ap-3794	142	15	of	of	ADP
ap-3794	142	16	points	point	NOUN
ap-3794	142	17	in	in	ADP
ap-3794	142	18	i	i	PRON
ap-3794	142	19	:	:	PUNCT
ap-3794	142	20	(	(	PUNCT
ap-3794	142	21	a	a	X
ap-3794	142	22	)	)	PUNCT
ap-3794	142	23	r(a−	r(a−	PROPN
ap-3794	142	24	ε	ε	PROPN
ap-3794	142	25	)	)	PUNCT
ap-3794	142	26	=	=	SYM
ap-3794	143	1	ωb→ac	ωb→ac	ADJ
ap-3794	143	2	(	(	PUNCT
ap-3794	143	3	r(a	r(a	PROPN
ap-3794	143	4	+	+	CCONJ
ap-3794	143	5	ε	ε	PROPN
ap-3794	143	6	)	)	PUNCT
ap-3794	143	7	)	)	PUNCT
ap-3794	143	8	,	,	PUNCT
ap-3794	144	1	(	(	PUNCT
ap-3794	144	2	b	b	X
ap-3794	144	3	)	)	PUNCT
ap-3794	144	4	r(a	r(a	VERB
ap-3794	144	5	+	+	CCONJ
ap-3794	144	6	ε	ε	PROPN
ap-3794	144	7	)	)	PUNCT
ap-3794	144	8	=	=	SYM
ap-3794	145	1	ωac→b	ωac→b	NOUN
ap-3794	145	2	(	(	PUNCT
ap-3794	145	3	r(a−	r(a−	PROPN
ap-3794	145	4	ε	ε	PROPN
ap-3794	145	5	)	)	PUNCT
ap-3794	145	6	)	)	PUNCT
ap-3794	145	7	,	,	PUNCT
ap-3794	145	8	(	(	PUNCT
ap-3794	145	9	c	c	X
ap-3794	145	10	)	)	PUNCT
ap-3794	145	11	r(b−	r(b−	NOUN
ap-3794	145	12	ε	ε	PROPN
ap-3794	145	13	)	)	PUNCT
ap-3794	145	14	=	=	PUNCT
ap-3794	145	15	ωca→b	ωca→b	NUM
ap-3794	145	16	(	(	PUNCT
ap-3794	145	17	r(b	r(b	PROPN
ap-3794	145	18	+	+	CCONJ
ap-3794	145	19	ε	ε	PROPN
ap-3794	145	20	)	)	PUNCT
ap-3794	145	21	)	)	PUNCT
ap-3794	145	22	,	,	PUNCT
ap-3794	145	23	(	(	PUNCT
ap-3794	145	24	d	d	X
ap-3794	145	25	)	)	PUNCT
ap-3794	145	26	r(b	r(b	PROPN
ap-3794	145	27	+	+	CCONJ
ap-3794	145	28	ε	ε	PROPN
ap-3794	145	29	)	)	PUNCT
ap-3794	145	30	=	=	NOUN
ap-3794	145	31	ωb→ca	ωb→ca	NOUN
ap-3794	145	32	(	(	PUNCT
ap-3794	145	33	r(b−	r(b−	PROPN
ap-3794	145	34	ε	ε	PROPN
ap-3794	145	35	)	)	PUNCT
ap-3794	145	36	)	)	PUNCT
ap-3794	145	37	,	,	PUNCT
ap-3794	145	38	(	(	PUNCT
ap-3794	145	39	e	e	NOUN
ap-3794	145	40	)	)	PUNCT
ap-3794	145	41	r(d	r(d	PROPN
ap-3794	145	42	+	+	CCONJ
ap-3794	145	43	ε	ε	PROPN
ap-3794	145	44	)	)	PUNCT
ap-3794	145	45	=	=	SYM
ap-3794	146	1	r(d−	r(d−	NOUN
ap-3794	146	2	ε)r(δ	ε)r(δ	ADV
ap-3794	146	3	−	−	PROPN
ap-3794	146	4	ε	ε	PROPN
ap-3794	146	5	)	)	PUNCT
ap-3794	146	6	,	,	PUNCT
ap-3794	146	7	(	(	PUNCT
ap-3794	146	8	f	f	X
ap-3794	146	9	)	)	PUNCT
ap-3794	146	10	r(c−	r(c−	PROPN
ap-3794	146	11	ε	ε	PROPN
ap-3794	146	12	)	)	PUNCT
ap-3794	146	13	=	=	PUNCT
ap-3794	147	1	r(c	r(c	ADJ
ap-3794	147	2	+	+	CCONJ
ap-3794	147	3	ε)r(γ	ε)r(γ	VERB
ap-3794	147	4	+	+	CCONJ
ap-3794	147	5	ε	ε	PROPN
ap-3794	147	6	)	)	PUNCT
ap-3794	147	7	,	,	PUNCT
ap-3794	147	8	where	where	SCONJ
ap-3794	147	9	a	a	DET
ap-3794	147	10	,	,	PUNCT
ap-3794	147	11	b	b	NOUN
ap-3794	147	12	,	,	PUNCT
ap-3794	147	13	c	c	X
ap-3794	147	14	,	,	PUNCT
ap-3794	147	15	d	d	PROPN
ap-3794	147	16	are	be	AUX
ap-3794	147	17	given	give	VERB
ap-3794	147	18	in	in	ADP
ap-3794	147	19	lemma	lemma	PROPN
ap-3794	147	20	3.2	3.2	NUM
ap-3794	147	21	.	.	PUNCT
ap-3794	147	22	proof	proof	NOUN
ap-3794	147	23	.	.	PUNCT
ap-3794	148	1	we	we	PRON
ap-3794	148	2	will	will	AUX
ap-3794	148	3	first	first	ADV
ap-3794	148	4	demonstrate	demonstrate	VERB
ap-3794	148	5	the	the	DET
ap-3794	148	6	proof	proof	NOUN
ap-3794	148	7	of	of	ADP
ap-3794	148	8	the	the	DET
ap-3794	148	9	case	case	NOUN
ap-3794	148	10	(	(	PUNCT
ap-3794	148	11	a	a	NOUN
ap-3794	148	12	)	)	PUNCT
ap-3794	148	13	.	.	PUNCT
ap-3794	149	1	let	let	VERB
ap-3794	149	2	k	k	NOUN
ap-3794	150	1	=	=	PUNCT
ap-3794	151	1	[	[	X
ap-3794	151	2	a	a	DET
ap-3794	151	3	−	−	PROPN
ap-3794	151	4	ε	ε	PROPN
ap-3794	151	5	,	,	PUNCT
ap-3794	151	6	a	a	PRON
ap-3794	151	7	+	+	X
ap-3794	151	8	ε	ε	X
ap-3794	151	9	]	]	PUNCT
ap-3794	151	10	with	with	ADP
ap-3794	151	11	ε	ε	PROPN
ap-3794	151	12	chosen	choose	VERB
ap-3794	151	13	such	such	ADJ
ap-3794	151	14	that	that	SCONJ
ap-3794	151	15	k	k	PROPN
ap-3794	151	16	⊂	⊂	PROPN
ap-3794	152	1	i	i	PROPN
ap-3794	152	2	and	and	CCONJ
ap-3794	152	3	α	α	PRON
ap-3794	152	4	,	,	PUNCT
ap-3794	152	5	β	β	X
ap-3794	152	6	,	,	PUNCT
ap-3794	152	7	γ	γ	PROPN
ap-3794	152	8	,	,	PUNCT
ap-3794	152	9	δ	δ	PROPN
ap-3794	152	10	6∈	6∈	PROPN
ap-3794	152	11	t	t	PROPN
ap-3794	152	12	i(k	i(k	PROPN
ap-3794	152	13	)	)	PUNCT
ap-3794	152	14	for	for	ADP
ap-3794	152	15	all	all	PRON
ap-3794	152	16	0	0	NUM
ap-3794	152	17	≤	≤	NUM
ap-3794	153	1	i	i	PRON
ap-3794	153	2	≤	≤	PUNCT
ap-3794	153	3	kα	kα	VERB
ap-3794	153	4	with	with	ADP
ap-3794	153	5	the	the	DET
ap-3794	153	6	only	only	ADJ
ap-3794	153	7	exception	exception	NOUN
ap-3794	153	8	of	of	ADP
ap-3794	153	9	t	t	PROPN
ap-3794	153	10	kα(a	kα(a	NOUN
ap-3794	153	11	)	)	PUNCT
ap-3794	153	12	=	=	SYM
ap-3794	154	1	α	α	X
ap-3794	154	2	.	.	PUNCT
ap-3794	155	1	(	(	PUNCT
ap-3794	155	2	7	7	NUM
ap-3794	155	3	)	)	PUNCT
ap-3794	155	4	for	for	ADP
ap-3794	155	5	simplicity	simplicity	NOUN
ap-3794	155	6	,	,	PUNCT
ap-3794	155	7	denote	denote	VERB
ap-3794	155	8	t	t	PROPN
ap-3794	155	9	=	=	SYM
ap-3794	155	10	max	max	PROPN
ap-3794	155	11	{	{	PUNCT
ap-3794	155	12	ri(x	ri(x	NUM
ap-3794	155	13	)	)	PUNCT
ap-3794	155	14	:	:	PUNCT
ap-3794	156	1	x	x	PUNCT
ap-3794	156	2	∈	∈	X
ap-3794	156	3	k	k	X
ap-3794	156	4	}	}	PUNCT
ap-3794	156	5	the	the	DET
ap-3794	156	6	maximal	maximal	ADJ
ap-3794	156	7	return	return	NOUN
ap-3794	156	8	time	time	NOUN
ap-3794	156	9	.	.	PUNCT
ap-3794	157	1	the	the	DET
ap-3794	157	2	existence	existence	NOUN
ap-3794	157	3	of	of	ADP
ap-3794	157	4	such	such	ADJ
ap-3794	157	5	ε	ε	PROPN
ap-3794	157	6	follows	follow	VERB
ap-3794	157	7	trivially	trivially	ADV
ap-3794	157	8	from	from	ADP
ap-3794	157	9	the	the	DET
ap-3794	157	10	definition	definition	NOUN
ap-3794	157	11	of	of	ADP
ap-3794	157	12	the	the	DET
ap-3794	157	13	interval	interval	NOUN
ap-3794	157	14	exchange	exchange	NOUN
ap-3794	157	15	transformation	transformation	NOUN
ap-3794	157	16	and	and	CCONJ
ap-3794	157	17	the	the	DET
ap-3794	157	18	assumptions	assumption	NOUN
ap-3794	157	19	of	of	ADP
ap-3794	157	20	the	the	DET
ap-3794	157	21	lemma	lemma	PROPN
ap-3794	157	22	.	.	PUNCT
ap-3794	158	1	let	let	VERB
ap-3794	158	2	k−	k−	PROPN
ap-3794	158	3	=	=	PUNCT
ap-3794	159	1	[	[	X
ap-3794	159	2	a−ε	a−ε	PROPN
ap-3794	159	3	,	,	PUNCT
ap-3794	159	4	a	a	PRON
ap-3794	159	5	)	)	PUNCT
ap-3794	159	6	and	and	CCONJ
ap-3794	159	7	k+	k+	X
ap-3794	160	1	=	=	PUNCT
ap-3794	161	1	[	[	X
ap-3794	161	2	a	a	X
ap-3794	161	3	,	,	PUNCT
ap-3794	161	4	a+ε	a+ε	PROPN
ap-3794	161	5	]	]	PUNCT
ap-3794	161	6	.	.	PUNCT
ap-3794	162	1	it	it	PRON
ap-3794	162	2	follows	follow	VERB
ap-3794	162	3	from	from	ADP
ap-3794	162	4	the	the	DET
ap-3794	162	5	definition	definition	NOUN
ap-3794	162	6	of	of	ADP
ap-3794	162	7	a	a	PRON
ap-3794	162	8	and	and	CCONJ
ap-3794	162	9	condition	condition	NOUN
ap-3794	162	10	(	(	PUNCT
ap-3794	162	11	7	7	NUM
ap-3794	162	12	)	)	PUNCT
ap-3794	163	1	that	that	SCONJ
ap-3794	163	2	for	for	ADP
ap-3794	163	3	all	all	PRON
ap-3794	163	4	i	i	PRON
ap-3794	163	5	such	such	ADJ
ap-3794	163	6	that	that	SCONJ
ap-3794	163	7	0	0	NUM
ap-3794	163	8	<	<	X
ap-3794	164	1	i	i	VERB
ap-3794	164	2	≤	≤	NUM
ap-3794	164	3	kα	kα	VERB
ap-3794	164	4	we	we	PRON
ap-3794	164	5	have	have	VERB
ap-3794	164	6	t	t	PROPN
ap-3794	164	7	i(k	i(k	PROPN
ap-3794	164	8	)	)	PUNCT
ap-3794	164	9	∩	∩	NOUN
ap-3794	165	1	i	i	PRON
ap-3794	165	2	=	=	PUNCT
ap-3794	165	3	∅.	∅.	VERB
ap-3794	165	4	moreover	moreover	ADV
ap-3794	165	5	,	,	PUNCT
ap-3794	165	6	condition	condition	NOUN
ap-3794	165	7	(	(	PUNCT
ap-3794	165	8	7	7	NUM
ap-3794	165	9	)	)	PUNCT
ap-3794	165	10	implies	imply	VERB
ap-3794	165	11	that	that	SCONJ
ap-3794	165	12	all	all	DET
ap-3794	165	13	such	such	ADJ
ap-3794	165	14	t	t	NOUN
ap-3794	165	15	i(k	i(k	PROPN
ap-3794	165	16	)	)	PUNCT
ap-3794	165	17	are	be	AUX
ap-3794	165	18	intervals	interval	NOUN
ap-3794	165	19	.	.	PUNCT
ap-3794	166	1	it	it	PRON
ap-3794	166	2	implies	imply	VERB
ap-3794	166	3	that	that	SCONJ
ap-3794	166	4	for	for	ADP
ap-3794	166	5	any	any	DET
ap-3794	166	6	x	x	NOUN
ap-3794	166	7	,	,	PUNCT
ap-3794	166	8	y	y	PROPN
ap-3794	166	9	∈	∈	PROPN
ap-3794	166	10	k	k	PROPN
ap-3794	166	11	,	,	PUNCT
ap-3794	166	12	the	the	DET
ap-3794	166	13	prefixes	prefix	NOUN
ap-3794	166	14	of	of	ADP
ap-3794	166	15	r(x	r(x	PROPN
ap-3794	166	16	)	)	PUNCT
ap-3794	166	17	and	and	CCONJ
ap-3794	166	18	r(y	r(y	VERB
ap-3794	166	19	)	)	PUNCT
ap-3794	166	20	of	of	ADP
ap-3794	166	21	length	length	NOUN
ap-3794	166	22	kα	kα	PROPN
ap-3794	167	1	+	+	CCONJ
ap-3794	167	2	1	1	NUM
ap-3794	167	3	are	be	AUX
ap-3794	167	4	the	the	DET
ap-3794	167	5	same	same	ADJ
ap-3794	167	6	.	.	PUNCT
ap-3794	168	1	denote	denote	VERB
ap-3794	168	2	this	this	DET
ap-3794	168	3	prefix	prefix	NOUN
ap-3794	168	4	by	by	ADP
ap-3794	168	5	w.	w.	PROPN
ap-3794	168	6	the	the	DET
ap-3794	168	7	definition	definition	NOUN
ap-3794	168	8	of	of	ADP
ap-3794	168	9	kα	kα	PROPN
ap-3794	168	10	implies	imply	VERB
ap-3794	168	11	that	that	SCONJ
ap-3794	168	12	α	α	PROPN
ap-3794	168	13	∈	∈	PROPN
ap-3794	168	14	t	t	NOUN
ap-3794	168	15	kα(k	kα(k	NOUN
ap-3794	168	16	)	)	PUNCT
ap-3794	168	17	.	.	PUNCT
ap-3794	169	1	since	since	SCONJ
ap-3794	169	2	t	t	PROPN
ap-3794	169	3	kα(k+	kα(k+	PROPN
ap-3794	169	4	)	)	PUNCT
ap-3794	170	1	=	=	PUNCT
ap-3794	171	1	[	[	X
ap-3794	171	2	α	α	X
ap-3794	171	3	,	,	PUNCT
ap-3794	171	4	α+	α+	X
ap-3794	171	5	ε	ε	X
ap-3794	171	6	]	]	X
ap-3794	171	7	⊂	⊂	PROPN
ap-3794	171	8	jb	jb	INTJ
ap-3794	171	9	,	,	PUNCT
ap-3794	171	10	we	we	PRON
ap-3794	171	11	obtain	obtain	VERB
ap-3794	171	12	t	t	NOUN
ap-3794	171	13	kα+1(k+	kα+1(k+	NOUN
ap-3794	171	14	)	)	PUNCT
ap-3794	172	1	=	=	PUNCT
ap-3794	172	2	[	[	PUNCT
ap-3794	172	3	t	t	X
ap-3794	172	4	(	(	PUNCT
ap-3794	172	5	α	α	NOUN
ap-3794	172	6	)	)	PUNCT
ap-3794	172	7	,	,	PUNCT
ap-3794	172	8	t	t	PROPN
ap-3794	172	9	(	(	PUNCT
ap-3794	172	10	α	α	NOUN
ap-3794	172	11	)	)	PUNCT
ap-3794	173	1	+	+	NUM
ap-3794	173	2	ε	ε	PROPN
ap-3794	173	3	)	)	PUNCT
ap-3794	173	4	.	.	PUNCT
ap-3794	174	1	furthermore	furthermore	ADV
ap-3794	174	2	,	,	PUNCT
ap-3794	174	3	since	since	SCONJ
ap-3794	174	4	t	t	PROPN
ap-3794	174	5	kα(k−	kα(k−	PROPN
ap-3794	174	6	)	)	PUNCT
ap-3794	174	7	=	=	PUNCT
ap-3794	175	1	[	[	X
ap-3794	175	2	α	α	X
ap-3794	175	3	−	−	PROPN
ap-3794	175	4	ε	ε	PROPN
ap-3794	175	5	,	,	PUNCT
ap-3794	175	6	α	α	X
ap-3794	175	7	)	)	PUNCT
ap-3794	175	8	⊂	⊂	PROPN
ap-3794	175	9	ja	ja	PROPN
ap-3794	175	10	,	,	PUNCT
ap-3794	175	11	we	we	PRON
ap-3794	175	12	obtain	obtain	VERB
ap-3794	175	13	t	t	PROPN
ap-3794	175	14	kα+1(k−	kα+1(k−	NOUN
ap-3794	175	15	)	)	PUNCT
ap-3794	176	1	=	=	PUNCT
ap-3794	177	1	[	[	X
ap-3794	177	2	1−	1−	NUM
ap-3794	177	3	ε	ε	PROPN
ap-3794	177	4	,	,	PUNCT
ap-3794	177	5	1	1	NUM
ap-3794	177	6	)	)	PUNCT
ap-3794	177	7	⊂	⊂	PROPN
ap-3794	177	8	jc	jc	PROPN
ap-3794	177	9	,	,	PUNCT
ap-3794	177	10	and	and	CCONJ
ap-3794	177	11	thus	thus	ADV
ap-3794	177	12	t	t	PROPN
ap-3794	177	13	kα+2(k−	kα+2(k−	NOUN
ap-3794	177	14	)	)	PUNCT
ap-3794	178	1	=	=	PUNCT
ap-3794	178	2	[	[	PUNCT
ap-3794	178	3	t	t	X
ap-3794	178	4	(	(	PUNCT
ap-3794	178	5	α)−	α)−	PROPN
ap-3794	178	6	ε	ε	PROPN
ap-3794	178	7	,	,	PUNCT
ap-3794	178	8	t	t	PROPN
ap-3794	178	9	(	(	PUNCT
ap-3794	178	10	α	α	NOUN
ap-3794	178	11	)	)	PUNCT
ap-3794	178	12	)	)	PUNCT
ap-3794	178	13	.	.	PUNCT
ap-3794	179	1	this	this	PRON
ap-3794	179	2	implies	imply	VERB
ap-3794	179	3	that	that	SCONJ
ap-3794	179	4	the	the	DET
ap-3794	179	5	set	set	NOUN
ap-3794	179	6	k	k	NOUN
ap-3794	179	7	′	′	NUM
ap-3794	179	8	=	=	SYM
ap-3794	179	9	t	t	PROPN
ap-3794	179	10	kα+2(k−	kα+2(k−	NOUN
ap-3794	179	11	)	)	PUNCT
ap-3794	179	12	∪	∪	ADP
ap-3794	179	13	t	t	NOUN
ap-3794	179	14	kα+1(k+	kα+1(k+	NOUN
ap-3794	179	15	)	)	PUNCT
ap-3794	179	16	=	=	PUNCT
ap-3794	180	1	[	[	X
ap-3794	180	2	t	t	X
ap-3794	180	3	(	(	PUNCT
ap-3794	180	4	α)−	α)−	PROPN
ap-3794	180	5	ε	ε	PROPN
ap-3794	180	6	,	,	PUNCT
ap-3794	180	7	t	t	PROPN
ap-3794	180	8	(	(	PUNCT
ap-3794	180	9	α	α	NOUN
ap-3794	180	10	)	)	PUNCT
ap-3794	180	11	+	+	CCONJ
ap-3794	181	1	ε	ε	X
ap-3794	181	2	]	]	X
ap-3794	181	3	is	be	AUX
ap-3794	181	4	an	an	DET
ap-3794	181	5	interval	interval	NOUN
ap-3794	181	6	.	.	PUNCT
ap-3794	182	1	as	as	ADP
ap-3794	182	2	above	above	ADV
ap-3794	182	3	,	,	PUNCT
ap-3794	182	4	condition	condition	NOUN
ap-3794	182	5	(	(	PUNCT
ap-3794	182	6	7	7	NUM
ap-3794	182	7	)	)	PUNCT
ap-3794	182	8	implies	imply	VERB
ap-3794	182	9	that	that	SCONJ
ap-3794	182	10	the	the	DET
ap-3794	182	11	set	set	NOUN
ap-3794	182	12	t	t	PROPN
ap-3794	182	13	i(k	i(k	PROPN
ap-3794	182	14	′	′	NOUN
ap-3794	182	15	)	)	PUNCT
ap-3794	182	16	is	be	AUX
ap-3794	182	17	an	an	DET
ap-3794	182	18	interval	interval	NOUN
ap-3794	182	19	for	for	ADP
ap-3794	182	20	all	all	PRON
ap-3794	182	21	i	i	PRON
ap-3794	182	22	such	such	ADJ
ap-3794	182	23	that	that	SCONJ
ap-3794	182	24	0	0	NUM
ap-3794	182	25	≤	≤	NUM
ap-3794	182	26	i	i	PRON
ap-3794	182	27	≤	≤	ADJ
ap-3794	182	28	t−kα−1	t−kα−1	ADJ
ap-3794	182	29	.	.	PUNCT
ap-3794	183	1	it	it	PRON
ap-3794	183	2	follows	follow	VERB
ap-3794	183	3	that	that	SCONJ
ap-3794	183	4	min	min	NOUN
ap-3794	183	5	{	{	PUNCT
ap-3794	183	6	i	i	PRON
ap-3794	183	7	:	:	PUNCT
ap-3794	183	8	t	t	PROPN
ap-3794	183	9	i(k	i(k	PROPN
ap-3794	183	10	′	′	NOUN
ap-3794	183	11	)	)	PUNCT
ap-3794	183	12	∩k	∩k	NOUN
ap-3794	183	13	6=	6=	NOUN
ap-3794	183	14	∅	∅	NOUN
ap-3794	183	15	}	}	PUNCT
ap-3794	183	16	=	=	PUNCT
ap-3794	183	17	t−	t−	PROPN
ap-3794	184	1	kα	kα	NOUN
ap-3794	184	2	−	−	PROPN
ap-3794	184	3	2	2	NUM
ap-3794	184	4	and	and	CCONJ
ap-3794	184	5	condition	condition	NOUN
ap-3794	184	6	(	(	PUNCT
ap-3794	184	7	7	7	X
ap-3794	184	8	)	)	PUNCT
ap-3794	184	9	moreover	moreover	ADV
ap-3794	184	10	implies	imply	VERB
ap-3794	184	11	that	that	SCONJ
ap-3794	184	12	t	t	PROPN
ap-3794	184	13	t−kα−2(k	t−kα−2(k	PROPN
ap-3794	184	14	′	′	NUM
ap-3794	184	15	)	)	PUNCT
ap-3794	185	1	⊂	⊂	PROPN
ap-3794	185	2	k.	k.	PROPN
ap-3794	186	1	thus	thus	ADV
ap-3794	186	2	,	,	PUNCT
ap-3794	186	3	the	the	DET
ap-3794	186	4	iterations	iteration	NOUN
ap-3794	186	5	x	x	NOUN
ap-3794	186	6	,	,	PUNCT
ap-3794	186	7	t	t	PROPN
ap-3794	186	8	(	(	PUNCT
ap-3794	186	9	x	x	NOUN
ap-3794	186	10	)	)	PUNCT
ap-3794	186	11	,	,	PUNCT
ap-3794	186	12	.	.	PUNCT
ap-3794	186	13	.	.	PUNCT
ap-3794	186	14	.	.	PUNCT
ap-3794	187	1	,	,	PUNCT
ap-3794	187	2	t	t	PROPN
ap-3794	187	3	t−kα−2(x	t−kα−2(x	NOUN
ap-3794	187	4	)	)	PUNCT
ap-3794	187	5	of	of	ADP
ap-3794	187	6	every	every	DET
ap-3794	187	7	x	x	SYM
ap-3794	187	8	∈	∈	PROPN
ap-3794	187	9	k	k	NOUN
ap-3794	187	10	′	′	NOUN
ap-3794	187	11	are	be	AUX
ap-3794	187	12	coded	code	VERB
ap-3794	187	13	by	by	ADP
ap-3794	187	14	the	the	DET
ap-3794	187	15	same	same	ADJ
ap-3794	187	16	word	word	NOUN
ap-3794	187	17	,	,	PUNCT
ap-3794	187	18	say	say	VERB
ap-3794	187	19	v.	v.	SCONJ
ap-3794	187	20	the	the	DET
ap-3794	187	21	whole	whole	ADJ
ap-3794	187	22	situation	situation	NOUN
ap-3794	187	23	is	be	AUX
ap-3794	187	24	depicted	depict	VERB
ap-3794	187	25	in	in	ADP
ap-3794	187	26	figure	figure	NOUN
ap-3794	187	27	1	1	NUM
ap-3794	187	28	.	.	PUNCT
ap-3794	188	1	from	from	ADP
ap-3794	188	2	what	what	PRON
ap-3794	188	3	is	be	AUX
ap-3794	188	4	said	say	VERB
ap-3794	188	5	above	above	ADV
ap-3794	188	6	,	,	PUNCT
ap-3794	188	7	we	we	PRON
ap-3794	188	8	can	can	AUX
ap-3794	188	9	write	write	VERB
ap-3794	188	10	down	down	ADP
ap-3794	188	11	the	the	DET
ap-3794	188	12	i	i	NOUN
ap-3794	188	13	-	-	PUNCT
ap-3794	188	14	itineraries	itinerary	NOUN
ap-3794	188	15	of	of	ADP
ap-3794	188	16	points	point	NOUN
ap-3794	188	17	from	from	ADP
ap-3794	188	18	k	k	PROPN
ap-3794	188	19	,	,	PUNCT
ap-3794	188	20	r(x	r(x	PROPN
ap-3794	188	21	)	)	PUNCT
ap-3794	189	1	=	=	PRON
ap-3794	189	2	{	{	PUNCT
ap-3794	189	3	wacv	wacv	NOUN
ap-3794	189	4	if	if	SCONJ
ap-3794	189	5	x	x	PROPN
ap-3794	189	6	∈	∈	PROPN
ap-3794	189	7	k−	k−	PROPN
ap-3794	189	8	,	,	PUNCT
ap-3794	189	9	wbv	wbv	VERB
ap-3794	189	10	if	if	SCONJ
ap-3794	189	11	x	x	X
ap-3794	189	12	∈	∈	PROPN
ap-3794	189	13	k+	k+	NOUN
ap-3794	189	14	.	.	PUNCT
ap-3794	190	1	this	this	PRON
ap-3794	190	2	finishes	finish	VERB
ap-3794	190	3	the	the	DET
ap-3794	190	4	proof	proof	NOUN
ap-3794	190	5	of	of	ADP
ap-3794	190	6	(	(	PUNCT
ap-3794	190	7	a	a	NOUN
ap-3794	190	8	)	)	PUNCT
ap-3794	190	9	.	.	PUNCT
ap-3794	191	1	the	the	DET
ap-3794	191	2	claim	claim	NOUN
ap-3794	191	3	in	in	ADP
ap-3794	191	4	item	item	NOUN
ap-3794	191	5	(	(	PUNCT
ap-3794	191	6	c	c	X
ap-3794	191	7	)	)	PUNCT
ap-3794	191	8	is	be	AUX
ap-3794	191	9	analogous	analogous	ADJ
ap-3794	191	10	to	to	ADP
ap-3794	191	11	(	(	PUNCT
ap-3794	191	12	a	a	NOUN
ap-3794	191	13	)	)	PUNCT
ap-3794	191	14	.	.	PUNCT
ap-3794	192	1	cases	case	NOUN
ap-3794	192	2	(	(	PUNCT
ap-3794	192	3	b	b	NOUN
ap-3794	192	4	)	)	PUNCT
ap-3794	192	5	and	and	CCONJ
ap-3794	192	6	(	(	PUNCT
ap-3794	192	7	d	d	X
ap-3794	192	8	)	)	PUNCT
ap-3794	192	9	are	be	AUX
ap-3794	192	10	derived	derive	VERB
ap-3794	192	11	from	from	ADP
ap-3794	192	12	(	(	PUNCT
ap-3794	192	13	a	a	X
ap-3794	192	14	)	)	PUNCT
ap-3794	192	15	and	and	CCONJ
ap-3794	192	16	(	(	PUNCT
ap-3794	192	17	c	c	NOUN
ap-3794	192	18	)	)	PUNCT
ap-3794	192	19	by	by	ADP
ap-3794	192	20	the	the	DET
ap-3794	192	21	use	use	NOUN
ap-3794	192	22	of	of	ADP
ap-3794	192	23	equivalence	equivalence	NOUN
ap-3794	192	24	(	(	PUNCT
ap-3794	192	25	6	6	NUM
ap-3794	192	26	)	)	PUNCT
ap-3794	192	27	.	.	PUNCT
ap-3794	193	1	let	let	VERB
ap-3794	193	2	us	we	PRON
ap-3794	193	3	now	now	ADV
ap-3794	193	4	demonstrate	demonstrate	VERB
ap-3794	193	5	the	the	DET
ap-3794	193	6	proof	proof	NOUN
ap-3794	193	7	of	of	ADP
ap-3794	193	8	the	the	DET
ap-3794	193	9	case	case	NOUN
ap-3794	193	10	(	(	PUNCT
ap-3794	193	11	e	e	NOUN
ap-3794	193	12	)	)	PUNCT
ap-3794	193	13	.	.	PUNCT
ap-3794	194	1	denote	denote	NOUN
ap-3794	194	2	s	s	PART
ap-3794	194	3	=	=	NOUN
ap-3794	194	4	min{n	min{n	NOUN
ap-3794	194	5	∈	∈	NOUN
ap-3794	194	6	z+	z+	NUM
ap-3794	194	7	:	:	PUNCT
ap-3794	194	8	tn(δ	tn(δ	X
ap-3794	194	9	)	)	PUNCT
ap-3794	194	10	∈	∈	PROPN
ap-3794	195	1	i	i	PRON
ap-3794	195	2	}	}	PUNCT
ap-3794	195	3	.	.	PUNCT
ap-3794	196	1	let	let	VERB
ap-3794	196	2	k	k	NOUN
ap-3794	196	3	=	=	PUNCT
ap-3794	197	1	[	[	X
ap-3794	197	2	d−	d−	PROPN
ap-3794	197	3	ε	ε	PROPN
ap-3794	197	4	,	,	PUNCT
ap-3794	197	5	d	d	PROPN
ap-3794	197	6	+	+	CCONJ
ap-3794	197	7	ε	ε	X
ap-3794	197	8	]	]	PUNCT
ap-3794	197	9	with	with	ADP
ap-3794	197	10	ε	ε	PROPN
ap-3794	197	11	chosen	choose	VERB
ap-3794	197	12	such	such	ADJ
ap-3794	197	13	that	that	SCONJ
ap-3794	197	14	k	k	PROPN
ap-3794	197	15	⊂	⊂	PROPN
ap-3794	198	1	i	i	PROPN
ap-3794	198	2	and	and	CCONJ
ap-3794	198	3	α	α	PRON
ap-3794	198	4	,	,	PUNCT
ap-3794	198	5	β	β	X
ap-3794	198	6	,	,	PUNCT
ap-3794	198	7	γ	γ	PROPN
ap-3794	198	8	,	,	PUNCT
ap-3794	198	9	δ	δ	PROPN
ap-3794	198	10	6∈	6∈	PROPN
ap-3794	198	11	t	t	PROPN
ap-3794	198	12	i(k	i(k	PROPN
ap-3794	198	13	)	)	PUNCT
ap-3794	198	14	for	for	ADP
ap-3794	198	15	all	all	PRON
ap-3794	198	16	0	0	NUM
ap-3794	198	17	≤	≤	NUM
ap-3794	198	18	i	i	PRON
ap-3794	198	19	≤	≤	ADJ
ap-3794	198	20	kδ	kδ	ADP
ap-3794	199	1	+	+	X
ap-3794	199	2	s	s	VERB
ap-3794	199	3	with	with	ADP
ap-3794	199	4	the	the	DET
ap-3794	199	5	only	only	ADJ
ap-3794	199	6	exception	exception	NOUN
ap-3794	199	7	of	of	ADP
ap-3794	199	8	t	t	PROPN
ap-3794	199	9	kδ(d	kδ(d	PUNCT
ap-3794	199	10	)	)	PUNCT
ap-3794	200	1	=	=	PUNCT
ap-3794	200	2	δ	δ	PROPN
ap-3794	200	3	.	.	PUNCT
ap-3794	201	1	(	(	PUNCT
ap-3794	201	2	8)	8)	NUM
ap-3794	201	3	the	the	DET
ap-3794	201	4	existence	existence	NOUN
ap-3794	201	5	of	of	ADP
ap-3794	201	6	such	such	ADJ
ap-3794	201	7	ε	ε	PROPN
ap-3794	201	8	follows	follow	VERB
ap-3794	201	9	trivially	trivially	ADV
ap-3794	201	10	from	from	ADP
ap-3794	201	11	the	the	DET
ap-3794	201	12	definition	definition	NOUN
ap-3794	201	13	of	of	ADP
ap-3794	201	14	the	the	DET
ap-3794	201	15	interval	interval	NOUN
ap-3794	201	16	exchange	exchange	NOUN
ap-3794	201	17	transformation	transformation	NOUN
ap-3794	201	18	and	and	CCONJ
ap-3794	201	19	the	the	DET
ap-3794	201	20	assumptions	assumption	NOUN
ap-3794	201	21	of	of	ADP
ap-3794	201	22	the	the	DET
ap-3794	201	23	lemma	lemma	PROPN
ap-3794	201	24	.	.	PUNCT
ap-3794	202	1	464	464	NUM
ap-3794	202	2	vol	vol	NOUN
ap-3794	202	3	.	.	PUNCT
ap-3794	203	1	56	56	NUM
ap-3794	203	2	no	no	NOUN
ap-3794	203	3	.	.	PUNCT
ap-3794	204	1	6/2016	6/2016	NUM
ap-3794	204	2	itineraries	itinerary	NOUN
ap-3794	204	3	induced	induce	VERB
ap-3794	204	4	by	by	ADP
ap-3794	204	5	exchange	exchange	NOUN
ap-3794	204	6	of	of	ADP
ap-3794	204	7	three	three	NUM
ap-3794	204	8	intervals	interval	NOUN
ap-3794	204	9	0	0	NUM
ap-3794	204	10	1α	1α	NUM
ap-3794	204	11	βγ	βγ	NUM
ap-3794	204	12	δ	δ	PROPN
ap-3794	204	13	a	a	PRON
ap-3794	204	14	a	a	DET
ap-3794	204	15	−	−	PROPN
ap-3794	204	16	ε	ε	PROPN
ap-3794	204	17	a	a	PRON
ap-3794	204	18	+	+	X
ap-3794	204	19	ε	ε	PROPN
ap-3794	204	20	0	0	NUM
ap-3794	204	21	1α	1α	NUM
ap-3794	204	22	βγ	βγ	PROPN
ap-3794	204	23	δ	δ	PROPN
ap-3794	204	24	tkα	tkα	X
ap-3794	204	25	(	(	PUNCT
ap-3794	204	26	a	a	NOUN
ap-3794	204	27	)	)	PUNCT
ap-3794	204	28	=	=	SYM
ap-3794	204	29	α	α	PROPN
ap-3794	204	30	tkα	tkα	NOUN
ap-3794	204	31	(	(	PUNCT
ap-3794	204	32	a	a	DET
ap-3794	204	33	−	−	PROPN
ap-3794	204	34	ε	ε	PROPN
ap-3794	204	35	)	)	PUNCT
ap-3794	204	36	tkα	tkα	NOUN
ap-3794	204	37	(	(	PUNCT
ap-3794	204	38	a	a	DET
ap-3794	204	39	+	+	X
ap-3794	204	40	ε	ε	NOUN
ap-3794	204	41	)	)	PUNCT
ap-3794	204	42	tkα	tkα	PROPN
ap-3794	204	43	tkα	tkα	NOUN
ap-3794	204	44	0	0	NUM
ap-3794	204	45	1α	1α	NUM
ap-3794	204	46	βγ	βγ	NUM
ap-3794	204	47	δ	δ	PROPN
ap-3794	204	48	tkα+1(a	tkα+1(a	NOUN
ap-3794	204	49	−	−	PROPN
ap-3794	204	50	ε	ε	PROPN
ap-3794	204	51	)	)	PUNCT
ap-3794	204	52	t	t	NOUN
ap-3794	204	53	0	0	NUM
ap-3794	204	54	1α	1α	NUM
ap-3794	204	55	βγ	βγ	PROPN
ap-3794	204	56	δ	δ	PROPN
ap-3794	204	57	tkα+2(a	tkα+2(a	VERB
ap-3794	204	58	−	−	PROPN
ap-3794	204	59	ε	ε	PROPN
ap-3794	204	60	)	)	PUNCT
ap-3794	204	61	tkα+1(a	tkα+1(a	NOUN
ap-3794	204	62	+	+	CCONJ
ap-3794	204	63	ε	ε	PROPN
ap-3794	204	64	)	)	PUNCT
ap-3794	204	65	t	t	PROPN
ap-3794	204	66	t	t	NOUN
ap-3794	204	67	0	0	NUM
ap-3794	204	68	1α	1α	NUM
ap-3794	205	1	βγ	βγ	NUM
ap-3794	205	2	δ	δ	PROPN
ap-3794	205	3	t	t	PROPN
ap-3794	205	4	t(a	t(a	NOUN
ap-3794	205	5	−	−	PROPN
ap-3794	205	6	ε	ε	PROPN
ap-3794	205	7	)	)	PUNCT
ap-3794	205	8	t	t	NOUN
ap-3794	205	9	t−1(a	t−1(a	NOUN
ap-3794	206	1	+	+	CCONJ
ap-3794	206	2	ε	ε	PROPN
ap-3794	206	3	)	)	PUNCT
ap-3794	206	4	t	t	PROPN
ap-3794	206	5	t−kα−2	t−kα−2	PROPN
ap-3794	206	6	t	t	PROPN
ap-3794	206	7	t−kα−2	t−kα−2	PROPN
ap-3794	206	8	.	.	PUNCT
ap-3794	207	1	figure	figure	VERB
ap-3794	207	2	1	1	NUM
ap-3794	207	3	.	.	PUNCT
ap-3794	208	1	situation	situation	NOUN
ap-3794	208	2	in	in	ADP
ap-3794	208	3	the	the	DET
ap-3794	208	4	proof	proof	NOUN
ap-3794	208	5	of	of	ADP
ap-3794	208	6	lemma	lemma	PROPN
ap-3794	208	7	4.2	4.2	NUM
ap-3794	208	8	,	,	PUNCT
ap-3794	208	9	case	case	NOUN
ap-3794	208	10	(	(	PUNCT
ap-3794	208	11	a	a	NOUN
ap-3794	208	12	)	)	PUNCT
ap-3794	208	13	.	.	PUNCT
ap-3794	209	1	condition	condition	NOUN
ap-3794	209	2	(	(	PUNCT
ap-3794	209	3	8)	8)	NUM
ap-3794	209	4	implies	imply	VERB
ap-3794	209	5	that	that	SCONJ
ap-3794	209	6	t	t	PROPN
ap-3794	209	7	i(k	i(k	PROPN
ap-3794	209	8	)	)	PUNCT
ap-3794	209	9	is	be	AUX
ap-3794	209	10	an	an	DET
ap-3794	209	11	interval	interval	NOUN
ap-3794	209	12	for	for	ADP
ap-3794	209	13	all	all	PRON
ap-3794	209	14	i	i	PRON
ap-3794	209	15	such	such	ADJ
ap-3794	209	16	that	that	SCONJ
ap-3794	209	17	0	0	NUM
ap-3794	209	18	<	<	X
ap-3794	209	19	i	i	PROPN
ap-3794	209	20	≤	≤	PROPN
ap-3794	209	21	kδ+s	kδ+s	NUM
ap-3794	209	22	.	.	PUNCT
ap-3794	210	1	moreover	moreover	ADV
ap-3794	210	2	,	,	PUNCT
ap-3794	210	3	t	t	NOUN
ap-3794	210	4	i(k)∩i	i(k)∩i	NOUN
ap-3794	210	5	=	=	SYM
ap-3794	210	6	∅	∅	NOUN
ap-3794	210	7	for	for	ADP
ap-3794	210	8	all	all	PRON
ap-3794	210	9	i	i	PRON
ap-3794	210	10	such	such	ADJ
ap-3794	210	11	that	that	SCONJ
ap-3794	210	12	0	0	NUM
ap-3794	210	13	<	<	X
ap-3794	211	1	i	i	X
ap-3794	211	2	<	<	X
ap-3794	211	3	kδ	kδ	VERB
ap-3794	211	4	.	.	PUNCT
ap-3794	212	1	we	we	PRON
ap-3794	212	2	obtain	obtain	VERB
ap-3794	212	3	t	t	PROPN
ap-3794	212	4	kδ	kδ	NOUN
ap-3794	212	5	(	(	PUNCT
ap-3794	212	6	k)∩i	k)∩i	PROPN
ap-3794	212	7	=	=	PUNCT
ap-3794	213	1	[	[	X
ap-3794	213	2	δ−ε	δ−ε	X
ap-3794	213	3	,	,	PUNCT
ap-3794	213	4	δ	δ	PROPN
ap-3794	213	5	)	)	PUNCT
ap-3794	213	6	.	.	PUNCT
ap-3794	214	1	in	in	ADP
ap-3794	214	2	other	other	ADJ
ap-3794	214	3	words	word	NOUN
ap-3794	214	4	,	,	PUNCT
ap-3794	214	5	the	the	DET
ap-3794	214	6	i	i	NOUN
ap-3794	214	7	-	-	PUNCT
ap-3794	214	8	itineraries	itinerary	NOUN
ap-3794	214	9	of	of	ADP
ap-3794	214	10	all	all	DET
ap-3794	214	11	points	point	NOUN
ap-3794	214	12	of	of	ADP
ap-3794	214	13	k	k	X
ap-3794	214	14	start	start	VERB
ap-3794	214	15	with	with	ADP
ap-3794	214	16	a	a	DET
ap-3794	214	17	prefix	prefix	NOUN
ap-3794	214	18	of	of	ADP
ap-3794	214	19	length	length	NOUN
ap-3794	214	20	kδ	kδ	NOUN
ap-3794	214	21	which	which	PRON
ap-3794	214	22	is	be	AUX
ap-3794	214	23	equal	equal	ADJ
ap-3794	214	24	to	to	ADP
ap-3794	214	25	r(d	r(d	NOUN
ap-3794	214	26	−	−	PROPN
ap-3794	214	27	ε	ε	PROPN
ap-3794	214	28	)	)	PUNCT
ap-3794	214	29	.	.	PUNCT
ap-3794	215	1	condition	condition	NOUN
ap-3794	215	2	(	(	PUNCT
ap-3794	215	3	8)	8)	NUM
ap-3794	215	4	and	and	CCONJ
ap-3794	215	5	the	the	DET
ap-3794	215	6	definition	definition	NOUN
ap-3794	215	7	of	of	ADP
ap-3794	215	8	s	s	PRON
ap-3794	215	9	implies	imply	VERB
ap-3794	215	10	that	that	SCONJ
ap-3794	215	11	for	for	SCONJ
ap-3794	215	12	all	all	PRON
ap-3794	215	13	i	i	PRON
ap-3794	215	14	such	such	ADJ
ap-3794	215	15	that	that	SCONJ
ap-3794	215	16	kδ	kδ	NOUN
ap-3794	215	17	<	<	X
ap-3794	216	1	i	i	PRON
ap-3794	216	2	<	<	X
ap-3794	216	3	s	s	X
ap-3794	217	1	+	+	CCONJ
ap-3794	217	2	kδ	kδ	VERB
ap-3794	217	3	we	we	PRON
ap-3794	217	4	have	have	VERB
ap-3794	217	5	t	t	PROPN
ap-3794	217	6	i(k	i(k	PROPN
ap-3794	217	7	)	)	PUNCT
ap-3794	218	1	⊂	⊂	PROPN
ap-3794	218	2	jx	jx	PROPN
ap-3794	218	3	for	for	ADP
ap-3794	218	4	some	some	DET
ap-3794	218	5	x	x	SYM
ap-3794	218	6	∈	∈	PROPN
ap-3794	218	7	{	{	PUNCT
ap-3794	218	8	a	a	DET
ap-3794	218	9	,	,	PUNCT
ap-3794	218	10	b	b	NOUN
ap-3794	218	11	,	,	PUNCT
ap-3794	218	12	c	c	NOUN
ap-3794	218	13	}	}	PUNCT
ap-3794	218	14	and	and	CCONJ
ap-3794	218	15	t	t	PROPN
ap-3794	218	16	i(k	i(k	PROPN
ap-3794	218	17	)	)	PUNCT
ap-3794	218	18	∩	∩	NOUN
ap-3794	218	19	i	i	PRON
ap-3794	218	20	=	=	PUNCT
ap-3794	218	21	∅.	∅.	VERB
ap-3794	218	22	moreover	moreover	ADV
ap-3794	218	23	,	,	PUNCT
ap-3794	218	24	t	t	PROPN
ap-3794	218	25	i(k	i(k	PROPN
ap-3794	218	26	)	)	PUNCT
ap-3794	219	1	⊂	⊂	PROPN
ap-3794	219	2	i	i	PRON
ap-3794	219	3	for	for	ADP
ap-3794	219	4	i	i	PRON
ap-3794	219	5	=	=	PUNCT
ap-3794	219	6	kδ	kδ	PROPN
ap-3794	219	7	+	+	CCONJ
ap-3794	219	8	s.	s.	PROPN
ap-3794	219	9	thus	thus	ADV
ap-3794	219	10	,	,	PUNCT
ap-3794	219	11	the	the	DET
ap-3794	219	12	iterations	iteration	NOUN
ap-3794	219	13	of	of	ADP
ap-3794	219	14	points	point	NOUN
ap-3794	219	15	of	of	ADP
ap-3794	219	16	t	t	PROPN
ap-3794	219	17	kδ	kδ	PROPN
ap-3794	219	18	(	(	PUNCT
ap-3794	219	19	k	k	NOUN
ap-3794	219	20	)	)	PUNCT
ap-3794	219	21	=	=	PUNCT
ap-3794	220	1	[	[	X
ap-3794	220	2	δ−	δ−	PROPN
ap-3794	220	3	ε	ε	PROPN
ap-3794	220	4	,	,	PUNCT
ap-3794	220	5	δ)∪	δ)∪	NOUN
ap-3794	220	6	t	t	NOUN
ap-3794	220	7	kδ	kδ	NOUN
ap-3794	221	1	[	[	X
ap-3794	221	2	d	d	X
ap-3794	221	3	,	,	PUNCT
ap-3794	221	4	d	d	PROPN
ap-3794	221	5	+	+	CCONJ
ap-3794	221	6	ε	ε	PROPN
ap-3794	221	7	]	]	PUNCT
ap-3794	221	8	are	be	AUX
ap-3794	221	9	coded	code	VERB
ap-3794	221	10	by	by	ADP
ap-3794	221	11	the	the	DET
ap-3794	221	12	same	same	ADJ
ap-3794	221	13	word	word	NOUN
ap-3794	221	14	of	of	ADP
ap-3794	221	15	length	length	NOUN
ap-3794	221	16	s	s	PROPN
ap-3794	221	17	,	,	PUNCT
ap-3794	221	18	namely	namely	ADV
ap-3794	221	19	r(δ	r(δ	PROPN
ap-3794	221	20	−	−	PROPN
ap-3794	221	21	ε	ε	PROPN
ap-3794	221	22	)	)	PUNCT
ap-3794	221	23	.	.	PUNCT
ap-3794	222	1	altogether	altogether	ADV
ap-3794	222	2	,	,	PUNCT
ap-3794	222	3	we	we	PRON
ap-3794	222	4	can	can	AUX
ap-3794	222	5	conclude	conclude	VERB
ap-3794	222	6	that	that	SCONJ
ap-3794	222	7	the	the	DET
ap-3794	222	8	i	i	PROPN
ap-3794	222	9	-	-	PUNCT
ap-3794	222	10	itinerary	itinerary	NOUN
ap-3794	222	11	of	of	ADP
ap-3794	222	12	points	point	NOUN
ap-3794	222	13	in	in	ADP
ap-3794	222	14	the	the	DET
ap-3794	222	15	interval	interval	NOUN
ap-3794	222	16	[	[	X
ap-3794	222	17	d	d	X
ap-3794	222	18	,	,	PUNCT
ap-3794	222	19	d	d	PROPN
ap-3794	222	20	+	+	CCONJ
ap-3794	222	21	ε	ε	X
ap-3794	222	22	]	]	PUNCT
ap-3794	222	23	is	be	AUX
ap-3794	222	24	equal	equal	ADJ
ap-3794	222	25	to	to	ADP
ap-3794	222	26	r(d−	r(d−	PROPN
ap-3794	222	27	ε)r(δ	ε)r(δ	ADV
ap-3794	222	28	−	−	PROPN
ap-3794	222	29	ε	ε	PROPN
ap-3794	222	30	)	)	PUNCT
ap-3794	222	31	.	.	PUNCT
ap-3794	223	1	the	the	DET
ap-3794	223	2	situation	situation	NOUN
ap-3794	223	3	is	be	AUX
ap-3794	223	4	depicted	depict	VERB
ap-3794	223	5	in	in	ADP
ap-3794	223	6	figure	figure	NOUN
ap-3794	223	7	2	2	NUM
ap-3794	223	8	.	.	PUNCT
ap-3794	223	9	case	case	NOUN
ap-3794	223	10	(	(	PUNCT
ap-3794	223	11	f	f	X
ap-3794	223	12	)	)	PUNCT
ap-3794	223	13	can	can	AUX
ap-3794	223	14	be	be	AUX
ap-3794	223	15	treated	treat	VERB
ap-3794	223	16	in	in	ADP
ap-3794	223	17	a	a	DET
ap-3794	223	18	way	way	NOUN
ap-3794	223	19	analogous	analogous	ADJ
ap-3794	223	20	to	to	PART
ap-3794	223	21	case	case	NOUN
ap-3794	223	22	(	(	PUNCT
ap-3794	223	23	e	e	NOUN
ap-3794	223	24	)	)	PUNCT
ap-3794	223	25	.	.	PUNCT
ap-3794	224	1	now	now	ADV
ap-3794	224	2	we	we	PRON
ap-3794	224	3	can	can	AUX
ap-3794	224	4	prove	prove	VERB
ap-3794	224	5	the	the	DET
ap-3794	224	6	main	main	ADJ
ap-3794	224	7	theorem	theorem	NOUN
ap-3794	224	8	describing	describe	VERB
ap-3794	224	9	the	the	DET
ap-3794	224	10	return	return	NOUN
ap-3794	224	11	times	time	NOUN
ap-3794	224	12	in	in	ADP
ap-3794	224	13	3iet	3iet	NUM
ap-3794	224	14	.	.	PUNCT
ap-3794	225	1	in	in	ADP
ap-3794	225	2	the	the	DET
ap-3794	225	3	proof	proof	NOUN
ap-3794	225	4	,	,	PUNCT
ap-3794	225	5	it	it	PRON
ap-3794	225	6	is	be	AUX
ap-3794	225	7	sufficient	sufficient	ADJ
ap-3794	225	8	to	to	PART
ap-3794	225	9	focus	focus	VERB
ap-3794	225	10	on	on	ADP
ap-3794	225	11	the	the	DET
ap-3794	225	12	case	case	NOUN
ap-3794	225	13	when	when	SCONJ
ap-3794	225	14	#	#	NOUN
ap-3794	225	15	iti	iti	NOUN
ap-3794	225	16	=	=	SYM
ap-3794	225	17	5	5	NUM
ap-3794	225	18	,	,	PUNCT
ap-3794	225	19	since	since	ADV
ap-3794	225	20	,	,	PUNCT
ap-3794	225	21	as	as	SCONJ
ap-3794	225	22	we	we	PRON
ap-3794	225	23	have	have	AUX
ap-3794	225	24	seen	see	VERB
ap-3794	225	25	from	from	ADP
ap-3794	225	26	proposition	proposition	NOUN
ap-3794	225	27	3.4	3.4	NUM
ap-3794	225	28	,	,	PUNCT
ap-3794	225	29	the	the	DET
ap-3794	225	30	set	set	NOUN
ap-3794	225	31	of	of	ADP
ap-3794	225	32	i	i	PROPN
ap-3794	225	33	-	-	PUNCT
ap-3794	225	34	itineraries	itinerary	NOUN
ap-3794	225	35	,	,	PUNCT
ap-3794	225	36	and	and	CCONJ
ap-3794	225	37	thus	thus	ADV
ap-3794	225	38	also	also	ADV
ap-3794	225	39	their	their	PRON
ap-3794	225	40	return	return	NOUN
ap-3794	225	41	times	time	NOUN
ap-3794	225	42	,	,	PUNCT
ap-3794	225	43	for	for	ADP
ap-3794	225	44	the	the	DET
ap-3794	225	45	other	other	ADJ
ap-3794	225	46	cases	case	NOUN
ap-3794	225	47	are	be	AUX
ap-3794	225	48	only	only	ADV
ap-3794	225	49	a	a	DET
ap-3794	225	50	subset	subset	NOUN
ap-3794	225	51	of	of	ADP
ap-3794	225	52	itĩ	itĩ	NOUN
ap-3794	225	53	for	for	ADP
ap-3794	225	54	some	some	DET
ap-3794	225	55	“	"	PUNCT
ap-3794	225	56	close	close	ADJ
ap-3794	225	57	enough	enough	ADV
ap-3794	225	58	”	"	PUNCT
ap-3794	225	59	generic	generic	ADJ
ap-3794	225	60	subinterval	subinterval	NOUN
ap-3794	225	61	ĩ	ĩ	PROPN
ap-3794	225	62	⊂	⊂	PUNCT
ap-3794	226	1	[	[	X
ap-3794	226	2	0	0	NUM
ap-3794	226	3	,	,	PUNCT
ap-3794	226	4	1	1	NUM
ap-3794	226	5	)	)	PUNCT
ap-3794	226	6	.	.	PUNCT
ap-3794	227	1	so	so	ADV
ap-3794	227	2	throughout	throughout	ADP
ap-3794	227	3	the	the	DET
ap-3794	227	4	rest	rest	NOUN
ap-3794	227	5	of	of	ADP
ap-3794	227	6	this	this	DET
ap-3794	227	7	section	section	NOUN
ap-3794	227	8	,	,	PUNCT
ap-3794	227	9	suppose	suppose	VERB
ap-3794	227	10	that	that	SCONJ
ap-3794	227	11	#	#	NOUN
ap-3794	227	12	iti	iti	NOUN
ap-3794	227	13	=	=	NOUN
ap-3794	227	14	5	5	X
ap-3794	227	15	.	.	PUNCT
ap-3794	228	1	this	this	DET
ap-3794	228	2	means	mean	VERB
ap-3794	228	3	by	by	ADP
ap-3794	228	4	lemma	lemma	PROPN
ap-3794	228	5	3.2	3.2	NUM
ap-3794	228	6	that	that	PRON
ap-3794	228	7	points	point	VERB
ap-3794	228	8	a	a	DET
ap-3794	228	9	,	,	PUNCT
ap-3794	228	10	b	b	NOUN
ap-3794	228	11	,	,	PUNCT
ap-3794	228	12	c	c	NOUN
ap-3794	228	13	,	,	PUNCT
ap-3794	228	14	d	d	PRON
ap-3794	228	15	lie	lie	VERB
ap-3794	228	16	in	in	ADP
ap-3794	228	17	the	the	DET
ap-3794	228	18	interior	interior	NOUN
ap-3794	228	19	of	of	ADP
ap-3794	228	20	the	the	DET
ap-3794	228	21	interval	interval	NOUN
ap-3794	229	1	i	i	PRON
ap-3794	229	2	=	=	PUNCT
ap-3794	230	1	[	[	X
ap-3794	230	2	γ	γ	X
ap-3794	230	3	,	,	PUNCT
ap-3794	230	4	δ	δ	PROPN
ap-3794	230	5	)	)	PUNCT
ap-3794	230	6	and	and	CCONJ
ap-3794	230	7	are	be	AUX
ap-3794	230	8	mutually	mutually	ADV
ap-3794	230	9	distinct	distinct	ADJ
ap-3794	230	10	.	.	PUNCT
ap-3794	231	1	moreover	moreover	ADV
ap-3794	231	2	,	,	PUNCT
ap-3794	231	3	by	by	ADP
ap-3794	231	4	proposition	proposition	NOUN
ap-3794	231	5	3.3	3.3	NUM
ap-3794	231	6	,	,	PUNCT
ap-3794	231	7	we	we	PRON
ap-3794	231	8	have	have	VERB
ap-3794	231	9	d	d	NOUN
ap-3794	231	10	<	<	X
ap-3794	231	11	c.	c.	NOUN
ap-3794	231	12	such	such	ADJ
ap-3794	231	13	conditions	condition	NOUN
ap-3794	231	14	imply	imply	VERB
ap-3794	231	15	12	12	NUM
ap-3794	231	16	possible	possible	ADJ
ap-3794	231	17	orderings	ordering	NOUN
ap-3794	231	18	of	of	ADP
ap-3794	231	19	a	a	DET
ap-3794	231	20	,	,	PUNCT
ap-3794	231	21	b	b	NOUN
ap-3794	231	22	,	,	PUNCT
ap-3794	231	23	c	c	NOUN
ap-3794	231	24	,	,	PUNCT
ap-3794	231	25	d	d	NUM
ap-3794	231	26	which	which	PRON
ap-3794	231	27	give	give	VERB
ap-3794	231	28	rise	rise	NOUN
ap-3794	231	29	to	to	ADP
ap-3794	231	30	12	12	NUM
ap-3794	231	31	cases	case	NOUN
ap-3794	231	32	in	in	ADP
ap-3794	231	33	the	the	DET
ap-3794	231	34	study	study	NOUN
ap-3794	231	35	of	of	ADP
ap-3794	231	36	return	return	NOUN
ap-3794	231	37	times	time	NOUN
ap-3794	231	38	.	.	PUNCT
ap-3794	232	1	we	we	PRON
ap-3794	232	2	will	will	AUX
ap-3794	232	3	describe	describe	VERB
ap-3794	232	4	them	they	PRON
ap-3794	232	5	in	in	ADP
ap-3794	232	6	the	the	DET
ap-3794	232	7	proof	proof	NOUN
ap-3794	232	8	of	of	ADP
ap-3794	232	9	theorem	theorem	ADJ
ap-3794	232	10	4.1	4.1	NUM
ap-3794	232	11	as	as	ADP
ap-3794	232	12	cases	case	NOUN
ap-3794	232	13	(	(	PUNCT
ap-3794	232	14	i)–(xii	i)–(xii	NOUN
ap-3794	232	15	)	)	PUNCT
ap-3794	232	16	and	and	CCONJ
ap-3794	232	17	then	then	ADV
ap-3794	232	18	show	show	VERB
ap-3794	232	19	in	in	ADP
ap-3794	232	20	example	example	NOUN
ap-3794	232	21	4.5	4.5	NUM
ap-3794	232	22	that	that	PRON
ap-3794	232	23	all	all	DET
ap-3794	232	24	12	12	NUM
ap-3794	232	25	cases	case	NOUN
ap-3794	232	26	may	may	AUX
ap-3794	232	27	occur	occur	VERB
ap-3794	232	28	.	.	PUNCT
ap-3794	233	1	remark	remark	PROPN
ap-3794	233	2	4.3	4.3	NUM
ap-3794	233	3	.	.	PUNCT
ap-3794	234	1	note	note	VERB
ap-3794	234	2	that	that	SCONJ
ap-3794	234	3	if	if	SCONJ
ap-3794	234	4	γ	γ	X
ap-3794	234	5	=	=	SYM
ap-3794	234	6	0	0	NUM
ap-3794	234	7	,	,	PUNCT
ap-3794	234	8	i.e.	i.e.	X
ap-3794	234	9	we	we	PRON
ap-3794	234	10	induce	induce	VERB
ap-3794	234	11	on	on	ADP
ap-3794	234	12	an	an	DET
ap-3794	234	13	interval	interval	NOUN
ap-3794	235	1	i	i	NOUN
ap-3794	235	2	=	=	PUNCT
ap-3794	236	1	[	[	X
ap-3794	236	2	0	0	NUM
ap-3794	236	3	,	,	PUNCT
ap-3794	236	4	δ	δ	PROPN
ap-3794	236	5	)	)	PUNCT
ap-3794	236	6	,	,	PUNCT
ap-3794	236	7	we	we	PRON
ap-3794	236	8	have	have	VERB
ap-3794	236	9	t−1(γ	t−1(γ	ADV
ap-3794	236	10	)	)	PUNCT
ap-3794	237	1	=	=	SYM
ap-3794	237	2	β	β	NOUN
ap-3794	237	3	and	and	CCONJ
ap-3794	237	4	therefore	therefore	ADV
ap-3794	237	5	necessarily	necessarily	ADV
ap-3794	237	6	b	b	PROPN
ap-3794	237	7	=	=	SYM
ap-3794	237	8	c.	c.	PROPN
ap-3794	237	9	thus	thus	ADV
ap-3794	237	10	there	there	PRON
ap-3794	237	11	are	be	VERB
ap-3794	237	12	at	at	ADP
ap-3794	237	13	most	most	ADJ
ap-3794	237	14	four	four	NUM
ap-3794	237	15	iitineraries	iitinerarie	NOUN
ap-3794	237	16	.	.	PUNCT
ap-3794	238	1	due	due	ADP
ap-3794	238	2	to	to	ADP
ap-3794	238	3	proposition	proposition	NOUN
ap-3794	238	4	3.5	3.5	NUM
ap-3794	238	5	,	,	PUNCT
ap-3794	238	6	a	a	DET
ap-3794	238	7	similar	similar	ADJ
ap-3794	238	8	situation	situation	NOUN
ap-3794	238	9	happens	happen	VERB
ap-3794	238	10	if	if	SCONJ
ap-3794	238	11	δ	δ	PROPN
ap-3794	238	12	=	=	NOUN
ap-3794	238	13	1	1	X
ap-3794	238	14	.	.	PUNCT
ap-3794	238	15	proof	proof	NOUN
ap-3794	238	16	of	of	ADP
ap-3794	238	17	theorem	theorem	NOUN
ap-3794	238	18	4.1	4.1	NUM
ap-3794	238	19	.	.	PUNCT
ap-3794	239	1	we	we	PRON
ap-3794	239	2	will	will	AUX
ap-3794	239	3	discuss	discuss	VERB
ap-3794	239	4	the	the	DET
ap-3794	239	5	12	12	NUM
ap-3794	239	6	possibilities	possibility	NOUN
ap-3794	239	7	of	of	ADP
ap-3794	239	8	ordering	ordering	NOUN
ap-3794	239	9	of	of	ADP
ap-3794	239	10	points	point	NOUN
ap-3794	239	11	a	a	DET
ap-3794	239	12	,	,	PUNCT
ap-3794	239	13	b	b	NOUN
ap-3794	239	14	,	,	PUNCT
ap-3794	239	15	c	c	X
ap-3794	239	16	,	,	PUNCT
ap-3794	239	17	d	d	NOUN
ap-3794	239	18	in	in	ADP
ap-3794	239	19	the	the	DET
ap-3794	239	20	interior	interior	NOUN
ap-3794	239	21	of	of	ADP
ap-3794	239	22	the	the	DET
ap-3794	239	23	interval	interval	NOUN
ap-3794	239	24	[	[	X
ap-3794	239	25	γ	γ	X
ap-3794	239	26	,	,	PUNCT
ap-3794	239	27	δ	δ	PROPN
ap-3794	239	28	)	)	PUNCT
ap-3794	239	29	with	with	ADP
ap-3794	239	30	the	the	DET
ap-3794	239	31	condition	condition	NOUN
ap-3794	239	32	d	d	X
ap-3794	239	33	<	<	X
ap-3794	239	34	c.	c.	NOUN
ap-3794	239	35	the	the	DET
ap-3794	239	36	structure	structure	NOUN
ap-3794	239	37	of	of	ADP
ap-3794	239	38	the	the	DET
ap-3794	239	39	set	set	NOUN
ap-3794	239	40	of	of	ADP
ap-3794	239	41	i	i	PROPN
ap-3794	239	42	-	-	PUNCT
ap-3794	239	43	itineraries	itinerary	NOUN
ap-3794	239	44	will	will	AUX
ap-3794	239	45	be	be	AUX
ap-3794	239	46	best	well	ADV
ap-3794	239	47	shown	show	VERB
ap-3794	239	48	in	in	ADP
ap-3794	239	49	terms	term	NOUN
ap-3794	239	50	of	of	ADP
ap-3794	239	51	i	i	NOUN
ap-3794	239	52	-	-	PUNCT
ap-3794	239	53	itineraries	itinerary	NOUN
ap-3794	239	54	of	of	ADP
ap-3794	239	55	points	point	NOUN
ap-3794	239	56	in	in	ADP
ap-3794	239	57	the	the	DET
ap-3794	239	58	left	left	ADJ
ap-3794	239	59	neighbourhood	neighbourhood	NOUN
ap-3794	239	60	of	of	ADP
ap-3794	239	61	the	the	DET
ap-3794	239	62	point	point	NOUN
ap-3794	239	63	d	d	NOUN
ap-3794	239	64	and	and	CCONJ
ap-3794	239	65	right	right	ADJ
ap-3794	239	66	neighbourhood	neighbourhood	NOUN
ap-3794	239	67	of	of	ADP
ap-3794	239	68	the	the	DET
ap-3794	239	69	point	point	NOUN
ap-3794	239	70	c.	c.	NOUN
ap-3794	239	71	for	for	ADP
ap-3794	239	72	simplicity	simplicity	NOUN
ap-3794	239	73	,	,	PUNCT
ap-3794	239	74	we	we	PRON
ap-3794	239	75	thus	thus	ADV
ap-3794	239	76	denote	denote	VERB
ap-3794	239	77	for	for	ADP
ap-3794	239	78	sufficiently	sufficiently	ADV
ap-3794	239	79	small	small	ADJ
ap-3794	239	80	positive	positive	ADJ
ap-3794	239	81	ε	ε	PROPN
ap-3794	239	82	r1	r1	NOUN
ap-3794	239	83	=	=	PUNCT
ap-3794	239	84	r(d−	r(d−	PROPN
ap-3794	239	85	ε	ε	PROPN
ap-3794	239	86	)	)	PUNCT
ap-3794	239	87	,	,	PUNCT
ap-3794	239	88	r2	r2	NOUN
ap-3794	239	89	=	=	PUNCT
ap-3794	240	1	r(c	r(c	PROPN
ap-3794	240	2	+	+	NUM
ap-3794	240	3	ε	ε	PROPN
ap-3794	240	4	)	)	PUNCT
ap-3794	240	5	and	and	CCONJ
ap-3794	240	6	|r1|	|r1|	PROPN
ap-3794	240	7	=	=	SYM
ap-3794	240	8	t1	t1	PROPN
ap-3794	240	9	,	,	PUNCT
ap-3794	240	10	|r2|	|r2|	NOUN
ap-3794	240	11	=	=	NOUN
ap-3794	240	12	t2	t2	NOUN
ap-3794	240	13	.	.	PUNCT
ap-3794	241	1	in	in	ADP
ap-3794	241	2	order	order	NOUN
ap-3794	241	3	to	to	PART
ap-3794	241	4	be	be	AUX
ap-3794	241	5	allowed	allow	VERB
ap-3794	241	6	to	to	PART
ap-3794	241	7	use	use	VERB
ap-3794	241	8	lemma	lemma	PROPN
ap-3794	241	9	4.2	4.2	NUM
ap-3794	241	10	,	,	PUNCT
ap-3794	241	11	we	we	PRON
ap-3794	241	12	will	will	AUX
ap-3794	241	13	assume	assume	VERB
ap-3794	241	14	that	that	SCONJ
ap-3794	241	15	the	the	DET
ap-3794	241	16	orbits	orbit	NOUN
ap-3794	241	17	of	of	ADP
ap-3794	241	18	points	point	NOUN
ap-3794	241	19	α	α	PROPN
ap-3794	241	20	,	,	PUNCT
ap-3794	241	21	β	β	X
ap-3794	241	22	,	,	PUNCT
ap-3794	241	23	γ	γ	PROPN
ap-3794	241	24	and	and	CCONJ
ap-3794	241	25	δ	δ	PROPN
ap-3794	241	26	are	be	AUX
ap-3794	241	27	mutually	mutually	ADV
ap-3794	241	28	disjoint	disjoint	ADJ
ap-3794	241	29	.	.	PUNCT
ap-3794	242	1	otherwise	otherwise	ADV
ap-3794	242	2	,	,	PUNCT
ap-3794	242	3	we	we	PRON
ap-3794	242	4	use	use	VERB
ap-3794	242	5	proposition	proposition	NOUN
ap-3794	242	6	3.4	3.4	NUM
ap-3794	242	7	to	to	PART
ap-3794	242	8	find	find	VERB
ap-3794	242	9	a	a	DET
ap-3794	242	10	modified	modify	VERB
ap-3794	242	11	interval	interval	NOUN
ap-3794	242	12	ĩ	ĩ	PROPN
ap-3794	242	13	where	where	SCONJ
ap-3794	242	14	this	this	PRON
ap-3794	242	15	is	be	AUX
ap-3794	242	16	satisfied	satisfied	ADJ
ap-3794	242	17	and	and	CCONJ
ap-3794	242	18	itĩ	itĩ	ADP
ap-3794	242	19	=	=	PROPN
ap-3794	242	20	iti	iti	PROPN
ap-3794	242	21	.	.	PUNCT
ap-3794	243	1	(	(	PUNCT
ap-3794	243	2	i	i	NOUN
ap-3794	243	3	)	)	PUNCT
ap-3794	243	4	let	let	VERB
ap-3794	243	5	a	a	DET
ap-3794	243	6	<	<	X
ap-3794	243	7	b	b	X
ap-3794	243	8	<	<	X
ap-3794	243	9	d	d	X
ap-3794	243	10	<	<	X
ap-3794	243	11	c.	c.	NOUN
ap-3794	243	12	we	we	PRON
ap-3794	243	13	know	know	VERB
ap-3794	243	14	that	that	SCONJ
ap-3794	243	15	r(x	r(x	PROPN
ap-3794	243	16	)	)	PUNCT
ap-3794	243	17	is	be	AUX
ap-3794	243	18	constant	constant	ADJ
ap-3794	243	19	on	on	ADP
ap-3794	243	20	the	the	DET
ap-3794	243	21	intervals	interval	NOUN
ap-3794	243	22	[	[	X
ap-3794	243	23	γ	γ	X
ap-3794	243	24	,	,	PUNCT
ap-3794	243	25	a	a	PRON
ap-3794	243	26	)	)	PUNCT
ap-3794	243	27	,	,	PUNCT
ap-3794	244	1	[	[	X
ap-3794	244	2	a	a	DET
ap-3794	244	3	,	,	PUNCT
ap-3794	244	4	b	b	NOUN
ap-3794	244	5	)	)	PUNCT
ap-3794	244	6	,	,	PUNCT
ap-3794	245	1	[	[	X
ap-3794	245	2	b	b	X
ap-3794	245	3	,	,	PUNCT
ap-3794	245	4	d	d	NOUN
ap-3794	245	5	)	)	PUNCT
ap-3794	245	6	,	,	PUNCT
ap-3794	245	7	[	[	X
ap-3794	245	8	d	d	X
ap-3794	245	9	,	,	PUNCT
ap-3794	245	10	c	c	NOUN
ap-3794	245	11	)	)	PUNCT
ap-3794	245	12	,	,	PUNCT
ap-3794	245	13	and	and	CCONJ
ap-3794	245	14	[	[	X
ap-3794	245	15	c	c	X
ap-3794	245	16	,	,	PUNCT
ap-3794	245	17	δ	δ	PROPN
ap-3794	245	18	)	)	PUNCT
ap-3794	245	19	.	.	PUNCT
ap-3794	246	1	by	by	ADP
ap-3794	246	2	definition	definition	NOUN
ap-3794	246	3	r(x	r(x	PROPN
ap-3794	246	4	)	)	PUNCT
ap-3794	246	5	=	=	SYM
ap-3794	246	6	r2	r2	PROPN
ap-3794	246	7	for	for	ADP
ap-3794	246	8	x	x	PROPN
ap-3794	246	9	∈	∈	PROPN
ap-3794	246	10	[	[	X
ap-3794	246	11	c	c	X
ap-3794	246	12	,	,	PUNCT
ap-3794	246	13	δ	δ	PROPN
ap-3794	246	14	)	)	PUNCT
ap-3794	246	15	and	and	CCONJ
ap-3794	246	16	r(x	r(x	NOUN
ap-3794	246	17	)	)	PUNCT
ap-3794	246	18	=	=	PROPN
ap-3794	246	19	r1	r1	PROPN
ap-3794	246	20	for	for	ADP
ap-3794	246	21	x	x	PROPN
ap-3794	246	22	∈	∈	PROPN
ap-3794	246	23	[	[	X
ap-3794	246	24	b	b	X
ap-3794	246	25	,	,	PUNCT
ap-3794	246	26	d	d	NOUN
ap-3794	246	27	)	)	PUNCT
ap-3794	246	28	.	.	PUNCT
ap-3794	247	1	we	we	PRON
ap-3794	247	2	can	can	AUX
ap-3794	247	3	derive	derive	VERB
ap-3794	247	4	from	from	ADP
ap-3794	247	5	rule	rule	NOUN
ap-3794	247	6	(	(	PUNCT
ap-3794	247	7	e	e	NOUN
ap-3794	247	8	)	)	PUNCT
ap-3794	247	9	of	of	ADP
ap-3794	247	10	lemma	lemma	PROPN
ap-3794	247	11	4.2	4.2	NUM
ap-3794	247	12	that	that	PRON
ap-3794	247	13	if	if	SCONJ
ap-3794	247	14	x	x	X
ap-3794	247	15	∈	∈	PROPN
ap-3794	247	16	[	[	X
ap-3794	247	17	d	d	X
ap-3794	247	18	,	,	PUNCT
ap-3794	247	19	c	c	NOUN
ap-3794	247	20	)	)	PUNCT
ap-3794	247	21	,	,	PUNCT
ap-3794	247	22	then	then	ADV
ap-3794	247	23	r(x	r(x	PROPN
ap-3794	247	24	)	)	PUNCT
ap-3794	247	25	=	=	PUNCT
ap-3794	248	1	r1r2	r1r2	VERB
ap-3794	248	2	.	.	PUNCT
ap-3794	248	3	further	far	ADV
ap-3794	248	4	,	,	PUNCT
ap-3794	248	5	we	we	PRON
ap-3794	248	6	use	use	VERB
ap-3794	248	7	rule	rule	NOUN
ap-3794	248	8	(	(	PUNCT
ap-3794	248	9	c	c	NOUN
ap-3794	248	10	)	)	PUNCT
ap-3794	248	11	to	to	ADP
ap-3794	248	12	465	465	NUM
ap-3794	248	13	z.	z.	NOUN
ap-3794	248	14	masáková	masáková	PROPN
ap-3794	248	15	,	,	PUNCT
ap-3794	248	16	e.	e.	PROPN
ap-3794	248	17	pelantová	pelantová	PROPN
ap-3794	248	18	,	,	PUNCT
ap-3794	248	19	š	š	PROPN
ap-3794	248	20	.	.	PROPN
ap-3794	248	21	starosta	starosta	PROPN
ap-3794	248	22	acta	acta	PROPN
ap-3794	248	23	polytechnica	polytechnica	PROPN
ap-3794	248	24	0	0	NUM
ap-3794	248	25	1α	1α	NUM
ap-3794	249	1	βγ	βγ	NUM
ap-3794	249	2	δ	δ	PROPN
ap-3794	250	1	d	d	PROPN
ap-3794	250	2	d	d	X
ap-3794	250	3	−	−	PROPN
ap-3794	250	4	ε	ε	PROPN
ap-3794	251	1	d	d	PROPN
ap-3794	251	2	+	+	CCONJ
ap-3794	251	3	ε	ε	PROPN
ap-3794	251	4	0	0	NUM
ap-3794	251	5	1α	1α	NUM
ap-3794	251	6	βγ	βγ	PROPN
ap-3794	251	7	δ	δ	PROPN
ap-3794	251	8	tkδ	tkδ	VERB
ap-3794	251	9	(	(	PUNCT
ap-3794	251	10	d	d	X
ap-3794	251	11	−	−	PROPN
ap-3794	251	12	ε	ε	PROPN
ap-3794	251	13	)	)	PUNCT
ap-3794	251	14	tkδ	tkδ	VERB
ap-3794	251	15	(	(	PUNCT
ap-3794	251	16	d	d	NOUN
ap-3794	251	17	+	+	CCONJ
ap-3794	251	18	ε	ε	PROPN
ap-3794	251	19	)	)	PUNCT
ap-3794	251	20	tkδ	tkδ	VERB
ap-3794	251	21	tkδ	tkδ	VERB
ap-3794	251	22	0	0	NUM
ap-3794	251	23	1α	1α	NUM
ap-3794	252	1	βγ	βγ	NUM
ap-3794	252	2	δ	δ	PROPN
ap-3794	252	3	t	t	VERB
ap-3794	252	4	t(δ	t(δ	PROPN
ap-3794	252	5	−	−	PROPN
ap-3794	252	6	ε	ε	PROPN
ap-3794	252	7	)	)	PUNCT
ap-3794	252	8	t	t	NOUN
ap-3794	252	9	t(δ	t(δ	PROPN
ap-3794	252	10	+	+	CCONJ
ap-3794	252	11	ε	ε	PROPN
ap-3794	252	12	)	)	PUNCT
ap-3794	252	13	t	t	PROPN
ap-3794	252	14	t	t	PROPN
ap-3794	252	15	t	t	PROPN
ap-3794	252	16	t	t	PROPN
ap-3794	252	17	.	.	PUNCT
ap-3794	253	1	figure	figure	NOUN
ap-3794	253	2	2	2	NUM
ap-3794	253	3	.	.	PUNCT
ap-3794	253	4	situation	situation	NOUN
ap-3794	253	5	in	in	ADP
ap-3794	253	6	the	the	DET
ap-3794	253	7	proof	proof	NOUN
ap-3794	253	8	of	of	ADP
ap-3794	253	9	lemma	lemma	PROPN
ap-3794	253	10	4.2	4.2	NUM
ap-3794	253	11	,	,	PUNCT
ap-3794	253	12	case	case	NOUN
ap-3794	253	13	(	(	PUNCT
ap-3794	253	14	e	e	NOUN
ap-3794	253	15	)	)	PUNCT
ap-3794	253	16	.	.	PUNCT
ap-3794	254	1	show	show	VERB
ap-3794	254	2	that	that	SCONJ
ap-3794	254	3	r(x	r(x	NOUN
ap-3794	254	4	)	)	PUNCT
ap-3794	254	5	=	=	SYM
ap-3794	254	6	ωca→b(r1	ωca→b(r1	NOUN
ap-3794	254	7	)	)	PUNCT
ap-3794	254	8	for	for	ADP
ap-3794	254	9	x	x	PROPN
ap-3794	254	10	∈	∈	PROPN
ap-3794	254	11	[	[	X
ap-3794	254	12	a	a	DET
ap-3794	254	13	,	,	PUNCT
ap-3794	254	14	b	b	NOUN
ap-3794	254	15	)	)	PUNCT
ap-3794	254	16	and	and	CCONJ
ap-3794	254	17	further	far	ADV
ap-3794	254	18	by	by	ADP
ap-3794	254	19	applying	apply	VERB
ap-3794	254	20	rule	rule	NOUN
ap-3794	254	21	(	(	PUNCT
ap-3794	254	22	a	a	X
ap-3794	254	23	)	)	PUNCT
ap-3794	254	24	,	,	PUNCT
ap-3794	254	25	we	we	PRON
ap-3794	254	26	obtain	obtain	VERB
ap-3794	254	27	that	that	DET
ap-3794	254	28	r(x	r(x	NOUN
ap-3794	254	29	)	)	PUNCT
ap-3794	255	1	=	=	SYM
ap-3794	255	2	ωb→ac	ωb→ac	ADJ
ap-3794	255	3	(	(	PUNCT
ap-3794	255	4	ωca→b(r1	ωca→b(r1	NOUN
ap-3794	255	5	)	)	PUNCT
ap-3794	255	6	)	)	PUNCT
ap-3794	256	1	for	for	ADP
ap-3794	256	2	x	x	PROPN
ap-3794	256	3	∈	∈	PROPN
ap-3794	256	4	[	[	X
ap-3794	256	5	γ	γ	X
ap-3794	256	6	,	,	PUNCT
ap-3794	256	7	a	a	PRON
ap-3794	256	8	)	)	PUNCT
ap-3794	256	9	.	.	PUNCT
ap-3794	257	1	summarized	summarize	VERB
ap-3794	257	2	,	,	PUNCT
ap-3794	257	3	r(x	r(x	PROPN
ap-3794	257	4	)	)	PUNCT
ap-3794	257	5	=	=	PUNCT
ap-3794	258	1			NOUN
ap-3794	258	2	ωb→ac	ωb→ac	ADJ
ap-3794	258	3	(	(	PUNCT
ap-3794	258	4	ωca→b(r1	ωca→b(r1	NOUN
ap-3794	258	5	)	)	PUNCT
ap-3794	258	6	)	)	PUNCT
ap-3794	259	1	for	for	ADP
ap-3794	259	2	x	x	PROPN
ap-3794	259	3	∈	∈	PROPN
ap-3794	259	4	[	[	X
ap-3794	259	5	γ	γ	X
ap-3794	259	6	,	,	PUNCT
ap-3794	259	7	a	a	PRON
ap-3794	259	8	)	)	PUNCT
ap-3794	259	9	,	,	PUNCT
ap-3794	259	10	ωca→b(r1	ωca→b(r1	NOUN
ap-3794	259	11	)	)	PUNCT
ap-3794	259	12	for	for	ADP
ap-3794	259	13	x	x	PROPN
ap-3794	259	14	∈	∈	PROPN
ap-3794	259	15	[	[	X
ap-3794	259	16	a	a	DET
ap-3794	259	17	,	,	PUNCT
ap-3794	259	18	b	b	NOUN
ap-3794	259	19	)	)	PUNCT
ap-3794	259	20	,	,	PUNCT
ap-3794	259	21	r1	r1	NOUN
ap-3794	259	22	for	for	ADP
ap-3794	259	23	x	x	PROPN
ap-3794	259	24	∈	∈	PROPN
ap-3794	259	25	[	[	X
ap-3794	259	26	b	b	X
ap-3794	259	27	,	,	PUNCT
ap-3794	259	28	d	d	NOUN
ap-3794	259	29	)	)	PUNCT
ap-3794	259	30	,	,	PUNCT
ap-3794	259	31	r1r2	r1r2	VERB
ap-3794	259	32	for	for	ADP
ap-3794	259	33	x	x	PROPN
ap-3794	259	34	∈	∈	PROPN
ap-3794	259	35	[	[	X
ap-3794	259	36	d	d	X
ap-3794	259	37	,	,	PUNCT
ap-3794	259	38	c	c	NOUN
ap-3794	259	39	)	)	PUNCT
ap-3794	259	40	,	,	PUNCT
ap-3794	259	41	r2	r2	VERB
ap-3794	259	42	for	for	ADP
ap-3794	259	43	x	x	PROPN
ap-3794	259	44	∈	∈	PROPN
ap-3794	259	45	[	[	X
ap-3794	259	46	c	c	X
ap-3794	259	47	,	,	PUNCT
ap-3794	259	48	δ	δ	PROPN
ap-3794	259	49	)	)	PUNCT
ap-3794	259	50	.	.	PUNCT
ap-3794	260	1	it	it	PRON
ap-3794	260	2	is	be	AUX
ap-3794	260	3	easy	easy	ADJ
ap-3794	260	4	to	to	PART
ap-3794	260	5	see	see	VERB
ap-3794	260	6	that	that	SCONJ
ap-3794	260	7	the	the	DET
ap-3794	260	8	lengths	length	NOUN
ap-3794	260	9	of	of	ADP
ap-3794	260	10	the	the	DET
ap-3794	260	11	above	above	ADJ
ap-3794	260	12	iitineraries	iitinerarie	NOUN
ap-3794	260	13	are	be	AUX
ap-3794	260	14	t1	t1	NOUN
ap-3794	260	15	,	,	PUNCT
ap-3794	260	16	t1	t1	NOUN
ap-3794	260	17	−	−	NOUN
ap-3794	260	18	1	1	NUM
ap-3794	260	19	,	,	PUNCT
ap-3794	260	20	t1	t1	PROPN
ap-3794	260	21	,	,	PUNCT
ap-3794	260	22	t1	t1	NOUN
ap-3794	260	23	+	+	CCONJ
ap-3794	260	24	t2	t2	NOUN
ap-3794	260	25	,	,	PUNCT
ap-3794	260	26	t2	t2	NOUN
ap-3794	260	27	,	,	PUNCT
ap-3794	260	28	respectively	respectively	ADV
ap-3794	260	29	.	.	PUNCT
ap-3794	261	1	for	for	ADP
ap-3794	261	2	that	that	PRON
ap-3794	261	3	,	,	PUNCT
ap-3794	261	4	realize	realize	VERB
ap-3794	261	5	that	that	SCONJ
ap-3794	261	6	by	by	ADP
ap-3794	261	7	definition	definition	NOUN
ap-3794	261	8	(	(	PUNCT
ap-3794	261	9	4	4	NUM
ap-3794	261	10	)	)	PUNCT
ap-3794	261	11	and	and	CCONJ
ap-3794	261	12	(	(	PUNCT
ap-3794	261	13	5	5	NUM
ap-3794	261	14	)	)	PUNCT
ap-3794	261	15	of	of	ADP
ap-3794	261	16	the	the	DET
ap-3794	261	17	action	action	NOUN
ap-3794	261	18	of	of	ADP
ap-3794	261	19	ωxy→z	ωxy→z	NOUN
ap-3794	261	20	and	and	CCONJ
ap-3794	261	21	ωz→xy	ωz→xy	NUM
ap-3794	261	22	,	,	PUNCT
ap-3794	261	23	the	the	DET
ap-3794	261	24	length	length	NOUN
ap-3794	261	25	of	of	ADP
ap-3794	261	26	the	the	DET
ap-3794	261	27	word	word	NOUN
ap-3794	261	28	ωb→ac	ωb→ac	PROPN
ap-3794	261	29	(	(	PUNCT
ap-3794	261	30	ωca→b(r1	ωca→b(r1	NOUN
ap-3794	261	31	)	)	PUNCT
ap-3794	261	32	)	)	PUNCT
ap-3794	261	33	is	be	AUX
ap-3794	261	34	equal	equal	ADJ
ap-3794	261	35	to	to	ADP
ap-3794	261	36	the	the	DET
ap-3794	261	37	length	length	NOUN
ap-3794	261	38	of	of	ADP
ap-3794	261	39	the	the	DET
ap-3794	261	40	itinerary	itinerary	ADJ
ap-3794	261	41	r1	r1	PROPN
ap-3794	261	42	,	,	PUNCT
ap-3794	261	43	i.e.	i.e.	X
ap-3794	261	44	t1	t1	NOUN
ap-3794	261	45	.	.	PUNCT
ap-3794	262	1	setting	set	VERB
ap-3794	262	2	r1	r1	PROPN
ap-3794	262	3	=	=	PUNCT
ap-3794	262	4	t1	t1	NOUN
ap-3794	262	5	−	−	NOUN
ap-3794	262	6	1	1	NUM
ap-3794	262	7	and	and	CCONJ
ap-3794	262	8	r2	r2	PROPN
ap-3794	262	9	=	=	SYM
ap-3794	262	10	t2	t2	PROPN
ap-3794	262	11	,	,	PUNCT
ap-3794	262	12	we	we	PRON
ap-3794	262	13	obtain	obtain	VERB
ap-3794	262	14	the	the	DET
ap-3794	262	15	desired	desire	VERB
ap-3794	262	16	return	return	NOUN
ap-3794	262	17	times	time	NOUN
ap-3794	262	18	.	.	PUNCT
ap-3794	263	1	the	the	DET
ap-3794	263	2	proofs	proof	NOUN
ap-3794	263	3	of	of	ADP
ap-3794	263	4	the	the	DET
ap-3794	263	5	other	other	ADJ
ap-3794	263	6	cases	case	NOUN
ap-3794	263	7	are	be	AUX
ap-3794	263	8	analogous	analogous	ADJ
ap-3794	263	9	,	,	PUNCT
ap-3794	263	10	we	we	PRON
ap-3794	263	11	state	state	VERB
ap-3794	263	12	the	the	DET
ap-3794	263	13	results	result	NOUN
ap-3794	263	14	in	in	ADP
ap-3794	263	15	terms	term	NOUN
ap-3794	263	16	of	of	ADP
ap-3794	263	17	r1	r1	NOUN
ap-3794	263	18	and	and	CCONJ
ap-3794	263	19	r2	r2	PROPN
ap-3794	263	20	.	.	PUNCT
ap-3794	264	1	(	(	PUNCT
ap-3794	264	2	ii	ii	NOUN
ap-3794	264	3	)	)	PUNCT
ap-3794	264	4	let	let	VERB
ap-3794	264	5	d	d	NOUN
ap-3794	264	6	<	<	X
ap-3794	264	7	c	c	X
ap-3794	264	8	<	<	X
ap-3794	264	9	a	a	DET
ap-3794	264	10	<	<	X
ap-3794	264	11	b.	b.	NOUN
ap-3794	264	12	we	we	PRON
ap-3794	264	13	obtain	obtain	VERB
ap-3794	264	14	r(x	r(x	NOUN
ap-3794	264	15	)	)	PUNCT
ap-3794	264	16	=	=	SYM
ap-3794	264	17			NUM
ap-3794	264	18	r1	r1	PROPN
ap-3794	264	19	for	for	ADP
ap-3794	264	20	x	x	PROPN
ap-3794	264	21	∈	∈	PROPN
ap-3794	264	22	[	[	X
ap-3794	264	23	γ	γ	X
ap-3794	264	24	,	,	PUNCT
ap-3794	264	25	d	d	NOUN
ap-3794	264	26	)	)	PUNCT
ap-3794	264	27	,	,	PUNCT
ap-3794	264	28	r2r1	r2r1	VERB
ap-3794	264	29	for	for	ADP
ap-3794	264	30	x	x	SYM
ap-3794	264	31	∈	∈	PROPN
ap-3794	264	32	[	[	X
ap-3794	264	33	d	d	X
ap-3794	264	34	,	,	PUNCT
ap-3794	264	35	c	c	NOUN
ap-3794	264	36	)	)	PUNCT
ap-3794	264	37	,	,	PUNCT
ap-3794	264	38	r2	r2	VERB
ap-3794	264	39	for	for	ADP
ap-3794	264	40	x	x	PROPN
ap-3794	264	41	∈	∈	PROPN
ap-3794	265	1	[	[	X
ap-3794	265	2	c	c	X
ap-3794	265	3	,	,	PUNCT
ap-3794	265	4	a	a	PRON
ap-3794	265	5	)	)	PUNCT
ap-3794	265	6	,	,	PUNCT
ap-3794	265	7	ωac→b(r2	ωac→b(r2	NOUN
ap-3794	265	8	)	)	PUNCT
ap-3794	265	9	for	for	ADP
ap-3794	265	10	x	x	PROPN
ap-3794	265	11	∈	∈	PROPN
ap-3794	265	12	[	[	X
ap-3794	265	13	a	a	DET
ap-3794	265	14	,	,	PUNCT
ap-3794	265	15	b	b	NOUN
ap-3794	265	16	)	)	PUNCT
ap-3794	265	17	,	,	PUNCT
ap-3794	265	18	ωb→ca	ωb→ca	NOUN
ap-3794	265	19	(	(	PUNCT
ap-3794	265	20	ωac→b(r2	ωac→b(r2	NOUN
ap-3794	265	21	)	)	PUNCT
ap-3794	265	22	)	)	PUNCT
ap-3794	265	23	for	for	ADP
ap-3794	265	24	x	x	PROPN
ap-3794	265	25	∈	∈	PROPN
ap-3794	265	26	[	[	X
ap-3794	265	27	b	b	X
ap-3794	265	28	,	,	PUNCT
ap-3794	265	29	δ	δ	PROPN
ap-3794	265	30	)	)	PUNCT
ap-3794	265	31	,	,	PUNCT
ap-3794	265	32	with	with	ADP
ap-3794	265	33	lengths	length	NOUN
ap-3794	265	34	t1	t1	VERB
ap-3794	265	35	,	,	PUNCT
ap-3794	265	36	t1	t1	NOUN
ap-3794	265	37	+	+	CCONJ
ap-3794	265	38	t2	t2	NOUN
ap-3794	265	39	,	,	PUNCT
ap-3794	265	40	t2	t2	NOUN
ap-3794	265	41	,	,	PUNCT
ap-3794	265	42	t2	t2	NOUN
ap-3794	265	43	−	−	PROPN
ap-3794	265	44	1	1	NUM
ap-3794	265	45	,	,	PUNCT
ap-3794	265	46	t2	t2	NOUN
ap-3794	265	47	,	,	PUNCT
ap-3794	265	48	respectively	respectively	ADV
ap-3794	265	49	.	.	PUNCT
ap-3794	266	1	we	we	PRON
ap-3794	266	2	set	set	VERB
ap-3794	266	3	r1	r1	PROPN
ap-3794	266	4	=	=	PROPN
ap-3794	266	5	t1	t1	PROPN
ap-3794	266	6	and	and	CCONJ
ap-3794	266	7	r2	r2	PROPN
ap-3794	266	8	=	=	SYM
ap-3794	266	9	t2	t2	PROPN
ap-3794	266	10	−	−	PROPN
ap-3794	266	11	1	1	NUM
ap-3794	266	12	.	.	PUNCT
ap-3794	267	1	(	(	PUNCT
ap-3794	267	2	iii	iii	X
ap-3794	267	3	)	)	PUNCT
ap-3794	267	4	let	let	VERB
ap-3794	267	5	b	b	X
ap-3794	267	6	<	<	X
ap-3794	267	7	a	a	PRON
ap-3794	267	8	<	<	X
ap-3794	267	9	d	d	X
ap-3794	267	10	<	<	X
ap-3794	267	11	c.	c.	PROPN
ap-3794	267	12	a	a	DET
ap-3794	267	13	discussion	discussion	NOUN
ap-3794	267	14	as	as	ADP
ap-3794	267	15	above	above	ADV
ap-3794	267	16	leads	lead	NOUN
ap-3794	267	17	to	to	ADP
ap-3794	267	18	r(x	r(x	NOUN
ap-3794	267	19	)	)	PUNCT
ap-3794	267	20	=	=	PUNCT
ap-3794	268	1			X
ap-3794	268	2	ωca→b	ωca→b	PUNCT
ap-3794	268	3	(	(	PUNCT
ap-3794	268	4	ωb→ac(r1	ωb→ac(r1	PROPN
ap-3794	268	5	)	)	PUNCT
ap-3794	268	6	)	)	PUNCT
ap-3794	269	1	for	for	ADP
ap-3794	269	2	x	x	PROPN
ap-3794	269	3	∈	∈	PROPN
ap-3794	269	4	[	[	X
ap-3794	269	5	γ	γ	X
ap-3794	269	6	,	,	PUNCT
ap-3794	269	7	b	b	NOUN
ap-3794	269	8	)	)	PUNCT
ap-3794	269	9	,	,	PUNCT
ap-3794	269	10	ωb→ac(r1	ωb→ac(r1	PROPN
ap-3794	269	11	)	)	PUNCT
ap-3794	269	12	for	for	ADP
ap-3794	269	13	x	x	PROPN
ap-3794	269	14	∈	∈	PROPN
ap-3794	270	1	[	[	X
ap-3794	270	2	b	b	NOUN
ap-3794	270	3	,	,	PUNCT
ap-3794	270	4	a	a	PRON
ap-3794	270	5	)	)	PUNCT
ap-3794	270	6	,	,	PUNCT
ap-3794	270	7	r1	r1	NOUN
ap-3794	270	8	for	for	ADP
ap-3794	270	9	x	x	PROPN
ap-3794	270	10	∈	∈	PROPN
ap-3794	270	11	[	[	X
ap-3794	270	12	a	a	X
ap-3794	270	13	,	,	PUNCT
ap-3794	270	14	d	d	NOUN
ap-3794	270	15	)	)	PUNCT
ap-3794	270	16	,	,	PUNCT
ap-3794	270	17	r1r2	r1r2	VERB
ap-3794	270	18	for	for	ADP
ap-3794	270	19	x	x	PROPN
ap-3794	270	20	∈	∈	PROPN
ap-3794	271	1	[	[	X
ap-3794	271	2	d	d	X
ap-3794	271	3	,	,	PUNCT
ap-3794	271	4	c	c	NOUN
ap-3794	271	5	)	)	PUNCT
ap-3794	271	6	,	,	PUNCT
ap-3794	271	7	r2	r2	VERB
ap-3794	271	8	for	for	ADP
ap-3794	271	9	x	x	PROPN
ap-3794	271	10	∈	∈	PROPN
ap-3794	271	11	[	[	X
ap-3794	271	12	c	c	X
ap-3794	271	13	,	,	PUNCT
ap-3794	271	14	δ	δ	PROPN
ap-3794	271	15	)	)	PUNCT
ap-3794	271	16	,	,	PUNCT
ap-3794	271	17	with	with	ADP
ap-3794	271	18	the	the	DET
ap-3794	271	19	corresponding	correspond	VERB
ap-3794	271	20	lengths	length	NOUN
ap-3794	271	21	t1	t1	VERB
ap-3794	271	22	,	,	PUNCT
ap-3794	271	23	t1	t1	NOUN
ap-3794	271	24	+	+	NOUN
ap-3794	271	25	1	1	NUM
ap-3794	271	26	,	,	PUNCT
ap-3794	271	27	t1	t1	PROPN
ap-3794	271	28	,	,	PUNCT
ap-3794	272	1	t1	t1	NOUN
ap-3794	272	2	+	+	CCONJ
ap-3794	272	3	t2	t2	NOUN
ap-3794	272	4	,	,	PUNCT
ap-3794	272	5	t2	t2	NOUN
ap-3794	272	6	,	,	PUNCT
ap-3794	272	7	respectively	respectively	ADV
ap-3794	272	8	.	.	PUNCT
ap-3794	273	1	we	we	PRON
ap-3794	273	2	set	set	VERB
ap-3794	273	3	r1	r1	PROPN
ap-3794	273	4	=	=	PROPN
ap-3794	273	5	t1	t1	PROPN
ap-3794	273	6	and	and	CCONJ
ap-3794	273	7	r2	r2	PROPN
ap-3794	273	8	=	=	SYM
ap-3794	273	9	t2	t2	PROPN
ap-3794	273	10	.	.	PUNCT
ap-3794	274	1	(	(	PUNCT
ap-3794	274	2	iv	iv	X
ap-3794	274	3	)	)	PUNCT
ap-3794	274	4	let	let	VERB
ap-3794	274	5	d	d	X
ap-3794	274	6	<	<	X
ap-3794	274	7	c	c	X
ap-3794	274	8	<	<	X
ap-3794	274	9	b	b	X
ap-3794	274	10	<	<	X
ap-3794	274	11	a.	a.	NOUN
ap-3794	274	12	we	we	PRON
ap-3794	274	13	obtain	obtain	VERB
ap-3794	274	14	r(x	r(x	NOUN
ap-3794	274	15	)	)	PUNCT
ap-3794	274	16	=	=	SYM
ap-3794	274	17			NUM
ap-3794	274	18	r1	r1	PROPN
ap-3794	274	19	for	for	ADP
ap-3794	274	20	x	x	PROPN
ap-3794	274	21	∈	∈	PROPN
ap-3794	274	22	[	[	X
ap-3794	274	23	γ	γ	X
ap-3794	274	24	,	,	PUNCT
ap-3794	274	25	d	d	NOUN
ap-3794	274	26	)	)	PUNCT
ap-3794	274	27	,	,	PUNCT
ap-3794	274	28	r2r1	r2r1	VERB
ap-3794	274	29	for	for	ADP
ap-3794	274	30	x	x	SYM
ap-3794	274	31	∈	∈	PROPN
ap-3794	274	32	[	[	X
ap-3794	274	33	d	d	X
ap-3794	274	34	,	,	PUNCT
ap-3794	274	35	c	c	NOUN
ap-3794	274	36	)	)	PUNCT
ap-3794	274	37	,	,	PUNCT
ap-3794	274	38	r2	r2	VERB
ap-3794	274	39	for	for	ADP
ap-3794	274	40	x	x	PROPN
ap-3794	274	41	∈	∈	PROPN
ap-3794	275	1	[	[	X
ap-3794	275	2	c	c	X
ap-3794	275	3	,	,	PUNCT
ap-3794	275	4	b	b	NOUN
ap-3794	275	5	)	)	PUNCT
ap-3794	275	6	,	,	PUNCT
ap-3794	275	7	ωb→ca(r2	ωb→ca(r2	NOUN
ap-3794	275	8	)	)	PUNCT
ap-3794	275	9	for	for	ADP
ap-3794	275	10	x	x	PROPN
ap-3794	275	11	∈	∈	PROPN
ap-3794	275	12	[	[	X
ap-3794	275	13	b	b	NOUN
ap-3794	275	14	,	,	PUNCT
ap-3794	275	15	a	a	PRON
ap-3794	275	16	)	)	PUNCT
ap-3794	275	17	,	,	PUNCT
ap-3794	275	18	ωac→b	ωac→b	NOUN
ap-3794	275	19	(	(	PUNCT
ap-3794	275	20	ωb→ca(r2	ωb→ca(r2	NOUN
ap-3794	275	21	)	)	PUNCT
ap-3794	275	22	)	)	PUNCT
ap-3794	275	23	for	for	ADP
ap-3794	275	24	x	x	PROPN
ap-3794	275	25	∈	∈	PROPN
ap-3794	275	26	[	[	X
ap-3794	275	27	a	a	X
ap-3794	275	28	,	,	PUNCT
ap-3794	275	29	δ	δ	PROPN
ap-3794	275	30	)	)	PUNCT
ap-3794	275	31	,	,	PUNCT
ap-3794	275	32	with	with	ADP
ap-3794	275	33	lengths	length	NOUN
ap-3794	275	34	t1	t1	VERB
ap-3794	275	35	,	,	PUNCT
ap-3794	275	36	t1	t1	NOUN
ap-3794	275	37	+	+	CCONJ
ap-3794	275	38	t2	t2	NOUN
ap-3794	275	39	,	,	PUNCT
ap-3794	275	40	t2	t2	NOUN
ap-3794	275	41	,	,	PUNCT
ap-3794	275	42	t2	t2	NOUN
ap-3794	275	43	+	+	CCONJ
ap-3794	275	44	1	1	NUM
ap-3794	275	45	,	,	PUNCT
ap-3794	275	46	t2	t2	NOUN
ap-3794	275	47	,	,	PUNCT
ap-3794	275	48	respectively	respectively	ADV
ap-3794	275	49	.	.	PUNCT
ap-3794	276	1	we	we	PRON
ap-3794	276	2	set	set	VERB
ap-3794	276	3	r1	r1	PROPN
ap-3794	276	4	=	=	PROPN
ap-3794	276	5	t1	t1	PROPN
ap-3794	276	6	and	and	CCONJ
ap-3794	276	7	r2	r2	PROPN
ap-3794	276	8	=	=	SYM
ap-3794	276	9	t2	t2	PROPN
ap-3794	276	10	.	.	PUNCT
ap-3794	277	1	(	(	PUNCT
ap-3794	277	2	v	v	NOUN
ap-3794	277	3	)	)	PUNCT
ap-3794	277	4	let	let	VERB
ap-3794	277	5	a	a	DET
ap-3794	277	6	<	<	X
ap-3794	277	7	d	d	X
ap-3794	277	8	<	<	X
ap-3794	277	9	b	b	X
ap-3794	277	10	<	<	X
ap-3794	277	11	c.	c.	PROPN
ap-3794	277	12	we	we	PRON
ap-3794	277	13	obtain	obtain	VERB
ap-3794	277	14	r(x	r(x	NOUN
ap-3794	277	15	)	)	PUNCT
ap-3794	277	16	=	=	PUNCT
ap-3794	277	17			NUM
ap-3794	277	18	ωb→ac(r1	ωb→ac(r1	PROPN
ap-3794	277	19	)	)	PUNCT
ap-3794	277	20	for	for	ADP
ap-3794	277	21	x	x	PROPN
ap-3794	277	22	∈	∈	PROPN
ap-3794	277	23	[	[	X
ap-3794	277	24	γ	γ	X
ap-3794	277	25	,	,	PUNCT
ap-3794	277	26	a	a	PRON
ap-3794	277	27	)	)	PUNCT
ap-3794	277	28	,	,	PUNCT
ap-3794	277	29	r1	r1	NOUN
ap-3794	277	30	for	for	ADP
ap-3794	277	31	x	x	PROPN
ap-3794	277	32	∈	∈	PROPN
ap-3794	277	33	[	[	X
ap-3794	277	34	a	a	X
ap-3794	277	35	,	,	PUNCT
ap-3794	277	36	d	d	NOUN
ap-3794	277	37	)	)	PUNCT
ap-3794	277	38	,	,	PUNCT
ap-3794	277	39	r1r2	r1r2	VERB
ap-3794	277	40	for	for	ADP
ap-3794	277	41	x	x	PROPN
ap-3794	277	42	∈	∈	PROPN
ap-3794	278	1	[	[	X
ap-3794	278	2	d	d	X
ap-3794	278	3	,	,	PUNCT
ap-3794	278	4	b	b	NOUN
ap-3794	278	5	)	)	PUNCT
ap-3794	278	6	,	,	PUNCT
ap-3794	278	7	r2ωb→ac(r1	r2ωb→ac(r1	PROPN
ap-3794	278	8	)	)	PUNCT
ap-3794	278	9	for	for	ADP
ap-3794	278	10	x	x	PROPN
ap-3794	278	11	∈	∈	PROPN
ap-3794	278	12	[	[	X
ap-3794	278	13	b	b	X
ap-3794	278	14	,	,	PUNCT
ap-3794	278	15	c	c	NOUN
ap-3794	278	16	)	)	PUNCT
ap-3794	278	17	,	,	PUNCT
ap-3794	278	18	r2	r2	VERB
ap-3794	278	19	for	for	ADP
ap-3794	278	20	x	x	PROPN
ap-3794	278	21	∈	∈	PROPN
ap-3794	278	22	[	[	X
ap-3794	278	23	c	c	X
ap-3794	278	24	,	,	PUNCT
ap-3794	278	25	δ	δ	PROPN
ap-3794	278	26	)	)	PUNCT
ap-3794	278	27	,	,	PUNCT
ap-3794	278	28	with	with	ADP
ap-3794	278	29	lengths	length	NOUN
ap-3794	278	30	t1	t1	VERB
ap-3794	278	31	+	+	CCONJ
ap-3794	278	32	1	1	NUM
ap-3794	278	33	,	,	PUNCT
ap-3794	278	34	t1	t1	PROPN
ap-3794	278	35	,	,	PUNCT
ap-3794	279	1	t1	t1	NOUN
ap-3794	279	2	+	+	CCONJ
ap-3794	279	3	t2	t2	NOUN
ap-3794	279	4	,	,	PUNCT
ap-3794	279	5	t1	t1	NOUN
ap-3794	279	6	+	+	CCONJ
ap-3794	279	7	t2	t2	NOUN
ap-3794	279	8	+	+	CCONJ
ap-3794	279	9	1	1	NUM
ap-3794	279	10	,	,	PUNCT
ap-3794	279	11	t2	t2	NOUN
ap-3794	279	12	,	,	PUNCT
ap-3794	279	13	respectively	respectively	ADV
ap-3794	279	14	.	.	PUNCT
ap-3794	280	1	we	we	PRON
ap-3794	280	2	set	set	VERB
ap-3794	280	3	r1	r1	PROPN
ap-3794	280	4	=	=	PROPN
ap-3794	280	5	t1	t1	PROPN
ap-3794	280	6	and	and	CCONJ
ap-3794	280	7	r2	r2	PROPN
ap-3794	280	8	=	=	SYM
ap-3794	280	9	t2	t2	PROPN
ap-3794	280	10	.	.	PUNCT
ap-3794	281	1	(	(	PUNCT
ap-3794	281	2	vi	vi	X
ap-3794	281	3	)	)	PUNCT
ap-3794	281	4	let	let	VERB
ap-3794	281	5	d	d	X
ap-3794	281	6	<	<	X
ap-3794	281	7	a	a	PRON
ap-3794	281	8	<	<	X
ap-3794	281	9	c	c	X
ap-3794	281	10	<	<	X
ap-3794	281	11	b.	b.	PROPN
ap-3794	281	12	we	we	PRON
ap-3794	281	13	obtain	obtain	VERB
ap-3794	281	14	r(x	r(x	NOUN
ap-3794	281	15	)	)	PUNCT
ap-3794	282	1	=	=	SYM
ap-3794	282	2			NUM
ap-3794	282	3	r1	r1	PROPN
ap-3794	282	4	for	for	ADP
ap-3794	282	5	x	x	PROPN
ap-3794	282	6	∈	∈	PROPN
ap-3794	282	7	[	[	X
ap-3794	282	8	γ	γ	X
ap-3794	282	9	,	,	PUNCT
ap-3794	282	10	d	d	NOUN
ap-3794	282	11	)	)	PUNCT
ap-3794	282	12	,	,	PUNCT
ap-3794	282	13	r1ωb→ca(r2	r1ωb→ca(r2	NOUN
ap-3794	282	14	)	)	PUNCT
ap-3794	282	15	for	for	ADP
ap-3794	282	16	x	x	PROPN
ap-3794	282	17	∈	∈	PROPN
ap-3794	283	1	[	[	X
ap-3794	283	2	d	d	X
ap-3794	283	3	,	,	PUNCT
ap-3794	283	4	a	a	PRON
ap-3794	283	5	)	)	PUNCT
ap-3794	283	6	,	,	PUNCT
ap-3794	283	7	r2r1	r2r1	VERB
ap-3794	283	8	for	for	ADP
ap-3794	283	9	x	x	PROPN
ap-3794	283	10	∈	∈	PROPN
ap-3794	283	11	[	[	X
ap-3794	283	12	a	a	X
ap-3794	283	13	,	,	PUNCT
ap-3794	283	14	c	c	NOUN
ap-3794	283	15	)	)	PUNCT
ap-3794	283	16	,	,	PUNCT
ap-3794	283	17	r2	r2	VERB
ap-3794	283	18	for	for	ADP
ap-3794	283	19	x	x	PROPN
ap-3794	283	20	∈	∈	PROPN
ap-3794	284	1	[	[	X
ap-3794	284	2	c	c	X
ap-3794	284	3	,	,	PUNCT
ap-3794	284	4	b	b	NOUN
ap-3794	284	5	)	)	PUNCT
ap-3794	284	6	,	,	PUNCT
ap-3794	284	7	ωb→ca(r2	ωb→ca(r2	NOUN
ap-3794	284	8	)	)	PUNCT
ap-3794	284	9	for	for	ADP
ap-3794	284	10	x	x	PROPN
ap-3794	284	11	∈	∈	PROPN
ap-3794	284	12	[	[	X
ap-3794	284	13	b	b	X
ap-3794	284	14	,	,	PUNCT
ap-3794	284	15	δ	δ	PROPN
ap-3794	284	16	)	)	PUNCT
ap-3794	284	17	,	,	PUNCT
ap-3794	284	18	with	with	ADP
ap-3794	284	19	lengths	length	NOUN
ap-3794	284	20	t1	t1	VERB
ap-3794	284	21	,	,	PUNCT
ap-3794	284	22	t1	t1	NOUN
ap-3794	284	23	+	+	CCONJ
ap-3794	284	24	t2	t2	NOUN
ap-3794	284	25	+	+	CCONJ
ap-3794	284	26	1	1	NUM
ap-3794	284	27	,	,	PUNCT
ap-3794	284	28	t1	t1	NOUN
ap-3794	284	29	+	+	CCONJ
ap-3794	284	30	t2	t2	NOUN
ap-3794	284	31	,	,	PUNCT
ap-3794	284	32	t2	t2	NOUN
ap-3794	284	33	,	,	PUNCT
ap-3794	284	34	t2	t2	NOUN
ap-3794	284	35	+	+	CCONJ
ap-3794	284	36	1	1	NUM
ap-3794	284	37	,	,	PUNCT
ap-3794	284	38	respectively	respectively	ADV
ap-3794	284	39	.	.	PUNCT
ap-3794	285	1	we	we	PRON
ap-3794	285	2	set	set	VERB
ap-3794	285	3	r1	r1	PROPN
ap-3794	285	4	=	=	PROPN
ap-3794	285	5	t1	t1	PROPN
ap-3794	285	6	and	and	CCONJ
ap-3794	285	7	r2	r2	PROPN
ap-3794	285	8	=	=	SYM
ap-3794	285	9	t2	t2	PROPN
ap-3794	285	10	.	.	PUNCT
ap-3794	286	1	(	(	PUNCT
ap-3794	286	2	vii	vii	PROPN
ap-3794	286	3	)	)	PUNCT
ap-3794	286	4	let	let	VERB
ap-3794	286	5	b	b	NOUN
ap-3794	286	6	<	<	X
ap-3794	286	7	d	d	X
ap-3794	286	8	<	<	X
ap-3794	286	9	a	a	DET
ap-3794	286	10	<	<	X
ap-3794	286	11	c.	c.	NOUN
ap-3794	286	12	we	we	PRON
ap-3794	286	13	obtain	obtain	VERB
ap-3794	286	14	r(x	r(x	NOUN
ap-3794	286	15	)	)	PUNCT
ap-3794	286	16	=	=	PUNCT
ap-3794	286	17			NUM
ap-3794	286	18	ωca→b(r1	ωca→b(r1	NUM
ap-3794	286	19	)	)	PUNCT
ap-3794	286	20	for	for	ADP
ap-3794	286	21	x	x	PROPN
ap-3794	286	22	∈	∈	PROPN
ap-3794	286	23	[	[	X
ap-3794	286	24	γ	γ	X
ap-3794	286	25	,	,	PUNCT
ap-3794	286	26	b	b	NOUN
ap-3794	286	27	)	)	PUNCT
ap-3794	286	28	,	,	PUNCT
ap-3794	286	29	r1	r1	NOUN
ap-3794	286	30	for	for	ADP
ap-3794	286	31	x	x	PROPN
ap-3794	286	32	∈	∈	PROPN
ap-3794	286	33	[	[	X
ap-3794	286	34	b	b	X
ap-3794	286	35	,	,	PUNCT
ap-3794	286	36	d	d	NOUN
ap-3794	286	37	)	)	PUNCT
ap-3794	286	38	,	,	PUNCT
ap-3794	286	39	r1r2	r1r2	VERB
ap-3794	286	40	for	for	ADP
ap-3794	286	41	x	x	PROPN
ap-3794	286	42	∈	∈	PROPN
ap-3794	287	1	[	[	X
ap-3794	287	2	d	d	X
ap-3794	287	3	,	,	PUNCT
ap-3794	287	4	a	a	PRON
ap-3794	287	5	)	)	PUNCT
ap-3794	287	6	,	,	PUNCT
ap-3794	287	7	r2ωca→b(r1	r2ωca→b(r1	NUM
ap-3794	287	8	)	)	PUNCT
ap-3794	287	9	for	for	ADP
ap-3794	287	10	x	x	PROPN
ap-3794	287	11	∈	∈	PROPN
ap-3794	287	12	[	[	X
ap-3794	287	13	a	a	X
ap-3794	287	14	,	,	PUNCT
ap-3794	287	15	c	c	NOUN
ap-3794	287	16	)	)	PUNCT
ap-3794	287	17	,	,	PUNCT
ap-3794	287	18	r2	r2	VERB
ap-3794	287	19	for	for	ADP
ap-3794	287	20	x	x	PROPN
ap-3794	287	21	∈	∈	PROPN
ap-3794	287	22	[	[	X
ap-3794	287	23	c	c	X
ap-3794	287	24	,	,	PUNCT
ap-3794	287	25	δ	δ	PROPN
ap-3794	287	26	)	)	PUNCT
ap-3794	287	27	,	,	PUNCT
ap-3794	287	28	466	466	NUM
ap-3794	287	29	vol	vol	NOUN
ap-3794	287	30	.	.	PUNCT
ap-3794	288	1	56	56	NUM
ap-3794	288	2	no	no	NOUN
ap-3794	288	3	.	.	PUNCT
ap-3794	289	1	6/2016	6/2016	NUM
ap-3794	289	2	itineraries	itinerary	NOUN
ap-3794	289	3	induced	induce	VERB
ap-3794	289	4	by	by	ADP
ap-3794	289	5	exchange	exchange	NOUN
ap-3794	289	6	of	of	ADP
ap-3794	289	7	three	three	NUM
ap-3794	289	8	intervals	interval	NOUN
ap-3794	289	9	with	with	ADP
ap-3794	289	10	lengths	length	NOUN
ap-3794	289	11	t1	t1	VERB
ap-3794	289	12	−	−	NOUN
ap-3794	289	13	1	1	NUM
ap-3794	289	14	,	,	PUNCT
ap-3794	289	15	t1	t1	PROPN
ap-3794	289	16	,	,	PUNCT
ap-3794	289	17	t1	t1	NOUN
ap-3794	289	18	+	+	CCONJ
ap-3794	289	19	t2	t2	NOUN
ap-3794	289	20	,	,	PUNCT
ap-3794	289	21	t1	t1	NOUN
ap-3794	289	22	+	+	CCONJ
ap-3794	289	23	t2	t2	PROPN
ap-3794	289	24	−	−	PROPN
ap-3794	289	25	1	1	NUM
ap-3794	289	26	,	,	PUNCT
ap-3794	289	27	t2	t2	NOUN
ap-3794	289	28	,	,	PUNCT
ap-3794	289	29	respectively	respectively	ADV
ap-3794	289	30	.	.	PUNCT
ap-3794	290	1	we	we	PRON
ap-3794	290	2	set	set	VERB
ap-3794	290	3	r1	r1	PROPN
ap-3794	290	4	=	=	PUNCT
ap-3794	290	5	t1	t1	NOUN
ap-3794	290	6	−	−	NOUN
ap-3794	290	7	1	1	NUM
ap-3794	290	8	and	and	CCONJ
ap-3794	290	9	r2	r2	PROPN
ap-3794	290	10	=	=	SYM
ap-3794	290	11	t2	t2	PROPN
ap-3794	290	12	.	.	PUNCT
ap-3794	291	1	(	(	PUNCT
ap-3794	291	2	viii	viii	NOUN
ap-3794	291	3	)	)	PUNCT
ap-3794	291	4	let	let	VERB
ap-3794	292	1	d	d	NOUN
ap-3794	292	2	<	<	X
ap-3794	292	3	b	b	X
ap-3794	292	4	<	<	X
ap-3794	292	5	c	c	X
ap-3794	292	6	<	<	X
ap-3794	292	7	a.	a.	NOUN
ap-3794	292	8	we	we	PRON
ap-3794	292	9	obtain	obtain	VERB
ap-3794	292	10	r(x	r(x	NOUN
ap-3794	292	11	)	)	PUNCT
ap-3794	292	12	=	=	SYM
ap-3794	292	13			NUM
ap-3794	292	14	r1	r1	PROPN
ap-3794	292	15	for	for	ADP
ap-3794	292	16	x	x	PROPN
ap-3794	292	17	∈	∈	PROPN
ap-3794	292	18	[	[	X
ap-3794	292	19	γ	γ	X
ap-3794	292	20	,	,	PUNCT
ap-3794	292	21	d	d	NOUN
ap-3794	292	22	)	)	PUNCT
ap-3794	292	23	,	,	PUNCT
ap-3794	292	24	r1ωac→b(r2	r1ωac→b(r2	NOUN
ap-3794	292	25	)	)	PUNCT
ap-3794	292	26	for	for	ADP
ap-3794	292	27	x	x	PROPN
ap-3794	292	28	∈	∈	PROPN
ap-3794	292	29	[	[	X
ap-3794	292	30	d	d	X
ap-3794	292	31	,	,	PUNCT
ap-3794	292	32	b	b	NOUN
ap-3794	292	33	)	)	PUNCT
ap-3794	292	34	,	,	PUNCT
ap-3794	292	35	r2r1	r2r1	VERB
ap-3794	292	36	for	for	ADP
ap-3794	292	37	x	x	PROPN
ap-3794	292	38	∈	∈	PROPN
ap-3794	292	39	[	[	X
ap-3794	292	40	b	b	X
ap-3794	292	41	,	,	PUNCT
ap-3794	292	42	c	c	NOUN
ap-3794	292	43	)	)	PUNCT
ap-3794	292	44	,	,	PUNCT
ap-3794	292	45	r2	r2	VERB
ap-3794	292	46	for	for	ADP
ap-3794	292	47	x	x	PROPN
ap-3794	292	48	∈	∈	PROPN
ap-3794	293	1	[	[	X
ap-3794	293	2	c	c	X
ap-3794	293	3	,	,	PUNCT
ap-3794	293	4	a	a	PRON
ap-3794	293	5	)	)	PUNCT
ap-3794	293	6	,	,	PUNCT
ap-3794	293	7	ωac→b(r2	ωac→b(r2	NOUN
ap-3794	293	8	)	)	PUNCT
ap-3794	293	9	for	for	ADP
ap-3794	293	10	x	x	PROPN
ap-3794	293	11	∈	∈	PROPN
ap-3794	293	12	[	[	X
ap-3794	293	13	a	a	X
ap-3794	293	14	,	,	PUNCT
ap-3794	293	15	δ	δ	PROPN
ap-3794	293	16	)	)	PUNCT
ap-3794	293	17	,	,	PUNCT
ap-3794	293	18	with	with	ADP
ap-3794	293	19	lengths	length	NOUN
ap-3794	293	20	t1	t1	VERB
ap-3794	293	21	,	,	PUNCT
ap-3794	293	22	t1	t1	NOUN
ap-3794	293	23	+	+	CCONJ
ap-3794	293	24	t2	t2	PROPN
ap-3794	293	25	−	−	PROPN
ap-3794	293	26	1	1	NUM
ap-3794	293	27	,	,	PUNCT
ap-3794	293	28	t1	t1	NOUN
ap-3794	293	29	+	+	CCONJ
ap-3794	293	30	t2	t2	NOUN
ap-3794	293	31	,	,	PUNCT
ap-3794	293	32	t2	t2	NOUN
ap-3794	293	33	,	,	PUNCT
ap-3794	293	34	t2	t2	NOUN
ap-3794	293	35	−	−	PROPN
ap-3794	293	36	1	1	NUM
ap-3794	293	37	,	,	PUNCT
ap-3794	293	38	respectively	respectively	ADV
ap-3794	293	39	.	.	PUNCT
ap-3794	294	1	we	we	PRON
ap-3794	294	2	set	set	VERB
ap-3794	294	3	r1	r1	PROPN
ap-3794	294	4	=	=	PROPN
ap-3794	294	5	t1	t1	PROPN
ap-3794	294	6	and	and	CCONJ
ap-3794	294	7	r2	r2	PROPN
ap-3794	294	8	=	=	SYM
ap-3794	294	9	t2	t2	PROPN
ap-3794	294	10	−	−	PROPN
ap-3794	294	11	1	1	NUM
ap-3794	294	12	.	.	PUNCT
ap-3794	295	1	(	(	PUNCT
ap-3794	295	2	ix	ix	ADV
ap-3794	295	3	)	)	PUNCT
ap-3794	295	4	let	let	VERB
ap-3794	295	5	a	a	DET
ap-3794	295	6	<	<	X
ap-3794	295	7	d	d	X
ap-3794	295	8	<	<	X
ap-3794	295	9	c	c	X
ap-3794	295	10	<	<	X
ap-3794	295	11	b.	b.	PROPN
ap-3794	296	1	we	we	PRON
ap-3794	296	2	obtain	obtain	VERB
ap-3794	296	3	r(x	r(x	NOUN
ap-3794	296	4	)	)	PUNCT
ap-3794	296	5	=	=	PUNCT
ap-3794	296	6			NUM
ap-3794	296	7	ωb→ac(r1	ωb→ac(r1	PROPN
ap-3794	296	8	)	)	PUNCT
ap-3794	296	9	for	for	ADP
ap-3794	296	10	x	x	PROPN
ap-3794	296	11	∈	∈	PROPN
ap-3794	296	12	[	[	X
ap-3794	296	13	γ	γ	X
ap-3794	296	14	,	,	PUNCT
ap-3794	296	15	a	a	PRON
ap-3794	296	16	)	)	PUNCT
ap-3794	296	17	,	,	PUNCT
ap-3794	296	18	r1	r1	NOUN
ap-3794	296	19	for	for	ADP
ap-3794	296	20	x	x	PROPN
ap-3794	296	21	∈	∈	PROPN
ap-3794	296	22	[	[	X
ap-3794	296	23	a	a	X
ap-3794	296	24	,	,	PUNCT
ap-3794	296	25	d	d	NOUN
ap-3794	296	26	)	)	PUNCT
ap-3794	296	27	,	,	PUNCT
ap-3794	296	28	r1ωb→ca(r2	r1ωb→ca(r2	NOUN
ap-3794	296	29	)	)	PUNCT
ap-3794	296	30	for	for	ADP
ap-3794	296	31	x	x	PROPN
ap-3794	296	32	∈	∈	PROPN
ap-3794	296	33	[	[	X
ap-3794	296	34	d	d	X
ap-3794	296	35	,	,	PUNCT
ap-3794	296	36	c	c	NOUN
ap-3794	296	37	)	)	PUNCT
ap-3794	296	38	,	,	PUNCT
ap-3794	296	39	r2	r2	VERB
ap-3794	296	40	for	for	ADP
ap-3794	296	41	x	x	PROPN
ap-3794	296	42	∈	∈	PROPN
ap-3794	297	1	[	[	X
ap-3794	297	2	c	c	X
ap-3794	297	3	,	,	PUNCT
ap-3794	297	4	b	b	NOUN
ap-3794	297	5	)	)	PUNCT
ap-3794	297	6	,	,	PUNCT
ap-3794	297	7	ωb→ca(r2	ωb→ca(r2	NOUN
ap-3794	297	8	)	)	PUNCT
ap-3794	297	9	for	for	ADP
ap-3794	297	10	x	x	PROPN
ap-3794	297	11	∈	∈	PROPN
ap-3794	297	12	[	[	X
ap-3794	297	13	b	b	X
ap-3794	297	14	,	,	PUNCT
ap-3794	297	15	δ	δ	PROPN
ap-3794	297	16	)	)	PUNCT
ap-3794	297	17	,	,	PUNCT
ap-3794	297	18	with	with	ADP
ap-3794	297	19	lengths	length	NOUN
ap-3794	297	20	t1	t1	VERB
ap-3794	297	21	+	+	CCONJ
ap-3794	297	22	1	1	NUM
ap-3794	297	23	,	,	PUNCT
ap-3794	297	24	t1	t1	PROPN
ap-3794	297	25	,	,	PUNCT
ap-3794	297	26	t1	t1	NOUN
ap-3794	297	27	+	+	CCONJ
ap-3794	297	28	t2	t2	NOUN
ap-3794	297	29	+	+	CCONJ
ap-3794	297	30	1	1	NUM
ap-3794	297	31	,	,	PUNCT
ap-3794	297	32	t2	t2	NOUN
ap-3794	297	33	,	,	PUNCT
ap-3794	297	34	t2	t2	NOUN
ap-3794	297	35	+	+	CCONJ
ap-3794	297	36	1	1	NUM
ap-3794	297	37	,	,	PUNCT
ap-3794	297	38	respectively	respectively	ADV
ap-3794	297	39	.	.	PUNCT
ap-3794	298	1	we	we	PRON
ap-3794	298	2	set	set	VERB
ap-3794	298	3	r1	r1	PROPN
ap-3794	298	4	=	=	PROPN
ap-3794	298	5	t1	t1	PROPN
ap-3794	298	6	and	and	CCONJ
ap-3794	298	7	r2	r2	PROPN
ap-3794	298	8	=	=	SYM
ap-3794	298	9	t2	t2	PROPN
ap-3794	298	10	.	.	PUNCT
ap-3794	299	1	(	(	PUNCT
ap-3794	299	2	x	x	X
ap-3794	299	3	)	)	PUNCT
ap-3794	299	4	let	let	VERB
ap-3794	299	5	b	b	NOUN
ap-3794	299	6	<	<	X
ap-3794	299	7	d	d	X
ap-3794	299	8	<	<	X
ap-3794	299	9	c	c	X
ap-3794	299	10	<	<	X
ap-3794	299	11	a.	a.	NOUN
ap-3794	299	12	we	we	PRON
ap-3794	299	13	obtain	obtain	VERB
ap-3794	299	14	r(x	r(x	NOUN
ap-3794	299	15	)	)	PUNCT
ap-3794	299	16	=	=	PUNCT
ap-3794	299	17			NUM
ap-3794	299	18	ωca→b(r1	ωca→b(r1	NUM
ap-3794	299	19	)	)	PUNCT
ap-3794	299	20	for	for	ADP
ap-3794	299	21	x	x	PROPN
ap-3794	299	22	∈	∈	PROPN
ap-3794	299	23	[	[	X
ap-3794	299	24	γ	γ	X
ap-3794	299	25	,	,	PUNCT
ap-3794	299	26	b	b	NOUN
ap-3794	299	27	)	)	PUNCT
ap-3794	299	28	,	,	PUNCT
ap-3794	299	29	r1	r1	NOUN
ap-3794	299	30	for	for	ADP
ap-3794	299	31	x	x	PROPN
ap-3794	299	32	∈	∈	PROPN
ap-3794	299	33	[	[	X
ap-3794	299	34	b	b	X
ap-3794	299	35	,	,	PUNCT
ap-3794	299	36	d	d	NOUN
ap-3794	299	37	)	)	PUNCT
ap-3794	299	38	,	,	PUNCT
ap-3794	299	39	r1ωac→b(r2	r1ωac→b(r2	NOUN
ap-3794	299	40	)	)	PUNCT
ap-3794	299	41	for	for	ADP
ap-3794	299	42	x	x	PROPN
ap-3794	299	43	∈	∈	PROPN
ap-3794	299	44	[	[	X
ap-3794	299	45	d	d	X
ap-3794	299	46	,	,	PUNCT
ap-3794	299	47	c	c	NOUN
ap-3794	299	48	)	)	PUNCT
ap-3794	299	49	,	,	PUNCT
ap-3794	299	50	r2	r2	VERB
ap-3794	299	51	for	for	ADP
ap-3794	299	52	x	x	PROPN
ap-3794	299	53	∈	∈	PROPN
ap-3794	300	1	[	[	X
ap-3794	300	2	c	c	X
ap-3794	300	3	,	,	PUNCT
ap-3794	300	4	a	a	PRON
ap-3794	300	5	)	)	PUNCT
ap-3794	300	6	,	,	PUNCT
ap-3794	300	7	ωac→b(r2	ωac→b(r2	NOUN
ap-3794	300	8	)	)	PUNCT
ap-3794	300	9	for	for	ADP
ap-3794	300	10	x	x	PROPN
ap-3794	300	11	∈	∈	PROPN
ap-3794	300	12	[	[	X
ap-3794	300	13	a	a	X
ap-3794	300	14	,	,	PUNCT
ap-3794	300	15	δ	δ	PROPN
ap-3794	300	16	)	)	PUNCT
ap-3794	300	17	,	,	PUNCT
ap-3794	300	18	with	with	ADP
ap-3794	300	19	lengths	length	NOUN
ap-3794	300	20	t1−	t1−	NOUN
ap-3794	300	21	1	1	NUM
ap-3794	300	22	,	,	PUNCT
ap-3794	300	23	t1	t1	PROPN
ap-3794	300	24	,	,	PUNCT
ap-3794	300	25	t1	t1	NOUN
ap-3794	300	26	+	+	CCONJ
ap-3794	300	27	t2−	t2−	NOUN
ap-3794	300	28	1	1	NUM
ap-3794	300	29	,	,	PUNCT
ap-3794	300	30	t2	t2	NOUN
ap-3794	300	31	,	,	PUNCT
ap-3794	300	32	t2−	t2−	NOUN
ap-3794	300	33	1	1	NUM
ap-3794	300	34	,	,	PUNCT
ap-3794	300	35	respectively	respectively	ADV
ap-3794	300	36	.	.	PUNCT
ap-3794	301	1	we	we	PRON
ap-3794	301	2	set	set	VERB
ap-3794	301	3	r1	r1	PROPN
ap-3794	301	4	=	=	PUNCT
ap-3794	301	5	t1	t1	NOUN
ap-3794	301	6	−	−	NOUN
ap-3794	301	7	1	1	NUM
ap-3794	301	8	and	and	CCONJ
ap-3794	301	9	r2	r2	PROPN
ap-3794	301	10	=	=	SYM
ap-3794	301	11	t2	t2	PROPN
ap-3794	301	12	−	−	PROPN
ap-3794	301	13	1	1	NUM
ap-3794	301	14	.	.	PUNCT
ap-3794	302	1	(	(	PUNCT
ap-3794	302	2	xi	xi	X
ap-3794	302	3	)	)	PUNCT
ap-3794	302	4	let	let	VERB
ap-3794	302	5	d	d	X
ap-3794	302	6	<	<	X
ap-3794	302	7	a	a	DET
ap-3794	302	8	<	<	X
ap-3794	302	9	b	b	X
ap-3794	302	10	<	<	X
ap-3794	302	11	c.	c.	NOUN
ap-3794	302	12	we	we	PRON
ap-3794	302	13	obtain	obtain	VERB
ap-3794	302	14	r(x	r(x	NOUN
ap-3794	302	15	)	)	PUNCT
ap-3794	303	1	=	=	SYM
ap-3794	303	2			NUM
ap-3794	303	3	r1	r1	PROPN
ap-3794	303	4	for	for	ADP
ap-3794	303	5	x	x	PROPN
ap-3794	303	6	∈	∈	PROPN
ap-3794	303	7	[	[	X
ap-3794	303	8	γ	γ	X
ap-3794	303	9	,	,	PUNCT
ap-3794	303	10	d	d	NOUN
ap-3794	303	11	)	)	PUNCT
ap-3794	303	12	,	,	PUNCT
ap-3794	303	13	r1r2	r1r2	VERB
ap-3794	303	14	for	for	ADP
ap-3794	303	15	x	x	PROPN
ap-3794	303	16	∈	∈	PROPN
ap-3794	304	1	[	[	X
ap-3794	304	2	d	d	X
ap-3794	304	3	,	,	PUNCT
ap-3794	304	4	a	a	PRON
ap-3794	304	5	)	)	PUNCT
ap-3794	304	6	,	,	PUNCT
ap-3794	304	7	ωca→b(r2r1	ωca→b(r2r1	NOUN
ap-3794	304	8	)	)	PUNCT
ap-3794	304	9	for	for	ADP
ap-3794	304	10	x	x	PROPN
ap-3794	304	11	∈	∈	PROPN
ap-3794	304	12	[	[	X
ap-3794	304	13	a	a	DET
ap-3794	304	14	,	,	PUNCT
ap-3794	304	15	b	b	NOUN
ap-3794	304	16	)	)	PUNCT
ap-3794	304	17	,	,	PUNCT
ap-3794	304	18	r2r1	r2r1	VERB
ap-3794	304	19	for	for	ADP
ap-3794	304	20	x	x	PROPN
ap-3794	304	21	∈	∈	PROPN
ap-3794	304	22	[	[	X
ap-3794	304	23	b	b	X
ap-3794	304	24	,	,	PUNCT
ap-3794	304	25	c	c	NOUN
ap-3794	304	26	)	)	PUNCT
ap-3794	304	27	,	,	PUNCT
ap-3794	304	28	r2	r2	VERB
ap-3794	304	29	for	for	ADP
ap-3794	304	30	x	x	PROPN
ap-3794	304	31	∈	∈	PROPN
ap-3794	304	32	[	[	X
ap-3794	304	33	c	c	X
ap-3794	304	34	,	,	PUNCT
ap-3794	304	35	δ	δ	PROPN
ap-3794	304	36	)	)	PUNCT
ap-3794	304	37	,	,	PUNCT
ap-3794	304	38	with	with	ADP
ap-3794	304	39	lengths	length	NOUN
ap-3794	304	40	t1	t1	VERB
ap-3794	304	41	,	,	PUNCT
ap-3794	304	42	t1	t1	NOUN
ap-3794	304	43	+	+	CCONJ
ap-3794	304	44	t2	t2	NOUN
ap-3794	304	45	,	,	PUNCT
ap-3794	304	46	t1	t1	NOUN
ap-3794	304	47	+	+	CCONJ
ap-3794	304	48	t2	t2	PROPN
ap-3794	304	49	−	−	PROPN
ap-3794	304	50	1	1	NUM
ap-3794	304	51	,	,	PUNCT
ap-3794	304	52	t1	t1	NOUN
ap-3794	304	53	+	+	CCONJ
ap-3794	304	54	t2	t2	NOUN
ap-3794	304	55	,	,	PUNCT
ap-3794	304	56	t2	t2	NOUN
ap-3794	304	57	,	,	PUNCT
ap-3794	304	58	respectively	respectively	ADV
ap-3794	304	59	.	.	PUNCT
ap-3794	305	1	we	we	PRON
ap-3794	305	2	set	set	VERB
ap-3794	305	3	r1	r1	PROPN
ap-3794	305	4	=	=	PUNCT
ap-3794	305	5	t1	t1	NOUN
ap-3794	305	6	−	−	NOUN
ap-3794	305	7	1	1	NUM
ap-3794	305	8	and	and	CCONJ
ap-3794	305	9	r2	r2	PROPN
ap-3794	305	10	=	=	SYM
ap-3794	305	11	t2	t2	PROPN
ap-3794	305	12	.	.	PUNCT
ap-3794	306	1	(	(	PUNCT
ap-3794	306	2	xii	xii	NOUN
ap-3794	306	3	)	)	PUNCT
ap-3794	306	4	let	let	VERB
ap-3794	306	5	d	d	NOUN
ap-3794	306	6	<	<	X
ap-3794	306	7	b	b	X
ap-3794	306	8	<	<	X
ap-3794	306	9	a	a	DET
ap-3794	306	10	<	<	X
ap-3794	306	11	c.	c.	NOUN
ap-3794	306	12	we	we	PRON
ap-3794	306	13	obtain	obtain	VERB
ap-3794	306	14	r(x	r(x	NOUN
ap-3794	306	15	)	)	PUNCT
ap-3794	306	16	=	=	SYM
ap-3794	306	17			NUM
ap-3794	306	18	r1	r1	PROPN
ap-3794	306	19	for	for	ADP
ap-3794	306	20	x	x	PROPN
ap-3794	306	21	∈	∈	PROPN
ap-3794	306	22	[	[	X
ap-3794	306	23	γ	γ	X
ap-3794	306	24	,	,	PUNCT
ap-3794	306	25	d	d	NOUN
ap-3794	306	26	)	)	PUNCT
ap-3794	306	27	,	,	PUNCT
ap-3794	306	28	r1r2	r1r2	VERB
ap-3794	306	29	for	for	ADP
ap-3794	306	30	x	x	PROPN
ap-3794	306	31	∈	∈	PROPN
ap-3794	307	1	[	[	X
ap-3794	307	2	d	d	X
ap-3794	307	3	,	,	PUNCT
ap-3794	307	4	b	b	NOUN
ap-3794	307	5	)	)	PUNCT
ap-3794	307	6	,	,	PUNCT
ap-3794	307	7	ωb→ac(r2r1	ωb→ac(r2r1	NOUN
ap-3794	307	8	)	)	PUNCT
ap-3794	307	9	for	for	ADP
ap-3794	307	10	x	x	PROPN
ap-3794	307	11	∈	∈	PROPN
ap-3794	307	12	[	[	X
ap-3794	307	13	b	b	NOUN
ap-3794	307	14	,	,	PUNCT
ap-3794	307	15	a	a	PRON
ap-3794	307	16	)	)	PUNCT
ap-3794	307	17	,	,	PUNCT
ap-3794	307	18	r2r1	r2r1	VERB
ap-3794	307	19	for	for	ADP
ap-3794	307	20	x	x	PROPN
ap-3794	307	21	∈	∈	PROPN
ap-3794	307	22	[	[	X
ap-3794	307	23	a	a	X
ap-3794	307	24	,	,	PUNCT
ap-3794	307	25	c	c	NOUN
ap-3794	307	26	)	)	PUNCT
ap-3794	307	27	,	,	PUNCT
ap-3794	307	28	r2	r2	VERB
ap-3794	307	29	for	for	ADP
ap-3794	307	30	x	x	PROPN
ap-3794	307	31	∈	∈	PROPN
ap-3794	307	32	[	[	X
ap-3794	307	33	c	c	X
ap-3794	307	34	,	,	PUNCT
ap-3794	307	35	δ	δ	PROPN
ap-3794	307	36	)	)	PUNCT
ap-3794	307	37	,	,	PUNCT
ap-3794	307	38	with	with	ADP
ap-3794	307	39	lengths	length	NOUN
ap-3794	307	40	t1	t1	VERB
ap-3794	307	41	,	,	PUNCT
ap-3794	308	1	t1	t1	NOUN
ap-3794	308	2	+	+	CCONJ
ap-3794	308	3	t2	t2	NOUN
ap-3794	308	4	,	,	PUNCT
ap-3794	308	5	t1	t1	NOUN
ap-3794	308	6	+	+	CCONJ
ap-3794	308	7	t2	t2	NOUN
ap-3794	309	1	+	+	CCONJ
ap-3794	310	1	1	1	NUM
ap-3794	310	2	,	,	PUNCT
ap-3794	310	3	t1	t1	NOUN
ap-3794	310	4	+	+	CCONJ
ap-3794	310	5	t2	t2	NOUN
ap-3794	310	6	,	,	PUNCT
ap-3794	310	7	t2	t2	NOUN
ap-3794	310	8	,	,	PUNCT
ap-3794	310	9	respectively	respectively	ADV
ap-3794	310	10	.	.	PUNCT
ap-3794	311	1	we	we	PRON
ap-3794	311	2	set	set	VERB
ap-3794	311	3	r1	r1	PROPN
ap-3794	311	4	=	=	PROPN
ap-3794	311	5	t1	t1	PROPN
ap-3794	311	6	and	and	CCONJ
ap-3794	311	7	r2	r2	PROPN
ap-3794	311	8	=	=	SYM
ap-3794	311	9	t2	t2	PROPN
ap-3794	311	10	.	.	PUNCT
ap-3794	312	1	remark	remark	PROPN
ap-3794	312	2	4.4	4.4	NUM
ap-3794	312	3	.	.	PUNCT
ap-3794	313	1	when	when	SCONJ
ap-3794	313	2	describing	describe	VERB
ap-3794	313	3	the	the	DET
ap-3794	313	4	i	i	NOUN
ap-3794	313	5	-	-	NOUN
ap-3794	313	6	itineraries	itinerary	NOUN
ap-3794	313	7	using	use	VERB
ap-3794	313	8	the	the	DET
ap-3794	313	9	words	word	NOUN
ap-3794	313	10	r1	r1	PROPN
ap-3794	313	11	,	,	PUNCT
ap-3794	313	12	r2	r2	PROPN
ap-3794	313	13	,	,	PUNCT
ap-3794	313	14	we	we	PRON
ap-3794	313	15	could	could	AUX
ap-3794	313	16	apply	apply	VERB
ap-3794	313	17	the	the	DET
ap-3794	313	18	rules	rule	NOUN
ap-3794	313	19	of	of	ADP
ap-3794	313	20	γ	γ	PROPN
ap-3794	313	21	δ	δ	PROPN
ap-3794	313	22	type	type	NOUN
ap-3794	313	23	lengths	length	NOUN
ap-3794	313	24	6	6	NUM
ap-3794	313	25	25	25	NUM
ap-3794	313	26	99	99	NUM
ap-3794	313	27	100	100	NUM
ap-3794	313	28	a	a	DET
ap-3794	313	29	<	<	X
ap-3794	313	30	b	b	X
ap-3794	313	31	<	<	X
ap-3794	313	32	d	d	X
ap-3794	313	33	<	<	X
ap-3794	313	34	c	c	PROPN
ap-3794	314	1	[	[	X
ap-3794	314	2	2	2	NUM
ap-3794	314	3	,	,	PUNCT
ap-3794	314	4	1	1	NUM
ap-3794	314	5	,	,	PUNCT
ap-3794	314	6	2	2	NUM
ap-3794	314	7	,	,	PUNCT
ap-3794	314	8	3	3	NUM
ap-3794	314	9	,	,	PUNCT
ap-3794	314	10	1	1	NUM
ap-3794	314	11	]	]	SYM
ap-3794	314	12	29	29	NUM
ap-3794	314	13	100	100	NUM
ap-3794	314	14	71	71	NUM
ap-3794	314	15	100	100	NUM
ap-3794	315	1	d	d	NOUN
ap-3794	315	2	<	<	X
ap-3794	315	3	c	c	X
ap-3794	315	4	<	<	X
ap-3794	315	5	a	a	PRON
ap-3794	315	6	<	<	X
ap-3794	315	7	b	b	X
ap-3794	316	1	[	[	X
ap-3794	316	2	1	1	NUM
ap-3794	316	3	,	,	PUNCT
ap-3794	316	4	15	15	NUM
ap-3794	316	5	,	,	PUNCT
ap-3794	316	6	14	14	NUM
ap-3794	316	7	,	,	PUNCT
ap-3794	316	8	13	13	NUM
ap-3794	316	9	,	,	PUNCT
ap-3794	316	10	14	14	NUM
ap-3794	316	11	]	]	SYM
ap-3794	316	12	77	77	NUM
ap-3794	316	13	100	100	NUM
ap-3794	316	14	4	4	NUM
ap-3794	316	15	5	5	NUM
ap-3794	316	16	b	b	NOUN
ap-3794	316	17	<	<	X
ap-3794	316	18	a	a	DET
ap-3794	316	19	<	<	X
ap-3794	316	20	d	d	X
ap-3794	316	21	<	<	X
ap-3794	316	22	c	c	PROPN
ap-3794	317	1	[	[	X
ap-3794	317	2	88	88	NUM
ap-3794	317	3	,	,	PUNCT
ap-3794	317	4	89	89	NUM
ap-3794	317	5	,	,	PUNCT
ap-3794	317	6	88	88	NUM
ap-3794	317	7	,	,	PUNCT
ap-3794	317	8	109	109	NUM
ap-3794	317	9	,	,	PUNCT
ap-3794	317	10	21	21	NUM
ap-3794	317	11	]	]	SYM
ap-3794	317	12	7	7	NUM
ap-3794	317	13	25	25	NUM
ap-3794	317	14	3	3	NUM
ap-3794	317	15	4	4	NUM
ap-3794	317	16	d	d	NOUN
ap-3794	317	17	<	<	X
ap-3794	317	18	c	c	X
ap-3794	317	19	<	<	X
ap-3794	317	20	b	b	X
ap-3794	317	21	<	<	X
ap-3794	317	22	a	a	DET
ap-3794	317	23	[	[	X
ap-3794	317	24	1	1	NUM
ap-3794	317	25	,	,	PUNCT
ap-3794	317	26	13	13	NUM
ap-3794	317	27	,	,	PUNCT
ap-3794	317	28	12	12	NUM
ap-3794	317	29	,	,	PUNCT
ap-3794	317	30	13	13	NUM
ap-3794	317	31	,	,	PUNCT
ap-3794	317	32	12	12	NUM
ap-3794	317	33	]	]	SYM
ap-3794	317	34	1	1	NUM
ap-3794	317	35	100	100	NUM
ap-3794	317	36	3	3	NUM
ap-3794	317	37	4	4	NUM
ap-3794	317	38	a	a	DET
ap-3794	317	39	<	<	X
ap-3794	317	40	d	d	X
ap-3794	317	41	<	<	X
ap-3794	317	42	b	b	X
ap-3794	317	43	<	<	X
ap-3794	317	44	c	c	PROPN
ap-3794	318	1	[	[	X
ap-3794	318	2	2	2	NUM
ap-3794	318	3	,	,	PUNCT
ap-3794	318	4	1	1	NUM
ap-3794	318	5	,	,	PUNCT
ap-3794	318	6	2	2	NUM
ap-3794	318	7	,	,	PUNCT
ap-3794	318	8	3	3	NUM
ap-3794	318	9	,	,	PUNCT
ap-3794	318	10	1	1	NUM
ap-3794	318	11	]	]	SYM
ap-3794	318	12	1	1	NUM
ap-3794	318	13	100	100	NUM
ap-3794	318	14	29	29	NUM
ap-3794	318	15	100	100	NUM
ap-3794	318	16	d	d	ADP
ap-3794	318	17	<	<	X
ap-3794	318	18	a	a	X
ap-3794	318	19	<	<	X
ap-3794	318	20	c	c	X
ap-3794	318	21	<	<	X
ap-3794	318	22	b	b	X
ap-3794	319	1	[	[	X
ap-3794	319	2	2	2	NUM
ap-3794	319	3	,	,	PUNCT
ap-3794	319	4	14	14	NUM
ap-3794	319	5	,	,	PUNCT
ap-3794	319	6	13	13	NUM
ap-3794	319	7	,	,	PUNCT
ap-3794	319	8	11	11	NUM
ap-3794	319	9	,	,	PUNCT
ap-3794	319	10	12	12	NUM
ap-3794	319	11	]	]	SYM
ap-3794	319	12	1	1	NUM
ap-3794	319	13	4	4	NUM
ap-3794	319	14	99	99	NUM
ap-3794	319	15	100	100	NUM
ap-3794	319	16	b	b	NOUN
ap-3794	319	17	<	<	X
ap-3794	319	18	d	d	X
ap-3794	319	19	<	<	X
ap-3794	319	20	a	a	PRON
ap-3794	319	21	<	<	X
ap-3794	319	22	c	c	NOUN
ap-3794	320	1	[	[	X
ap-3794	320	2	1	1	NUM
ap-3794	320	3	,	,	PUNCT
ap-3794	320	4	2	2	NUM
ap-3794	320	5	,	,	PUNCT
ap-3794	320	6	3	3	NUM
ap-3794	320	7	,	,	PUNCT
ap-3794	320	8	2	2	NUM
ap-3794	320	9	,	,	PUNCT
ap-3794	320	10	1	1	NUM
ap-3794	320	11	]	]	SYM
ap-3794	320	12	71	71	NUM
ap-3794	320	13	100	100	NUM
ap-3794	320	14	99	99	NUM
ap-3794	320	15	100	100	NUM
ap-3794	321	1	d	d	NOUN
ap-3794	321	2	<	<	X
ap-3794	321	3	b	b	X
ap-3794	321	4	<	<	X
ap-3794	321	5	c	c	X
ap-3794	321	6	<	<	X
ap-3794	321	7	a	a	DET
ap-3794	321	8	[	[	X
ap-3794	321	9	2	2	NUM
ap-3794	321	10	,	,	PUNCT
ap-3794	321	11	13	13	NUM
ap-3794	321	12	,	,	PUNCT
ap-3794	321	13	14	14	NUM
ap-3794	321	14	,	,	PUNCT
ap-3794	321	15	12	12	NUM
ap-3794	321	16	,	,	PUNCT
ap-3794	321	17	11	11	NUM
ap-3794	321	18	]	]	SYM
ap-3794	321	19	1	1	NUM
ap-3794	321	20	25	25	NUM
ap-3794	321	21	37	37	NUM
ap-3794	321	22	50	50	NUM
ap-3794	321	23	a	a	DET
ap-3794	321	24	<	<	X
ap-3794	321	25	d	d	X
ap-3794	321	26	<	<	X
ap-3794	321	27	c	c	X
ap-3794	321	28	<	<	X
ap-3794	321	29	b	b	X
ap-3794	322	1	[	[	X
ap-3794	322	2	2	2	NUM
ap-3794	322	3	,	,	PUNCT
ap-3794	322	4	1	1	NUM
ap-3794	322	5	,	,	PUNCT
ap-3794	322	6	4	4	NUM
ap-3794	322	7	,	,	PUNCT
ap-3794	322	8	2	2	NUM
ap-3794	322	9	,	,	PUNCT
ap-3794	322	10	3	3	NUM
ap-3794	322	11	]	]	SYM
ap-3794	322	12	29	29	NUM
ap-3794	322	13	100	100	NUM
ap-3794	322	14	99	99	NUM
ap-3794	322	15	100	100	NUM
ap-3794	322	16	b	b	NOUN
ap-3794	322	17	<	<	X
ap-3794	322	18	d	d	X
ap-3794	322	19	<	<	X
ap-3794	322	20	c	c	X
ap-3794	322	21	<	<	X
ap-3794	322	22	a	a	DET
ap-3794	322	23	[	[	X
ap-3794	322	24	1	1	NUM
ap-3794	322	25	,	,	PUNCT
ap-3794	322	26	2	2	NUM
ap-3794	322	27	,	,	PUNCT
ap-3794	322	28	4	4	NUM
ap-3794	322	29	,	,	PUNCT
ap-3794	322	30	3	3	NUM
ap-3794	322	31	,	,	PUNCT
ap-3794	322	32	2	2	NUM
ap-3794	322	33	]	]	SYM
ap-3794	322	34	1	1	NUM
ap-3794	322	35	100	100	NUM
ap-3794	322	36	99	99	NUM
ap-3794	322	37	100	100	NUM
ap-3794	322	38	d	d	ADP
ap-3794	322	39	<	<	X
ap-3794	322	40	a	a	DET
ap-3794	322	41	<	<	X
ap-3794	322	42	b	b	X
ap-3794	322	43	<	<	X
ap-3794	322	44	c	c	PROPN
ap-3794	323	1	[	[	X
ap-3794	323	2	1	1	NUM
ap-3794	323	3	,	,	PUNCT
ap-3794	323	4	2	2	NUM
ap-3794	323	5	,	,	PUNCT
ap-3794	323	6	1	1	NUM
ap-3794	323	7	,	,	PUNCT
ap-3794	323	8	2	2	NUM
ap-3794	323	9	,	,	PUNCT
ap-3794	323	10	1	1	NUM
ap-3794	323	11	]	]	SYM
ap-3794	323	12	1	1	NUM
ap-3794	323	13	4	4	NUM
ap-3794	323	14	3	3	NUM
ap-3794	323	15	4	4	NUM
ap-3794	323	16	d	d	NOUN
ap-3794	323	17	<	<	X
ap-3794	323	18	b	b	X
ap-3794	323	19	<	<	X
ap-3794	323	20	a	a	PRON
ap-3794	323	21	<	<	X
ap-3794	323	22	c	c	X
ap-3794	324	1	[	[	X
ap-3794	324	2	1	1	NUM
ap-3794	324	3	,	,	PUNCT
ap-3794	324	4	12	12	NUM
ap-3794	324	5	,	,	PUNCT
ap-3794	324	6	13	13	NUM
ap-3794	324	7	,	,	PUNCT
ap-3794	324	8	12	12	NUM
ap-3794	324	9	,	,	PUNCT
ap-3794	324	10	11	11	NUM
ap-3794	324	11	]	]	SYM
ap-3794	324	12	table	table	NOUN
ap-3794	324	13	1	1	NUM
ap-3794	324	14	.	.	PUNCT
ap-3794	325	1	the	the	DET
ap-3794	325	2	cases	case	NOUN
ap-3794	325	3	(	(	PUNCT
ap-3794	325	4	i)–(xii	i)–(xii	NOUN
ap-3794	325	5	)	)	PUNCT
ap-3794	325	6	from	from	ADP
ap-3794	325	7	the	the	DET
ap-3794	325	8	proof	proof	NOUN
ap-3794	325	9	of	of	ADP
ap-3794	325	10	theorem	theorem	NOUN
ap-3794	325	11	4.1	4.1	NUM
ap-3794	325	12	for	for	ADP
ap-3794	325	13	α	α	NOUN
ap-3794	325	14	=	=	SYM
ap-3794	325	15	1	1	NUM
ap-3794	325	16	5	5	NUM
ap-3794	325	17	√	√	NUM
ap-3794	325	18	5	5	NUM
ap-3794	325	19	−	−	NOUN
ap-3794	325	20	1	1	NUM
ap-3794	325	21	5	5	NUM
ap-3794	325	22	,	,	PUNCT
ap-3794	325	23	β	β	X
ap-3794	325	24	=	=	SYM
ap-3794	325	25	−	−	PROPN
ap-3794	325	26	1	1	NUM
ap-3794	325	27	6	6	NUM
ap-3794	325	28	√	√	NUM
ap-3794	325	29	5	5	NUM
ap-3794	325	30	+	+	CCONJ
ap-3794	325	31	2	2	NUM
ap-3794	325	32	3	3	NUM
ap-3794	325	33	as	as	ADP
ap-3794	325	34	in	in	ADP
ap-3794	325	35	example	example	NOUN
ap-3794	325	36	4.5	4.5	NUM
ap-3794	325	37	.	.	PUNCT
ap-3794	326	1	the	the	DET
ap-3794	326	2	endpoints	endpoint	NOUN
ap-3794	326	3	of	of	ADP
ap-3794	326	4	the	the	DET
ap-3794	326	5	interval	interval	NOUN
ap-3794	326	6	i	i	PRON
ap-3794	327	1	=	=	PUNCT
ap-3794	328	1	[	[	X
ap-3794	328	2	γ	γ	X
ap-3794	328	3	,	,	PUNCT
ap-3794	328	4	δ	δ	PROPN
ap-3794	328	5	)	)	PUNCT
ap-3794	328	6	are	be	AUX
ap-3794	328	7	in	in	ADP
ap-3794	328	8	the	the	DET
ap-3794	328	9	first	first	ADJ
ap-3794	328	10	and	and	CCONJ
ap-3794	328	11	second	second	ADJ
ap-3794	328	12	column	column	NOUN
ap-3794	328	13	.	.	PUNCT
ap-3794	329	1	the	the	DET
ap-3794	329	2	last	last	ADJ
ap-3794	329	3	column	column	NOUN
ap-3794	329	4	contains	contain	VERB
ap-3794	329	5	a	a	DET
ap-3794	329	6	list	list	NOUN
ap-3794	329	7	of	of	ADP
ap-3794	329	8	lengths	length	NOUN
ap-3794	329	9	of	of	ADP
ap-3794	329	10	i	i	NOUN
ap-3794	329	11	-	-	PUNCT
ap-3794	329	12	itineraries	itinerary	NOUN
ap-3794	329	13	of	of	ADP
ap-3794	329	14	all	all	DET
ap-3794	329	15	5	5	NUM
ap-3794	329	16	subintervals	subinterval	NOUN
ap-3794	329	17	of	of	ADP
ap-3794	329	18	i	i	PRON
ap-3794	329	19	starting	start	VERB
ap-3794	329	20	from	from	ADP
ap-3794	329	21	the	the	DET
ap-3794	329	22	leftmost	leftmost	PROPN
ap-3794	329	23	one	one	NUM
ap-3794	329	24	.	.	PUNCT
ap-3794	330	1	lemma	lemma	PROPN
ap-3794	330	2	4.2	4.2	NUM
ap-3794	330	3	in	in	ADP
ap-3794	330	4	a	a	DET
ap-3794	330	5	different	different	ADJ
ap-3794	330	6	order	order	NOUN
ap-3794	330	7	.	.	PUNCT
ap-3794	331	1	by	by	ADP
ap-3794	331	2	doing	do	VERB
ap-3794	331	3	so	so	ADV
ap-3794	331	4	,	,	PUNCT
ap-3794	331	5	we	we	PRON
ap-3794	331	6	would	would	AUX
ap-3794	331	7	obtain	obtain	VERB
ap-3794	331	8	the	the	DET
ap-3794	331	9	itineraries	itinerary	NOUN
ap-3794	331	10	expressed	express	VERB
ap-3794	331	11	differently	differently	ADV
ap-3794	331	12	,	,	PUNCT
ap-3794	331	13	which	which	PRON
ap-3794	331	14	yields	yield	VERB
ap-3794	331	15	interesting	interesting	ADJ
ap-3794	331	16	relations	relation	NOUN
ap-3794	331	17	between	between	ADP
ap-3794	331	18	words	word	NOUN
ap-3794	331	19	r1	r1	PROPN
ap-3794	331	20	,	,	PUNCT
ap-3794	331	21	r2	r2	PROPN
ap-3794	331	22	.	.	PUNCT
ap-3794	332	1	for	for	ADP
ap-3794	332	2	example	example	NOUN
ap-3794	332	3	,	,	PUNCT
ap-3794	332	4	in	in	ADP
ap-3794	332	5	the	the	DET
ap-3794	332	6	case	case	NOUN
ap-3794	332	7	(	(	PUNCT
ap-3794	332	8	ix	ix	PROPN
ap-3794	332	9	)	)	PUNCT
ap-3794	332	10	,	,	PUNCT
ap-3794	332	11	we	we	PRON
ap-3794	332	12	derive	derive	VERB
ap-3794	332	13	that	that	SCONJ
ap-3794	332	14	the	the	DET
ap-3794	332	15	i	i	PROPN
ap-3794	332	16	-	-	PUNCT
ap-3794	332	17	itinerary	itinerary	NOUN
ap-3794	332	18	of	of	ADP
ap-3794	332	19	x	x	SYM
ap-3794	332	20	∈	∈	PROPN
ap-3794	332	21	[	[	X
ap-3794	332	22	d	d	X
ap-3794	332	23	,	,	PUNCT
ap-3794	332	24	c	c	NOUN
ap-3794	332	25	)	)	PUNCT
ap-3794	332	26	is	be	AUX
ap-3794	332	27	r(x	r(x	PROPN
ap-3794	332	28	)	)	PUNCT
ap-3794	332	29	=	=	SYM
ap-3794	332	30	r1ωb→ca(r2	r1ωb→ca(r2	NOUN
ap-3794	332	31	)	)	PUNCT
ap-3794	332	32	=	=	SYM
ap-3794	332	33	r2ωb→ac(r1	r2ωb→ac(r1	PROPN
ap-3794	332	34	)	)	PUNCT
ap-3794	332	35	.	.	PUNCT
ap-3794	333	1	note	note	VERB
ap-3794	333	2	also	also	ADV
ap-3794	333	3	the	the	DET
ap-3794	333	4	symmetries	symmetry	NOUN
ap-3794	333	5	between	between	ADP
ap-3794	333	6	the	the	DET
ap-3794	333	7	cases	case	NOUN
ap-3794	333	8	(	(	PUNCT
ap-3794	333	9	i	i	NOUN
ap-3794	333	10	)	)	PUNCT
ap-3794	333	11	and	and	CCONJ
ap-3794	333	12	(	(	PUNCT
ap-3794	333	13	ii	ii	NOUN
ap-3794	333	14	)	)	PUNCT
ap-3794	333	15	,	,	PUNCT
ap-3794	333	16	(	(	PUNCT
ap-3794	333	17	iii	iii	NOUN
ap-3794	333	18	)	)	PUNCT
ap-3794	333	19	and	and	CCONJ
ap-3794	333	20	(	(	PUNCT
ap-3794	333	21	iv	iv	X
ap-3794	333	22	)	)	PUNCT
ap-3794	333	23	,	,	PUNCT
ap-3794	333	24	(	(	PUNCT
ap-3794	333	25	v	v	NOUN
ap-3794	333	26	)	)	PUNCT
ap-3794	333	27	and	and	CCONJ
ap-3794	333	28	(	(	PUNCT
ap-3794	333	29	vi	vi	NOUN
ap-3794	333	30	)	)	PUNCT
ap-3794	333	31	,	,	PUNCT
ap-3794	333	32	(	(	PUNCT
ap-3794	333	33	vii	vii	PROPN
ap-3794	333	34	)	)	PUNCT
ap-3794	333	35	and	and	CCONJ
ap-3794	333	36	(	(	PUNCT
ap-3794	333	37	viii	viii	NOUN
ap-3794	333	38	)	)	PUNCT
ap-3794	333	39	,	,	PUNCT
ap-3794	333	40	in	in	ADP
ap-3794	333	41	consequence	consequence	NOUN
ap-3794	333	42	of	of	ADP
ap-3794	333	43	proposition	proposition	NOUN
ap-3794	333	44	3.5	3.5	NUM
ap-3794	333	45	.	.	PUNCT
ap-3794	334	1	indeed	indeed	ADV
ap-3794	334	2	,	,	PUNCT
ap-3794	334	3	if	if	SCONJ
ap-3794	334	4	we	we	PRON
ap-3794	334	5	exchange	exchange	VERB
ap-3794	334	6	the	the	DET
ap-3794	334	7	pair	pair	NOUN
ap-3794	334	8	of	of	ADP
ap-3794	334	9	points	point	NOUN
ap-3794	334	10	d	d	X
ap-3794	334	11	↔	↔	PROPN
ap-3794	334	12	c	c	PROPN
ap-3794	334	13	,	,	PUNCT
ap-3794	334	14	b	b	PROPN
ap-3794	334	15	↔	↔	PROPN
ap-3794	334	16	a	a	PRON
ap-3794	334	17	,	,	PUNCT
ap-3794	334	18	letters	letter	VERB
ap-3794	334	19	a	a	DET
ap-3794	334	20	↔	↔	PROPN
ap-3794	334	21	c	c	NOUN
ap-3794	334	22	,	,	PUNCT
ap-3794	334	23	and	and	CCONJ
ap-3794	334	24	finally	finally	ADV
ap-3794	334	25	the	the	DET
ap-3794	334	26	inequalities	inequality	NOUN
ap-3794	334	27	“	"	PUNCT
ap-3794	334	28	<	<	X
ap-3794	334	29	”	"	PUNCT
ap-3794	334	30	and	and	CCONJ
ap-3794	334	31	“	"	PUNCT
ap-3794	334	32	>	>	PUNCT
ap-3794	334	33	”	"	PUNCT
ap-3794	334	34	,	,	PUNCT
ap-3794	334	35	we	we	PRON
ap-3794	334	36	obtain	obtain	VERB
ap-3794	334	37	a	a	DET
ap-3794	334	38	symmetric	symmetric	ADJ
ap-3794	334	39	situation	situation	NOUN
ap-3794	334	40	in	in	ADP
ap-3794	334	41	the	the	DET
ap-3794	334	42	list	list	NOUN
ap-3794	334	43	of	of	ADP
ap-3794	334	44	cases	case	NOUN
ap-3794	334	45	we	we	PRON
ap-3794	334	46	discussed	discuss	VERB
ap-3794	334	47	in	in	ADP
ap-3794	334	48	the	the	DET
ap-3794	334	49	proof	proof	NOUN
ap-3794	334	50	.	.	PUNCT
ap-3794	335	1	in	in	ADP
ap-3794	335	2	this	this	DET
ap-3794	335	3	sense	sense	NOUN
ap-3794	335	4	,	,	PUNCT
ap-3794	335	5	each	each	PRON
ap-3794	335	6	of	of	ADP
ap-3794	335	7	cases	case	NOUN
ap-3794	335	8	(	(	PUNCT
ap-3794	335	9	ix	ix	X
ap-3794	335	10	)	)	PUNCT
ap-3794	335	11	up	up	ADP
ap-3794	335	12	to	to	ADP
ap-3794	335	13	(	(	PUNCT
ap-3794	335	14	xii	xii	NOUN
ap-3794	335	15	)	)	PUNCT
ap-3794	335	16	is	be	AUX
ap-3794	335	17	symmetric	symmetric	ADJ
ap-3794	335	18	to	to	ADP
ap-3794	335	19	itself	itself	PRON
ap-3794	335	20	.	.	PUNCT
ap-3794	336	1	example	example	NOUN
ap-3794	336	2	4.5	4.5	NUM
ap-3794	336	3	.	.	PUNCT
ap-3794	337	1	set	set	VERB
ap-3794	337	2	α	α	NOUN
ap-3794	337	3	=	=	SYM
ap-3794	337	4	1	1	NUM
ap-3794	337	5	5	5	NUM
ap-3794	337	6	√	√	NUM
ap-3794	337	7	5−	5−	NUM
ap-3794	337	8	1	1	NUM
ap-3794	337	9	5	5	NUM
ap-3794	337	10	and	and	CCONJ
ap-3794	337	11	β	β	X
ap-3794	337	12	=	=	SYM
ap-3794	338	1	−	−	PROPN
ap-3794	338	2	1	1	NUM
ap-3794	338	3	6	6	NUM
ap-3794	338	4	√	√	NUM
ap-3794	338	5	5	5	NUM
ap-3794	338	6	+	+	CCONJ
ap-3794	338	7	2	2	NUM
ap-3794	338	8	3	3	NUM
ap-3794	338	9	.	.	PUNCT
ap-3794	339	1	table	table	NOUN
ap-3794	339	2	1	1	NUM
ap-3794	339	3	shows	show	VERB
ap-3794	339	4	12	12	NUM
ap-3794	339	5	choices	choice	NOUN
ap-3794	339	6	of	of	ADP
ap-3794	339	7	i	i	PRON
ap-3794	339	8	=	=	PUNCT
ap-3794	340	1	[	[	X
ap-3794	340	2	γ	γ	X
ap-3794	340	3	,	,	PUNCT
ap-3794	340	4	δ	δ	PROPN
ap-3794	340	5	)	)	PUNCT
ap-3794	340	6	which	which	PRON
ap-3794	340	7	produce	produce	VERB
ap-3794	340	8	12	12	NUM
ap-3794	340	9	distinct	distinct	ADJ
ap-3794	340	10	orders	order	NOUN
ap-3794	340	11	of	of	ADP
ap-3794	340	12	the	the	DET
ap-3794	340	13	points	point	NOUN
ap-3794	340	14	a	a	DET
ap-3794	340	15	,	,	PUNCT
ap-3794	340	16	b	b	NOUN
ap-3794	340	17	,	,	PUNCT
ap-3794	340	18	c	c	PROPN
ap-3794	340	19	and	and	CCONJ
ap-3794	340	20	d	d	PROPN
ap-3794	340	21	,	,	PUNCT
ap-3794	340	22	shown	show	VERB
ap-3794	340	23	in	in	ADP
ap-3794	340	24	the	the	DET
ap-3794	340	25	third	third	ADJ
ap-3794	340	26	column	column	NOUN
ap-3794	340	27	.	.	PUNCT
ap-3794	341	1	the	the	DET
ap-3794	341	2	last	last	ADJ
ap-3794	341	3	column	column	NOUN
ap-3794	341	4	contains	contain	VERB
ap-3794	341	5	the	the	DET
ap-3794	341	6	respective	respective	ADJ
ap-3794	341	7	lengths	length	NOUN
ap-3794	341	8	of	of	ADP
ap-3794	341	9	the	the	DET
ap-3794	341	10	5	5	NUM
ap-3794	341	11	distinct	distinct	ADJ
ap-3794	341	12	i	i	NOUN
ap-3794	341	13	-	-	PUNCT
ap-3794	341	14	itineraries	itinerary	NOUN
ap-3794	341	15	.	.	PUNCT
ap-3794	342	1	let	let	VERB
ap-3794	342	2	us	we	PRON
ap-3794	342	3	describe	describe	VERB
ap-3794	342	4	in	in	ADP
ap-3794	342	5	detail	detail	NOUN
ap-3794	342	6	one	one	NUM
ap-3794	342	7	of	of	ADP
ap-3794	342	8	the	the	DET
ap-3794	342	9	cases	case	NOUN
ap-3794	342	10	,	,	PUNCT
ap-3794	342	11	namely	namely	ADV
ap-3794	342	12	the	the	DET
ap-3794	342	13	case	case	NOUN
ap-3794	342	14	b	b	X
ap-3794	342	15	<	<	X
ap-3794	342	16	d	d	X
ap-3794	342	17	<	<	X
ap-3794	342	18	c	c	X
ap-3794	342	19	<	<	X
ap-3794	342	20	a.	a.	NOUN
ap-3794	342	21	the	the	DET
ap-3794	342	22	induced	induced	ADJ
ap-3794	342	23	interval	interval	NOUN
ap-3794	342	24	is	be	AUX
ap-3794	342	25	determined	determine	VERB
ap-3794	342	26	by	by	ADP
ap-3794	342	27	setting	set	VERB
ap-3794	342	28	γ	γ	X
ap-3794	342	29	=	=	SYM
ap-3794	342	30	29	29	NUM
ap-3794	342	31	100	100	NUM
ap-3794	342	32	and	and	CCONJ
ap-3794	342	33	δ	δ	NOUN
ap-3794	342	34	=	=	NOUN
ap-3794	342	35	99	99	NUM
ap-3794	342	36	100	100	NUM
ap-3794	342	37	.	.	PUNCT
ap-3794	343	1	one	one	PRON
ap-3794	343	2	can	can	AUX
ap-3794	343	3	verify	verify	VERB
ap-3794	343	4	that	that	DET
ap-3794	343	5	b	b	X
ap-3794	343	6	=	=	SYM
ap-3794	343	7	t−0(β	t−0(β	PROPN
ap-3794	343	8	)	)	PUNCT
ap-3794	343	9	=	=	SYM
ap-3794	344	1	1	1	NUM
ap-3794	344	2	6	6	NUM
ap-3794	344	3	√	√	NUM
ap-3794	344	4	5	5	NUM
ap-3794	344	5	+	+	CCONJ
ap-3794	344	6	1	1	NUM
ap-3794	344	7	3	3	NUM
ap-3794	344	8	≈	≈	PROPN
ap-3794	344	9	0.706011329583298	0.706011329583298	NUM
ap-3794	344	10	;	;	PUNCT
ap-3794	344	11	d	d	PROPN
ap-3794	344	12	=	=	SYM
ap-3794	344	13	t−2(δ	t−2(δ	PROPN
ap-3794	344	14	)	)	PUNCT
ap-3794	344	15	=	=	PUNCT
ap-3794	345	1	11	11	NUM
ap-3794	345	2	30	30	NUM
ap-3794	345	3	√	√	NUM
ap-3794	345	4	5	5	NUM
ap-3794	345	5	+	+	CCONJ
ap-3794	345	6	37	37	NUM
ap-3794	345	7	300	300	NUM
ap-3794	345	8	≈	≈	PROPN
ap-3794	345	9	0.943224925083256	0.943224925083256	NUM
ap-3794	345	10	;	;	PUNCT
ap-3794	345	11	c	c	X
ap-3794	345	12	=	=	SYM
ap-3794	345	13	t−3(γ	t−3(γ	PROPN
ap-3794	345	14	)	)	PUNCT
ap-3794	346	1	=	=	SYM
ap-3794	347	1	8	8	NUM
ap-3794	347	2	15	15	NUM
ap-3794	347	3	√	√	NOUN
ap-3794	347	4	5−	5−	NUM
ap-3794	347	5	73	73	NUM
ap-3794	347	6	300	300	NUM
ap-3794	347	7	≈	≈	PROPN
ap-3794	347	8	0.949236254666554	0.949236254666554	NUM
ap-3794	347	9	;	;	PUNCT
ap-3794	347	10	a	a	DET
ap-3794	347	11	=	=	SYM
ap-3794	347	12	t−1(α	t−1(α	PROPN
ap-3794	347	13	)	)	PUNCT
ap-3794	347	14	=	=	PUNCT
ap-3794	348	1	11	11	NUM
ap-3794	348	2	30	30	NUM
ap-3794	348	3	√	√	NOUN
ap-3794	348	4	5	5	NUM
ap-3794	348	5	+	+	CCONJ
ap-3794	348	6	2	2	NUM
ap-3794	348	7	15	15	NUM
ap-3794	348	8	≈	≈	PROPN
ap-3794	348	9	0.953224925083256	0.953224925083256	NUM
ap-3794	348	10	.	.	PUNCT
ap-3794	349	1	it	it	PRON
ap-3794	349	2	corresponds	correspond	VERB
ap-3794	349	3	to	to	ADP
ap-3794	349	4	the	the	DET
ap-3794	349	5	case	case	NOUN
ap-3794	349	6	(	(	PUNCT
ap-3794	349	7	x	x	X
ap-3794	349	8	)	)	PUNCT
ap-3794	349	9	in	in	ADP
ap-3794	349	10	the	the	DET
ap-3794	349	11	proof	proof	NOUN
ap-3794	349	12	of	of	ADP
ap-3794	349	13	theorem	theorem	NOUN
ap-3794	349	14	4.1	4.1	NUM
ap-3794	349	15	with	with	ADP
ap-3794	349	16	r1	r1	PROPN
ap-3794	349	17	=	=	PUNCT
ap-3794	349	18	ca	can	AUX
ap-3794	349	19	and	and	CCONJ
ap-3794	349	20	r2	r2	PROPN
ap-3794	349	21	=	=	SYM
ap-3794	349	22	cac	cac	PROPN
ap-3794	349	23	.	.	PUNCT
ap-3794	350	1	the	the	DET
ap-3794	350	2	i467	i467	PROPN
ap-3794	350	3	z.	z.	PROPN
ap-3794	350	4	masáková	masáková	PROPN
ap-3794	350	5	,	,	PUNCT
ap-3794	350	6	e.	e.	PROPN
ap-3794	350	7	pelantová	pelantová	PROPN
ap-3794	350	8	,	,	PUNCT
ap-3794	350	9	š	š	PROPN
ap-3794	350	10	.	.	PROPN
ap-3794	350	11	starosta	starosta	PROPN
ap-3794	350	12	acta	acta	PROPN
ap-3794	350	13	polytechnica	polytechnica	PROPN
ap-3794	350	14	itinerary	itinerary	NOUN
ap-3794	350	15	of	of	ADP
ap-3794	350	16	a	a	DET
ap-3794	350	17	point	point	NOUN
ap-3794	350	18	x	x	X
ap-3794	350	19	∈	∈	NOUN
ap-3794	351	1	i	i	PRON
ap-3794	351	2	=	=	X
ap-3794	352	1	[	[	X
ap-3794	352	2	γ	γ	X
ap-3794	352	3	,	,	PUNCT
ap-3794	352	4	δ	δ	PROPN
ap-3794	352	5	)	)	PUNCT
ap-3794	352	6	is	be	AUX
ap-3794	352	7	r(x	r(x	PROPN
ap-3794	352	8	)	)	PUNCT
ap-3794	352	9	=	=	PUNCT
ap-3794	353	1			NUM
ap-3794	353	2	b	b	PROPN
ap-3794	353	3	for	for	ADP
ap-3794	353	4	x	x	PROPN
ap-3794	353	5	∈	∈	PROPN
ap-3794	353	6	[	[	X
ap-3794	353	7	γ	γ	X
ap-3794	353	8	,	,	PUNCT
ap-3794	353	9	b	b	NOUN
ap-3794	353	10	)	)	PUNCT
ap-3794	353	11	,	,	PUNCT
ap-3794	353	12	ca	ca	NOUN
ap-3794	353	13	for	for	ADP
ap-3794	353	14	x	x	PROPN
ap-3794	353	15	∈	∈	PROPN
ap-3794	353	16	[	[	X
ap-3794	353	17	b	b	X
ap-3794	353	18	,	,	PUNCT
ap-3794	353	19	d	d	NOUN
ap-3794	353	20	)	)	PUNCT
ap-3794	353	21	,	,	PUNCT
ap-3794	353	22	cacb	cacb	VERB
ap-3794	353	23	for	for	ADP
ap-3794	353	24	x	x	PROPN
ap-3794	353	25	∈	∈	PROPN
ap-3794	353	26	[	[	X
ap-3794	353	27	d	d	X
ap-3794	353	28	,	,	PUNCT
ap-3794	353	29	c	c	NOUN
ap-3794	353	30	)	)	PUNCT
ap-3794	353	31	,	,	PUNCT
ap-3794	353	32	cac	cac	PROPN
ap-3794	353	33	for	for	ADP
ap-3794	353	34	x	x	PROPN
ap-3794	353	35	∈	∈	PROPN
ap-3794	354	1	[	[	X
ap-3794	354	2	c	c	X
ap-3794	354	3	,	,	PUNCT
ap-3794	354	4	a	a	PRON
ap-3794	354	5	)	)	PUNCT
ap-3794	354	6	,	,	PUNCT
ap-3794	354	7	cb	cb	PROPN
ap-3794	354	8	for	for	ADP
ap-3794	354	9	x	x	PROPN
ap-3794	354	10	∈	∈	PROPN
ap-3794	354	11	[	[	X
ap-3794	354	12	a	a	X
ap-3794	354	13	,	,	PUNCT
ap-3794	354	14	δ	δ	PROPN
ap-3794	354	15	)	)	PUNCT
ap-3794	354	16	.	.	PUNCT
ap-3794	355	1	5	5	X
ap-3794	355	2	.	.	X
ap-3794	355	3	description	description	NOUN
ap-3794	355	4	of	of	ADP
ap-3794	355	5	the	the	DET
ap-3794	355	6	case	case	NOUN
ap-3794	355	7	of	of	ADP
ap-3794	355	8	three	three	NUM
ap-3794	355	9	i	i	NOUN
ap-3794	355	10	-	-	PUNCT
ap-3794	355	11	itineraries	itinerarie	VERB
ap-3794	355	12	the	the	DET
ap-3794	355	13	cases	case	NOUN
ap-3794	355	14	(	(	PUNCT
ap-3794	355	15	i)–(xii	i)–(xii	NOUN
ap-3794	355	16	)	)	PUNCT
ap-3794	355	17	in	in	ADP
ap-3794	355	18	the	the	DET
ap-3794	355	19	proof	proof	NOUN
ap-3794	355	20	of	of	ADP
ap-3794	355	21	theorem	theorem	ADJ
ap-3794	355	22	4.1	4.1	NUM
ap-3794	355	23	correspond	correspond	NOUN
ap-3794	355	24	to	to	ADP
ap-3794	355	25	the	the	DET
ap-3794	355	26	generic	generic	ADJ
ap-3794	355	27	instances	instance	NOUN
ap-3794	355	28	of	of	ADP
ap-3794	355	29	a	a	DET
ap-3794	355	30	subinterval	subinterval	NOUN
ap-3794	355	31	i	i	PRON
ap-3794	355	32	in	in	ADP
ap-3794	355	33	a	a	DET
ap-3794	355	34	non	non	ADJ
ap-3794	355	35	-	-	ADJ
ap-3794	355	36	degenerate	degenerate	ADJ
ap-3794	355	37	3iet	3iet	NUM
ap-3794	355	38	which	which	PRON
ap-3794	355	39	lead	lead	VERB
ap-3794	355	40	to	to	ADP
ap-3794	355	41	5	5	NUM
ap-3794	355	42	different	different	ADJ
ap-3794	355	43	i	i	NOUN
ap-3794	355	44	-	-	PUNCT
ap-3794	355	45	itineraries	itinerary	NOUN
ap-3794	355	46	.	.	PUNCT
ap-3794	356	1	let	let	VERB
ap-3794	356	2	us	we	PRON
ap-3794	356	3	focus	focus	VERB
ap-3794	356	4	on	on	ADP
ap-3794	356	5	the	the	DET
ap-3794	356	6	cases	case	NOUN
ap-3794	356	7	where	where	SCONJ
ap-3794	356	8	,	,	PUNCT
ap-3794	356	9	on	on	ADP
ap-3794	356	10	the	the	DET
ap-3794	356	11	contrary	contrary	NOUN
ap-3794	356	12	,	,	PUNCT
ap-3794	356	13	the	the	DET
ap-3794	356	14	set	set	NOUN
ap-3794	356	15	of	of	ADP
ap-3794	356	16	i	i	PROPN
ap-3794	356	17	-	-	PUNCT
ap-3794	356	18	itineraries	itinerary	NOUN
ap-3794	356	19	has	have	VERB
ap-3794	356	20	only	only	ADV
ap-3794	356	21	3	3	NUM
ap-3794	356	22	elements	element	NOUN
ap-3794	356	23	.	.	PUNCT
ap-3794	357	1	first	first	ADV
ap-3794	357	2	we	we	PRON
ap-3794	357	3	recall	recall	VERB
ap-3794	357	4	two	two	NUM
ap-3794	357	5	reasons	reason	NOUN
ap-3794	357	6	why	why	SCONJ
ap-3794	357	7	such	such	ADJ
ap-3794	357	8	cases	case	NOUN
ap-3794	357	9	are	be	AUX
ap-3794	357	10	interesting	interesting	ADJ
ap-3794	357	11	.	.	PUNCT
ap-3794	358	1	for	for	ADP
ap-3794	358	2	a	a	DET
ap-3794	358	3	factor	factor	NOUN
ap-3794	358	4	w	w	NOUN
ap-3794	358	5	from	from	ADP
ap-3794	358	6	the	the	DET
ap-3794	358	7	language	language	NOUN
ap-3794	358	8	of	of	ADP
ap-3794	358	9	a	a	DET
ap-3794	358	10	nondegenerate	nondegenerate	ADJ
ap-3794	358	11	3iet	3iet	NUM
ap-3794	358	12	transformation	transformation	NOUN
ap-3794	358	13	t	t	NOUN
ap-3794	358	14	,	,	PUNCT
ap-3794	358	15	denote	denote	VERB
ap-3794	358	16	[	[	X
ap-3794	358	17	w	w	X
ap-3794	358	18	]	]	X
ap-3794	358	19	=	=	SYM
ap-3794	358	20	{	{	PUNCT
ap-3794	358	21	ρ	ρ	PROPN
ap-3794	358	22	∈	∈	PROPN
ap-3794	359	1	[	[	X
ap-3794	359	2	0	0	NUM
ap-3794	359	3	,	,	PUNCT
ap-3794	359	4	1	1	NUM
ap-3794	359	5	)	)	PUNCT
ap-3794	359	6	:	:	PUNCT
ap-3794	359	7	w	w	NOUN
ap-3794	359	8	is	be	AUX
ap-3794	359	9	a	a	DET
ap-3794	359	10	prefix	prefix	NOUN
ap-3794	359	11	of	of	ADP
ap-3794	359	12	uρ	uρ	ADP
ap-3794	359	13	}	}	PUNCT
ap-3794	359	14	.	.	PUNCT
ap-3794	360	1	it	it	PRON
ap-3794	360	2	is	be	AUX
ap-3794	360	3	easy	easy	ADJ
ap-3794	360	4	to	to	PART
ap-3794	360	5	see	see	VERB
ap-3794	360	6	that	that	SCONJ
ap-3794	360	7	[	[	X
ap-3794	360	8	w	w	X
ap-3794	360	9	]	]	X
ap-3794	360	10	–	–	PUNCT
ap-3794	360	11	usually	usually	ADV
ap-3794	360	12	called	call	VERB
ap-3794	360	13	the	the	DET
ap-3794	360	14	cylinder	cylinder	NOUN
ap-3794	360	15	of	of	ADP
ap-3794	360	16	w	w	PROPN
ap-3794	360	17	–	–	PUNCT
ap-3794	360	18	is	be	AUX
ap-3794	360	19	a	a	DET
ap-3794	360	20	semi	semi	ADJ
ap-3794	360	21	-	-	ADJ
ap-3794	360	22	closed	closed	ADJ
ap-3794	360	23	interval	interval	NOUN
ap-3794	360	24	and	and	CCONJ
ap-3794	360	25	its	its	PRON
ap-3794	360	26	boundaries	boundary	NOUN
ap-3794	360	27	belong	belong	VERB
ap-3794	360	28	to	to	ADP
ap-3794	360	29	the	the	DET
ap-3794	360	30	set	set	NOUN
ap-3794	360	31	{	{	PUNCT
ap-3794	360	32	t−i(z	t−i(z	NOUN
ap-3794	360	33	)	)	PUNCT
ap-3794	360	34	:	:	PUNCT
ap-3794	361	1	0	0	NUM
ap-3794	361	2	≤	≤	X
ap-3794	362	1	i	i	PRON
ap-3794	362	2	<	<	X
ap-3794	362	3	n	n	CCONJ
ap-3794	362	4	,	,	PUNCT
ap-3794	362	5	z	z	PROPN
ap-3794	362	6	∈	∈	PROPN
ap-3794	362	7	{	{	PUNCT
ap-3794	362	8	α	α	NOUN
ap-3794	362	9	,	,	PUNCT
ap-3794	362	10	β	β	NOUN
ap-3794	362	11	}	}	PUNCT
ap-3794	362	12	}	}	PUNCT
ap-3794	362	13	.	.	PUNCT
ap-3794	363	1	clearly	clearly	ADV
ap-3794	363	2	,	,	PUNCT
ap-3794	363	3	a	a	DET
ap-3794	363	4	factor	factor	NOUN
ap-3794	363	5	v	v	NOUN
ap-3794	363	6	is	be	AUX
ap-3794	363	7	a	a	DET
ap-3794	363	8	return	return	NOUN
ap-3794	363	9	word	word	NOUN
ap-3794	363	10	to	to	ADP
ap-3794	363	11	the	the	DET
ap-3794	363	12	factor	factor	NOUN
ap-3794	363	13	w	w	NOUN
ap-3794	364	1	if	if	SCONJ
ap-3794	365	1	and	and	CCONJ
ap-3794	365	2	only	only	ADV
ap-3794	365	3	if	if	SCONJ
ap-3794	365	4	v	v	NOUN
ap-3794	365	5	is	be	AUX
ap-3794	365	6	a	a	DET
ap-3794	365	7	[	[	X
ap-3794	365	8	w]-itinerary	w]-itinerary	NOUN
ap-3794	365	9	.	.	PUNCT
ap-3794	366	1	it	it	PRON
ap-3794	366	2	is	be	AUX
ap-3794	366	3	well	well	ADV
ap-3794	366	4	known	known	ADJ
ap-3794	366	5	[	[	X
ap-3794	366	6	16	16	NUM
ap-3794	366	7	]	]	PUNCT
ap-3794	366	8	that	that	SCONJ
ap-3794	366	9	any	any	DET
ap-3794	366	10	factor	factor	NOUN
ap-3794	366	11	of	of	ADP
ap-3794	366	12	an	an	DET
ap-3794	366	13	infinite	infinite	ADJ
ap-3794	366	14	word	word	NOUN
ap-3794	366	15	coding	code	VERB
ap-3794	366	16	a	a	DET
ap-3794	366	17	non	non	ADJ
ap-3794	366	18	-	-	ADJ
ap-3794	366	19	degenerate	degenerate	ADJ
ap-3794	366	20	3iet	3iet	PROPN
ap-3794	366	21	has	have	VERB
ap-3794	366	22	exactly	exactly	ADV
ap-3794	366	23	three	three	NUM
ap-3794	366	24	return	return	NOUN
ap-3794	366	25	words	word	NOUN
ap-3794	366	26	and	and	CCONJ
ap-3794	366	27	thus	thus	ADV
ap-3794	366	28	the	the	DET
ap-3794	366	29	set	set	ADJ
ap-3794	366	30	it[w	it[w	PROPN
ap-3794	366	31	]	]	PUNCT
ap-3794	366	32	has	have	VERB
ap-3794	366	33	three	three	NUM
ap-3794	366	34	elements	element	NOUN
ap-3794	366	35	.	.	PUNCT
ap-3794	367	1	the	the	DET
ap-3794	367	2	second	second	ADJ
ap-3794	367	3	reason	reason	NOUN
ap-3794	367	4	why	why	SCONJ
ap-3794	367	5	to	to	PART
ap-3794	367	6	study	study	VERB
ap-3794	367	7	intervals	interval	NOUN
ap-3794	367	8	i	i	PRON
ap-3794	367	9	yielding	yield	VERB
ap-3794	367	10	three	three	NUM
ap-3794	367	11	i	i	PRON
ap-3794	367	12	-	-	PUNCT
ap-3794	367	13	itineraries	itinerary	NOUN
ap-3794	367	14	is	be	AUX
ap-3794	367	15	that	that	SCONJ
ap-3794	367	16	any	any	DET
ap-3794	367	17	morphism	morphism	NOUN
ap-3794	367	18	fixing	fix	VERB
ap-3794	367	19	a	a	DET
ap-3794	367	20	nondegenerate	nondegenerate	ADJ
ap-3794	367	21	3iet	3iet	NUM
ap-3794	367	22	word	word	NOUN
ap-3794	367	23	corresponds	correspond	VERB
ap-3794	367	24	to	to	ADP
ap-3794	367	25	such	such	DET
ap-3794	367	26	an	an	DET
ap-3794	367	27	interval	interval	NOUN
ap-3794	367	28	i.	i.	NOUN
ap-3794	367	29	details	detail	NOUN
ap-3794	367	30	of	of	ADP
ap-3794	367	31	this	this	DET
ap-3794	367	32	correspondence	correspondence	NOUN
ap-3794	367	33	will	will	AUX
ap-3794	367	34	be	be	AUX
ap-3794	367	35	explained	explain	VERB
ap-3794	367	36	further	far	ADV
ap-3794	367	37	in	in	ADP
ap-3794	367	38	this	this	DET
ap-3794	367	39	section	section	NOUN
ap-3794	367	40	.	.	PUNCT
ap-3794	368	1	proposition	proposition	NOUN
ap-3794	368	2	5.1	5.1	NUM
ap-3794	368	3	.	.	PUNCT
ap-3794	369	1	let	let	VERB
ap-3794	369	2	t	t	PROPN
ap-3794	369	3	be	be	AUX
ap-3794	369	4	a	a	DET
ap-3794	369	5	non	non	ADJ
ap-3794	369	6	-	-	ADJ
ap-3794	369	7	degenerate	degenerate	ADJ
ap-3794	369	8	3iet	3iet	NOUN
ap-3794	369	9	and	and	CCONJ
ap-3794	369	10	let	let	VERB
ap-3794	369	11	i	i	PRON
ap-3794	369	12	=	=	PUNCT
ap-3794	370	1	[	[	X
ap-3794	370	2	γ	γ	X
ap-3794	370	3	,	,	PUNCT
ap-3794	370	4	δ	δ	PROPN
ap-3794	370	5	)	)	PUNCT
ap-3794	370	6	⊂	⊂	PROPN
ap-3794	371	1	[	[	X
ap-3794	371	2	0	0	NUM
ap-3794	371	3	,	,	PUNCT
ap-3794	371	4	1	1	NUM
ap-3794	371	5	)	)	PUNCT
ap-3794	371	6	be	be	AUX
ap-3794	371	7	such	such	ADJ
ap-3794	371	8	that	that	SCONJ
ap-3794	371	9	#	#	NOUN
ap-3794	371	10	iti	iti	NOUN
ap-3794	371	11	=	=	NOUN
ap-3794	371	12	3	3	X
ap-3794	371	13	.	.	X
ap-3794	371	14	one	one	NUM
ap-3794	371	15	of	of	ADP
ap-3794	371	16	the	the	DET
ap-3794	371	17	following	follow	VERB
ap-3794	371	18	cases	case	NOUN
ap-3794	371	19	occurs	occur	VERB
ap-3794	371	20	:	:	PUNCT
ap-3794	371	21	(	(	PUNCT
ap-3794	371	22	i	i	NOUN
ap-3794	371	23	)	)	PUNCT
ap-3794	371	24	b	b	X
ap-3794	372	1	=	=	SYM
ap-3794	372	2	d	d	X
ap-3794	372	3	<	<	X
ap-3794	372	4	a	a	X
ap-3794	372	5	=	=	SYM
ap-3794	372	6	c	c	PROPN
ap-3794	372	7	and	and	CCONJ
ap-3794	372	8	r(x	r(x	PROPN
ap-3794	372	9	)	)	PUNCT
ap-3794	372	10	=	=	SYM
ap-3794	373	1			PROPN
ap-3794	373	2	r1	r1	NOUN
ap-3794	373	3	for	for	ADP
ap-3794	373	4	x	x	PROPN
ap-3794	373	5	∈	∈	PROPN
ap-3794	373	6	[	[	X
ap-3794	373	7	γ	γ	X
ap-3794	373	8	,	,	PUNCT
ap-3794	373	9	b	b	NOUN
ap-3794	373	10	)	)	PUNCT
ap-3794	373	11	,	,	PUNCT
ap-3794	373	12	ωb→ca(r1r2	ωb→ca(r1r2	NUM
ap-3794	373	13	)	)	PUNCT
ap-3794	373	14	=	=	SYM
ap-3794	373	15	ωb→ac(r2r1	ωb→ac(r2r1	NOUN
ap-3794	373	16	)	)	PUNCT
ap-3794	373	17	for	for	ADP
ap-3794	373	18	x	x	PROPN
ap-3794	373	19	∈	∈	PROPN
ap-3794	373	20	[	[	X
ap-3794	373	21	b	b	NOUN
ap-3794	373	22	,	,	PUNCT
ap-3794	373	23	a	a	NOUN
ap-3794	373	24	)	)	PUNCT
ap-3794	373	25	,	,	PUNCT
ap-3794	373	26	r2	r2	NOUN
ap-3794	373	27	for	for	ADP
ap-3794	373	28	x	x	PROPN
ap-3794	373	29	∈	∈	PROPN
ap-3794	373	30	[	[	X
ap-3794	373	31	a	a	X
ap-3794	373	32	,	,	PUNCT
ap-3794	373	33	δ	δ	PROPN
ap-3794	373	34	)	)	PUNCT
ap-3794	373	35	;	;	PUNCT
ap-3794	373	36	(	(	PUNCT
ap-3794	373	37	ii	ii	NOUN
ap-3794	373	38	)	)	PUNCT
ap-3794	373	39	a	a	DET
ap-3794	373	40	=	=	SYM
ap-3794	373	41	d	d	X
ap-3794	373	42	<	<	X
ap-3794	373	43	b	b	PROPN
ap-3794	373	44	=	=	SYM
ap-3794	373	45	c	c	PROPN
ap-3794	373	46	and	and	CCONJ
ap-3794	373	47	r(x	r(x	PROPN
ap-3794	373	48	)	)	PUNCT
ap-3794	373	49	=	=	SYM
ap-3794	374	1			PROPN
ap-3794	374	2	r1	r1	NOUN
ap-3794	374	3	for	for	ADP
ap-3794	374	4	x	x	PROPN
ap-3794	374	5	∈	∈	PROPN
ap-3794	374	6	[	[	X
ap-3794	374	7	γ	γ	X
ap-3794	374	8	,	,	PUNCT
ap-3794	374	9	a	a	PRON
ap-3794	374	10	)	)	PUNCT
ap-3794	374	11	,	,	PUNCT
ap-3794	374	12	ωac→b(r1r2	ωac→b(r1r2	NUM
ap-3794	374	13	)	)	PUNCT
ap-3794	374	14	=	=	SYM
ap-3794	374	15	ωca→b(r2r1	ωca→b(r2r1	NOUN
ap-3794	374	16	)	)	PUNCT
ap-3794	374	17	for	for	ADP
ap-3794	374	18	x	x	PROPN
ap-3794	374	19	∈	∈	PROPN
ap-3794	374	20	[	[	X
ap-3794	374	21	a	a	DET
ap-3794	374	22	,	,	PUNCT
ap-3794	374	23	b	b	NOUN
ap-3794	374	24	)	)	PUNCT
ap-3794	374	25	,	,	PUNCT
ap-3794	374	26	r2	r2	PROPN
ap-3794	374	27	for	for	ADP
ap-3794	374	28	x	x	PROPN
ap-3794	374	29	∈	∈	PROPN
ap-3794	374	30	[	[	X
ap-3794	374	31	b	b	X
ap-3794	374	32	,	,	PUNCT
ap-3794	374	33	δ	δ	PROPN
ap-3794	374	34	)	)	PUNCT
ap-3794	374	35	;	;	PUNCT
ap-3794	374	36	(	(	PUNCT
ap-3794	374	37	iii	iii	X
ap-3794	374	38	)	)	PUNCT
ap-3794	374	39	b	b	NOUN
ap-3794	374	40	<	<	X
ap-3794	374	41	a	a	X
ap-3794	374	42	=	=	NOUN
ap-3794	374	43	c	c	NOUN
ap-3794	374	44	=	=	SYM
ap-3794	374	45	d	d	PROPN
ap-3794	374	46	and	and	CCONJ
ap-3794	374	47	r(x	r(x	PROPN
ap-3794	374	48	)	)	PUNCT
ap-3794	374	49	=	=	SYM
ap-3794	375	1			PRON
ap-3794	375	2	ωca→b(r1	ωca→b(r1	NOUN
ap-3794	375	3	)	)	PUNCT
ap-3794	375	4	for	for	ADP
ap-3794	375	5	x	x	PROPN
ap-3794	375	6	∈	∈	PROPN
ap-3794	375	7	[	[	X
ap-3794	375	8	γ	γ	X
ap-3794	375	9	,	,	PUNCT
ap-3794	375	10	b	b	NOUN
ap-3794	375	11	)	)	PUNCT
ap-3794	375	12	,	,	PUNCT
ap-3794	375	13	r1	r1	NOUN
ap-3794	375	14	for	for	ADP
ap-3794	375	15	x	x	PROPN
ap-3794	375	16	∈	∈	PROPN
ap-3794	375	17	[	[	X
ap-3794	375	18	b	b	NOUN
ap-3794	375	19	,	,	PUNCT
ap-3794	375	20	a	a	NOUN
ap-3794	375	21	)	)	PUNCT
ap-3794	375	22	,	,	PUNCT
ap-3794	375	23	r2	r2	NOUN
ap-3794	375	24	for	for	ADP
ap-3794	375	25	x	x	PROPN
ap-3794	375	26	∈	∈	PROPN
ap-3794	375	27	[	[	X
ap-3794	375	28	a	a	X
ap-3794	375	29	,	,	PUNCT
ap-3794	375	30	δ	δ	PROPN
ap-3794	375	31	)	)	PUNCT
ap-3794	375	32	;	;	PUNCT
ap-3794	375	33	(	(	PUNCT
ap-3794	375	34	iv	iv	X
ap-3794	375	35	)	)	PUNCT
ap-3794	375	36	b	b	NOUN
ap-3794	375	37	=	=	SYM
ap-3794	375	38	c	c	NOUN
ap-3794	375	39	=	=	SYM
ap-3794	376	1	d	d	X
ap-3794	376	2	<	<	X
ap-3794	376	3	a	a	PROPN
ap-3794	376	4	and	and	CCONJ
ap-3794	376	5	r(x	r(x	NOUN
ap-3794	376	6	)	)	PUNCT
ap-3794	376	7	=	=	PUNCT
ap-3794	377	1			PROPN
ap-3794	377	2	r1	r1	VERB
ap-3794	377	3	for	for	ADP
ap-3794	377	4	x	x	PROPN
ap-3794	377	5	∈	∈	PROPN
ap-3794	377	6	[	[	X
ap-3794	377	7	γ	γ	X
ap-3794	377	8	,	,	PUNCT
ap-3794	377	9	a	a	PRON
ap-3794	377	10	)	)	PUNCT
ap-3794	377	11	,	,	PUNCT
ap-3794	377	12	r2	r2	NOUN
ap-3794	377	13	for	for	ADP
ap-3794	377	14	x	x	PROPN
ap-3794	377	15	∈	∈	PROPN
ap-3794	377	16	[	[	X
ap-3794	377	17	a	a	DET
ap-3794	377	18	,	,	PUNCT
ap-3794	377	19	b	b	NOUN
ap-3794	377	20	)	)	PUNCT
ap-3794	377	21	,	,	PUNCT
ap-3794	377	22	ωac→b(r2	ωac→b(r2	NOUN
ap-3794	377	23	)	)	PUNCT
ap-3794	377	24	for	for	ADP
ap-3794	377	25	x	x	PROPN
ap-3794	377	26	∈	∈	PROPN
ap-3794	377	27	[	[	X
ap-3794	377	28	b	b	X
ap-3794	377	29	,	,	PUNCT
ap-3794	377	30	δ	δ	PROPN
ap-3794	377	31	)	)	PUNCT
ap-3794	377	32	;	;	PUNCT
ap-3794	377	33	(	(	PUNCT
ap-3794	377	34	v	v	NOUN
ap-3794	377	35	)	)	PUNCT
ap-3794	377	36	a	a	PRON
ap-3794	377	37	=	=	NOUN
ap-3794	377	38	c	c	NOUN
ap-3794	377	39	=	=	SYM
ap-3794	378	1	d	d	X
ap-3794	378	2	<	<	X
ap-3794	378	3	b	b	PROPN
ap-3794	378	4	and	and	CCONJ
ap-3794	378	5	r(x	r(x	NOUN
ap-3794	378	6	)	)	PUNCT
ap-3794	378	7	=	=	PUNCT
ap-3794	379	1			PROPN
ap-3794	379	2	r1	r1	VERB
ap-3794	379	3	for	for	ADP
ap-3794	379	4	x	x	PROPN
ap-3794	379	5	∈	∈	PROPN
ap-3794	379	6	[	[	X
ap-3794	379	7	γ	γ	X
ap-3794	379	8	,	,	PUNCT
ap-3794	379	9	a	a	PRON
ap-3794	379	10	)	)	PUNCT
ap-3794	379	11	,	,	PUNCT
ap-3794	379	12	r2	r2	NOUN
ap-3794	379	13	for	for	ADP
ap-3794	379	14	x	x	PROPN
ap-3794	379	15	∈	∈	PROPN
ap-3794	379	16	[	[	X
ap-3794	379	17	a	a	DET
ap-3794	379	18	,	,	PUNCT
ap-3794	379	19	b	b	NOUN
ap-3794	379	20	)	)	PUNCT
ap-3794	379	21	,	,	PUNCT
ap-3794	379	22	ωb→ca(r2	ωb→ca(r2	NOUN
ap-3794	379	23	)	)	PUNCT
ap-3794	379	24	for	for	ADP
ap-3794	379	25	x	x	PROPN
ap-3794	379	26	∈	∈	PROPN
ap-3794	379	27	[	[	X
ap-3794	379	28	b	b	X
ap-3794	379	29	,	,	PUNCT
ap-3794	379	30	δ	δ	PROPN
ap-3794	379	31	)	)	PUNCT
ap-3794	379	32	;	;	PUNCT
ap-3794	379	33	(	(	PUNCT
ap-3794	379	34	vi	vi	X
ap-3794	379	35	)	)	PUNCT
ap-3794	379	36	a	a	DET
ap-3794	379	37	<	<	X
ap-3794	379	38	b	b	X
ap-3794	379	39	=	=	SYM
ap-3794	379	40	c	c	NOUN
ap-3794	379	41	=	=	SYM
ap-3794	379	42	d	d	PROPN
ap-3794	379	43	and	and	CCONJ
ap-3794	379	44	r(x	r(x	PROPN
ap-3794	379	45	)	)	PUNCT
ap-3794	379	46	=	=	SYM
ap-3794	380	1			PROPN
ap-3794	380	2	ωb→ac(r1	ωb→ac(r1	PROPN
ap-3794	380	3	)	)	PUNCT
ap-3794	380	4	for	for	ADP
ap-3794	380	5	x	x	PROPN
ap-3794	380	6	∈	∈	PROPN
ap-3794	380	7	[	[	X
ap-3794	380	8	γ	γ	X
ap-3794	380	9	,	,	PUNCT
ap-3794	380	10	a	a	PRON
ap-3794	380	11	)	)	PUNCT
ap-3794	380	12	,	,	PUNCT
ap-3794	380	13	r1	r1	NOUN
ap-3794	380	14	for	for	ADP
ap-3794	380	15	x	x	PROPN
ap-3794	380	16	∈	∈	PROPN
ap-3794	380	17	[	[	X
ap-3794	380	18	a	a	DET
ap-3794	380	19	,	,	PUNCT
ap-3794	380	20	b	b	NOUN
ap-3794	380	21	)	)	PUNCT
ap-3794	380	22	,	,	PUNCT
ap-3794	380	23	r2	r2	PROPN
ap-3794	380	24	for	for	ADP
ap-3794	380	25	x	x	PROPN
ap-3794	380	26	∈	∈	PROPN
ap-3794	380	27	[	[	X
ap-3794	380	28	b	b	X
ap-3794	380	29	,	,	PUNCT
ap-3794	380	30	δ	δ	PROPN
ap-3794	380	31	)	)	PUNCT
ap-3794	380	32	.	.	PUNCT
ap-3794	381	1	sketch	sketch	NOUN
ap-3794	381	2	of	of	ADP
ap-3794	381	3	a	a	DET
ap-3794	381	4	proof	proof	NOUN
ap-3794	381	5	.	.	PUNCT
ap-3794	382	1	since	since	SCONJ
ap-3794	382	2	by	by	ADP
ap-3794	382	3	lemma	lemma	PROPN
ap-3794	382	4	3.2	3.2	NUM
ap-3794	382	5	the	the	DET
ap-3794	382	6	subintervals	subinterval	NOUN
ap-3794	382	7	of	of	ADP
ap-3794	382	8	i	i	PRON
ap-3794	382	9	corresponding	correspond	VERB
ap-3794	382	10	to	to	ADP
ap-3794	382	11	the	the	DET
ap-3794	382	12	same	same	ADJ
ap-3794	382	13	itinerary	itinerary	NOUN
ap-3794	382	14	are	be	AUX
ap-3794	382	15	delimited	delimit	VERB
ap-3794	382	16	by	by	ADP
ap-3794	382	17	the	the	DET
ap-3794	382	18	points	point	NOUN
ap-3794	382	19	a	a	DET
ap-3794	382	20	,	,	PUNCT
ap-3794	382	21	b	b	NOUN
ap-3794	382	22	,	,	PUNCT
ap-3794	382	23	c	c	PROPN
ap-3794	382	24	and	and	CCONJ
ap-3794	382	25	d	d	X
ap-3794	382	26	,	,	PUNCT
ap-3794	382	27	we	we	PRON
ap-3794	382	28	may	may	AUX
ap-3794	382	29	have	have	VERB
ap-3794	382	30	#	#	NOUN
ap-3794	382	31	iti	iti	NOUN
ap-3794	382	32	=	=	NOUN
ap-3794	382	33	3	3	NUM
ap-3794	382	34	only	only	ADV
ap-3794	382	35	if	if	SCONJ
ap-3794	382	36	some	some	PRON
ap-3794	382	37	of	of	ADP
ap-3794	382	38	these	these	DET
ap-3794	382	39	points	point	NOUN
ap-3794	382	40	coincide	coincide	NOUN
ap-3794	382	41	,	,	PUNCT
ap-3794	382	42	more	more	ADV
ap-3794	382	43	precisely	precisely	ADV
ap-3794	382	44	if	if	SCONJ
ap-3794	382	45	#	#	NOUN
ap-3794	382	46	{	{	PUNCT
ap-3794	382	47	a	a	DET
ap-3794	382	48	,	,	PUNCT
ap-3794	382	49	b	b	NOUN
ap-3794	382	50	,	,	PUNCT
ap-3794	382	51	c	c	X
ap-3794	382	52	,	,	PUNCT
ap-3794	382	53	d	d	NOUN
ap-3794	382	54	}	}	PUNCT
ap-3794	382	55	=	=	SYM
ap-3794	382	56	2	2	X
ap-3794	382	57	.	.	X
ap-3794	383	1	the	the	DET
ap-3794	383	2	non	non	NOUN
ap-3794	383	3	-	-	NOUN
ap-3794	383	4	degeneracy	degeneracy	NOUN
ap-3794	383	5	of	of	ADP
ap-3794	383	6	the	the	DET
ap-3794	383	7	considered	considered	ADJ
ap-3794	383	8	3iet	3iet	PROPN
ap-3794	383	9	implies	imply	VERB
ap-3794	383	10	that	that	SCONJ
ap-3794	383	11	always	always	ADV
ap-3794	383	12	a	a	DET
ap-3794	383	13	6=	6=	PROPN
ap-3794	383	14	b	b	PROPN
ap-3794	383	15	,	,	PUNCT
ap-3794	383	16	which	which	PRON
ap-3794	383	17	further	far	ADV
ap-3794	383	18	limits	limit	VERB
ap-3794	383	19	the	the	DET
ap-3794	383	20	discussion	discussion	NOUN
ap-3794	383	21	.	.	PUNCT
ap-3794	384	1	the	the	DET
ap-3794	384	2	six	six	NUM
ap-3794	384	3	cases	case	NOUN
ap-3794	384	4	listed	list	VERB
ap-3794	384	5	in	in	ADP
ap-3794	384	6	the	the	DET
ap-3794	384	7	statement	statement	NOUN
ap-3794	384	8	are	be	AUX
ap-3794	384	9	the	the	DET
ap-3794	384	10	possibilities	possibility	NOUN
ap-3794	384	11	of	of	ADP
ap-3794	384	12	how	how	SCONJ
ap-3794	384	13	this	this	PRON
ap-3794	384	14	may	may	AUX
ap-3794	384	15	happen	happen	VERB
ap-3794	384	16	,	,	PUNCT
ap-3794	384	17	respecting	respect	VERB
ap-3794	384	18	the	the	DET
ap-3794	384	19	condition	condition	NOUN
ap-3794	384	20	d	d	ADP
ap-3794	384	21	<	<	X
ap-3794	384	22	c	c	PROPN
ap-3794	384	23	or	or	CCONJ
ap-3794	384	24	d	d	NOUN
ap-3794	384	25	=	=	PROPN
ap-3794	384	26	c.	c.	NOUN
ap-3794	384	27	in	in	SCONJ
ap-3794	384	28	order	order	NOUN
ap-3794	384	29	to	to	PART
ap-3794	384	30	describe	describe	VERB
ap-3794	384	31	the	the	DET
ap-3794	384	32	itineraries	itinerary	NOUN
ap-3794	384	33	,	,	PUNCT
ap-3794	384	34	denote	denote	VERB
ap-3794	384	35	again	again	ADV
ap-3794	384	36	r1	r1	PROPN
ap-3794	384	37	=	=	PUNCT
ap-3794	384	38	r(d−	r(d−	PROPN
ap-3794	384	39	ε	ε	PROPN
ap-3794	384	40	)	)	PUNCT
ap-3794	384	41	and	and	CCONJ
ap-3794	384	42	r2	r2	NOUN
ap-3794	384	43	=	=	PUNCT
ap-3794	385	1	r(c	r(c	PROPN
ap-3794	385	2	+	+	NUM
ap-3794	385	3	ε	ε	PROPN
ap-3794	385	4	)	)	PUNCT
ap-3794	385	5	for	for	ADP
ap-3794	385	6	ε	ε	PROPN
ap-3794	385	7	>	>	X
ap-3794	385	8	0	0	PUNCT
ap-3794	385	9	sufficiently	sufficiently	ADV
ap-3794	385	10	small	small	ADJ
ap-3794	385	11	.	.	PUNCT
ap-3794	386	1	one	one	PRON
ap-3794	386	2	can	can	AUX
ap-3794	386	3	then	then	ADV
ap-3794	386	4	follow	follow	VERB
ap-3794	386	5	the	the	DET
ap-3794	386	6	ideas	idea	NOUN
ap-3794	386	7	of	of	ADP
ap-3794	386	8	the	the	DET
ap-3794	386	9	proof	proof	NOUN
ap-3794	386	10	of	of	ADP
ap-3794	386	11	lemma	lemma	PROPN
ap-3794	386	12	4.2	4.2	NUM
ap-3794	386	13	.	.	PUNCT
ap-3794	387	1	5.1	5.1	NUM
ap-3794	387	2	.	.	PUNCT
ap-3794	388	1	return	return	VERB
ap-3794	388	2	words	word	NOUN
ap-3794	388	3	to	to	ADP
ap-3794	388	4	factors	factor	NOUN
ap-3794	388	5	of	of	ADP
ap-3794	388	6	a	a	DET
ap-3794	388	7	3iet	3iet	PROPN
ap-3794	388	8	let	let	VERB
ap-3794	388	9	us	we	PRON
ap-3794	388	10	apply	apply	VERB
ap-3794	388	11	proposition	proposition	NOUN
ap-3794	388	12	5.1	5.1	NUM
ap-3794	388	13	in	in	ADP
ap-3794	388	14	order	order	NOUN
ap-3794	388	15	to	to	PART
ap-3794	388	16	provide	provide	VERB
ap-3794	388	17	the	the	DET
ap-3794	388	18	description	description	NOUN
ap-3794	388	19	of	of	ADP
ap-3794	388	20	return	return	NOUN
ap-3794	388	21	words	word	NOUN
ap-3794	388	22	to	to	ADP
ap-3794	388	23	factors	factor	NOUN
ap-3794	388	24	of	of	ADP
ap-3794	388	25	a	a	DET
ap-3794	388	26	non	non	ADJ
ap-3794	388	27	-	-	ADJ
ap-3794	388	28	degenerate	degenerate	ADJ
ap-3794	388	29	3iet	3iet	NUM
ap-3794	388	30	word	word	NOUN
ap-3794	388	31	.	.	PUNCT
ap-3794	389	1	if	if	SCONJ
ap-3794	389	2	a	a	DET
ap-3794	389	3	factor	factor	NOUN
ap-3794	389	4	w	w	NOUN
ap-3794	389	5	has	have	VERB
ap-3794	389	6	a	a	DET
ap-3794	389	7	unique	unique	ADJ
ap-3794	389	8	right	right	ADJ
ap-3794	389	9	prolongation	prolongation	NOUN
ap-3794	389	10	in	in	ADP
ap-3794	389	11	the	the	DET
ap-3794	389	12	language	language	NOUN
ap-3794	389	13	l(t	l(t	PROPN
ap-3794	389	14	)	)	PUNCT
ap-3794	389	15	,	,	PUNCT
ap-3794	389	16	i.e.	i.e.	X
ap-3794	389	17	there	there	PRON
ap-3794	389	18	exists	exist	VERB
ap-3794	389	19	only	only	ADV
ap-3794	389	20	one	one	NUM
ap-3794	389	21	letter	letter	NOUN
ap-3794	389	22	a	a	DET
ap-3794	389	23	∈	∈	PROPN
ap-3794	389	24	a	a	DET
ap-3794	389	25	such	such	ADJ
ap-3794	389	26	that	that	DET
ap-3794	389	27	wa	wa	PROPN
ap-3794	389	28	∈	∈	PROPN
ap-3794	389	29	l(t	l(t	PROPN
ap-3794	389	30	)	)	PUNCT
ap-3794	389	31	,	,	PUNCT
ap-3794	389	32	then	then	ADV
ap-3794	389	33	the	the	DET
ap-3794	389	34	set	set	NOUN
ap-3794	389	35	of	of	ADP
ap-3794	389	36	return	return	NOUN
ap-3794	389	37	words	word	NOUN
ap-3794	389	38	to	to	ADP
ap-3794	389	39	w	w	PROPN
ap-3794	389	40	and	and	CCONJ
ap-3794	389	41	the	the	DET
ap-3794	389	42	set	set	NOUN
ap-3794	389	43	of	of	ADP
ap-3794	389	44	return	return	NOUN
ap-3794	389	45	words	word	NOUN
ap-3794	389	46	to	to	ADP
ap-3794	389	47	wa	wa	ADJ
ap-3794	389	48	coincide	coincide	NOUN
ap-3794	389	49	.	.	PUNCT
ap-3794	390	1	and	and	CCONJ
ap-3794	390	2	(	(	PUNCT
ap-3794	390	3	almost	almost	ADV
ap-3794	390	4	)	)	PUNCT
ap-3794	390	5	analogously	analogously	ADV
ap-3794	390	6	,	,	PUNCT
ap-3794	390	7	if	if	SCONJ
ap-3794	390	8	a	a	DET
ap-3794	390	9	factor	factor	NOUN
ap-3794	390	10	w	w	NOUN
ap-3794	390	11	has	have	VERB
ap-3794	390	12	a	a	DET
ap-3794	390	13	unique	unique	ADJ
ap-3794	390	14	left	leave	VERB
ap-3794	390	15	prolongation	prolongation	NOUN
ap-3794	390	16	in	in	ADP
ap-3794	390	17	the	the	DET
ap-3794	390	18	language	language	NOUN
ap-3794	390	19	l(t	l(t	PROPN
ap-3794	390	20	)	)	PUNCT
ap-3794	390	21	,	,	PUNCT
ap-3794	390	22	say	say	VERB
ap-3794	390	23	aw	aw	INTJ
ap-3794	390	24	for	for	ADP
ap-3794	390	25	some	some	DET
ap-3794	390	26	a	a	DET
ap-3794	390	27	∈	∈	PROPN
ap-3794	390	28	a	a	PRON
ap-3794	390	29	,	,	PUNCT
ap-3794	390	30	then	then	ADV
ap-3794	390	31	a	a	DET
ap-3794	390	32	word	word	NOUN
ap-3794	390	33	v	v	NOUN
ap-3794	390	34	is	be	AUX
ap-3794	390	35	a	a	DET
ap-3794	390	36	return	return	NOUN
ap-3794	390	37	word	word	NOUN
ap-3794	390	38	to	to	ADP
ap-3794	390	39	w	w	VERB
ap-3794	390	40	if	if	SCONJ
ap-3794	391	1	and	and	CCONJ
ap-3794	391	2	only	only	ADV
ap-3794	391	3	if	if	SCONJ
ap-3794	391	4	ava−1	ava−1	PROPN
ap-3794	391	5	is	be	AUX
ap-3794	391	6	a	a	DET
ap-3794	391	7	return	return	NOUN
ap-3794	391	8	word	word	NOUN
ap-3794	391	9	to	to	ADP
ap-3794	391	10	aw	aw	INTJ
ap-3794	391	11	.	.	PUNCT
ap-3794	392	1	consequently	consequently	ADV
ap-3794	392	2	,	,	PUNCT
ap-3794	392	3	to	to	PART
ap-3794	392	4	describe	describe	VERB
ap-3794	392	5	the	the	DET
ap-3794	392	6	structure	structure	NOUN
ap-3794	392	7	of	of	ADP
ap-3794	392	8	return	return	NOUN
ap-3794	392	9	words	word	NOUN
ap-3794	392	10	to	to	ADP
ap-3794	392	11	a	a	DET
ap-3794	392	12	given	give	VERB
ap-3794	392	13	factor	factor	NOUN
ap-3794	392	14	w	w	NOUN
ap-3794	392	15	,	,	PUNCT
ap-3794	392	16	we	we	PRON
ap-3794	392	17	can	can	AUX
ap-3794	392	18	restrict	restrict	VERB
ap-3794	392	19	to	to	ADP
ap-3794	392	20	factors	factor	NOUN
ap-3794	392	21	which	which	PRON
ap-3794	392	22	have	have	VERB
ap-3794	392	23	at	at	ADV
ap-3794	392	24	least	least	ADV
ap-3794	392	25	two	two	NUM
ap-3794	392	26	right	right	ADJ
ap-3794	392	27	and	and	CCONJ
ap-3794	392	28	at	at	ADV
ap-3794	392	29	least	least	ADJ
ap-3794	392	30	two	two	NUM
ap-3794	392	31	left	left	ADJ
ap-3794	392	32	prolongations	prolongation	NOUN
ap-3794	392	33	.	.	PUNCT
ap-3794	393	1	such	such	ADJ
ap-3794	393	2	factors	factor	NOUN
ap-3794	393	3	are	be	AUX
ap-3794	393	4	called	call	VERB
ap-3794	393	5	bispecial	bispecial	ADJ
ap-3794	393	6	.	.	PUNCT
ap-3794	394	1	it	it	PRON
ap-3794	394	2	is	be	AUX
ap-3794	394	3	readily	readily	ADV
ap-3794	394	4	seen	see	VERB
ap-3794	394	5	that	that	SCONJ
ap-3794	394	6	the	the	DET
ap-3794	394	7	language	language	NOUN
ap-3794	394	8	of	of	ADP
ap-3794	394	9	an	an	DET
ap-3794	394	10	aperiodic	aperiodic	ADJ
ap-3794	394	11	recurrent	recurrent	NOUN
ap-3794	394	12	infinite	infinite	ADJ
ap-3794	394	13	word	word	NOUN
ap-3794	394	14	u	u	NOUN
ap-3794	394	15	contains	contain	VERB
ap-3794	394	16	infinitely	infinitely	ADV
ap-3794	394	17	many	many	ADJ
ap-3794	394	18	bispecial	bispecial	ADJ
ap-3794	394	19	factors	factor	NOUN
ap-3794	394	20	.	.	PUNCT
ap-3794	395	1	before	before	ADP
ap-3794	395	2	giving	give	VERB
ap-3794	395	3	the	the	DET
ap-3794	395	4	description	description	NOUN
ap-3794	395	5	of	of	ADP
ap-3794	395	6	return	return	NOUN
ap-3794	395	7	words	word	NOUN
ap-3794	395	8	to	to	ADP
ap-3794	395	9	bispecial	bispecial	ADJ
ap-3794	395	10	factors	factor	NOUN
ap-3794	395	11	,	,	PUNCT
ap-3794	395	12	we	we	PRON
ap-3794	395	13	state	state	VERB
ap-3794	395	14	the	the	DET
ap-3794	395	15	following	follow	VERB
ap-3794	395	16	lemma	lemma	PROPN
ap-3794	395	17	.	.	PUNCT
ap-3794	396	1	let	let	VERB
ap-3794	396	2	us	we	PRON
ap-3794	396	3	recall	recall	VERB
ap-3794	396	4	that	that	PRON
ap-3794	396	5	for	for	ADP
ap-3794	396	6	a	a	DET
ap-3794	396	7	word	word	NOUN
ap-3794	396	8	w	w	ADP
ap-3794	396	9	the	the	DET
ap-3794	396	10	notation	notation	NOUN
ap-3794	396	11	w	w	PROPN
ap-3794	396	12	denotes	denote	VERB
ap-3794	396	13	the	the	DET
ap-3794	396	14	reversal	reversal	NOUN
ap-3794	396	15	of	of	ADP
ap-3794	396	16	w	w	NOUN
ap-3794	396	17	while	while	NOUN
ap-3794	396	18	for	for	ADP
ap-3794	396	19	an	an	DET
ap-3794	396	20	interval	interval	NOUN
ap-3794	397	1	[	[	X
ap-3794	397	2	c	c	X
ap-3794	397	3	,	,	PUNCT
ap-3794	397	4	d	d	NOUN
ap-3794	397	5	)	)	PUNCT
ap-3794	397	6	the	the	DET
ap-3794	397	7	notation	notation	NOUN
ap-3794	397	8	[	[	X
ap-3794	397	9	c	c	X
ap-3794	397	10	,	,	PUNCT
ap-3794	397	11	d	d	NOUN
ap-3794	397	12	)	)	PUNCT
ap-3794	397	13	denotes	denote	VERB
ap-3794	397	14	the	the	DET
ap-3794	397	15	interval	interval	NOUN
ap-3794	398	1	[	[	X
ap-3794	398	2	1−	1−	NUM
ap-3794	398	3	d	d	PROPN
ap-3794	398	4	,	,	PUNCT
ap-3794	398	5	1−	1−	NUM
ap-3794	398	6	c	c	NOUN
ap-3794	398	7	)	)	PUNCT
ap-3794	398	8	.	.	PUNCT
ap-3794	399	1	lemma	lemma	PROPN
ap-3794	399	2	5.2	5.2	NUM
ap-3794	399	3	.	.	PUNCT
ap-3794	400	1	let	let	VERB
ap-3794	400	2	w	w	PART
ap-3794	400	3	belong	belong	VERB
ap-3794	400	4	to	to	ADP
ap-3794	400	5	the	the	DET
ap-3794	400	6	language	language	NOUN
ap-3794	400	7	of	of	ADP
ap-3794	400	8	a	a	DET
ap-3794	400	9	nondegenerate	nondegenerate	NOUN
ap-3794	400	10	3iet	3iet	PROPN
ap-3794	400	11	t	t	NOUN
ap-3794	400	12	.	.	PUNCT
ap-3794	401	1	denote	denote	VERB
ap-3794	401	2	n	n	PROPN
ap-3794	401	3	=	=	SYM
ap-3794	401	4	|w|	|w|	PROPN
ap-3794	401	5	.	.	PROPN
ap-3794	402	1	for	for	ADP
ap-3794	402	2	the	the	DET
ap-3794	402	3	cylinder	cylinder	NOUN
ap-3794	402	4	of	of	ADP
ap-3794	402	5	its	its	PRON
ap-3794	402	6	reversal	reversal	NOUN
ap-3794	402	7	w	w	NOUN
ap-3794	402	8	,	,	PUNCT
ap-3794	402	9	one	one	PRON
ap-3794	402	10	has	have	VERB
ap-3794	402	11	[	[	X
ap-3794	402	12	w	w	X
ap-3794	402	13	]	]	X
ap-3794	402	14	=	=	SYM
ap-3794	402	15	tn	tn	PROPN
ap-3794	402	16	(	(	PUNCT
ap-3794	402	17	[	[	X
ap-3794	402	18	w	w	X
ap-3794	402	19	]	]	X
ap-3794	402	20	)	)	PUNCT
ap-3794	402	21	.	.	PUNCT
ap-3794	403	1	468	468	NUM
ap-3794	403	2	vol	vol	NOUN
ap-3794	403	3	.	.	PUNCT
ap-3794	404	1	56	56	NUM
ap-3794	404	2	no	no	NOUN
ap-3794	404	3	.	.	PUNCT
ap-3794	405	1	6/2016	6/2016	NUM
ap-3794	405	2	itineraries	itinerary	NOUN
ap-3794	405	3	induced	induce	VERB
ap-3794	405	4	by	by	ADP
ap-3794	405	5	exchange	exchange	NOUN
ap-3794	405	6	of	of	ADP
ap-3794	405	7	three	three	NUM
ap-3794	405	8	intervals	interval	NOUN
ap-3794	405	9	proof	proof	NOUN
ap-3794	405	10	.	.	PUNCT
ap-3794	406	1	according	accord	VERB
ap-3794	406	2	to	to	ADP
ap-3794	406	3	the	the	DET
ap-3794	406	4	definition	definition	NOUN
ap-3794	406	5	of	of	ADP
ap-3794	406	6	[	[	X
ap-3794	406	7	w	w	X
ap-3794	406	8	]	]	X
ap-3794	406	9	,	,	PUNCT
ap-3794	406	10	for	for	ADP
ap-3794	406	11	each	each	DET
ap-3794	406	12	[	[	X
ap-3794	406	13	w]-itinerary	w]-itinerary	ADJ
ap-3794	406	14	r	r	NOUN
ap-3794	406	15	,	,	PUNCT
ap-3794	406	16	the	the	DET
ap-3794	406	17	word	word	NOUN
ap-3794	406	18	rw	rw	NOUN
ap-3794	406	19	belongs	belong	VERB
ap-3794	406	20	to	to	ADP
ap-3794	406	21	the	the	DET
ap-3794	406	22	language	language	NOUN
ap-3794	406	23	and	and	CCONJ
ap-3794	406	24	w	w	NOUN
ap-3794	406	25	occurs	occur	VERB
ap-3794	406	26	in	in	ADP
ap-3794	406	27	rw	rw	NOUN
ap-3794	406	28	exactly	exactly	ADV
ap-3794	406	29	twice	twice	ADV
ap-3794	406	30	,	,	PUNCT
ap-3794	406	31	as	as	ADP
ap-3794	406	32	a	a	DET
ap-3794	406	33	prefix	prefix	NOUN
ap-3794	406	34	and	and	CCONJ
ap-3794	406	35	as	as	ADP
ap-3794	406	36	a	a	DET
ap-3794	406	37	suffix	suffix	NOUN
ap-3794	406	38	.	.	PUNCT
ap-3794	407	1	in	in	ADP
ap-3794	407	2	other	other	ADJ
ap-3794	407	3	words	word	NOUN
ap-3794	407	4	r	r	NOUN
ap-3794	407	5	is	be	AUX
ap-3794	407	6	a	a	DET
ap-3794	407	7	return	return	NOUN
ap-3794	407	8	word	word	NOUN
ap-3794	407	9	to	to	ADP
ap-3794	407	10	w.	w.	PROPN
ap-3794	407	11	moreover	moreover	ADV
ap-3794	407	12	,	,	PUNCT
ap-3794	407	13	[	[	X
ap-3794	407	14	w	w	X
ap-3794	407	15	]	]	X
ap-3794	407	16	is	be	AUX
ap-3794	407	17	the	the	DET
ap-3794	407	18	maximal	maximal	ADJ
ap-3794	407	19	(	(	PUNCT
ap-3794	407	20	with	with	ADP
ap-3794	407	21	respect	respect	NOUN
ap-3794	407	22	to	to	ADP
ap-3794	407	23	inclusion	inclusion	NOUN
ap-3794	407	24	)	)	PUNCT
ap-3794	407	25	interval	interval	NOUN
ap-3794	407	26	with	with	ADP
ap-3794	407	27	this	this	DET
ap-3794	407	28	property	property	NOUN
ap-3794	407	29	.	.	PUNCT
ap-3794	408	1	it	it	PRON
ap-3794	408	2	follows	follow	VERB
ap-3794	408	3	also	also	ADV
ap-3794	408	4	that	that	SCONJ
ap-3794	408	5	if	if	SCONJ
ap-3794	408	6	r	r	NOUN
ap-3794	408	7	is	be	AUX
ap-3794	408	8	an	an	DET
ap-3794	408	9	[	[	X
ap-3794	408	10	w]-itinerary	w]-itinerary	ADJ
ap-3794	408	11	,	,	PUNCT
ap-3794	408	12	then	then	ADV
ap-3794	408	13	the	the	DET
ap-3794	408	14	word	word	NOUN
ap-3794	408	15	w−1rw	w−1rw	NOUN
ap-3794	408	16	is	be	AUX
ap-3794	408	17	a	a	DET
ap-3794	408	18	tn([w])-itinerary	tn([w])-itinerary	PROPN
ap-3794	408	19	.	.	PUNCT
ap-3794	409	1	applying	apply	VERB
ap-3794	409	2	proposition	proposition	NOUN
ap-3794	409	3	3.5	3.5	NUM
ap-3794	409	4	to	to	ADP
ap-3794	409	5	the	the	DET
ap-3794	409	6	interval	interval	NOUN
ap-3794	409	7	tn([w	tn([w	PROPN
ap-3794	409	8	]	]	PUNCT
ap-3794	409	9	)	)	PUNCT
ap-3794	409	10	we	we	PRON
ap-3794	409	11	obtain	obtain	VERB
ap-3794	409	12	that	that	PRON
ap-3794	409	13	s	s	VERB
ap-3794	409	14	:	:	PUNCT
ap-3794	409	15	=	=	SYM
ap-3794	409	16	w−1rw	w−1rw	NOUN
ap-3794	409	17	is	be	AUX
ap-3794	409	18	an	an	DET
ap-3794	409	19	tn([w])-itinerary	tn([w])-itinerary	NOUN
ap-3794	409	20	.	.	PUNCT
ap-3794	410	1	since	since	SCONJ
ap-3794	410	2	the	the	DET
ap-3794	410	3	word	word	NOUN
ap-3794	410	4	sw	sw	PROPN
ap-3794	410	5	=	=	PUNCT
ap-3794	410	6	rw	rw	PROPN
ap-3794	410	7	has	have	VERB
ap-3794	410	8	a	a	DET
ap-3794	410	9	prefix	prefix	NOUN
ap-3794	410	10	w	w	NOUN
ap-3794	410	11	and	and	CCONJ
ap-3794	410	12	a	a	DET
ap-3794	410	13	suffix	suffix	PROPN
ap-3794	410	14	w	w	NOUN
ap-3794	410	15	,	,	PUNCT
ap-3794	410	16	with	with	ADP
ap-3794	410	17	no	no	DET
ap-3794	410	18	other	other	ADJ
ap-3794	410	19	occurrences	occurrence	NOUN
ap-3794	410	20	of	of	ADP
ap-3794	410	21	w	w	NOUN
ap-3794	410	22	,	,	PUNCT
ap-3794	410	23	the	the	DET
ap-3794	410	24	word	word	NOUN
ap-3794	410	25	s	s	VERB
ap-3794	410	26	is	be	AUX
ap-3794	410	27	a	a	DET
ap-3794	410	28	return	return	NOUN
ap-3794	410	29	word	word	NOUN
ap-3794	410	30	to	to	ADP
ap-3794	410	31	w	w	NOUN
ap-3794	410	32	and	and	CCONJ
ap-3794	410	33	thus	thus	ADV
ap-3794	410	34	by	by	ADP
ap-3794	410	35	definition	definition	NOUN
ap-3794	410	36	of	of	ADP
ap-3794	410	37	the	the	DET
ap-3794	410	38	cylinder	cylinder	NOUN
ap-3794	410	39	,	,	PUNCT
ap-3794	410	40	s	s	PART
ap-3794	410	41	=	=	PUNCT
ap-3794	410	42	w−1rw	w−1rw	NOUN
ap-3794	410	43	belongs	belong	VERB
ap-3794	410	44	to	to	ADP
ap-3794	410	45	[	[	X
ap-3794	410	46	w]-itinerary	w]-itinerary	ADJ
ap-3794	410	47	for	for	ADP
ap-3794	410	48	any	any	DET
ap-3794	410	49	tn([w])-itinerary	tn([w])-itinerary	PROPN
ap-3794	410	50	s.	s.	PROPN
ap-3794	410	51	from	from	ADP
ap-3794	410	52	the	the	DET
ap-3794	410	53	maximality	maximality	NOUN
ap-3794	410	54	of	of	ADP
ap-3794	410	55	the	the	DET
ap-3794	410	56	cylinder	cylinder	NOUN
ap-3794	410	57	we	we	PRON
ap-3794	410	58	have	have	VERB
ap-3794	410	59	tn([w	tn([w	PROPN
ap-3794	410	60	]	]	X
ap-3794	410	61	)	)	PUNCT
ap-3794	410	62	⊂	⊂	PROPN
ap-3794	411	1	[	[	X
ap-3794	411	2	w	w	X
ap-3794	411	3	]	]	X
ap-3794	411	4	.	.	PUNCT
ap-3794	412	1	since	since	SCONJ
ap-3794	412	2	the	the	DET
ap-3794	412	3	lengths	length	NOUN
ap-3794	412	4	of	of	ADP
ap-3794	412	5	the	the	DET
ap-3794	412	6	intervals	interval	NOUN
ap-3794	412	7	[	[	X
ap-3794	412	8	w	w	X
ap-3794	412	9	]	]	X
ap-3794	412	10	and	and	CCONJ
ap-3794	412	11	tn([w	tn([w	PROPN
ap-3794	412	12	]	]	PUNCT
ap-3794	412	13	)	)	PUNCT
ap-3794	412	14	coincide	coincide	NOUN
ap-3794	412	15	we	we	PRON
ap-3794	412	16	see	see	VERB
ap-3794	412	17	,	,	PUNCT
ap-3794	412	18	in	in	ADP
ap-3794	412	19	particular	particular	ADJ
ap-3794	412	20	,	,	PUNCT
ap-3794	412	21	that	that	SCONJ
ap-3794	412	22	the	the	DET
ap-3794	412	23	length	length	NOUN
ap-3794	412	24	of	of	ADP
ap-3794	412	25	the	the	DET
ap-3794	412	26	interval	interval	NOUN
ap-3794	412	27	[	[	X
ap-3794	412	28	w	w	X
ap-3794	412	29	]	]	X
ap-3794	412	30	is	be	AUX
ap-3794	412	31	less	less	ADV
ap-3794	412	32	or	or	CCONJ
ap-3794	412	33	equal	equal	ADJ
ap-3794	412	34	to	to	ADP
ap-3794	412	35	the	the	DET
ap-3794	412	36	length	length	NOUN
ap-3794	412	37	of	of	ADP
ap-3794	412	38	the	the	DET
ap-3794	412	39	interval	interval	NOUN
ap-3794	412	40	[	[	X
ap-3794	412	41	w	w	X
ap-3794	412	42	]	]	X
ap-3794	412	43	.	.	PUNCT
ap-3794	413	1	but	but	CCONJ
ap-3794	413	2	from	from	ADP
ap-3794	413	3	the	the	DET
ap-3794	413	4	symmetry	symmetry	NOUN
ap-3794	413	5	of	of	ADP
ap-3794	413	6	the	the	DET
ap-3794	413	7	role	role	NOUN
ap-3794	413	8	w	w	NOUN
ap-3794	413	9	and	and	CCONJ
ap-3794	413	10	w	w	PROPN
ap-3794	413	11	,	,	PUNCT
ap-3794	413	12	their	their	PRON
ap-3794	413	13	length	length	NOUN
ap-3794	413	14	must	must	AUX
ap-3794	413	15	be	be	AUX
ap-3794	413	16	equal	equal	ADJ
ap-3794	413	17	and	and	CCONJ
ap-3794	413	18	thus	thus	ADV
ap-3794	413	19	tn([w	tn([w	PROPN
ap-3794	413	20	]	]	X
ap-3794	413	21	)	)	PUNCT
ap-3794	414	1	=	=	PUNCT
ap-3794	415	1	[	[	X
ap-3794	415	2	w	w	X
ap-3794	415	3	]	]	X
ap-3794	415	4	.	.	PUNCT
ap-3794	416	1	the	the	DET
ap-3794	416	2	language	language	NOUN
ap-3794	416	3	of	of	ADP
ap-3794	416	4	t	t	PROPN
ap-3794	416	5	contains	contain	VERB
ap-3794	416	6	two	two	NUM
ap-3794	416	7	types	type	NOUN
ap-3794	416	8	of	of	ADP
ap-3794	416	9	bispecial	bispecial	ADJ
ap-3794	416	10	factors	factor	NOUN
ap-3794	416	11	:	:	PUNCT
ap-3794	416	12	palindromic	palindromic	ADJ
ap-3794	416	13	and	and	CCONJ
ap-3794	416	14	non	non	ADJ
ap-3794	416	15	-	-	ADJ
ap-3794	416	16	palindromic	palindromic	ADJ
ap-3794	416	17	.	.	PUNCT
ap-3794	417	1	in	in	ADP
ap-3794	417	2	[	[	X
ap-3794	417	3	6	6	NUM
ap-3794	417	4	]	]	PUNCT
ap-3794	417	5	,	,	PUNCT
ap-3794	417	6	ferenczi	ferenczi	PROPN
ap-3794	417	7	,	,	PUNCT
ap-3794	417	8	holton	holton	PROPN
ap-3794	417	9	and	and	CCONJ
ap-3794	417	10	zamboni	zamboni	PROPN
ap-3794	417	11	studied	study	VERB
ap-3794	417	12	the	the	DET
ap-3794	417	13	structure	structure	NOUN
ap-3794	417	14	of	of	ADP
ap-3794	417	15	return	return	NOUN
ap-3794	417	16	words	word	NOUN
ap-3794	417	17	to	to	ADP
ap-3794	417	18	non	non	ADJ
ap-3794	417	19	-	-	ADJ
ap-3794	417	20	palindromic	palindromic	ADJ
ap-3794	417	21	bispecial	bispecial	ADJ
ap-3794	417	22	factors	factor	NOUN
ap-3794	417	23	.	.	PUNCT
ap-3794	418	1	the	the	DET
ap-3794	418	2	following	follow	VERB
ap-3794	418	3	proposition	proposition	NOUN
ap-3794	418	4	completes	complete	VERB
ap-3794	418	5	this	this	DET
ap-3794	418	6	description	description	NOUN
ap-3794	418	7	.	.	PUNCT
ap-3794	419	1	proposition	proposition	NOUN
ap-3794	419	2	5.3	5.3	NUM
ap-3794	419	3	.	.	PUNCT
ap-3794	420	1	let	let	VERB
ap-3794	420	2	w	w	NOUN
ap-3794	420	3	be	be	AUX
ap-3794	420	4	a	a	DET
ap-3794	420	5	bispecial	bispecial	ADJ
ap-3794	420	6	factor	factor	NOUN
ap-3794	420	7	.	.	PUNCT
ap-3794	421	1	if	if	SCONJ
ap-3794	421	2	w	w	NOUN
ap-3794	421	3	is	be	AUX
ap-3794	421	4	a	a	DET
ap-3794	421	5	palindrome	palindrome	NOUN
ap-3794	421	6	,	,	PUNCT
ap-3794	421	7	then	then	ADV
ap-3794	421	8	its	its	PRON
ap-3794	421	9	return	return	NOUN
ap-3794	421	10	words	word	NOUN
ap-3794	421	11	are	be	AUX
ap-3794	421	12	described	describe	VERB
ap-3794	421	13	by	by	ADP
ap-3794	421	14	the	the	DET
ap-3794	421	15	cases	case	NOUN
ap-3794	421	16	(	(	PUNCT
ap-3794	421	17	i	i	NOUN
ap-3794	421	18	)	)	PUNCT
ap-3794	421	19	and	and	CCONJ
ap-3794	421	20	(	(	PUNCT
ap-3794	421	21	ii	ii	NOUN
ap-3794	421	22	)	)	PUNCT
ap-3794	421	23	of	of	ADP
ap-3794	421	24	proposition	proposition	NOUN
ap-3794	421	25	5.1	5.1	NUM
ap-3794	421	26	.	.	PUNCT
ap-3794	422	1	if	if	SCONJ
ap-3794	422	2	w	w	NOUN
ap-3794	422	3	is	be	AUX
ap-3794	422	4	not	not	PART
ap-3794	422	5	a	a	DET
ap-3794	422	6	palindrome	palindrome	NOUN
ap-3794	422	7	,	,	PUNCT
ap-3794	422	8	then	then	ADV
ap-3794	422	9	its	its	PRON
ap-3794	422	10	return	return	NOUN
ap-3794	422	11	words	word	NOUN
ap-3794	422	12	are	be	AUX
ap-3794	422	13	described	describe	VERB
ap-3794	422	14	by	by	ADP
ap-3794	422	15	the	the	DET
ap-3794	422	16	cases	case	NOUN
ap-3794	422	17	(	(	PUNCT
ap-3794	422	18	iii	iii	NOUN
ap-3794	422	19	)	)	PUNCT
ap-3794	422	20	–	–	PUNCT
ap-3794	422	21	(	(	PUNCT
ap-3794	422	22	vi	vi	NOUN
ap-3794	422	23	)	)	PUNCT
ap-3794	422	24	of	of	ADP
ap-3794	422	25	proposition	proposition	NOUN
ap-3794	422	26	5.1	5.1	NUM
ap-3794	422	27	.	.	PUNCT
ap-3794	423	1	proof	proof	NOUN
ap-3794	423	2	.	.	PUNCT
ap-3794	424	1	let	let	VERB
ap-3794	424	2	w	w	NOUN
ap-3794	424	3	be	be	AUX
ap-3794	424	4	a	a	DET
ap-3794	424	5	bispecial	bispecial	ADJ
ap-3794	424	6	factor	factor	NOUN
ap-3794	424	7	.	.	PUNCT
ap-3794	425	1	if	if	SCONJ
ap-3794	425	2	w	w	NOUN
ap-3794	425	3	is	be	AUX
ap-3794	425	4	not	not	PART
ap-3794	425	5	a	a	DET
ap-3794	425	6	palindrome	palindrome	NOUN
ap-3794	425	7	,	,	PUNCT
ap-3794	425	8	the	the	DET
ap-3794	425	9	claim	claim	NOUN
ap-3794	425	10	follows	follow	VERB
ap-3794	425	11	from	from	ADP
ap-3794	425	12	theorem	theorem	ADJ
ap-3794	425	13	4.6	4.6	NUM
ap-3794	425	14	of	of	ADP
ap-3794	425	15	[	[	X
ap-3794	425	16	6	6	NUM
ap-3794	425	17	]	]	PUNCT
ap-3794	425	18	.	.	PUNCT
ap-3794	426	1	assume	assume	VERB
ap-3794	426	2	that	that	SCONJ
ap-3794	426	3	w	w	NOUN
ap-3794	426	4	is	be	AUX
ap-3794	426	5	a	a	DET
ap-3794	426	6	palindrome	palindrome	NOUN
ap-3794	426	7	and	and	CCONJ
ap-3794	426	8	let	let	VERB
ap-3794	426	9	[	[	X
ap-3794	426	10	w	w	X
ap-3794	426	11	]	]	X
ap-3794	426	12	=	=	PUNCT
ap-3794	427	1	[	[	X
ap-3794	427	2	t−`(l	t−`(l	NOUN
ap-3794	427	3	)	)	PUNCT
ap-3794	427	4	,	,	PUNCT
ap-3794	427	5	t−r(r	t−r(r	NOUN
ap-3794	427	6	)	)	PUNCT
ap-3794	427	7	)	)	PUNCT
ap-3794	427	8	with	with	ADP
ap-3794	427	9	l	l	NOUN
ap-3794	427	10	,	,	PUNCT
ap-3794	427	11	r	r	NOUN
ap-3794	427	12	∈	∈	PROPN
ap-3794	427	13	{	{	PUNCT
ap-3794	427	14	α	α	NOUN
ap-3794	427	15	,	,	PUNCT
ap-3794	427	16	β	β	NOUN
ap-3794	427	17	}	}	PUNCT
ap-3794	427	18	and	and	CCONJ
ap-3794	427	19	0	0	NUM
ap-3794	427	20	≤	≤	NUM
ap-3794	427	21	`	`	PUNCT
ap-3794	427	22	,	,	PUNCT
ap-3794	427	23	r	r	NOUN
ap-3794	427	24	<	<	X
ap-3794	427	25	|w|	|w|	PROPN
ap-3794	427	26	.	.	PUNCT
ap-3794	427	27	by	by	ADP
ap-3794	427	28	lemma	lemma	PROPN
ap-3794	427	29	5.2	5.2	NUM
ap-3794	427	30	we	we	PRON
ap-3794	427	31	have	have	VERB
ap-3794	427	32	[	[	X
ap-3794	427	33	w	w	X
ap-3794	427	34	]	]	X
ap-3794	427	35	=	=	SYM
ap-3794	427	36	t	t	PROPN
ap-3794	427	37	|w|	|w|	PROPN
ap-3794	427	38	(	(	PUNCT
ap-3794	427	39	[	[	X
ap-3794	427	40	w	w	X
ap-3794	427	41	]	]	X
ap-3794	427	42	)	)	PUNCT
ap-3794	427	43	.	.	PUNCT
ap-3794	428	1	since	since	SCONJ
ap-3794	428	2	w	w	PROPN
ap-3794	428	3	=	=	SYM
ap-3794	428	4	w	w	PROPN
ap-3794	428	5	,	,	PUNCT
ap-3794	428	6	we	we	PRON
ap-3794	428	7	have	have	VERB
ap-3794	428	8	iw	iw	NOUN
ap-3794	428	9	=	=	SYM
ap-3794	428	10	iw	iw	PROPN
ap-3794	428	11	,	,	PUNCT
ap-3794	428	12	and	and	CCONJ
ap-3794	428	13	thus	thus	ADV
ap-3794	428	14	iw	iw	ADJ
ap-3794	428	15	=	=	PUNCT
ap-3794	428	16	[	[	X
ap-3794	428	17	t−`(l	t−`(l	NOUN
ap-3794	428	18	)	)	PUNCT
ap-3794	428	19	,	,	PUNCT
ap-3794	428	20	t−r(r	t−r(r	NOUN
ap-3794	428	21	)	)	PUNCT
ap-3794	428	22	)	)	PUNCT
ap-3794	429	1	=	=	PUNCT
ap-3794	430	1	[	[	X
ap-3794	430	2	1−	1−	NUM
ap-3794	430	3	tn−r(r	tn−r(r	NOUN
ap-3794	430	4	)	)	PUNCT
ap-3794	430	5	,	,	PUNCT
ap-3794	430	6	1−	1−	NUM
ap-3794	430	7	tn−`(l	tn−`(l	NOUN
ap-3794	430	8	)	)	PUNCT
ap-3794	430	9	)	)	PUNCT
ap-3794	431	1	=	=	SYM
ap-3794	431	2	iw	iw	INTJ
ap-3794	431	3	.	.	PUNCT
ap-3794	432	1	since	since	SCONJ
ap-3794	432	2	the	the	DET
ap-3794	432	3	considered	considered	ADJ
ap-3794	432	4	3iet	3iet	PROPN
ap-3794	432	5	is	be	AUX
ap-3794	432	6	non	non	ADJ
ap-3794	432	7	-	-	ADJ
ap-3794	432	8	degenerate	degenerate	ADJ
ap-3794	432	9	,	,	PUNCT
ap-3794	432	10	the	the	DET
ap-3794	432	11	parameters	parameter	NOUN
ap-3794	432	12	α	α	PRON
ap-3794	432	13	,	,	PUNCT
ap-3794	432	14	β	β	X
ap-3794	432	15	satisfy	satisfy	NOUN
ap-3794	432	16	(	(	PUNCT
ap-3794	432	17	2	2	NUM
ap-3794	432	18	)	)	PUNCT
ap-3794	432	19	.	.	PUNCT
ap-3794	433	1	consequently	consequently	ADV
ap-3794	433	2	,	,	PUNCT
ap-3794	433	3	the	the	DET
ap-3794	433	4	equation	equation	NOUN
ap-3794	433	5	t−`(l	t−`(l	NOUN
ap-3794	433	6	)	)	PUNCT
ap-3794	433	7	=	=	SYM
ap-3794	433	8	1	1	NUM
ap-3794	433	9	−	−	PROPN
ap-3794	433	10	tn−r(r	tn−r(r	NOUN
ap-3794	433	11	)	)	PUNCT
ap-3794	433	12	has	have	VERB
ap-3794	433	13	a	a	DET
ap-3794	433	14	solution	solution	NOUN
ap-3794	433	15	if	if	SCONJ
ap-3794	433	16	and	and	CCONJ
ap-3794	433	17	only	only	ADV
ap-3794	433	18	if	if	SCONJ
ap-3794	433	19	r	r	NOUN
ap-3794	433	20	6=	6=	PUNCT
ap-3794	433	21	l.	l.	PROPN
ap-3794	433	22	thus	thus	ADV
ap-3794	433	23	,	,	PUNCT
ap-3794	433	24	we	we	PRON
ap-3794	433	25	have	have	VERB
ap-3794	433	26	neither	neither	CCONJ
ap-3794	433	27	a	a	DET
ap-3794	433	28	=	=	SYM
ap-3794	433	29	c	c	NOUN
ap-3794	433	30	=	=	SYM
ap-3794	433	31	d	d	PROPN
ap-3794	433	32	nor	nor	CCONJ
ap-3794	433	33	b	b	X
ap-3794	434	1	=	=	SYM
ap-3794	434	2	c	c	NOUN
ap-3794	434	3	=	=	SYM
ap-3794	434	4	d	d	PROPN
ap-3794	434	5	and	and	CCONJ
ap-3794	434	6	we	we	PRON
ap-3794	434	7	are	be	AUX
ap-3794	434	8	in	in	ADP
ap-3794	434	9	the	the	DET
ap-3794	434	10	case	case	NOUN
ap-3794	434	11	(	(	PUNCT
ap-3794	434	12	i	i	NOUN
ap-3794	434	13	)	)	PUNCT
ap-3794	434	14	or	or	CCONJ
ap-3794	434	15	(	(	PUNCT
ap-3794	434	16	ii	ii	NOUN
ap-3794	434	17	)	)	PUNCT
ap-3794	434	18	of	of	ADP
ap-3794	434	19	proposition	proposition	NOUN
ap-3794	434	20	5.1	5.1	NUM
ap-3794	434	21	.	.	PUNCT
ap-3794	435	1	5.2	5.2	NUM
ap-3794	435	2	.	.	PUNCT
ap-3794	435	3	substitutions	substitution	NOUN
ap-3794	435	4	fixing	fix	VERB
ap-3794	435	5	3iet	3iet	NUM
ap-3794	435	6	words	word	NOUN
ap-3794	435	7	another	another	DET
ap-3794	435	8	application	application	NOUN
ap-3794	435	9	of	of	ADP
ap-3794	435	10	proposition	proposition	NOUN
ap-3794	435	11	5.1	5.1	NUM
ap-3794	435	12	is	be	AUX
ap-3794	435	13	providing	provide	VERB
ap-3794	435	14	some	some	DET
ap-3794	435	15	information	information	NOUN
ap-3794	435	16	about	about	ADP
ap-3794	435	17	substitution	substitution	NOUN
ap-3794	435	18	having	have	VERB
ap-3794	435	19	as	as	ADP
ap-3794	435	20	a	a	DET
ap-3794	435	21	fixed	fix	VERB
ap-3794	435	22	point	point	NOUN
ap-3794	435	23	a	a	DET
ap-3794	435	24	non	non	ADJ
ap-3794	435	25	-	-	ADJ
ap-3794	435	26	degenerate	degenerate	ADJ
ap-3794	435	27	3iet	3iet	NUM
ap-3794	435	28	word	word	NOUN
ap-3794	435	29	.	.	PUNCT
ap-3794	436	1	a	a	DET
ap-3794	436	2	substitution	substitution	NOUN
ap-3794	436	3	over	over	ADP
ap-3794	436	4	an	an	DET
ap-3794	436	5	alphabet	alphabet	NOUN
ap-3794	436	6	a	a	PRON
ap-3794	436	7	is	be	AUX
ap-3794	436	8	a	a	DET
ap-3794	436	9	morphism	morphism	PROPN
ap-3794	436	10	η	η	PROPN
ap-3794	436	11	:	:	PUNCT
ap-3794	436	12	a∗	a∗	PROPN
ap-3794	436	13	→	→	SYM
ap-3794	436	14	a∗	a∗	NOUN
ap-3794	436	15	such	such	ADJ
ap-3794	436	16	that	that	DET
ap-3794	436	17	η(b	η(b	NOUN
ap-3794	436	18	)	)	PUNCT
ap-3794	436	19	6=	6=	ADP
ap-3794	436	20	ε	ε	PROPN
ap-3794	436	21	for	for	ADP
ap-3794	436	22	b	b	PROPN
ap-3794	436	23	∈	∈	PROPN
ap-3794	436	24	a	a	PRON
ap-3794	436	25	and	and	CCONJ
ap-3794	436	26	there	there	PRON
ap-3794	436	27	is	be	VERB
ap-3794	436	28	a	a	DET
ap-3794	436	29	letter	letter	NOUN
ap-3794	436	30	a	a	DET
ap-3794	436	31	∈	∈	NOUN
ap-3794	436	32	a	a	DET
ap-3794	436	33	satisfying	satisfying	ADJ
ap-3794	436	34	η(a	η(a	NOUN
ap-3794	436	35	)	)	PUNCT
ap-3794	436	36	=	=	SYM
ap-3794	437	1	aw	aw	INTJ
ap-3794	437	2	for	for	ADP
ap-3794	437	3	some	some	DET
ap-3794	437	4	non	non	ADJ
ap-3794	437	5	-	-	ADJ
ap-3794	437	6	empty	empty	ADJ
ap-3794	437	7	word	word	NOUN
ap-3794	437	8	w.	w.	NOUN
ap-3794	437	9	the	the	DET
ap-3794	437	10	action	action	NOUN
ap-3794	437	11	of	of	ADP
ap-3794	437	12	η	η	PROPN
ap-3794	437	13	can	can	AUX
ap-3794	437	14	be	be	AUX
ap-3794	437	15	naturally	naturally	ADV
ap-3794	437	16	extended	extend	VERB
ap-3794	437	17	to	to	PART
ap-3794	437	18	infinite	infinite	VERB
ap-3794	437	19	words	word	NOUN
ap-3794	437	20	u	u	NOUN
ap-3794	437	21	∈	∈	PROPN
ap-3794	437	22	an	an	PRON
ap-3794	437	23	by	by	ADP
ap-3794	437	24	setting	set	VERB
ap-3794	437	25	η(u	η(u	NOUN
ap-3794	437	26	)	)	PUNCT
ap-3794	437	27	=	=	SYM
ap-3794	437	28	η(u0)η(u1)η(u2	η(u0)η(u1)η(u2	NOUN
ap-3794	437	29	)	)	PUNCT
ap-3794	437	30	.	.	PUNCT
ap-3794	438	1	.	.	PUNCT
ap-3794	439	1	..	..	PUNCT
ap-3794	440	1	if	if	SCONJ
ap-3794	440	2	η(u	η(u	NOUN
ap-3794	440	3	)	)	PUNCT
ap-3794	440	4	=	=	SYM
ap-3794	440	5	u	u	NOUN
ap-3794	440	6	,	,	PUNCT
ap-3794	440	7	then	then	ADV
ap-3794	440	8	u	u	NOUN
ap-3794	440	9	is	be	AUX
ap-3794	440	10	said	say	VERB
ap-3794	440	11	to	to	PART
ap-3794	440	12	be	be	AUX
ap-3794	440	13	a	a	DET
ap-3794	440	14	fixed	fixed	ADJ
ap-3794	440	15	point	point	NOUN
ap-3794	440	16	of	of	ADP
ap-3794	440	17	η	η	PROPN
ap-3794	440	18	.	.	PROPN
ap-3794	440	19	obviously	obviously	ADV
ap-3794	440	20	,	,	PUNCT
ap-3794	440	21	a	a	DET
ap-3794	440	22	substitution	substitution	NOUN
ap-3794	440	23	always	always	ADV
ap-3794	440	24	has	have	VERB
ap-3794	440	25	the	the	DET
ap-3794	440	26	fixed	fix	VERB
ap-3794	440	27	point	point	NOUN
ap-3794	440	28	limn→∞	limn→∞	PROPN
ap-3794	440	29	ηn(a	ηn(a	NOUN
ap-3794	440	30	)	)	PUNCT
ap-3794	440	31	where	where	SCONJ
ap-3794	440	32	the	the	DET
ap-3794	440	33	limit	limit	NOUN
ap-3794	440	34	is	be	AUX
ap-3794	440	35	taken	take	VERB
ap-3794	440	36	over	over	ADP
ap-3794	440	37	the	the	DET
ap-3794	440	38	product	product	NOUN
ap-3794	440	39	topology	topology	NOUN
ap-3794	440	40	.	.	PUNCT
ap-3794	441	1	a	a	DET
ap-3794	441	2	substitution	substitution	NOUN
ap-3794	441	3	η	η	NOUN
ap-3794	441	4	is	be	AUX
ap-3794	441	5	primitive	primitive	ADJ
ap-3794	441	6	if	if	SCONJ
ap-3794	441	7	there	there	PRON
ap-3794	441	8	exists	exist	VERB
ap-3794	441	9	an	an	DET
ap-3794	441	10	integer	integer	NOUN
ap-3794	441	11	k	k	PROPN
ap-3794	441	12	such	such	ADJ
ap-3794	441	13	that	that	PRON
ap-3794	441	14	for	for	ADP
ap-3794	441	15	all	all	DET
ap-3794	441	16	a	a	PRON
ap-3794	441	17	,	,	PUNCT
ap-3794	441	18	b	b	X
ap-3794	441	19	∈	∈	PROPN
ap-3794	441	20	a	a	PRON
ap-3794	441	21	,	,	PUNCT
ap-3794	441	22	the	the	DET
ap-3794	441	23	letter	letter	NOUN
ap-3794	441	24	b	b	PROPN
ap-3794	441	25	occurs	occur	VERB
ap-3794	441	26	in	in	ADP
ap-3794	441	27	ηk(a	ηk(a	NOUN
ap-3794	441	28	)	)	PUNCT
ap-3794	441	29	.	.	PUNCT
ap-3794	442	1	3iet	3iet	NUM
ap-3794	442	2	words	word	NOUN
ap-3794	442	3	fixed	fix	VERB
ap-3794	442	4	by	by	ADP
ap-3794	442	5	a	a	DET
ap-3794	442	6	substitution	substitution	NOUN
ap-3794	442	7	were	be	AUX
ap-3794	442	8	studied	study	VERB
ap-3794	442	9	in	in	ADP
ap-3794	442	10	[	[	X
ap-3794	442	11	3	3	NUM
ap-3794	442	12	]	]	PUNCT
ap-3794	442	13	and	and	CCONJ
ap-3794	442	14	[	[	X
ap-3794	442	15	5	5	NUM
ap-3794	442	16	]	]	PUNCT
ap-3794	442	17	.	.	PUNCT
ap-3794	443	1	in	in	ADP
ap-3794	443	2	[	[	X
ap-3794	443	3	3	3	X
ap-3794	443	4	]	]	PUNCT
ap-3794	443	5	it	it	PRON
ap-3794	443	6	was	be	AUX
ap-3794	443	7	shown	show	VERB
ap-3794	443	8	that	that	SCONJ
ap-3794	443	9	a	a	DET
ap-3794	443	10	substitution	substitution	NOUN
ap-3794	443	11	fixing	fix	VERB
ap-3794	443	12	a	a	DET
ap-3794	443	13	non	non	ADJ
ap-3794	443	14	-	-	ADJ
ap-3794	443	15	degenerate	degenerate	ADJ
ap-3794	443	16	3iet	3iet	NUM
ap-3794	443	17	word	word	NOUN
ap-3794	443	18	corresponds	correspond	VERB
ap-3794	443	19	to	to	ADP
ap-3794	443	20	an	an	DET
ap-3794	443	21	interval	interval	NOUN
ap-3794	443	22	i	i	PRON
ap-3794	443	23	such	such	ADJ
ap-3794	443	24	that	that	SCONJ
ap-3794	443	25	the	the	DET
ap-3794	443	26	induced	induced	ADJ
ap-3794	443	27	transformation	transformation	NOUN
ap-3794	443	28	is	be	AUX
ap-3794	443	29	homothetic	homothetic	ADJ
ap-3794	443	30	to	to	ADP
ap-3794	443	31	the	the	DET
ap-3794	443	32	original	original	ADJ
ap-3794	443	33	one	one	NUM
ap-3794	443	34	.	.	PUNCT
ap-3794	444	1	more	more	ADV
ap-3794	444	2	precisely	precisely	ADV
ap-3794	444	3	,	,	PUNCT
ap-3794	444	4	we	we	PRON
ap-3794	444	5	have	have	VERB
ap-3794	444	6	the	the	DET
ap-3794	444	7	following	follow	VERB
ap-3794	444	8	theorem	theorem	VERB
ap-3794	444	9	.	.	PUNCT
ap-3794	444	10	theorem	theorem	VERB
ap-3794	444	11	5.4	5.4	NUM
ap-3794	445	1	[	[	X
ap-3794	445	2	3	3	NUM
ap-3794	445	3	]	]	PUNCT
ap-3794	445	4	.	.	PUNCT
ap-3794	446	1	let	let	VERB
ap-3794	446	2	ξ	ξ	X
ap-3794	446	3	be	be	AUX
ap-3794	446	4	a	a	DET
ap-3794	446	5	primitive	primitive	ADJ
ap-3794	446	6	substitution	substitution	NOUN
ap-3794	446	7	over	over	ADP
ap-3794	446	8	{	{	PUNCT
ap-3794	446	9	a	a	DET
ap-3794	446	10	,	,	PUNCT
ap-3794	446	11	b	b	NOUN
ap-3794	446	12	,	,	PUNCT
ap-3794	446	13	c	c	NOUN
ap-3794	446	14	}	}	PUNCT
ap-3794	446	15	and	and	CCONJ
ap-3794	446	16	let	let	VERB
ap-3794	446	17	t	t	PROPN
ap-3794	446	18	be	be	AUX
ap-3794	446	19	a	a	DET
ap-3794	446	20	non	non	ADJ
ap-3794	446	21	-	-	ADJ
ap-3794	446	22	degenerate	degenerate	ADJ
ap-3794	446	23	3iet	3iet	NUM
ap-3794	446	24	.	.	PUNCT
ap-3794	447	1	if	if	SCONJ
ap-3794	447	2	substitution	substitution	NOUN
ap-3794	447	3	ξ	ξ	PROPN
ap-3794	447	4	fixes	fix	VERB
ap-3794	447	5	the	the	DET
ap-3794	447	6	word	word	NOUN
ap-3794	447	7	uρ	uρ	ADP
ap-3794	447	8	coding	code	VERB
ap-3794	447	9	the	the	DET
ap-3794	447	10	orbit	orbit	NOUN
ap-3794	447	11	of	of	ADP
ap-3794	447	12	a	a	DET
ap-3794	447	13	point	point	NOUN
ap-3794	447	14	ρ	ρ	X
ap-3794	447	15	∈	∈	PROPN
ap-3794	448	1	[	[	X
ap-3794	448	2	0	0	NUM
ap-3794	448	3	,	,	PUNCT
ap-3794	448	4	1	1	NUM
ap-3794	448	5	)	)	PUNCT
ap-3794	448	6	under	under	ADP
ap-3794	448	7	t	t	PROPN
ap-3794	448	8	,	,	PUNCT
ap-3794	448	9	then	then	ADV
ap-3794	448	10	there	there	PRON
ap-3794	448	11	exists	exist	VERB
ap-3794	448	12	an	an	DET
ap-3794	448	13	interval	interval	NOUN
ap-3794	449	1	i	i	PRON
ap-3794	449	2	⊂	⊂	PROPN
ap-3794	450	1	[	[	X
ap-3794	450	2	0	0	NUM
ap-3794	450	3	,	,	PUNCT
ap-3794	450	4	1	1	NUM
ap-3794	450	5	)	)	PUNCT
ap-3794	450	6	such	such	ADJ
ap-3794	450	7	that	that	SCONJ
ap-3794	450	8	the	the	DET
ap-3794	450	9	induced	induced	ADJ
ap-3794	450	10	transformation	transformation	NOUN
ap-3794	450	11	ti	ti	NOUN
ap-3794	450	12	is	be	AUX
ap-3794	450	13	homothetic	homothetic	ADJ
ap-3794	450	14	to	to	ADP
ap-3794	450	15	t	t	PROPN
ap-3794	450	16	,	,	PUNCT
ap-3794	450	17	the	the	DET
ap-3794	450	18	set	set	NOUN
ap-3794	450	19	of	of	ADP
ap-3794	450	20	i	i	PROPN
ap-3794	450	21	-	-	PUNCT
ap-3794	450	22	itineraries	itinerary	NOUN
ap-3794	450	23	is	be	AUX
ap-3794	450	24	equal	equal	ADJ
ap-3794	450	25	to	to	ADP
ap-3794	450	26	iti	iti	PROPN
ap-3794	450	27	=	=	SYM
ap-3794	450	28	{	{	PUNCT
ap-3794	450	29	ra	ra	PROPN
ap-3794	450	30	,	,	PUNCT
ap-3794	450	31	rb	rb	PROPN
ap-3794	450	32	,	,	PUNCT
ap-3794	450	33	rc	rc	PROPN
ap-3794	450	34	}	}	PUNCT
ap-3794	450	35	,	,	PUNCT
ap-3794	450	36	and	and	CCONJ
ap-3794	450	37	the	the	DET
ap-3794	450	38	substitution	substitution	NOUN
ap-3794	450	39	ξ	ξ	NOUN
ap-3794	450	40	satisfies	satisfie	NOUN
ap-3794	450	41	either	either	CCONJ
ap-3794	450	42	η	η	PROPN
ap-3794	450	43	=	=	SYM
ap-3794	450	44	ξ	ξ	PROPN
ap-3794	450	45	or	or	CCONJ
ap-3794	450	46	η	η	PROPN
ap-3794	450	47	=	=	PROPN
ap-3794	450	48	ξ2	ξ2	PROPN
ap-3794	450	49	,	,	PUNCT
ap-3794	450	50	where	where	SCONJ
ap-3794	450	51	η(a	η(a	VERB
ap-3794	450	52	)	)	PUNCT
ap-3794	450	53	=	=	SYM
ap-3794	450	54	ra	ra	PROPN
ap-3794	450	55	,	,	PUNCT
ap-3794	450	56	η(b	η(b	ADJ
ap-3794	450	57	)	)	PUNCT
ap-3794	450	58	=	=	SYM
ap-3794	450	59	rb	rb	NOUN
ap-3794	450	60	and	and	CCONJ
ap-3794	450	61	η(c	η(c	ADJ
ap-3794	450	62	)	)	PUNCT
ap-3794	450	63	=	=	SYM
ap-3794	450	64	rc	rc	PROPN
ap-3794	450	65	.	.	PUNCT
ap-3794	451	1	using	use	VERB
ap-3794	451	2	the	the	DET
ap-3794	451	3	above	above	ADJ
ap-3794	451	4	theorem	theorem	NOUN
ap-3794	451	5	together	together	ADV
ap-3794	451	6	with	with	ADP
ap-3794	451	7	proposition	proposition	NOUN
ap-3794	451	8	5.1	5.1	NUM
ap-3794	451	9	,	,	PUNCT
ap-3794	451	10	one	one	PRON
ap-3794	451	11	can	can	AUX
ap-3794	451	12	derive	derive	VERB
ap-3794	451	13	information	information	NOUN
ap-3794	451	14	about	about	ADP
ap-3794	451	15	the	the	DET
ap-3794	451	16	itineraries	itinerary	NOUN
ap-3794	451	17	which	which	PRON
ap-3794	451	18	determine	determine	VERB
ap-3794	451	19	the	the	DET
ap-3794	451	20	substitution	substitution	NOUN
ap-3794	451	21	η	η	PROPN
ap-3794	451	22	.	.	PROPN
ap-3794	451	23	corollary	corollary	ADJ
ap-3794	451	24	5.5	5.5	NUM
ap-3794	451	25	.	.	PUNCT
ap-3794	452	1	let	let	VERB
ap-3794	452	2	η	η	PROPN
ap-3794	452	3	be	be	AUX
ap-3794	452	4	a	a	DET
ap-3794	452	5	primitive	primitive	ADJ
ap-3794	452	6	substitution	substitution	NOUN
ap-3794	452	7	as	as	ADP
ap-3794	452	8	in	in	ADP
ap-3794	452	9	theorem	theorem	ADJ
ap-3794	452	10	5.4	5.4	NUM
ap-3794	452	11	fixing	fix	VERB
ap-3794	452	12	a	a	DET
ap-3794	452	13	non	non	ADJ
ap-3794	452	14	-	-	ADJ
ap-3794	452	15	degenerate	degenerate	ADJ
ap-3794	452	16	3iet	3iet	NUM
ap-3794	452	17	word	word	NOUN
ap-3794	452	18	over	over	ADP
ap-3794	452	19	the	the	DET
ap-3794	452	20	alphabet	alphabet	NOUN
ap-3794	452	21	{	{	PUNCT
ap-3794	452	22	a	a	PROPN
ap-3794	452	23	,	,	PUNCT
ap-3794	452	24	b	b	NOUN
ap-3794	452	25	,	,	PUNCT
ap-3794	452	26	c	c	NOUN
ap-3794	452	27	}	}	PUNCT
ap-3794	452	28	.	.	PUNCT
ap-3794	453	1	we	we	PRON
ap-3794	453	2	have	have	VERB
ap-3794	453	3	η(b	η(b	ADV
ap-3794	453	4	)	)	PUNCT
ap-3794	453	5	=	=	SYM
ap-3794	454	1	ωac→b	ωac→b	NOUN
ap-3794	454	2	(	(	PUNCT
ap-3794	454	3	η(ac	η(ac	PROPN
ap-3794	454	4	)	)	PUNCT
ap-3794	454	5	)	)	PUNCT
ap-3794	455	1	=	=	PUNCT
ap-3794	455	2	ωca→b	ωca→b	PUNCT
ap-3794	455	3	(	(	PUNCT
ap-3794	455	4	η(ca	η(ca	NOUN
ap-3794	455	5	)	)	PUNCT
ap-3794	455	6	)	)	PUNCT
ap-3794	455	7	or	or	CCONJ
ap-3794	455	8	η(b	η(b	PROPN
ap-3794	455	9	)	)	PUNCT
ap-3794	455	10	=	=	SYM
ap-3794	455	11	ωb→ca	ωb→ca	NOUN
ap-3794	455	12	(	(	PUNCT
ap-3794	455	13	η(ac	η(ac	PROPN
ap-3794	455	14	)	)	PUNCT
ap-3794	455	15	)	)	PUNCT
ap-3794	456	1	=	=	SYM
ap-3794	456	2	ωb→ac	ωb→ac	ADJ
ap-3794	456	3	(	(	PUNCT
ap-3794	456	4	η(ca	η(ca	PROPN
ap-3794	456	5	)	)	PUNCT
ap-3794	456	6	)	)	PUNCT
ap-3794	456	7	.	.	PUNCT
ap-3794	457	1	proof	proof	NOUN
ap-3794	457	2	.	.	PUNCT
ap-3794	458	1	by	by	ADP
ap-3794	458	2	theorem	theorem	NOUN
ap-3794	458	3	5.4	5.4	NUM
ap-3794	458	4	,	,	PUNCT
ap-3794	458	5	η	η	PROPN
ap-3794	458	6	corresponds	correspond	VERB
ap-3794	458	7	to	to	ADP
ap-3794	458	8	an	an	DET
ap-3794	458	9	interval	interval	NOUN
ap-3794	458	10	i	i	PRON
ap-3794	458	11	such	such	ADJ
ap-3794	458	12	that	that	SCONJ
ap-3794	458	13	ti	ti	PROPN
ap-3794	458	14	is	be	AUX
ap-3794	458	15	homothetic	homothetic	ADJ
ap-3794	458	16	to	to	ADP
ap-3794	458	17	t	t	PROPN
ap-3794	458	18	.	.	PUNCT
ap-3794	459	1	since	since	SCONJ
ap-3794	459	2	t	t	PROPN
ap-3794	459	3	is	be	AUX
ap-3794	459	4	nondegenerate	nondegenerate	ADJ
ap-3794	459	5	,	,	PUNCT
ap-3794	459	6	also	also	ADV
ap-3794	459	7	ti	ti	PROPN
ap-3794	459	8	is	be	AUX
ap-3794	459	9	non	non	ADJ
ap-3794	459	10	-	-	ADJ
ap-3794	459	11	degenerate	degenerate	ADJ
ap-3794	459	12	,	,	PUNCT
ap-3794	459	13	and	and	CCONJ
ap-3794	459	14	therefore	therefore	ADV
ap-3794	459	15	its	its	PRON
ap-3794	459	16	discontinuity	discontinuity	NOUN
ap-3794	459	17	points	point	VERB
ap-3794	459	18	c	c	NOUN
ap-3794	459	19	,	,	PUNCT
ap-3794	459	20	d	d	NOUN
ap-3794	459	21	are	be	AUX
ap-3794	459	22	distinct	distinct	ADJ
ap-3794	459	23	.	.	PUNCT
ap-3794	460	1	by	by	ADP
ap-3794	460	2	proposition	proposition	NOUN
ap-3794	460	3	5.1	5.1	NUM
ap-3794	460	4	,	,	PUNCT
ap-3794	460	5	the	the	DET
ap-3794	460	6	three	three	NUM
ap-3794	460	7	i	i	NOUN
ap-3794	460	8	-	-	PUNCT
ap-3794	460	9	itineraries	itinerary	NOUN
ap-3794	460	10	are	be	AUX
ap-3794	460	11	of	of	ADP
ap-3794	460	12	the	the	DET
ap-3794	460	13	form	form	NOUN
ap-3794	460	14	given	give	VERB
ap-3794	460	15	by	by	ADP
ap-3794	460	16	cases	case	NOUN
ap-3794	460	17	(	(	PUNCT
ap-3794	460	18	i	i	NOUN
ap-3794	460	19	)	)	PUNCT
ap-3794	460	20	or	or	CCONJ
ap-3794	460	21	(	(	PUNCT
ap-3794	460	22	ii	ii	NOUN
ap-3794	460	23	)	)	PUNCT
ap-3794	460	24	.	.	PUNCT
ap-3794	461	1	example	example	NOUN
ap-3794	462	1	5.6	5.6	NUM
ap-3794	462	2	.	.	PUNCT
ap-3794	463	1	we	we	PRON
ap-3794	463	2	can	can	AUX
ap-3794	463	3	illustrate	illustrate	VERB
ap-3794	463	4	the	the	DET
ap-3794	463	5	above	above	ADJ
ap-3794	463	6	corollary	corollary	NOUN
ap-3794	463	7	on	on	ADP
ap-3794	463	8	the	the	DET
ap-3794	463	9	substitution	substitution	NOUN
ap-3794	463	10	η(a	η(a	VERB
ap-3794	463	11	)	)	PUNCT
ap-3794	463	12	=	=	SYM
ap-3794	463	13	bcacac	bcacac	NOUN
ap-3794	463	14	,	,	PUNCT
ap-3794	463	15	η(b	η(b	ADJ
ap-3794	463	16	)	)	PUNCT
ap-3794	463	17	=	=	SYM
ap-3794	463	18	bcacbbcac	bcacbbcac	NOUN
ap-3794	463	19	,	,	PUNCT
ap-3794	463	20	η(c	η(c	ADJ
ap-3794	463	21	)	)	PUNCT
ap-3794	463	22	=	=	SYM
ap-3794	463	23	bcac	bcac	NOUN
ap-3794	463	24	.	.	PUNCT
ap-3794	464	1	the	the	DET
ap-3794	464	2	morphism	morphism	PROPN
ap-3794	464	3	η	η	PROPN
ap-3794	464	4	satisfies	satisfy	VERB
ap-3794	464	5	the	the	DET
ap-3794	464	6	property	property	NOUN
ap-3794	464	7	given	give	VERB
ap-3794	464	8	in	in	ADP
ap-3794	464	9	corollary	corollary	ADJ
ap-3794	464	10	5.5	5.5	NUM
ap-3794	464	11	(	(	PUNCT
ap-3794	464	12	see	see	VERB
ap-3794	464	13	[	[	X
ap-3794	464	14	12	12	NUM
ap-3794	464	15	]	]	NUM
ap-3794	464	16	)	)	PUNCT
ap-3794	464	17	.	.	PUNCT
ap-3794	465	1	namely	namely	ADV
ap-3794	465	2	,	,	PUNCT
ap-3794	465	3	we	we	PRON
ap-3794	465	4	have	have	VERB
ap-3794	465	5	η(b	η(b	ADV
ap-3794	465	6	)	)	PUNCT
ap-3794	466	1	=	=	SYM
ap-3794	466	2	bcacbbcac	bcacbbcac	NOUN
ap-3794	466	3	=	=	SYM
ap-3794	466	4	ωac→b	ωac→b	NOUN
ap-3794	466	5	(	(	PUNCT
ap-3794	466	6	η(ac	η(ac	PROPN
ap-3794	466	7	)	)	PUNCT
ap-3794	466	8	)	)	PUNCT
ap-3794	467	1	=	=	PUNCT
ap-3794	467	2	ωac→b	ωac→b	NOUN
ap-3794	467	3	(	(	PUNCT
ap-3794	467	4	bcacacbcac	bcacacbcac	NOUN
ap-3794	467	5	)	)	PUNCT
ap-3794	467	6	=	=	PUNCT
ap-3794	467	7	ωca→b	ωca→b	NUM
ap-3794	467	8	(	(	PUNCT
ap-3794	467	9	η(ca	η(ca	NOUN
ap-3794	467	10	)	)	PUNCT
ap-3794	467	11	)	)	PUNCT
ap-3794	468	1	=	=	PUNCT
ap-3794	468	2	ωca→b	ωca→b	PUNCT
ap-3794	468	3	(	(	PUNCT
ap-3794	468	4	bcacbcacac	bcacbcacac	PROPN
ap-3794	468	5	)	)	PUNCT
ap-3794	468	6	.	.	PUNCT
ap-3794	469	1	469	469	NUM
ap-3794	469	2	z.	z.	PROPN
ap-3794	469	3	masáková	masáková	PROPN
ap-3794	469	4	,	,	PUNCT
ap-3794	469	5	e.	e.	PROPN
ap-3794	469	6	pelantová	pelantová	PROPN
ap-3794	469	7	,	,	PUNCT
ap-3794	469	8	š	š	PROPN
ap-3794	469	9	.	.	PROPN
ap-3794	469	10	starosta	starosta	PROPN
ap-3794	469	11	acta	acta	PROPN
ap-3794	469	12	polytechnica	polytechnica	PROPN
ap-3794	469	13	corollary	corollary	PROPN
ap-3794	469	14	5.5	5.5	NUM
ap-3794	469	15	implies	imply	VERB
ap-3794	469	16	a	a	DET
ap-3794	469	17	relation	relation	NOUN
ap-3794	469	18	of	of	ADP
ap-3794	469	19	numbers	number	NOUN
ap-3794	469	20	of	of	ADP
ap-3794	469	21	occurrences	occurrence	NOUN
ap-3794	469	22	of	of	ADP
ap-3794	469	23	letters	letter	NOUN
ap-3794	469	24	in	in	ADP
ap-3794	469	25	letter	letter	NOUN
ap-3794	469	26	images	image	NOUN
ap-3794	469	27	of	of	ADP
ap-3794	469	28	η	η	PROPN
ap-3794	469	29	which	which	PRON
ap-3794	469	30	may	may	AUX
ap-3794	469	31	be	be	AUX
ap-3794	469	32	used	use	VERB
ap-3794	469	33	to	to	PART
ap-3794	469	34	get	get	VERB
ap-3794	469	35	an	an	DET
ap-3794	469	36	interesting	interesting	ADJ
ap-3794	469	37	relation	relation	NOUN
ap-3794	469	38	for	for	ADP
ap-3794	469	39	the	the	DET
ap-3794	469	40	incidence	incidence	NOUN
ap-3794	469	41	matrix	matrix	NOUN
ap-3794	469	42	mη	mη	NOUN
ap-3794	469	43	of	of	ADP
ap-3794	469	44	η	η	PROPN
ap-3794	469	45	.	.	PUNCT
ap-3794	470	1	it	it	PRON
ap-3794	470	2	is	be	AUX
ap-3794	470	3	an	an	DET
ap-3794	470	4	integer	integer	NOUN
ap-3794	470	5	-	-	PUNCT
ap-3794	470	6	valued	value	VERB
ap-3794	470	7	matrix	matrix	NOUN
ap-3794	470	8	defined	define	VERB
ap-3794	470	9	by	by	ADP
ap-3794	470	10	(	(	PUNCT
ap-3794	470	11	mη)ab	mη)ab	PROPN
ap-3794	470	12	=	=	SYM
ap-3794	470	13	|η(a)|b	|η(a)|b	PROPN
ap-3794	470	14	for	for	ADP
ap-3794	470	15	a	a	DET
ap-3794	470	16	,	,	PUNCT
ap-3794	470	17	b	b	PROPN
ap-3794	470	18	∈	∈	NOUN
ap-3794	470	19	a.	a.	NOUN
ap-3794	470	20	as	as	ADP
ap-3794	470	21	a	a	DET
ap-3794	470	22	consequence	consequence	NOUN
ap-3794	470	23	of	of	ADP
ap-3794	470	24	corollary	corollary	ADJ
ap-3794	470	25	5.5	5.5	NUM
ap-3794	470	26	,	,	PUNCT
ap-3794	470	27	we	we	PRON
ap-3794	470	28	have	have	VERB
ap-3794	470	29	for	for	ADP
ap-3794	470	30	the	the	DET
ap-3794	470	31	columns	column	NOUN
ap-3794	470	32	of	of	ADP
ap-3794	470	33	the	the	DET
ap-3794	470	34	incidence	incidence	NOUN
ap-3794	470	35	matrix	matrix	NOUN
ap-3794	470	36	mη	mη	NOUN
ap-3794	470	37	that	that	PRON
ap-3794	470	38	mη	mη	NOUN
ap-3794	470	39			PROPN
ap-3794	470	40	1	1	NUM
ap-3794	470	41	−1	−1	NOUN
ap-3794	470	42	1	1	NUM
ap-3794	470	43			PROPN
ap-3794	470	44	=	=	SYM
ap-3794	470	45	|η(a)|a	|η(a)|a	NUM
ap-3794	470	46	|η(a)|b	|η(a)|b	PROPN
ap-3794	470	47	|η(a)|c	|η(a)|c	PROPN
ap-3794	470	48	−	−	ADP
ap-3794	471	1	|η(b)|a	|η(b)|a	VERB
ap-3794	471	2	|η(b)|b	|η(b)|b	NOUN
ap-3794	471	3	|η(b)|c	|η(b)|c	PROPN
ap-3794	471	4			PROPN
ap-3794	471	5	+	+	CCONJ
ap-3794	471	6	|η(c)|a	|η(c)|a	PROPN
ap-3794	471	7	|η(c)|b	|η(c)|b	PROPN
ap-3794	471	8	|η(c)|c	|η(c)|c	NOUN
ap-3794	471	9			PROPN
ap-3794	471	10	=	=	SYM
ap-3794	471	11	±	±	NUM
ap-3794	472	1			PROPN
ap-3794	472	2	1	1	NUM
ap-3794	472	3	−1	−1	NOUN
ap-3794	472	4	1	1	NUM
ap-3794	472	5			PROPN
ap-3794	472	6	.	.	PUNCT
ap-3794	473	1	thus	thus	ADV
ap-3794	473	2	,	,	PUNCT
ap-3794	473	3	(	(	PUNCT
ap-3794	473	4	1,−1	1,−1	NUM
ap-3794	473	5	,	,	PUNCT
ap-3794	473	6	1	1	NUM
ap-3794	473	7	)	)	PUNCT
ap-3794	473	8	>	>	X
ap-3794	473	9	is	be	AUX
ap-3794	473	10	an	an	DET
ap-3794	473	11	eigenvector	eigenvector	NOUN
ap-3794	473	12	of	of	ADP
ap-3794	473	13	mη	mη	NOUN
ap-3794	473	14	corresponding	correspond	VERB
ap-3794	473	15	to	to	ADP
ap-3794	473	16	the	the	DET
ap-3794	473	17	eigenvalue	eigenvalue	PROPN
ap-3794	473	18	1	1	NUM
ap-3794	473	19	and	and	CCONJ
ap-3794	473	20	−1	−1	NOUN
ap-3794	473	21	,	,	PUNCT
ap-3794	473	22	respectively	respectively	ADV
ap-3794	473	23	.	.	PUNCT
ap-3794	474	1	this	this	DET
ap-3794	474	2	fact	fact	NOUN
ap-3794	474	3	has	have	AUX
ap-3794	474	4	been	be	AUX
ap-3794	474	5	already	already	ADV
ap-3794	474	6	derived	derive	VERB
ap-3794	474	7	in	in	ADP
ap-3794	474	8	[	[	X
ap-3794	474	9	2	2	NUM
ap-3794	474	10	]	]	PUNCT
ap-3794	474	11	by	by	ADP
ap-3794	474	12	other	other	ADJ
ap-3794	474	13	methods	method	NOUN
ap-3794	474	14	.	.	PUNCT
ap-3794	475	1	6	6	X
ap-3794	475	2	.	.	X
ap-3794	475	3	gaps	gap	NOUN
ap-3794	475	4	and	and	CCONJ
ap-3794	475	5	distance	distance	NOUN
ap-3794	475	6	theorems	theorem	NOUN
ap-3794	475	7	let	let	VERB
ap-3794	475	8	us	we	PRON
ap-3794	475	9	reinterpret	reinterpret	VERB
ap-3794	475	10	the	the	DET
ap-3794	475	11	statement	statement	NOUN
ap-3794	475	12	of	of	ADP
ap-3794	475	13	the	the	DET
ap-3794	475	14	main	main	ADJ
ap-3794	475	15	result	result	NOUN
ap-3794	475	16	(	(	PUNCT
ap-3794	475	17	theorem	theorem	VERB
ap-3794	475	18	4.1	4.1	NUM
ap-3794	475	19	)	)	PUNCT
ap-3794	475	20	from	from	ADP
ap-3794	475	21	the	the	DET
ap-3794	475	22	point	point	NOUN
ap-3794	475	23	of	of	ADP
ap-3794	475	24	view	view	NOUN
ap-3794	475	25	of	of	ADP
ap-3794	475	26	three	three	NUM
ap-3794	475	27	gap	gap	NOUN
ap-3794	475	28	and	and	CCONJ
ap-3794	475	29	three	three	NUM
ap-3794	475	30	distance	distance	NOUN
ap-3794	475	31	theorems	theorem	NOUN
ap-3794	475	32	which	which	PRON
ap-3794	475	33	are	be	AUX
ap-3794	475	34	narrowly	narrowly	ADV
ap-3794	475	35	connected	connect	VERB
ap-3794	475	36	with	with	ADP
ap-3794	475	37	the	the	DET
ap-3794	475	38	exchange	exchange	NOUN
ap-3794	475	39	of	of	ADP
ap-3794	475	40	two	two	NUM
ap-3794	475	41	intervals	interval	NOUN
ap-3794	475	42	.	.	PUNCT
ap-3794	476	1	under	under	ADP
ap-3794	476	2	the	the	DET
ap-3794	476	3	name	name	NOUN
ap-3794	476	4	three	three	NUM
ap-3794	476	5	gap	gap	NOUN
ap-3794	476	6	theorem	theorem	VERB
ap-3794	476	7	one	one	PRON
ap-3794	476	8	usually	usually	ADV
ap-3794	476	9	refers	refer	VERB
ap-3794	476	10	to	to	ADP
ap-3794	476	11	the	the	DET
ap-3794	476	12	description	description	NOUN
ap-3794	476	13	of	of	ADP
ap-3794	476	14	gaps	gap	NOUN
ap-3794	476	15	between	between	ADP
ap-3794	476	16	neighbouring	neighbouring	ADJ
ap-3794	476	17	elements	element	NOUN
ap-3794	476	18	of	of	ADP
ap-3794	476	19	the	the	DET
ap-3794	476	20	set	set	PROPN
ap-3794	476	21	g(α	g(α	PROPN
ap-3794	476	22	,	,	PUNCT
ap-3794	476	23	δ	δ	PROPN
ap-3794	476	24	)	)	PUNCT
ap-3794	476	25	:	:	PUNCT
ap-3794	477	1	=	=	X
ap-3794	477	2	{	{	PUNCT
ap-3794	477	3	n	n	CCONJ
ap-3794	477	4	∈	∈	PROPN
ap-3794	477	5	n	n	NOUN
ap-3794	477	6	:	:	PUNCT
ap-3794	477	7	{	{	PUNCT
ap-3794	477	8	nα	nα	NOUN
ap-3794	477	9	}	}	PUNCT
ap-3794	477	10	<	<	X
ap-3794	477	11	δ	δ	X
ap-3794	477	12	}	}	PUNCT
ap-3794	477	13	⊂	⊂	PROPN
ap-3794	477	14	n	n	CCONJ
ap-3794	477	15	,	,	PUNCT
ap-3794	477	16	where	where	SCONJ
ap-3794	477	17	α	α	X
ap-3794	477	18	∈	∈	NOUN
ap-3794	477	19	r	r	NOUN
ap-3794	477	20	\q	\q	NOUN
ap-3794	477	21	,	,	PUNCT
ap-3794	477	22	δ	δ	PROPN
ap-3794	477	23	∈	∈	PROPN
ap-3794	477	24	(	(	PUNCT
ap-3794	477	25	0	0	NUM
ap-3794	477	26	,	,	PUNCT
ap-3794	477	27	1	1	NUM
ap-3794	477	28	)	)	PUNCT
ap-3794	477	29	,	,	PUNCT
ap-3794	477	30	see	see	VERB
ap-3794	477	31	[	[	X
ap-3794	477	32	15	15	NUM
ap-3794	477	33	]	]	PUNCT
ap-3794	477	34	.	.	PUNCT
ap-3794	478	1	sometimes	sometimes	ADV
ap-3794	478	2	one	one	PRON
ap-3794	478	3	uses	use	VERB
ap-3794	478	4	a	a	DET
ap-3794	478	5	more	more	ADV
ap-3794	478	6	general	general	ADJ
ap-3794	478	7	formulation	formulation	NOUN
ap-3794	478	8	,	,	PUNCT
ap-3794	478	9	namely	namely	ADV
ap-3794	478	10	the	the	DET
ap-3794	478	11	set	set	PROPN
ap-3794	478	12	g(α	g(α	PROPN
ap-3794	478	13	,	,	PUNCT
ap-3794	478	14	ρ	ρ	PROPN
ap-3794	478	15	,	,	PUNCT
ap-3794	478	16	γ	γ	X
ap-3794	478	17	,	,	PUNCT
ap-3794	478	18	δ	δ	PROPN
ap-3794	478	19	)	)	PUNCT
ap-3794	478	20	:	:	PUNCT
ap-3794	479	1	=	=	X
ap-3794	479	2	{	{	PUNCT
ap-3794	479	3	n	n	CCONJ
ap-3794	479	4	∈	∈	PROPN
ap-3794	479	5	n	n	NOUN
ap-3794	479	6	:	:	PUNCT
ap-3794	479	7	γ	γ	PROPN
ap-3794	479	8	≤	≤	NUM
ap-3794	479	9	{	{	PUNCT
ap-3794	479	10	nα+	nα+	NOUN
ap-3794	479	11	ρ	ρ	PROPN
ap-3794	479	12	}	}	PUNCT
ap-3794	479	13	<	<	X
ap-3794	479	14	δ	δ	X
ap-3794	479	15	}	}	PUNCT
ap-3794	479	16	⊂	⊂	PROPN
ap-3794	479	17	n	n	CCONJ
ap-3794	479	18	,	,	PUNCT
ap-3794	479	19	where	where	SCONJ
ap-3794	479	20	moreover	moreover	ADV
ap-3794	479	21	ρ	ρ	X
ap-3794	479	22	∈	∈	PROPN
ap-3794	479	23	r	r	NOUN
ap-3794	479	24	,	,	PUNCT
ap-3794	479	25	0	0	NUM
ap-3794	479	26	≤	≤	NUM
ap-3794	479	27	γ	γ	X
ap-3794	479	28	<	<	X
ap-3794	479	29	δ	δ	X
ap-3794	479	30	<	<	X
ap-3794	479	31	1	1	NUM
ap-3794	479	32	.	.	PUNCT
ap-3794	480	1	the	the	DET
ap-3794	480	2	three	three	NUM
ap-3794	480	3	gap	gap	NOUN
ap-3794	480	4	theorem	theorem	VERB
ap-3794	480	5	states	state	NOUN
ap-3794	480	6	that	that	SCONJ
ap-3794	480	7	there	there	PRON
ap-3794	480	8	exist	exist	VERB
ap-3794	480	9	integers	integer	NOUN
ap-3794	480	10	r1	r1	PROPN
ap-3794	480	11	,	,	PUNCT
ap-3794	480	12	r2	r2	NOUN
ap-3794	480	13	such	such	ADJ
ap-3794	480	14	that	that	SCONJ
ap-3794	480	15	gaps	gap	NOUN
ap-3794	480	16	between	between	ADP
ap-3794	480	17	neighbours	neighbour	NOUN
ap-3794	480	18	in	in	ADP
ap-3794	480	19	g(α	g(α	PROPN
ap-3794	480	20	,	,	PUNCT
ap-3794	480	21	ρ	ρ	PROPN
ap-3794	480	22	,	,	PUNCT
ap-3794	480	23	γ	γ	X
ap-3794	480	24	,	,	PUNCT
ap-3794	480	25	δ	δ	NOUN
ap-3794	480	26	)	)	PUNCT
ap-3794	480	27	take	take	VERB
ap-3794	480	28	at	at	ADV
ap-3794	480	29	most	most	ADV
ap-3794	480	30	three	three	NUM
ap-3794	480	31	values	value	NOUN
ap-3794	480	32	,	,	PUNCT
ap-3794	480	33	namely	namely	ADV
ap-3794	480	34	in	in	ADP
ap-3794	480	35	the	the	DET
ap-3794	480	36	set	set	NOUN
ap-3794	480	37	{	{	PUNCT
ap-3794	480	38	r1	r1	NOUN
ap-3794	480	39	,	,	PUNCT
ap-3794	480	40	r2	r2	PROPN
ap-3794	480	41	,	,	PUNCT
ap-3794	480	42	r1	r1	NOUN
ap-3794	480	43	+	+	CCONJ
ap-3794	480	44	r2	r2	NOUN
ap-3794	480	45	}	}	PUNCT
ap-3794	480	46	.	.	PUNCT
ap-3794	481	1	let	let	VERB
ap-3794	481	2	us	we	PRON
ap-3794	481	3	interpret	interpret	VERB
ap-3794	481	4	the	the	DET
ap-3794	481	5	three	three	NUM
ap-3794	481	6	gap	gap	NOUN
ap-3794	481	7	theorem	theorem	VERB
ap-3794	481	8	in	in	ADP
ap-3794	481	9	the	the	DET
ap-3794	481	10	framework	framework	NOUN
ap-3794	481	11	of	of	ADP
ap-3794	481	12	exchange	exchange	NOUN
ap-3794	481	13	of	of	ADP
ap-3794	481	14	two	two	NUM
ap-3794	481	15	intervals	interval	NOUN
ap-3794	481	16	j0	j0	NOUN
ap-3794	481	17	=	=	PUNCT
ap-3794	482	1	[	[	X
ap-3794	482	2	0	0	NUM
ap-3794	482	3	,	,	PUNCT
ap-3794	482	4	1	1	NUM
ap-3794	482	5	−	−	PROPN
ap-3794	482	6	α	α	NOUN
ap-3794	482	7	)	)	PUNCT
ap-3794	482	8	,	,	PUNCT
ap-3794	482	9	j1	j1	PROPN
ap-3794	482	10	=	=	PUNCT
ap-3794	483	1	[	[	X
ap-3794	483	2	1−	1−	NUM
ap-3794	483	3	α	α	NOUN
ap-3794	483	4	,	,	PUNCT
ap-3794	483	5	1	1	NUM
ap-3794	483	6	)	)	PUNCT
ap-3794	483	7	.	.	PUNCT
ap-3794	484	1	the	the	DET
ap-3794	484	2	transformation	transformation	NOUN
ap-3794	484	3	t	t	NOUN
ap-3794	484	4	:	:	PUNCT
ap-3794	485	1	[	[	X
ap-3794	485	2	0	0	NUM
ap-3794	485	3	,	,	PUNCT
ap-3794	485	4	1)→	1)→	NUM
ap-3794	485	5	[	[	X
ap-3794	485	6	0	0	NUM
ap-3794	485	7	,	,	PUNCT
ap-3794	485	8	1	1	NUM
ap-3794	485	9	)	)	PUNCT
ap-3794	485	10	is	be	AUX
ap-3794	485	11	of	of	ADP
ap-3794	485	12	the	the	DET
ap-3794	485	13	form	form	NOUN
ap-3794	485	14	t	t	PROPN
ap-3794	485	15	(	(	PUNCT
ap-3794	485	16	x	x	X
ap-3794	485	17	)	)	PUNCT
ap-3794	485	18	=	=	PRON
ap-3794	485	19	{	{	PUNCT
ap-3794	485	20	x+	x+	PROPN
ap-3794	485	21	α	α	NOUN
ap-3794	485	22	for	for	ADP
ap-3794	485	23	x	x	PROPN
ap-3794	485	24	∈	∈	PROPN
ap-3794	486	1	[	[	X
ap-3794	486	2	0	0	NUM
ap-3794	486	3	,	,	PUNCT
ap-3794	486	4	1−	1−	NUM
ap-3794	486	5	α	α	NOUN
ap-3794	486	6	)	)	PUNCT
ap-3794	486	7	,	,	PUNCT
ap-3794	486	8	x+	x+	X
ap-3794	486	9	α−	α−	ADP
ap-3794	486	10	1	1	NUM
ap-3794	486	11	for	for	ADP
ap-3794	486	12	x	x	PROPN
ap-3794	486	13	∈	∈	PROPN
ap-3794	487	1	[	[	X
ap-3794	487	2	1−	1−	NUM
ap-3794	487	3	α	α	NOUN
ap-3794	487	4	,	,	PUNCT
ap-3794	487	5	1	1	NUM
ap-3794	487	6	)	)	PUNCT
ap-3794	487	7	,	,	PUNCT
ap-3794	487	8	(	(	PUNCT
ap-3794	487	9	9	9	X
ap-3794	487	10	)	)	PUNCT
ap-3794	487	11	i.e.	i.e.	X
ap-3794	487	12	,	,	PUNCT
ap-3794	487	13	t	t	PROPN
ap-3794	487	14	(	(	PUNCT
ap-3794	487	15	x	x	X
ap-3794	487	16	)	)	PUNCT
ap-3794	487	17	=	=	PRON
ap-3794	487	18	{	{	PUNCT
ap-3794	487	19	x+	x+	NOUN
ap-3794	487	20	α	α	NOUN
ap-3794	487	21	}	}	PUNCT
ap-3794	487	22	.	.	PUNCT
ap-3794	488	1	therefore	therefore	ADV
ap-3794	488	2	we	we	PRON
ap-3794	488	3	can	can	AUX
ap-3794	488	4	write	write	VERB
ap-3794	488	5	g(α	g(α	PROPN
ap-3794	488	6	,	,	PUNCT
ap-3794	488	7	ρ	ρ	PROPN
ap-3794	488	8	,	,	PUNCT
ap-3794	488	9	γ	γ	X
ap-3794	488	10	,	,	PUNCT
ap-3794	488	11	δ	δ	PROPN
ap-3794	488	12	)	)	PUNCT
ap-3794	488	13	:	:	PUNCT
ap-3794	489	1	=	=	X
ap-3794	489	2	{	{	PUNCT
ap-3794	489	3	n	n	CCONJ
ap-3794	489	4	∈	∈	PROPN
ap-3794	489	5	n	n	CCONJ
ap-3794	489	6	:	:	PUNCT
ap-3794	489	7	tn(ρ	tn(ρ	X
ap-3794	489	8	)	)	PUNCT
ap-3794	489	9	∈	∈	PROPN
ap-3794	489	10	[	[	X
ap-3794	489	11	γ	γ	X
ap-3794	489	12	,	,	PUNCT
ap-3794	489	13	δ	δ	PROPN
ap-3794	489	14	)	)	PUNCT
ap-3794	489	15	}	}	PUNCT
ap-3794	489	16	,	,	PUNCT
ap-3794	489	17	(	(	PUNCT
ap-3794	489	18	10	10	NUM
ap-3794	489	19	)	)	PUNCT
ap-3794	489	20	and	and	CCONJ
ap-3794	489	21	the	the	DET
ap-3794	489	22	gaps	gap	NOUN
ap-3794	489	23	in	in	ADP
ap-3794	489	24	this	this	DET
ap-3794	489	25	set	set	NOUN
ap-3794	489	26	correspond	correspond	NOUN
ap-3794	489	27	to	to	PART
ap-3794	489	28	return	return	VERB
ap-3794	489	29	times	time	NOUN
ap-3794	489	30	to	to	ADP
ap-3794	489	31	the	the	DET
ap-3794	489	32	interval	interval	NOUN
ap-3794	489	33	[	[	X
ap-3794	489	34	γ	γ	X
ap-3794	489	35	,	,	PUNCT
ap-3794	489	36	δ	δ	PROPN
ap-3794	489	37	)	)	PUNCT
ap-3794	489	38	under	under	ADP
ap-3794	489	39	the	the	DET
ap-3794	489	40	transformation	transformation	NOUN
ap-3794	489	41	t	t	NOUN
ap-3794	489	42	.	.	PUNCT
ap-3794	490	1	our	our	PRON
ap-3794	490	2	theorem	theorem	ADJ
ap-3794	490	3	4.1	4.1	NUM
ap-3794	490	4	is	be	AUX
ap-3794	490	5	an	an	DET
ap-3794	490	6	analogue	analogue	NOUN
ap-3794	490	7	of	of	ADP
ap-3794	490	8	the	the	DET
ap-3794	490	9	three	three	NUM
ap-3794	490	10	gap	gap	NOUN
ap-3794	490	11	theorem	theorem	VERB
ap-3794	490	12	in	in	ADP
ap-3794	490	13	the	the	DET
ap-3794	490	14	form	form	NOUN
ap-3794	490	15	(	(	PUNCT
ap-3794	490	16	10	10	NUM
ap-3794	490	17	)	)	PUNCT
ap-3794	490	18	generalized	generalize	VERB
ap-3794	490	19	for	for	ADP
ap-3794	490	20	the	the	DET
ap-3794	490	21	case	case	NOUN
ap-3794	490	22	when	when	SCONJ
ap-3794	490	23	the	the	DET
ap-3794	490	24	transformation	transformation	NOUN
ap-3794	490	25	t	t	PROPN
ap-3794	490	26	is	be	AUX
ap-3794	490	27	a	a	DET
ap-3794	490	28	non	non	ADJ
ap-3794	490	29	-	-	ADJ
ap-3794	490	30	degenerate	degenerate	ADJ
ap-3794	490	31	3iet	3iet	NUM
ap-3794	490	32	.	.	PUNCT
ap-3794	491	1	we	we	PRON
ap-3794	491	2	see	see	VERB
ap-3794	491	3	that	that	SCONJ
ap-3794	491	4	there	there	PRON
ap-3794	491	5	are	be	VERB
ap-3794	491	6	5	5	NUM
ap-3794	491	7	gaps	gap	NOUN
ap-3794	491	8	,	,	PUNCT
ap-3794	491	9	but	but	CCONJ
ap-3794	491	10	still	still	ADV
ap-3794	491	11	expressed	express	VERB
ap-3794	491	12	using	use	VERB
ap-3794	491	13	two	two	NUM
ap-3794	491	14	basic	basic	ADJ
ap-3794	491	15	values	value	NOUN
ap-3794	491	16	r1	r1	NOUN
ap-3794	491	17	,	,	PUNCT
ap-3794	491	18	r2	r2	PROPN
ap-3794	491	19	.	.	PUNCT
ap-3794	492	1	the	the	DET
ap-3794	492	2	so	so	ADV
ap-3794	492	3	-	-	PUNCT
ap-3794	492	4	called	call	VERB
ap-3794	492	5	three	three	NUM
ap-3794	492	6	distance	distance	NOUN
ap-3794	492	7	theorem	theorem	NOUN
ap-3794	492	8	focuses	focus	VERB
ap-3794	492	9	on	on	ADP
ap-3794	492	10	distances	distance	NOUN
ap-3794	492	11	between	between	ADP
ap-3794	492	12	neighbours	neighbour	NOUN
ap-3794	492	13	of	of	ADP
ap-3794	492	14	the	the	DET
ap-3794	492	15	set	set	NOUN
ap-3794	492	16	d(α	d(α	PROPN
ap-3794	492	17	,	,	PUNCT
ap-3794	492	18	ρ	ρ	NOUN
ap-3794	492	19	,	,	PUNCT
ap-3794	492	20	n	n	CCONJ
ap-3794	492	21	)	)	PUNCT
ap-3794	492	22	:	:	PUNCT
ap-3794	493	1	=	=	X
ap-3794	493	2	{	{	PUNCT
ap-3794	493	3	{	{	PUNCT
ap-3794	493	4	αn+	αn+	NOUN
ap-3794	493	5	ρ	ρ	NOUN
ap-3794	493	6	}	}	PUNCT
ap-3794	493	7	:	:	PUNCT
ap-3794	493	8	n	n	CCONJ
ap-3794	493	9	∈	∈	PROPN
ap-3794	493	10	n	n	CCONJ
ap-3794	493	11	,	,	PUNCT
ap-3794	493	12	n	n	CCONJ
ap-3794	493	13	<	<	X
ap-3794	493	14	n	n	X
ap-3794	493	15	}	}	PUNCT
ap-3794	493	16	⊂	⊂	PROPN
ap-3794	494	1	[	[	X
ap-3794	494	2	0	0	NUM
ap-3794	494	3	,	,	PUNCT
ap-3794	494	4	1	1	NUM
ap-3794	494	5	)	)	PUNCT
ap-3794	494	6	.	.	PUNCT
ap-3794	495	1	the	the	DET
ap-3794	495	2	three	three	NUM
ap-3794	495	3	distance	distance	NOUN
ap-3794	495	4	theorem	theorem	NOUN
ap-3794	495	5	ensures	ensure	VERB
ap-3794	495	6	the	the	DET
ap-3794	495	7	existence	existence	NOUN
ap-3794	495	8	of	of	ADP
ap-3794	495	9	∆1,∆2	∆1,∆2	NOUN
ap-3794	495	10	>	>	X
ap-3794	495	11	0	0	NUM
ap-3794	495	12	such	such	ADJ
ap-3794	495	13	that	that	SCONJ
ap-3794	495	14	distances	distance	NOUN
ap-3794	495	15	between	between	ADP
ap-3794	495	16	neighbours	neighbour	NOUN
ap-3794	495	17	in	in	ADP
ap-3794	495	18	d(α	d(α	PROPN
ap-3794	495	19	,	,	PUNCT
ap-3794	495	20	ρ	ρ	NOUN
ap-3794	495	21	,	,	PUNCT
ap-3794	495	22	n	n	CCONJ
ap-3794	495	23	)	)	PUNCT
ap-3794	495	24	take	take	VERB
ap-3794	495	25	at	at	ADV
ap-3794	495	26	most	most	ADV
ap-3794	495	27	three	three	NUM
ap-3794	495	28	values	value	NOUN
ap-3794	495	29	,	,	PUNCT
ap-3794	495	30	namely	namely	ADV
ap-3794	495	31	in	in	ADP
ap-3794	495	32	{	{	PUNCT
ap-3794	495	33	∆1,∆2,∆1	∆1,∆2,∆1	NOUN
ap-3794	495	34	+	+	CCONJ
ap-3794	495	35	∆2	∆2	NOUN
ap-3794	495	36	}	}	PUNCT
ap-3794	495	37	.	.	PUNCT
ap-3794	496	1	in	in	ADP
ap-3794	496	2	the	the	DET
ap-3794	496	3	framework	framework	NOUN
ap-3794	496	4	of	of	ADP
ap-3794	496	5	2iet	2iet	PROPN
ap-3794	496	6	t	t	NOUN
ap-3794	496	7	,	,	PUNCT
ap-3794	496	8	we	we	PRON
ap-3794	496	9	can	can	AUX
ap-3794	496	10	write	write	VERB
ap-3794	496	11	for	for	ADP
ap-3794	496	12	the	the	DET
ap-3794	496	13	distances	distance	NOUN
ap-3794	496	14	d(α	d(α	PROPN
ap-3794	496	15	,	,	PUNCT
ap-3794	496	16	ρ	ρ	NOUN
ap-3794	496	17	,	,	PUNCT
ap-3794	496	18	n	n	CCONJ
ap-3794	496	19	)	)	PUNCT
ap-3794	496	20	:	:	PUNCT
ap-3794	497	1	=	=	PRON
ap-3794	497	2	{	{	PUNCT
ap-3794	497	3	tn(ρ	tn(ρ	PROPN
ap-3794	497	4	)	)	PUNCT
ap-3794	497	5	:	:	PUNCT
ap-3794	497	6	n	n	X
ap-3794	497	7	∈	∈	PROPN
ap-3794	497	8	n	n	CCONJ
ap-3794	497	9	,	,	PUNCT
ap-3794	497	10	n	n	CCONJ
ap-3794	497	11	<	<	X
ap-3794	497	12	n	n	X
ap-3794	497	13	}	}	PUNCT
ap-3794	497	14	⊂	⊂	PROPN
ap-3794	498	1	[	[	X
ap-3794	498	2	0	0	NUM
ap-3794	498	3	,	,	PUNCT
ap-3794	498	4	1	1	NUM
ap-3794	498	5	)	)	PUNCT
ap-3794	498	6	,	,	PUNCT
ap-3794	498	7	(	(	PUNCT
ap-3794	498	8	11	11	NUM
ap-3794	498	9	)	)	PUNCT
ap-3794	498	10	where	where	SCONJ
ap-3794	498	11	α	α	NOUN
ap-3794	498	12	is	be	AUX
ap-3794	498	13	the	the	DET
ap-3794	498	14	defining	define	VERB
ap-3794	498	15	parameter	parameter	NOUN
ap-3794	498	16	of	of	ADP
ap-3794	498	17	t	t	PROPN
ap-3794	498	18	as	as	ADP
ap-3794	498	19	in	in	ADP
ap-3794	498	20	(	(	PUNCT
ap-3794	498	21	9	9	NUM
ap-3794	498	22	)	)	PUNCT
ap-3794	498	23	,	,	PUNCT
ap-3794	498	24	and	and	CCONJ
ap-3794	498	25	ρ	ρ	NUM
ap-3794	498	26	∈	∈	PROPN
ap-3794	499	1	[	[	X
ap-3794	499	2	0	0	NUM
ap-3794	499	3	,	,	PUNCT
ap-3794	499	4	1	1	NUM
ap-3794	499	5	)	)	PUNCT
ap-3794	499	6	.	.	PUNCT
ap-3794	500	1	we	we	PRON
ap-3794	500	2	could	could	AUX
ap-3794	500	3	try	try	VERB
ap-3794	500	4	to	to	PART
ap-3794	500	5	study	study	VERB
ap-3794	500	6	the	the	DET
ap-3794	500	7	analogue	analogue	NOUN
ap-3794	500	8	of	of	ADP
ap-3794	500	9	the	the	DET
ap-3794	500	10	three	three	NUM
ap-3794	500	11	distance	distance	NOUN
ap-3794	500	12	theorem	theorem	VERB
ap-3794	500	13	in	in	ADP
ap-3794	500	14	the	the	DET
ap-3794	500	15	form	form	NOUN
ap-3794	500	16	(	(	PUNCT
ap-3794	500	17	11	11	NUM
ap-3794	500	18	)	)	PUNCT
ap-3794	500	19	for	for	ADP
ap-3794	500	20	exchanges	exchange	NOUN
ap-3794	500	21	of	of	ADP
ap-3794	500	22	three	three	NUM
ap-3794	500	23	intervals	interval	NOUN
ap-3794	500	24	.	.	PUNCT
ap-3794	501	1	in	in	ADP
ap-3794	501	2	fact	fact	NOUN
ap-3794	501	3	,	,	PUNCT
ap-3794	501	4	it	it	PRON
ap-3794	501	5	can	can	AUX
ap-3794	501	6	be	be	AUX
ap-3794	501	7	derived	derive	VERB
ap-3794	501	8	from	from	ADP
ap-3794	501	9	the	the	DET
ap-3794	501	10	results	result	NOUN
ap-3794	501	11	of	of	ADP
ap-3794	501	12	[	[	X
ap-3794	501	13	9	9	NUM
ap-3794	501	14	]	]	PUNCT
ap-3794	501	15	that	that	SCONJ
ap-3794	501	16	if	if	SCONJ
ap-3794	501	17	t	t	PROPN
ap-3794	501	18	is	be	AUX
ap-3794	501	19	a	a	DET
ap-3794	501	20	3iet	3iet	PROPN
ap-3794	501	21	with	with	ADP
ap-3794	501	22	discontinuity	discontinuity	NOUN
ap-3794	501	23	points	point	NOUN
ap-3794	501	24	α	α	PRON
ap-3794	501	25	,	,	PUNCT
ap-3794	501	26	β	β	NOUN
ap-3794	501	27	,	,	PUNCT
ap-3794	501	28	then	then	ADV
ap-3794	501	29	d(α	d(α	PROPN
ap-3794	501	30	,	,	PUNCT
ap-3794	501	31	β	β	X
ap-3794	501	32	,	,	PUNCT
ap-3794	501	33	ρ	ρ	PROPN
ap-3794	501	34	,	,	PUNCT
ap-3794	501	35	n	n	CCONJ
ap-3794	501	36	)	)	PUNCT
ap-3794	501	37	:	:	PUNCT
ap-3794	501	38	=	=	PRON
ap-3794	501	39	{	{	PUNCT
ap-3794	501	40	tn(ρ	tn(ρ	PROPN
ap-3794	501	41	)	)	PUNCT
ap-3794	501	42	:	:	PUNCT
ap-3794	501	43	n	n	X
ap-3794	501	44	∈	∈	PROPN
ap-3794	501	45	n	n	CCONJ
ap-3794	501	46	,	,	PUNCT
ap-3794	501	47	n	n	CCONJ
ap-3794	501	48	<	<	X
ap-3794	501	49	n	n	X
ap-3794	501	50	}	}	PUNCT
ap-3794	501	51	has	have	VERB
ap-3794	501	52	again	again	ADV
ap-3794	501	53	at	at	ADP
ap-3794	501	54	most	most	ADV
ap-3794	501	55	three	three	NUM
ap-3794	501	56	distances	distance	NOUN
ap-3794	501	57	∆1	∆1	PROPN
ap-3794	501	58	,	,	PUNCT
ap-3794	501	59	∆2	∆2	PROPN
ap-3794	501	60	,	,	PUNCT
ap-3794	501	61	and	and	CCONJ
ap-3794	501	62	∆1+∆2	∆1+∆2	PROPN
ap-3794	501	63	for	for	ADP
ap-3794	501	64	some	some	DET
ap-3794	501	65	positive	positive	ADJ
ap-3794	501	66	∆1,∆2	∆1,∆2	NOUN
ap-3794	501	67	.	.	PUNCT
ap-3794	502	1	the	the	DET
ap-3794	502	2	three	three	NUM
ap-3794	502	3	distance	distance	NOUN
ap-3794	502	4	theorem	theorem	NOUN
ap-3794	502	5	can	can	AUX
ap-3794	502	6	also	also	ADV
ap-3794	502	7	be	be	AUX
ap-3794	502	8	used	use	VERB
ap-3794	502	9	to	to	PART
ap-3794	502	10	derive	derive	VERB
ap-3794	502	11	that	that	SCONJ
ap-3794	502	12	the	the	DET
ap-3794	502	13	frequencies	frequency	NOUN
ap-3794	502	14	of	of	ADP
ap-3794	502	15	factors	factor	NOUN
ap-3794	502	16	of	of	ADP
ap-3794	502	17	length	length	NOUN
ap-3794	502	18	n	n	NOUN
ap-3794	502	19	in	in	ADP
ap-3794	502	20	a	a	DET
ap-3794	502	21	sturmian	sturmian	NOUN
ap-3794	502	22	word	word	NOUN
ap-3794	502	23	take	take	VERB
ap-3794	502	24	at	at	ADV
ap-3794	502	25	most	most	ADV
ap-3794	502	26	three	three	NUM
ap-3794	502	27	values	value	NOUN
ap-3794	502	28	.	.	PUNCT
ap-3794	503	1	recall	recall	VERB
ap-3794	503	2	that	that	SCONJ
ap-3794	503	3	the	the	DET
ap-3794	503	4	frequency	frequency	NOUN
ap-3794	503	5	of	of	ADP
ap-3794	503	6	a	a	DET
ap-3794	503	7	factor	factor	NOUN
ap-3794	503	8	w	w	NOUN
ap-3794	503	9	in	in	ADP
ap-3794	503	10	the	the	DET
ap-3794	503	11	infinite	infinite	ADJ
ap-3794	503	12	word	word	NOUN
ap-3794	503	13	u	u	NOUN
ap-3794	503	14	=	=	NOUN
ap-3794	503	15	u0u1u2	u0u1u2	NOUN
ap-3794	503	16	.	.	PUNCT
ap-3794	503	17	.	.	PUNCT
ap-3794	504	1	.	.	PUNCT
ap-3794	504	2	is	be	AUX
ap-3794	504	3	given	give	VERB
ap-3794	504	4	by	by	ADP
ap-3794	504	5	freq(w	freq(w	NOUN
ap-3794	504	6	)	)	PUNCT
ap-3794	504	7	:	:	PUNCT
ap-3794	505	1	=	=	PUNCT
ap-3794	505	2	lim	lim	PROPN
ap-3794	505	3	n→∞	n→∞	NUM
ap-3794	505	4	1	1	NUM
ap-3794	505	5	n	n	PROPN
ap-3794	505	6	(	(	PUNCT
ap-3794	505	7	#	#	SYM
ap-3794	505	8	{	{	PUNCT
ap-3794	505	9	0	0	NUM
ap-3794	505	10	≤	≤	NUM
ap-3794	506	1	i	i	PRON
ap-3794	506	2	<	<	X
ap-3794	506	3	n	n	X
ap-3794	506	4	:	:	PUNCT
ap-3794	506	5	w	w	NOUN
ap-3794	506	6	is	be	AUX
ap-3794	506	7	a	a	DET
ap-3794	506	8	prefix	prefix	NOUN
ap-3794	506	9	of	of	ADP
ap-3794	506	10	uiui+1	uiui+1	NOUN
ap-3794	506	11	.	.	PUNCT
ap-3794	506	12	.	.	PUNCT
ap-3794	506	13	.	.	PUNCT
ap-3794	507	1	}	}	PUNCT
ap-3794	507	2	)	)	PUNCT
ap-3794	507	3	,	,	PUNCT
ap-3794	507	4	if	if	SCONJ
ap-3794	507	5	the	the	DET
ap-3794	507	6	limit	limit	NOUN
ap-3794	507	7	exists	exist	VERB
ap-3794	507	8	.	.	PUNCT
ap-3794	508	1	it	it	PRON
ap-3794	508	2	is	be	AUX
ap-3794	508	3	a	a	DET
ap-3794	508	4	well	well	ADV
ap-3794	508	5	known	know	VERB
ap-3794	508	6	fact	fact	NOUN
ap-3794	508	7	that	that	SCONJ
ap-3794	508	8	the	the	DET
ap-3794	508	9	frequencies	frequency	NOUN
ap-3794	508	10	of	of	ADP
ap-3794	508	11	factors	factor	NOUN
ap-3794	508	12	of	of	ADP
ap-3794	508	13	length	length	NOUN
ap-3794	508	14	n	n	NOUN
ap-3794	508	15	in	in	ADP
ap-3794	508	16	a	a	DET
ap-3794	508	17	coding	coding	NOUN
ap-3794	508	18	of	of	ADP
ap-3794	508	19	an	an	DET
ap-3794	508	20	exchange	exchange	NOUN
ap-3794	508	21	of	of	ADP
ap-3794	508	22	intervals	interval	NOUN
ap-3794	508	23	are	be	AUX
ap-3794	508	24	given	give	VERB
ap-3794	508	25	by	by	ADP
ap-3794	508	26	the	the	DET
ap-3794	508	27	lengths	length	NOUN
ap-3794	508	28	of	of	ADP
ap-3794	508	29	cylinders	cylinder	NOUN
ap-3794	508	30	corresponding	correspond	VERB
ap-3794	508	31	to	to	ADP
ap-3794	508	32	the	the	DET
ap-3794	508	33	factors	factor	NOUN
ap-3794	508	34	.	.	PUNCT
ap-3794	509	1	the	the	DET
ap-3794	509	2	boundary	boundary	ADJ
ap-3794	509	3	points	point	NOUN
ap-3794	509	4	of	of	ADP
ap-3794	509	5	these	these	DET
ap-3794	509	6	cylinders	cylinder	NOUN
ap-3794	509	7	are	be	AUX
ap-3794	509	8	t−j(1	t−j(1	ADJ
ap-3794	509	9	−	−	PROPN
ap-3794	509	10	α	α	NOUN
ap-3794	509	11	)	)	PUNCT
ap-3794	509	12	,	,	PUNCT
ap-3794	509	13	for	for	ADP
ap-3794	509	14	j	j	PROPN
ap-3794	509	15	=	=	SYM
ap-3794	509	16	0	0	PROPN
ap-3794	509	17	,	,	PUNCT
ap-3794	509	18	.	.	PUNCT
ap-3794	509	19	.	.	PUNCT
ap-3794	510	1	.	.	PUNCT
ap-3794	511	1	,	,	PUNCT
ap-3794	512	1	n	n	CCONJ
ap-3794	512	2	−	−	PROPN
ap-3794	512	3	1	1	NUM
ap-3794	512	4	.	.	PUNCT
ap-3794	513	1	consequently	consequently	ADV
ap-3794	513	2	,	,	PUNCT
ap-3794	513	3	the	the	DET
ap-3794	513	4	distances	distance	NOUN
ap-3794	513	5	in	in	ADP
ap-3794	513	6	the	the	DET
ap-3794	513	7	set	set	NOUN
ap-3794	513	8	d(α	d(α	PROPN
ap-3794	513	9	,	,	PUNCT
ap-3794	513	10	1−	1−	NUM
ap-3794	513	11	α	α	NOUN
ap-3794	513	12	,	,	PUNCT
ap-3794	513	13	n	n	CCONJ
ap-3794	513	14	)	)	PUNCT
ap-3794	513	15	are	be	AUX
ap-3794	513	16	precisely	precisely	ADV
ap-3794	513	17	the	the	DET
ap-3794	513	18	frequencies	frequency	NOUN
ap-3794	513	19	of	of	ADP
ap-3794	513	20	factors	factor	NOUN
ap-3794	513	21	,	,	PUNCT
ap-3794	513	22	and	and	CCONJ
ap-3794	513	23	the	the	DET
ap-3794	513	24	three	three	NUM
ap-3794	513	25	distance	distance	NOUN
ap-3794	513	26	theorem	theorem	NOUN
ap-3794	513	27	implies	imply	VERB
ap-3794	513	28	the	the	DET
ap-3794	513	29	well	well	ADV
ap-3794	513	30	known	know	VERB
ap-3794	513	31	fact	fact	NOUN
ap-3794	513	32	that	that	SCONJ
ap-3794	513	33	sturmian	sturmian	NOUN
ap-3794	513	34	words	word	NOUN
ap-3794	513	35	have	have	AUX
ap-3794	513	36	for	for	ADP
ap-3794	513	37	each	each	DET
ap-3794	513	38	n	n	CCONJ
ap-3794	513	39	only	only	ADV
ap-3794	513	40	three	three	NUM
ap-3794	513	41	values	value	NOUN
ap-3794	513	42	of	of	ADP
ap-3794	513	43	frequencies	frequency	NOUN
ap-3794	513	44	of	of	ADP
ap-3794	513	45	factors	factor	NOUN
ap-3794	513	46	of	of	ADP
ap-3794	513	47	length	length	NOUN
ap-3794	513	48	n	n	CCONJ
ap-3794	513	49	,	,	PUNCT
ap-3794	513	50	namely	namely	ADV
ap-3794	513	51	%	%	NOUN
ap-3794	513	52	1	1	NUM
ap-3794	513	53	,	,	PUNCT
ap-3794	513	54	%	%	NOUN
ap-3794	513	55	2	2	NUM
ap-3794	513	56	,	,	PUNCT
ap-3794	513	57	%	%	NOUN
ap-3794	513	58	1	1	NUM
ap-3794	514	1	+	+	CCONJ
ap-3794	514	2	%	%	NOUN
ap-3794	514	3	2	2	NUM
ap-3794	514	4	.	.	PUNCT
ap-3794	515	1	the	the	DET
ap-3794	515	2	frequencies	frequency	NOUN
ap-3794	515	3	of	of	ADP
ap-3794	515	4	factors	factor	NOUN
ap-3794	515	5	of	of	ADP
ap-3794	515	6	length	length	NOUN
ap-3794	515	7	n	n	NOUN
ap-3794	515	8	in	in	ADP
ap-3794	515	9	3iet	3iet	NUM
ap-3794	515	10	words	word	NOUN
ap-3794	515	11	are	be	AUX
ap-3794	515	12	given	give	VERB
ap-3794	515	13	by	by	ADP
ap-3794	515	14	distances	distance	NOUN
ap-3794	515	15	between	between	ADP
ap-3794	515	16	neighbours	neighbour	NOUN
ap-3794	515	17	of	of	ADP
ap-3794	515	18	the	the	DET
ap-3794	515	19	set	set	NOUN
ap-3794	515	20	{	{	PUNCT
ap-3794	515	21	t−n(α	t−n(α	PROPN
ap-3794	515	22	)	)	PUNCT
ap-3794	515	23	:	:	PUNCT
ap-3794	516	1	n	n	X
ap-3794	516	2	∈	∈	PROPN
ap-3794	516	3	n	n	CCONJ
ap-3794	516	4	,	,	PUNCT
ap-3794	516	5	n	n	CCONJ
ap-3794	516	6	<	<	X
ap-3794	516	7	n	n	CCONJ
ap-3794	516	8	}	}	PUNCT
ap-3794	516	9	∪	∪	ADJ
ap-3794	516	10	{	{	PUNCT
ap-3794	516	11	t−n(β	t−n(β	NOUN
ap-3794	516	12	)	)	PUNCT
ap-3794	516	13	:	:	PUNCT
ap-3794	517	1	n	n	X
ap-3794	517	2	∈	∈	PROPN
ap-3794	517	3	n	n	CCONJ
ap-3794	517	4	,	,	PUNCT
ap-3794	517	5	n	n	CCONJ
ap-3794	517	6	<	<	X
ap-3794	517	7	n	n	X
ap-3794	517	8	}	}	PUNCT
ap-3794	517	9	.	.	PUNCT
ap-3794	518	1	in	in	ADP
ap-3794	518	2	[	[	X
ap-3794	518	3	4	4	X
ap-3794	518	4	]	]	PUNCT
ap-3794	518	5	it	it	PRON
ap-3794	518	6	is	be	AUX
ap-3794	518	7	shown	show	VERB
ap-3794	518	8	,	,	PUNCT
ap-3794	518	9	based	base	VERB
ap-3794	518	10	on	on	ADP
ap-3794	518	11	the	the	DET
ap-3794	518	12	study	study	NOUN
ap-3794	518	13	of	of	ADP
ap-3794	518	14	rauzy	rauzy	NOUN
ap-3794	518	15	graphs	graph	NOUN
ap-3794	518	16	,	,	PUNCT
ap-3794	518	17	that	that	SCONJ
ap-3794	518	18	the	the	DET
ap-3794	518	19	number	number	NOUN
ap-3794	518	20	of	of	ADP
ap-3794	518	21	distinct	distinct	ADJ
ap-3794	518	22	values	value	NOUN
ap-3794	518	23	of	of	ADP
ap-3794	518	24	frequencies	frequency	NOUN
ap-3794	518	25	in	in	ADP
ap-3794	518	26	infinite	infinite	ADJ
ap-3794	518	27	words	word	NOUN
ap-3794	518	28	with	with	ADP
ap-3794	518	29	reversal	reversal	NOUN
ap-3794	518	30	closed	close	VERB
ap-3794	518	31	language	language	NOUN
ap-3794	518	32	satisfies	satisfie	NOUN
ap-3794	518	33	#	#	SYM
ap-3794	518	34	{	{	PUNCT
ap-3794	518	35	freq(w	freq(w	PROPN
ap-3794	518	36	)	)	PUNCT
ap-3794	518	37	:	:	PUNCT
ap-3794	518	38	w	w	PROPN
ap-3794	518	39	∈	∈	PROPN
ap-3794	518	40	l(u	l(u	PROPN
ap-3794	518	41	)	)	PUNCT
ap-3794	518	42	,	,	PUNCT
ap-3794	518	43	|w|	|w|	ADJ
ap-3794	518	44	=	=	PUNCT
ap-3794	518	45	n	n	CCONJ
ap-3794	518	46	}	}	PUNCT
ap-3794	518	47	≤	≤	NUM
ap-3794	518	48	2	2	NUM
ap-3794	518	49	(	(	PUNCT
ap-3794	518	50	cu(n)−	cu(n)−	NOUN
ap-3794	518	51	cu(n−	cu(n−	PROPN
ap-3794	518	52	1	1	NUM
ap-3794	518	53	)	)	PUNCT
ap-3794	518	54	)	)	PUNCT
ap-3794	519	1	+	+	CCONJ
ap-3794	519	2	1	1	NUM
ap-3794	519	3	,	,	PUNCT
ap-3794	519	4	which	which	PRON
ap-3794	519	5	in	in	ADP
ap-3794	519	6	case	case	NOUN
ap-3794	519	7	of	of	ADP
ap-3794	519	8	3iet	3iet	NUM
ap-3794	519	9	words	word	NOUN
ap-3794	519	10	reduces	reduce	VERB
ap-3794	519	11	to	to	ADP
ap-3794	519	12	≤	≤	NUM
ap-3794	519	13	5	5	NUM
ap-3794	519	14	.	.	PUNCT
ap-3794	519	15	article	article	NOUN
ap-3794	519	16	[	[	X
ap-3794	519	17	7	7	X
ap-3794	519	18	]	]	PUNCT
ap-3794	519	19	shows	show	VERB
ap-3794	519	20	that	that	SCONJ
ap-3794	519	21	the	the	DET
ap-3794	519	22	set	set	NOUN
ap-3794	519	23	of	of	ADP
ap-3794	519	24	integers	integer	NOUN
ap-3794	519	25	n	n	PRON
ap-3794	519	26	for	for	ADP
ap-3794	519	27	which	which	PRON
ap-3794	519	28	this	this	DET
ap-3794	519	29	bound	bind	VERB
ap-3794	519	30	is	be	AUX
ap-3794	519	31	achieved	achieve	VERB
ap-3794	519	32	is	be	AUX
ap-3794	519	33	of	of	ADP
ap-3794	519	34	density	density	NOUN
ap-3794	519	35	1	1	NUM
ap-3794	519	36	in	in	ADP
ap-3794	519	37	n.	n.	NOUN
ap-3794	519	38	470	470	NUM
ap-3794	519	39	vol	vol	NOUN
ap-3794	519	40	.	.	PUNCT
ap-3794	520	1	56	56	NUM
ap-3794	520	2	no	no	NOUN
ap-3794	520	3	.	.	PUNCT
ap-3794	521	1	6/2016	6/2016	NUM
ap-3794	521	2	itineraries	itinerary	NOUN
ap-3794	521	3	induced	induce	VERB
ap-3794	521	4	by	by	ADP
ap-3794	521	5	exchange	exchange	NOUN
ap-3794	521	6	of	of	ADP
ap-3794	521	7	three	three	NUM
ap-3794	521	8	intervals	interval	NOUN
ap-3794	521	9	acknowledgements	acknowledgement	VERB
ap-3794	521	10	the	the	DET
ap-3794	521	11	authors	author	NOUN
ap-3794	521	12	acknowledge	acknowledge	VERB
ap-3794	521	13	financial	financial	ADJ
ap-3794	521	14	support	support	NOUN
ap-3794	521	15	by	by	ADP
ap-3794	521	16	the	the	DET
ap-3794	521	17	czech	czech	PROPN
ap-3794	521	18	science	science	PROPN
ap-3794	521	19	foundation	foundation	PROPN
ap-3794	521	20	grant	grant	PROPN
ap-3794	521	21	gačr	gačr	PROPN
ap-3794	521	22	13	13	NUM
ap-3794	521	23	-	-	PUNCT
ap-3794	521	24	03538s	03538s	NUM
ap-3794	521	25	.	.	PUNCT
ap-3794	522	1	references	reference	NOUN
ap-3794	522	2	[	[	X
ap-3794	522	3	1	1	NUM
ap-3794	522	4	]	]	PUNCT
ap-3794	522	5	p.	p.	NOUN
ap-3794	522	6	alessandri	alessandri	PROPN
ap-3794	522	7	and	and	CCONJ
ap-3794	522	8	v.	v.	ADP
ap-3794	522	9	berthé	berthé	ADJ
ap-3794	522	10	,	,	PUNCT
ap-3794	522	11	three	three	NUM
ap-3794	522	12	distance	distance	NOUN
ap-3794	522	13	theorems	theorem	NOUN
ap-3794	522	14	and	and	CCONJ
ap-3794	522	15	combinatorics	combinatoric	NOUN
ap-3794	522	16	on	on	ADP
ap-3794	522	17	words	word	NOUN
ap-3794	522	18	,	,	PUNCT
ap-3794	522	19	enseign	enseign	NOUN
ap-3794	522	20	.	.	PUNCT
ap-3794	523	1	math	math	NOUN
ap-3794	523	2	.	.	PUNCT
ap-3794	524	1	(	(	PUNCT
ap-3794	524	2	2	2	NUM
ap-3794	524	3	)	)	PUNCT
ap-3794	524	4	,	,	PUNCT
ap-3794	524	5	44	44	NUM
ap-3794	524	6	(	(	PUNCT
ap-3794	524	7	1998	1998	NUM
ap-3794	524	8	)	)	PUNCT
ap-3794	524	9	,	,	PUNCT
ap-3794	524	10	pp	pp	ADP
ap-3794	524	11	.	.	PUNCT
ap-3794	525	1	103–132	103–132	NUM
ap-3794	525	2	,	,	PUNCT
ap-3794	525	3	doi:10.5169	doi:10.5169	NOUN
ap-3794	525	4	/	/	SYM
ap-3794	525	5	seals-63900	seals-63900	NOUN
ap-3794	525	6	.	.	PUNCT
ap-3794	526	1	[	[	X
ap-3794	526	2	2	2	NUM
ap-3794	526	3	]	]	PUNCT
ap-3794	526	4	p.	p.	NOUN
ap-3794	526	5	ambrož	ambrož	PROPN
ap-3794	526	6	,	,	PUNCT
ap-3794	526	7	z.	z.	PROPN
ap-3794	526	8	masáková	masáková	PROPN
ap-3794	526	9	,	,	PUNCT
ap-3794	526	10	and	and	CCONJ
ap-3794	526	11	e.	e.	PROPN
ap-3794	526	12	pelantová	pelantová	PROPN
ap-3794	526	13	,	,	PUNCT
ap-3794	526	14	matrices	matrix	NOUN
ap-3794	526	15	of	of	ADP
ap-3794	526	16	3	3	NUM
ap-3794	526	17	-	-	PUNCT
ap-3794	526	18	iet	iet	NOUN
ap-3794	526	19	preserving	preserve	VERB
ap-3794	526	20	morphisms	morphism	NOUN
ap-3794	526	21	,	,	PUNCT
ap-3794	526	22	theor	theor	PROPN
ap-3794	526	23	.	.	PUNCT
ap-3794	527	1	comput	comput	PROPN
ap-3794	527	2	.	.	PUNCT
ap-3794	528	1	sci	sci	PROPN
ap-3794	528	2	.	.	PROPN
ap-3794	528	3	,	,	PUNCT
ap-3794	528	4	400	400	NUM
ap-3794	528	5	(	(	PUNCT
ap-3794	528	6	2008	2008	NUM
ap-3794	528	7	)	)	PUNCT
ap-3794	528	8	,	,	PUNCT
ap-3794	528	9	pp	pp	ADP
ap-3794	528	10	.	.	PUNCT
ap-3794	529	1	113–136	113–136	NUM
ap-3794	529	2	,	,	PUNCT
ap-3794	529	3	doi:10.1016	doi:10.1016	PROPN
ap-3794	529	4	/	/	SYM
ap-3794	529	5	j.tcs.2008.02.044	j.tcs.2008.02.044	PROPN
ap-3794	529	6	.	.	PUNCT
ap-3794	530	1	[	[	X
ap-3794	530	2	3	3	NUM
ap-3794	530	3	]	]	X
ap-3794	530	4	p.	p.	NOUN
ap-3794	530	5	arnoux	arnoux	NOUN
ap-3794	530	6	,	,	PUNCT
ap-3794	530	7	v.	v.	ADP
ap-3794	530	8	berthé	berthé	PROPN
ap-3794	530	9	,	,	PUNCT
ap-3794	530	10	z.	z.	PROPN
ap-3794	530	11	masáková	masáková	PROPN
ap-3794	530	12	,	,	PUNCT
ap-3794	530	13	and	and	CCONJ
ap-3794	530	14	e.	e.	PROPN
ap-3794	530	15	pelantová	pelantová	PROPN
ap-3794	530	16	,	,	PUNCT
ap-3794	530	17	sturm	sturm	PROPN
ap-3794	530	18	numbers	number	NOUN
ap-3794	530	19	and	and	CCONJ
ap-3794	530	20	substitution	substitution	NOUN
ap-3794	530	21	invariance	invariance	NOUN
ap-3794	530	22	of	of	ADP
ap-3794	530	23	3iet	3iet	NUM
ap-3794	530	24	words	word	NOUN
ap-3794	530	25	,	,	PUNCT
ap-3794	530	26	integers	integer	NOUN
ap-3794	530	27	,	,	PUNCT
ap-3794	530	28	8	8	NUM
ap-3794	530	29	(	(	PUNCT
ap-3794	530	30	2008	2008	NUM
ap-3794	530	31	)	)	PUNCT
ap-3794	530	32	,	,	PUNCT
ap-3794	531	1	http://eudml.org/doc/117362	http://eudml.org/doc/117362	PROPN
ap-3794	531	2	.	.	PUNCT
ap-3794	532	1	article	article	PROPN
ap-3794	532	2	a14	a14	PROPN
ap-3794	532	3	.	.	PUNCT
ap-3794	533	1	[	[	X
ap-3794	533	2	4	4	X
ap-3794	533	3	]	]	X
ap-3794	533	4	l.	l.	PROPN
ap-3794	533	5	balková	balková	PROPN
ap-3794	533	6	and	and	CCONJ
ap-3794	533	7	e.	e.	PROPN
ap-3794	533	8	pelantová	pelantová	PROPN
ap-3794	533	9	,	,	PUNCT
ap-3794	533	10	a	a	DET
ap-3794	533	11	note	note	NOUN
ap-3794	533	12	on	on	ADP
ap-3794	533	13	symmetries	symmetry	NOUN
ap-3794	533	14	in	in	ADP
ap-3794	533	15	the	the	DET
ap-3794	533	16	rauzy	rauzy	NOUN
ap-3794	533	17	graph	graph	NOUN
ap-3794	533	18	and	and	CCONJ
ap-3794	533	19	factor	factor	NOUN
ap-3794	533	20	frequencies	frequency	NOUN
ap-3794	533	21	,	,	PUNCT
ap-3794	533	22	theor	theor	PROPN
ap-3794	533	23	.	.	PUNCT
ap-3794	534	1	comput	comput	PROPN
ap-3794	534	2	.	.	PUNCT
ap-3794	535	1	sci	sci	PROPN
ap-3794	535	2	.	.	PROPN
ap-3794	535	3	,	,	PUNCT
ap-3794	535	4	410	410	NUM
ap-3794	535	5	(	(	PUNCT
ap-3794	535	6	2009	2009	NUM
ap-3794	535	7	)	)	PUNCT
ap-3794	535	8	,	,	PUNCT
ap-3794	535	9	pp	pp	ADP
ap-3794	535	10	.	.	PUNCT
ap-3794	536	1	2779–2783	2779–2783	NUM
ap-3794	536	2	,	,	PUNCT
ap-3794	536	3	doi:10.1016	doi:10.1016	PROPN
ap-3794	536	4	/	/	SYM
ap-3794	536	5	j.tcs.2009.04.002	j.tcs.2009.04.002	NOUN
ap-3794	536	6	.	.	PUNCT
ap-3794	537	1	[	[	X
ap-3794	537	2	5	5	NUM
ap-3794	537	3	]	]	PUNCT
ap-3794	537	4	p.	p.	NOUN
ap-3794	537	5	baláži	baláži	NOUN
ap-3794	537	6	,	,	PUNCT
ap-3794	537	7	z.	z.	PROPN
ap-3794	537	8	masáková	masáková	PROPN
ap-3794	537	9	,	,	PUNCT
ap-3794	537	10	and	and	CCONJ
ap-3794	537	11	e.	e.	PROPN
ap-3794	537	12	pelantová	pelantová	PROPN
ap-3794	537	13	,	,	PUNCT
ap-3794	537	14	characterization	characterization	NOUN
ap-3794	537	15	of	of	ADP
ap-3794	537	16	substitution	substitution	NOUN
ap-3794	537	17	invariant	invariant	ADJ
ap-3794	537	18	words	word	NOUN
ap-3794	537	19	coding	code	VERB
ap-3794	537	20	exchange	exchange	NOUN
ap-3794	537	21	of	of	ADP
ap-3794	537	22	three	three	NUM
ap-3794	537	23	intervals	interval	NOUN
ap-3794	537	24	,	,	PUNCT
ap-3794	537	25	integers	integer	NOUN
ap-3794	537	26	,	,	PUNCT
ap-3794	537	27	8	8	NUM
ap-3794	537	28	(	(	PUNCT
ap-3794	537	29	2008	2008	NUM
ap-3794	537	30	)	)	PUNCT
ap-3794	537	31	,	,	PUNCT
ap-3794	537	32	http://eudml.org/doc/117368	http://eudml.org/doc/117368	PROPN
ap-3794	537	33	.	.	PROPN
ap-3794	537	34	article	article	PROPN
ap-3794	537	35	a20	a20	PROPN
ap-3794	537	36	.	.	PUNCT
ap-3794	538	1	[	[	X
ap-3794	538	2	6	6	NUM
ap-3794	538	3	]	]	PUNCT
ap-3794	538	4	s.	s.	PROPN
ap-3794	538	5	ferenczi	ferenczi	PROPN
ap-3794	538	6	,	,	PUNCT
ap-3794	538	7	c.	c.	PROPN
ap-3794	538	8	holton	holton	PROPN
ap-3794	538	9	,	,	PUNCT
ap-3794	538	10	and	and	CCONJ
ap-3794	538	11	l.	l.	PROPN
ap-3794	538	12	q.	q.	PROPN
ap-3794	538	13	zamboni	zamboni	PROPN
ap-3794	538	14	,	,	PUNCT
ap-3794	538	15	structure	structure	NOUN
ap-3794	538	16	of	of	ADP
ap-3794	538	17	three	three	NUM
ap-3794	538	18	-	-	PUNCT
ap-3794	538	19	interval	interval	NOUN
ap-3794	538	20	exchange	exchange	NOUN
ap-3794	538	21	transformations	transformation	NOUN
ap-3794	538	22	ii	ii	NOUN
ap-3794	538	23	:	:	PUNCT
ap-3794	538	24	a	a	DET
ap-3794	538	25	combinatorial	combinatorial	ADJ
ap-3794	538	26	description	description	NOUN
ap-3794	538	27	of	of	ADP
ap-3794	538	28	the	the	DET
ap-3794	538	29	trajectories	trajectory	NOUN
ap-3794	538	30	,	,	PUNCT
ap-3794	538	31	j.	j.	PROPN
ap-3794	538	32	anal	anal	PROPN
ap-3794	538	33	.	.	PUNCT
ap-3794	538	34	math	math	PROPN
ap-3794	538	35	.	.	PUNCT
ap-3794	538	36	,	,	PUNCT
ap-3794	538	37	89	89	NUM
ap-3794	538	38	(	(	PUNCT
ap-3794	538	39	2003	2003	NUM
ap-3794	538	40	)	)	PUNCT
ap-3794	538	41	,	,	PUNCT
ap-3794	538	42	pp	pp	ADP
ap-3794	538	43	.	.	PUNCT
ap-3794	539	1	239–276	239–276	NUM
ap-3794	539	2	,	,	PUNCT
ap-3794	539	3	doi:10.1007	doi:10.1007	NOUN
ap-3794	539	4	/	/	SYM
ap-3794	539	5	bf02893083	bf02893083	NOUN
ap-3794	539	6	.	.	PUNCT
ap-3794	540	1	[	[	X
ap-3794	540	2	7	7	X
ap-3794	540	3	]	]	X
ap-3794	540	4	s.	s.	PROPN
ap-3794	540	5	ferenczi	ferenczi	PROPN
ap-3794	540	6	and	and	CCONJ
ap-3794	540	7	l.	l.	PROPN
ap-3794	540	8	q.	q.	PROPN
ap-3794	540	9	zamboni	zamboni	PROPN
ap-3794	540	10	,	,	PUNCT
ap-3794	540	11	structure	structure	NOUN
ap-3794	540	12	of	of	ADP
ap-3794	540	13	k	k	ADJ
ap-3794	540	14	-	-	PUNCT
ap-3794	540	15	interval	interval	NOUN
ap-3794	540	16	exchange	exchange	NOUN
ap-3794	540	17	transformations	transformation	NOUN
ap-3794	540	18	:	:	PUNCT
ap-3794	540	19	induction	induction	NOUN
ap-3794	540	20	,	,	PUNCT
ap-3794	540	21	trajectories	trajectory	NOUN
ap-3794	540	22	,	,	PUNCT
ap-3794	540	23	and	and	CCONJ
ap-3794	540	24	distance	distance	NOUN
ap-3794	540	25	theorems	theorem	NOUN
ap-3794	540	26	,	,	PUNCT
ap-3794	540	27	j.	j.	PROPN
ap-3794	540	28	anal	anal	PROPN
ap-3794	540	29	.	.	PUNCT
ap-3794	540	30	math	math	PROPN
ap-3794	540	31	.	.	PUNCT
ap-3794	540	32	,	,	PUNCT
ap-3794	540	33	112	112	NUM
ap-3794	540	34	(	(	PUNCT
ap-3794	540	35	2010	2010	NUM
ap-3794	540	36	)	)	PUNCT
ap-3794	540	37	,	,	PUNCT
ap-3794	540	38	pp	pp	ADP
ap-3794	540	39	.	.	PUNCT
ap-3794	541	1	289–328	289–328	NUM
ap-3794	541	2	,	,	PUNCT
ap-3794	541	3	doi:10.1007	doi:10.1007	NOUN
ap-3794	541	4	/	/	SYM
ap-3794	541	5	s11854	s11854	NOUN
ap-3794	541	6	-	-	PUNCT
ap-3794	541	7	010	010	NUM
ap-3794	541	8	-	-	PUNCT
ap-3794	541	9	0031	0031	NUM
ap-3794	541	10	-	-	PUNCT
ap-3794	541	11	2	2	NUM
ap-3794	541	12	.	.	PUNCT
ap-3794	542	1	[	[	X
ap-3794	542	2	8	8	NUM
ap-3794	542	3	]	]	X
ap-3794	542	4	j.	j.	PROPN
ap-3794	542	5	florek	florek	PROPN
ap-3794	542	6	and	and	CCONJ
ap-3794	542	7	k.	k.	PROPN
ap-3794	542	8	florek	florek	PROPN
ap-3794	542	9	,	,	PUNCT
ap-3794	542	10	billiard	billiard	PROPN
ap-3794	542	11	and	and	CCONJ
ap-3794	542	12	the	the	DET
ap-3794	542	13	five	five	NUM
ap-3794	542	14	-	-	PUNCT
ap-3794	542	15	gap	gap	NOUN
ap-3794	542	16	theorem	theorem	VERB
ap-3794	542	17	,	,	PUNCT
ap-3794	542	18	discrete	discrete	ADJ
ap-3794	542	19	math	math	NOUN
ap-3794	542	20	.	.	PUNCT
ap-3794	542	21	,	,	PUNCT
ap-3794	542	22	309	309	NUM
ap-3794	542	23	(	(	PUNCT
ap-3794	542	24	2009	2009	NUM
ap-3794	542	25	)	)	PUNCT
ap-3794	542	26	,	,	PUNCT
ap-3794	542	27	pp	pp	PROPN
ap-3794	542	28	.	.	PUNCT
ap-3794	543	1	4123–4129	4123–4129	NUM
ap-3794	543	2	,	,	PUNCT
ap-3794	543	3	doi:10.1016	doi:10.1016	PROPN
ap-3794	543	4	/	/	SYM
ap-3794	543	5	j.disc.2008.12.010	j.disc.2008.12.010	PROPN
ap-3794	543	6	.	.	PUNCT
ap-3794	544	1	[	[	X
ap-3794	544	2	9	9	NUM
ap-3794	544	3	]	]	PUNCT
ap-3794	544	4	l.	l.	PROPN
ap-3794	544	5	s.	s.	PROPN
ap-3794	544	6	guimond	guimond	PROPN
ap-3794	544	7	,	,	PUNCT
ap-3794	544	8	z.	z.	PROPN
ap-3794	544	9	masáková	masáková	PROPN
ap-3794	544	10	,	,	PUNCT
ap-3794	544	11	and	and	CCONJ
ap-3794	544	12	e.	e.	PROPN
ap-3794	544	13	pelantová	pelantová	PROPN
ap-3794	544	14	,	,	PUNCT
ap-3794	544	15	combinatorial	combinatorial	ADJ
ap-3794	544	16	properties	property	NOUN
ap-3794	544	17	of	of	ADP
ap-3794	544	18	infinite	infinite	ADJ
ap-3794	544	19	words	word	NOUN
ap-3794	544	20	associated	associate	VERB
ap-3794	544	21	with	with	ADP
ap-3794	544	22	cut	cut	VERB
ap-3794	544	23	-	-	PUNCT
ap-3794	544	24	and	and	CCONJ
ap-3794	544	25	-	-	PUNCT
ap-3794	544	26	project	project	NOUN
ap-3794	544	27	sequences	sequence	NOUN
ap-3794	544	28	,	,	PUNCT
ap-3794	544	29	j.	j.	PROPN
ap-3794	544	30	théor	théor	PROPN
ap-3794	544	31	.	.	PUNCT
ap-3794	544	32	nombres	nombre	NOUN
ap-3794	544	33	bordeaux	bordeaux	PROPN
ap-3794	544	34	,	,	PUNCT
ap-3794	544	35	15	15	NUM
ap-3794	544	36	(	(	PUNCT
ap-3794	544	37	2003	2003	NUM
ap-3794	544	38	)	)	PUNCT
ap-3794	544	39	,	,	PUNCT
ap-3794	544	40	pp	pp	ADP
ap-3794	544	41	.	.	PUNCT
ap-3794	545	1	697–725	697–725	NUM
ap-3794	545	2	,	,	PUNCT
ap-3794	545	3	doi:10.5802	doi:10.5802	PROPN
ap-3794	545	4	/	/	SYM
ap-3794	545	5	jtnb.422	jtnb.422	NOUN
ap-3794	545	6	.	.	PUNCT
ap-3794	546	1	[	[	X
ap-3794	546	2	10	10	NUM
ap-3794	546	3	]	]	X
ap-3794	546	4	a.	a.	NOUN
ap-3794	546	5	hof	hof	PROPN
ap-3794	546	6	,	,	PUNCT
ap-3794	546	7	o.	o.	PROPN
ap-3794	546	8	knill	knill	NOUN
ap-3794	546	9	,	,	PUNCT
ap-3794	546	10	and	and	CCONJ
ap-3794	546	11	b.	b.	PROPN
ap-3794	546	12	simon	simon	PROPN
ap-3794	546	13	,	,	PUNCT
ap-3794	546	14	singular	singular	ADJ
ap-3794	546	15	continuous	continuous	ADJ
ap-3794	546	16	spectrum	spectrum	NOUN
ap-3794	546	17	for	for	ADP
ap-3794	546	18	palindromic	palindromic	ADJ
ap-3794	546	19	schrödinger	schrödinger	ADJ
ap-3794	546	20	operators	operator	NOUN
ap-3794	546	21	,	,	PUNCT
ap-3794	546	22	comm	comm	NOUN
ap-3794	546	23	.	.	PUNCT
ap-3794	546	24	math	math	NOUN
ap-3794	546	25	.	.	PUNCT
ap-3794	547	1	phys	phy	NOUN
ap-3794	547	2	.	.	PUNCT
ap-3794	547	3	,	,	PUNCT
ap-3794	547	4	174	174	NUM
ap-3794	547	5	(	(	PUNCT
ap-3794	547	6	1995	1995	NUM
ap-3794	547	7	)	)	PUNCT
ap-3794	547	8	,	,	PUNCT
ap-3794	547	9	pp	pp	ADP
ap-3794	547	10	.	.	PUNCT
ap-3794	548	1	149–159	149–159	NUM
ap-3794	548	2	,	,	PUNCT
ap-3794	548	3	doi:10.1007	doi:10.1007	NOUN
ap-3794	548	4	/	/	SYM
ap-3794	548	5	bf02099468	bf02099468	NOUN
ap-3794	548	6	.	.	PUNCT
ap-3794	549	1	[	[	X
ap-3794	549	2	11	11	NUM
ap-3794	549	3	]	]	PUNCT
ap-3794	549	4	m.	m.	PROPN
ap-3794	549	5	keane	keane	PROPN
ap-3794	549	6	,	,	PUNCT
ap-3794	549	7	interval	interval	NOUN
ap-3794	549	8	exchange	exchange	NOUN
ap-3794	549	9	transformations	transformation	NOUN
ap-3794	549	10	,	,	PUNCT
ap-3794	549	11	math	math	NOUN
ap-3794	549	12	.	.	PUNCT
ap-3794	550	1	z.	z.	PROPN
ap-3794	550	2	,	,	PUNCT
ap-3794	550	3	141	141	NUM
ap-3794	550	4	(	(	PUNCT
ap-3794	550	5	1975	1975	NUM
ap-3794	550	6	)	)	PUNCT
ap-3794	550	7	,	,	PUNCT
ap-3794	550	8	pp	pp	PROPN
ap-3794	550	9	.	.	PUNCT
ap-3794	551	1	25–31	25–31	NUM
ap-3794	551	2	,	,	PUNCT
ap-3794	551	3	doi:10.1007	doi:10.1007	NOUN
ap-3794	551	4	/	/	SYM
ap-3794	551	5	bf01236981	bf01236981	NOUN
ap-3794	551	6	.	.	PUNCT
ap-3794	552	1	[	[	X
ap-3794	552	2	12	12	NUM
ap-3794	552	3	]	]	PUNCT
ap-3794	552	4	z.	z.	PROPN
ap-3794	552	5	masáková	masáková	PROPN
ap-3794	552	6	,	,	PUNCT
ap-3794	552	7	e.	e.	PROPN
ap-3794	552	8	pelantová	pelantová	PROPN
ap-3794	552	9	,	,	PUNCT
ap-3794	552	10	and	and	CCONJ
ap-3794	552	11	š	š	PROPN
ap-3794	552	12	.	.	PUNCT
ap-3794	552	13	starosta	starosta	PROPN
ap-3794	552	14	,	,	PUNCT
ap-3794	552	15	exchange	exchange	NOUN
ap-3794	552	16	of	of	ADP
ap-3794	552	17	three	three	NUM
ap-3794	552	18	intervals	interval	NOUN
ap-3794	552	19	:	:	PUNCT
ap-3794	552	20	substitutions	substitution	NOUN
ap-3794	552	21	and	and	CCONJ
ap-3794	552	22	palindromicity	palindromicity	NOUN
ap-3794	552	23	,	,	PUNCT
ap-3794	552	24	submitted	submit	VERB
ap-3794	552	25	.	.	PUNCT
ap-3794	553	1	[	[	X
ap-3794	553	2	13	13	NUM
ap-3794	553	3	]	]	PUNCT
ap-3794	553	4	z.	z.	PROPN
ap-3794	553	5	masáková	masáková	PROPN
ap-3794	553	6	and	and	CCONJ
ap-3794	553	7	e.	e.	PROPN
ap-3794	553	8	pelantová	pelantová	PROPN
ap-3794	553	9	,	,	PUNCT
ap-3794	553	10	itineraries	itinerary	NOUN
ap-3794	553	11	induced	induce	VERB
ap-3794	553	12	by	by	ADP
ap-3794	553	13	exchange	exchange	NOUN
ap-3794	553	14	of	of	ADP
ap-3794	553	15	two	two	NUM
ap-3794	553	16	intervals	interval	NOUN
ap-3794	553	17	,	,	PUNCT
ap-3794	553	18	acta	acta	PROPN
ap-3794	553	19	polytechnica	polytechnica	PROPN
ap-3794	553	20	,	,	PUNCT
ap-3794	553	21	53	53	NUM
ap-3794	553	22	(	(	PUNCT
ap-3794	553	23	2013	2013	NUM
ap-3794	553	24	)	)	PUNCT
ap-3794	553	25	,	,	PUNCT
ap-3794	553	26	pp	pp	ADP
ap-3794	553	27	.	.	PUNCT
ap-3794	554	1	444–449	444–449	NUM
ap-3794	554	2	,	,	PUNCT
ap-3794	554	3	doi:10.14311	doi:10.14311	NOUN
ap-3794	554	4	/	/	SYM
ap-3794	554	5	ap.2013.53.0444	ap.2013.53.0444	PROPN
ap-3794	554	6	.	.	PUNCT
ap-3794	555	1	[	[	X
ap-3794	555	2	14	14	NUM
ap-3794	555	3	]	]	X
ap-3794	555	4	n.	n.	PROPN
ap-3794	555	5	b.	b.	PROPN
ap-3794	555	6	slater	slater	PROPN
ap-3794	555	7	,	,	PUNCT
ap-3794	555	8	the	the	DET
ap-3794	555	9	distribution	distribution	NOUN
ap-3794	555	10	of	of	ADP
ap-3794	555	11	the	the	DET
ap-3794	555	12	integers	integer	NOUN
ap-3794	555	13	n	n	X
ap-3794	555	14	for	for	ADP
ap-3794	555	15	which	which	PRON
ap-3794	555	16	θn	θn	ADP
ap-3794	555	17	<	<	X
ap-3794	555	18	φ	φ	PROPN
ap-3794	555	19	,	,	PUNCT
ap-3794	555	20	proc	proc	PROPN
ap-3794	555	21	.	.	PUNCT
ap-3794	556	1	cambridge	cambridge	PROPN
ap-3794	556	2	philos	philos	PROPN
ap-3794	556	3	.	.	PUNCT
ap-3794	556	4	soc	soc	PROPN
ap-3794	556	5	.	.	PUNCT
ap-3794	557	1	,	,	PUNCT
ap-3794	557	2	46	46	NUM
ap-3794	557	3	(	(	PUNCT
ap-3794	557	4	1950	1950	NUM
ap-3794	557	5	)	)	PUNCT
ap-3794	557	6	,	,	PUNCT
ap-3794	557	7	pp	pp	ADP
ap-3794	557	8	.	.	PUNCT
ap-3794	558	1	525–534	525–534	NUM
ap-3794	558	2	,	,	PUNCT
ap-3794	558	3	doi:10.1017	doi:10.1017	X
ap-3794	558	4	/	/	SYM
ap-3794	558	5	s0305004100026086	s0305004100026086	NOUN
ap-3794	558	6	.	.	PUNCT
ap-3794	559	1	[	[	X
ap-3794	559	2	15	15	NUM
ap-3794	559	3	]	]	X
ap-3794	559	4	n.	n.	PROPN
ap-3794	559	5	b.	b.	PROPN
ap-3794	559	6	slater	slater	PROPN
ap-3794	559	7	,	,	PUNCT
ap-3794	559	8	gaps	gap	NOUN
ap-3794	559	9	and	and	CCONJ
ap-3794	559	10	steps	step	NOUN
ap-3794	559	11	for	for	ADP
ap-3794	559	12	the	the	DET
ap-3794	559	13	sequence	sequence	NOUN
ap-3794	559	14	nθ	nθ	NOUN
ap-3794	559	15	mod	mod	PROPN
ap-3794	559	16	1	1	NUM
ap-3794	559	17	,	,	PUNCT
ap-3794	559	18	math	math	NOUN
ap-3794	559	19	.	.	PUNCT
ap-3794	560	1	proc	proc	PROPN
ap-3794	560	2	.	.	PUNCT
ap-3794	561	1	cambridge	cambridge	PROPN
ap-3794	561	2	phil	phil	PROPN
ap-3794	561	3	.	.	PUNCT
ap-3794	562	1	soc	soc	PROPN
ap-3794	562	2	.	.	PUNCT
ap-3794	562	3	,	,	PUNCT
ap-3794	562	4	63	63	NUM
ap-3794	562	5	(	(	PUNCT
ap-3794	562	6	1967	1967	NUM
ap-3794	562	7	)	)	PUNCT
ap-3794	562	8	,	,	PUNCT
ap-3794	562	9	pp	pp	ADP
ap-3794	562	10	.	.	PUNCT
ap-3794	563	1	1115–1123	1115–1123	NUM
ap-3794	563	2	,	,	PUNCT
ap-3794	563	3	doi:10.1017	doi:10.1017	X
ap-3794	563	4	/	/	SYM
ap-3794	563	5	s0305004100042195	s0305004100042195	NOUN
ap-3794	563	6	.	.	PUNCT
ap-3794	564	1	[	[	X
ap-3794	564	2	16	16	NUM
ap-3794	564	3	]	]	X
ap-3794	564	4	l.	l.	PROPN
ap-3794	564	5	vuillon	vuillon	PROPN
ap-3794	564	6	,	,	PUNCT
ap-3794	564	7	on	on	ADP
ap-3794	564	8	the	the	DET
ap-3794	564	9	number	number	NOUN
ap-3794	564	10	of	of	ADP
ap-3794	564	11	return	return	NOUN
ap-3794	564	12	words	word	NOUN
ap-3794	564	13	in	in	ADP
ap-3794	564	14	infinite	infinite	ADJ
ap-3794	564	15	words	word	NOUN
ap-3794	564	16	constructed	construct	VERB
ap-3794	564	17	by	by	ADP
ap-3794	564	18	interval	interval	NOUN
ap-3794	564	19	exchange	exchange	NOUN
ap-3794	564	20	transformations	transformation	NOUN
ap-3794	564	21	,	,	PUNCT
ap-3794	564	22	pure	pure	ADJ
ap-3794	564	23	math	math	NOUN
ap-3794	564	24	.	.	PUNCT
ap-3794	565	1	appl	appl	PROPN
ap-3794	565	2	.	.	PUNCT
ap-3794	566	1	(	(	PUNCT
ap-3794	566	2	pu.m.a	pu.m.a	PROPN
ap-3794	566	3	.	.	PROPN
ap-3794	566	4	)	)	PUNCT
ap-3794	566	5	,	,	PUNCT
ap-3794	566	6	18	18	NUM
ap-3794	566	7	(	(	PUNCT
ap-3794	566	8	2007	2007	NUM
ap-3794	566	9	)	)	PUNCT
ap-3794	566	10	,	,	PUNCT
ap-3794	566	11	pp	pp	ADP
ap-3794	566	12	.	.	PUNCT
ap-3794	567	1	345–355	345–355	NUM
ap-3794	567	2	,	,	PUNCT
ap-3794	567	3	http://www.mat.unisi.it/	http://www.mat.unisi.it/	PROPN
ap-3794	567	4	newsito	newsito	VERB
ap-3794	567	5	/	/	SYM
ap-3794	567	6	puma	puma	NOUN
ap-3794	567	7	/	/	SYM
ap-3794	567	8	public_html/18_3_4	public_html/18_3_4	NOUN
ap-3794	567	9	/	/	SYM
ap-3794	567	10	vuillon.pdf	vuillon.pdf	PROPN
ap-3794	567	11	.	.	NOUN
ap-3794	567	12	471	471	NUM
ap-3794	567	13	http://dx.doi.org/10.5169/seals-63900	http://dx.doi.org/10.5169/seals-63900	NOUN
ap-3794	567	14	http://dx.doi.org/10.1016/j.tcs.2008.02.044	http://dx.doi.org/10.1016/j.tcs.2008.02.044	PROPN
ap-3794	567	15	http://eudml.org/doc/117362	http://eudml.org/doc/117362	PROPN
ap-3794	567	16	http://dx.doi.org/10.1016/j.tcs.2009.04.002	http://dx.doi.org/10.1016/j.tcs.2009.04.002	NOUN
ap-3794	567	17	http://eudml.org/doc/117368	http://eudml.org/doc/117368	PROPN
ap-3794	567	18	http://dx.doi.org/10.1007/bf02893083	http://dx.doi.org/10.1007/bf02893083	PROPN
ap-3794	567	19	http://dx.doi.org/10.1007/s11854-010-0031-2	http://dx.doi.org/10.1007/s11854-010-0031-2	PROPN
ap-3794	568	1	http://dx.doi.org/10.1016/j.disc.2008.12.010	http://dx.doi.org/10.1016/j.disc.2008.12.010	PROPN
ap-3794	568	2	http://dx.doi.org/10.5802/jtnb.422	http://dx.doi.org/10.5802/jtnb.422	NOUN
ap-3794	568	3	http://dx.doi.org/10.1007/bf02099468	http://dx.doi.org/10.1007/bf02099468	PROPN
ap-3794	568	4	http://dx.doi.org/10.1007/bf01236981	http://dx.doi.org/10.1007/bf01236981	VERB
ap-3794	568	5	http://dx.doi.org/10.14311/ap.2013.53.0444	http://dx.doi.org/10.14311/ap.2013.53.0444	X
ap-3794	568	6	http://dx.doi.org/10.1017/s0305004100026086	http://dx.doi.org/10.1017/s0305004100026086	PROPN
ap-3794	568	7	http://dx.doi.org/10.1017/s0305004100042195	http://dx.doi.org/10.1017/s0305004100042195	NOUN
ap-3794	568	8	http://www.mat.unisi.it/newsito/puma/public_html/18_3_4/vuillon.pdf	http://www.mat.unisi.it/newsito/puma/public_html/18_3_4/vuillon.pdf	PROPN
ap-3794	568	9	http://www.mat.unisi.it/newsito/puma/public_html/18_3_4/vuillon.pdf	http://www.mat.unisi.it/newsito/puma/public_html/18_3_4/vuillon.pdf	PROPN
ap-3794	568	10	acta	acta	PROPN
ap-3794	568	11	polytechnica	polytechnica	PROPN
ap-3794	568	12	56(6):462–471	56(6):462–471	PROPN
ap-3794	568	13	,	,	PUNCT
ap-3794	568	14	2016	2016	NUM
ap-3794	568	15	1	1	NUM
ap-3794	568	16	introduction	introduction	NOUN
ap-3794	568	17	2	2	NUM
ap-3794	568	18	preliminaries	preliminary	NOUN
ap-3794	568	19	2.1	2.1	NUM
ap-3794	568	20	combinatorics	combinatoric	NOUN
ap-3794	568	21	on	on	ADP
ap-3794	568	22	words	word	NOUN
ap-3794	568	23	2.2	2.2	NUM
ap-3794	568	24	exchange	exchange	NOUN
ap-3794	568	25	of	of	ADP
ap-3794	568	26	three	three	NUM
ap-3794	568	27	intervals	interval	NOUN
ap-3794	568	28	3	3	NUM
ap-3794	568	29	itineraries	itinerary	NOUN
ap-3794	568	30	in	in	ADP
ap-3794	568	31	exchange	exchange	NOUN
ap-3794	568	32	of	of	ADP
ap-3794	568	33	three	three	NUM
ap-3794	568	34	intervals	interval	NOUN
ap-3794	568	35	4	4	NUM
ap-3794	568	36	return	return	NOUN
ap-3794	568	37	time	time	NOUN
ap-3794	568	38	in	in	ADP
ap-3794	568	39	a	a	DET
ap-3794	568	40	3iet	3iet	NUM
ap-3794	568	41	5	5	NUM
ap-3794	568	42	description	description	NOUN
ap-3794	568	43	of	of	ADP
ap-3794	568	44	the	the	DET
ap-3794	568	45	case	case	NOUN
ap-3794	568	46	of	of	ADP
ap-3794	568	47	three	three	NUM
ap-3794	568	48	i	i	NOUN
ap-3794	568	49	-	-	PUNCT
ap-3794	568	50	itineraries	itinerary	NOUN
ap-3794	568	51	5.1	5.1	NUM
ap-3794	568	52	return	return	NOUN
ap-3794	568	53	words	word	NOUN
ap-3794	568	54	to	to	ADP
ap-3794	568	55	factors	factor	NOUN
ap-3794	568	56	of	of	ADP
ap-3794	568	57	a	a	DET
ap-3794	568	58	3iet	3iet	NUM
ap-3794	568	59	5.2	5.2	NUM
ap-3794	568	60	substitutions	substitution	NOUN
ap-3794	568	61	fixing	fix	VERB
ap-3794	568	62	3iet	3iet	NUM
ap-3794	568	63	words	word	NOUN
ap-3794	568	64	6	6	NUM
ap-3794	568	65	gaps	gap	NOUN
ap-3794	568	66	and	and	CCONJ
ap-3794	568	67	distance	distance	NOUN
ap-3794	568	68	theorems	theorem	NOUN
ap-3794	568	69	acknowledgements	acknowledgement	NOUN
ap-3794	568	70	references	reference	NOUN