id	sid	tid	token	lemma	pos
cana-1315	1	1	communications	communication	NOUN
cana-1315	1	2	on	on	ADP
cana-1315	1	3	applied	apply	VERB
cana-1315	1	4	nonlinear	nonlinear	ADJ
cana-1315	1	5	analysis	analysis	NOUN
cana-1315	1	6	issn	issn	NOUN
cana-1315	1	7	:	:	PUNCT
cana-1315	1	8	1074	1074	NUM
cana-1315	1	9	-	-	PUNCT
cana-1315	1	10	133x	133x	NUM
cana-1315	1	11	vol	vol	NOUN
cana-1315	1	12	31	31	NUM
cana-1315	1	13	no	no	NOUN
cana-1315	1	14	.	.	PUNCT
cana-1315	2	1	7s	7	NOUN
cana-1315	2	2	(	(	PUNCT
cana-1315	2	3	2024	2024	NUM
cana-1315	2	4	)	)	PUNCT
cana-1315	2	5	357	357	NUM
cana-1315	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1315	2	7	investigation	investigation	NOUN
cana-1315	2	8	on	on	ADP
cana-1315	2	9	anti	anti	ADJ
cana-1315	2	10	-	-	ADJ
cana-1315	2	11	fuzzy	fuzzy	ADJ
cana-1315	2	12	tssemiring	tssemiring	NOUN
cana-1315	2	13	of	of	ADP
cana-1315	2	14	a	a	DET
cana-1315	2	15	ter.semi	ter.semi	NOUN
cana-1315	2	16	-	-	PUNCT
cana-1315	2	17	ring	ring	NOUN
cana-1315	2	18	*	*	PROPN
cana-1315	2	19	1	1	NUM
cana-1315	2	20	g.	g.	PROPN
cana-1315	2	21	srinivasa	srinivasa	PROPN
cana-1315	2	22	rao	rao	PROPN
cana-1315	2	23	,	,	PUNCT
cana-1315	2	24	2	2	NUM
cana-1315	2	25	r.venkata	r.venkata	VERB
cana-1315	2	26	aravinda	aravinda	PROPN
cana-1315	2	27	raju	raju	PROPN
cana-1315	2	28	,	,	PUNCT
cana-1315	2	29	3	3	NUM
cana-1315	2	30	v.	v.	ADP
cana-1315	2	31	savithri	savithri	NOUN
cana-1315	2	32	,	,	PUNCT
cana-1315	2	33	4	4	NUM
cana-1315	2	34	s.	s.	NOUN
cana-1315	2	35	vinoth	vinoth	NOUN
cana-1315	2	36	*	*	PROPN
cana-1315	2	37	1	1	NUM
cana-1315	2	38	associate	associate	NOUN
cana-1315	2	39	professor	professor	NOUN
cana-1315	2	40	,	,	PUNCT
cana-1315	2	41	department	department	NOUN
cana-1315	2	42	of	of	ADP
cana-1315	2	43	mathematics	mathematic	NOUN
cana-1315	2	44	,	,	PUNCT
cana-1315	2	45	school	school	NOUN
cana-1315	2	46	of	of	ADP
cana-1315	2	47	applied	apply	VERB
cana-1315	2	48	sciences	sciences	PROPN
cana-1315	2	49	&	&	CCONJ
cana-1315	2	50	humanities	humanity	NOUN
cana-1315	2	51	,	,	PUNCT
cana-1315	2	52	vfstr	vfstr	NOUN
cana-1315	2	53	deemed	deem	VERB
cana-1315	2	54	to	to	PART
cana-1315	2	55	be	be	AUX
cana-1315	2	56	university	university	NOUN
cana-1315	2	57	,	,	PUNCT
cana-1315	2	58	vadlamudi	vadlamudi	NOUN
cana-1315	2	59	,	,	PUNCT
cana-1315	2	60	guntur	guntur	PROPN
cana-1315	2	61	(	(	PUNCT
cana-1315	2	62	dt	dt	PROPN
cana-1315	2	63	.	.	PUNCT
cana-1315	2	64	)	)	PUNCT
cana-1315	2	65	,	,	PUNCT
cana-1315	2	66	a.p	a.p	PROPN
cana-1315	2	67	.	.	PROPN
cana-1315	2	68	,	,	PUNCT
cana-1315	2	69	india.email:gsrinulakshmi77@gmail.com	india.email:gsrinulakshmi77@gmail.com	X
cana-1315	2	70	2	2	NUM
cana-1315	2	71	assistant	assistant	NOUN
cana-1315	2	72	professor	professor	NOUN
cana-1315	2	73	,	,	PUNCT
cana-1315	2	74	dvr	dvr	PROPN
cana-1315	2	75	&	&	CCONJ
cana-1315	2	76	dr	dr	PROPN
cana-1315	2	77	.	.	PROPN
cana-1315	2	78	hs	hs	PROPN
cana-1315	3	1	mic	mic	PROPN
cana-1315	3	2	college	college	PROPN
cana-1315	3	3	of	of	ADP
cana-1315	3	4	technology	technology	NOUN
cana-1315	3	5	,	,	PUNCT
cana-1315	3	6	kanchikacherla	kanchikacherla	PROPN
cana-1315	3	7	,	,	PUNCT
cana-1315	3	8	krishna	krishna	PROPN
cana-1315	3	9	district521180	district521180	PROPN
cana-1315	3	10	,	,	PUNCT
cana-1315	3	11	a.p	a.p	PROPN
cana-1315	3	12	,	,	PUNCT
cana-1315	3	13	india	india	PROPN
cana-1315	3	14	.	.	PUNCT
cana-1315	3	15	email	email	PROPN
cana-1315	3	16	:	:	PUNCT
cana-1315	3	17	ravindaraju.1@gmail.com	ravindaraju.1@gmail.com	PROPN
cana-1315	3	18	3	3	NUM
cana-1315	3	19	assistant	assistant	NOUN
cana-1315	3	20	professor	professor	NOUN
cana-1315	3	21	,	,	PUNCT
cana-1315	3	22	department	department	NOUN
cana-1315	3	23	of	of	ADP
cana-1315	3	24	mathematics	mathematics	PROPN
cana-1315	3	25	,	,	PUNCT
cana-1315	3	26	karpagam	karpagam	PROPN
cana-1315	3	27	academy	academy	PROPN
cana-1315	3	28	of	of	ADP
cana-1315	3	29	higher	high	ADJ
cana-1315	3	30	education	education	NOUN
cana-1315	3	31	,	,	PUNCT
cana-1315	3	32	(	(	PUNCT
cana-1315	3	33	deemed	deem	VERB
cana-1315	3	34	to	to	PART
cana-1315	3	35	be	be	AUX
cana-1315	3	36	university	university	NOUN
cana-1315	3	37	)	)	PUNCT
cana-1315	3	38	,	,	PUNCT
cana-1315	3	39	eachanari	eachanari	PROPN
cana-1315	3	40	,	,	PUNCT
cana-1315	3	41	coimbatore	coimbatore	PROPN
cana-1315	3	42	,	,	PUNCT
cana-1315	3	43	tamilnadu	tamilnadu	NOUN
cana-1315	3	44	,	,	PUNCT
cana-1315	3	45	india	india	PROPN
cana-1315	3	46	.	.	PUNCT
cana-1315	4	1	email:savithri.vijayakumar@kahedu.edu.in	email:savithri.vijayakumar@kahedu.edu.in	PROPN
cana-1315	4	2	4	4	NUM
cana-1315	4	3	assistant	assistant	NOUN
cana-1315	4	4	professor	professor	NOUN
cana-1315	4	5	,	,	PUNCT
cana-1315	4	6	department	department	NOUN
cana-1315	4	7	of	of	ADP
cana-1315	4	8	mathematics	mathematic	NOUN
cana-1315	4	9	,	,	PUNCT
cana-1315	4	10	school	school	NOUN
cana-1315	4	11	of	of	ADP
cana-1315	4	12	applied	apply	VERB
cana-1315	4	13	sciences	sciences	PROPN
cana-1315	4	14	&	&	CCONJ
cana-1315	4	15	humanities	humanity	NOUN
cana-1315	4	16	,	,	PUNCT
cana-1315	4	17	vfstr	vfstr	NOUN
cana-1315	4	18	deemed	deem	VERB
cana-1315	4	19	to	to	PART
cana-1315	4	20	be	be	AUX
cana-1315	4	21	university	university	NOUN
cana-1315	4	22	,	,	PUNCT
cana-1315	4	23	vadlamudi	vadlamudi	NOUN
cana-1315	4	24	,	,	PUNCT
cana-1315	4	25	guntur	guntur	PROPN
cana-1315	4	26	(	(	PUNCT
cana-1315	4	27	dt	dt	PROPN
cana-1315	4	28	.	.	PUNCT
cana-1315	4	29	)	)	PUNCT
cana-1315	4	30	,	,	PUNCT
cana-1315	4	31	a.p	a.p	PROPN
cana-1315	4	32	.	.	PROPN
cana-1315	4	33	,	,	PUNCT
cana-1315	4	34	india.email:vinomaths6@gmail.com	india.email:vinomaths6@gmail.com	X
cana-1315	5	1	article	article	PROPN
cana-1315	5	2	history	history	NOUN
cana-1315	5	3	:	:	PUNCT
cana-1315	5	4	received	receive	VERB
cana-1315	5	5	:	:	PUNCT
cana-1315	5	6	01	01	NUM
cana-1315	5	7	-	-	PUNCT
cana-1315	5	8	06	06	NUM
cana-1315	5	9	-	-	PUNCT
cana-1315	5	10	2024	2024	NUM
cana-1315	5	11	revised	revise	VERB
cana-1315	5	12	:	:	PUNCT
cana-1315	5	13	03	03	NUM
cana-1315	5	14	-	-	PUNCT
cana-1315	5	15	07	07	NUM
cana-1315	5	16	-	-	PUNCT
cana-1315	5	17	2024	2024	NUM
cana-1315	5	18	accepted	accept	VERB
cana-1315	5	19	:	:	PUNCT
cana-1315	5	20	29	29	NUM
cana-1315	5	21	-	-	SYM
cana-1315	5	22	07	07	NUM
cana-1315	5	23	-	-	PUNCT
cana-1315	5	24	2024	2024	NUM
cana-1315	5	25	abstract	abstract	NOUN
cana-1315	5	26	:	:	PUNCT
cana-1315	5	27	in	in	ADP
cana-1315	5	28	this	this	DET
cana-1315	5	29	article	article	NOUN
cana-1315	5	30	,	,	PUNCT
cana-1315	5	31	we	we	PRON
cana-1315	5	32	scrutinise	scrutinise	VERB
cana-1315	5	33	the	the	DET
cana-1315	5	34	algebraic	algebraic	ADJ
cana-1315	5	35	characteristics	characteristic	NOUN
cana-1315	5	36	of	of	ADP
cana-1315	5	37	the	the	DET
cana-1315	5	38	anti	anti	ADJ
cana-1315	5	39	-	-	ADJ
cana-1315	5	40	fuzzy	fuzzy	ADJ
cana-1315	5	41	ternary	ternary	ADJ
cana-1315	5	42	subsemi	subsemi	NOUN
cana-1315	5	43	-	-	PUNCT
cana-1315	5	44	ring	ring	NOUN
cana-1315	5	45	of	of	ADP
cana-1315	5	46	a	a	DET
cana-1315	5	47	ternary	ternary	ADJ
cana-1315	5	48	semi	semi	ADJ
cana-1315	5	49	-	-	ADJ
cana-1315	5	50	ring	ring	ADJ
cana-1315	5	51	and	and	CCONJ
cana-1315	5	52	explore	explore	VERB
cana-1315	5	53	many	many	ADJ
cana-1315	5	54	theorems	theorem	NOUN
cana-1315	5	55	inside	inside	ADP
cana-1315	5	56	it	it	PRON
cana-1315	5	57	.	.	PUNCT
cana-1315	6	1	keywords	keyword	NOUN
cana-1315	6	2	:	:	PUNCT
cana-1315	6	3	fuzzy	fuzzy	ADJ
cana-1315	6	4	set	set	NOUN
cana-1315	6	5	,	,	PUNCT
cana-1315	6	6	fuzzy	fuzzy	ADJ
cana-1315	6	7	ternary	ternary	ADJ
cana-1315	6	8	sub	sub	ADJ
cana-1315	6	9	-	-	ADJ
cana-1315	6	10	semi	semi	ADJ
cana-1315	6	11	-	-	ADJ
cana-1315	6	12	ring	ring	ADJ
cana-1315	6	13	,	,	PUNCT
cana-1315	6	14	anti	anti	ADJ
cana-1315	6	15	-	-	ADJ
cana-1315	6	16	fuzzy	fuzzy	ADJ
cana-1315	6	17	ternary	ternary	ADJ
cana-1315	6	18	sub	sub	ADJ
cana-1315	6	19	-	-	ADJ
cana-1315	6	20	semi	semi	ADJ
cana-1315	6	21	-	-	ADJ
cana-1315	6	22	ring	ring	ADJ
cana-1315	6	23	,	,	PUNCT
cana-1315	6	24	antifuzzy	antifuzzy	VERB
cana-1315	6	25	normal	normal	ADJ
cana-1315	6	26	ternary	ternary	ADJ
cana-1315	6	27	sub	sub	ADJ
cana-1315	6	28	-	-	ADJ
cana-1315	6	29	semi	semi	ADJ
cana-1315	6	30	-	-	ADJ
cana-1315	6	31	ring	ring	ADJ
cana-1315	6	32	,	,	PUNCT
cana-1315	6	33	homomorphism	homomorphism	NOUN
cana-1315	6	34	,	,	PUNCT
cana-1315	6	35	anti	anti	ADJ
cana-1315	6	36	-	-	ADJ
cana-1315	6	37	homomorphism	homomorphism	ADJ
cana-1315	6	38	,	,	PUNCT
cana-1315	6	39	isomorphism	isomorphism	NOUN
cana-1315	6	40	,	,	PUNCT
cana-1315	6	41	anti	anti	ADJ
cana-1315	6	42	-	-	ADJ
cana-1315	6	43	isomorphism	isomorphism	ADJ
cana-1315	6	44	.	.	PUNCT
cana-1315	7	1	2000	2000	NUM
cana-1315	7	2	ams	am	NOUN
cana-1315	7	3	subject	subject	ADJ
cana-1315	7	4	classification	classification	NOUN
cana-1315	7	5	:	:	PUNCT
cana-1315	7	6	03f55	03f55	NOUN
cana-1315	7	7	,	,	PUNCT
cana-1315	7	8	06d72	06d72	NOUN
cana-1315	7	9	,	,	PUNCT
cana-1315	7	10	08a72	08a72	NUM
cana-1315	7	11	.	.	PUNCT
cana-1315	8	1	1	1	X
cana-1315	8	2	.	.	X
cana-1315	8	3	introduction	introduction	NOUN
cana-1315	8	4	numerous	numerous	ADJ
cana-1315	8	5	ideas	idea	NOUN
cana-1315	8	6	exist	exist	VERB
cana-1315	8	7	for	for	ADP
cana-1315	8	8	universal	universal	ADJ
cana-1315	8	9	algebras	algebra	NOUN
cana-1315	8	10	that	that	PRON
cana-1315	8	11	extend	extend	VERB
cana-1315	8	12	an	an	DET
cana-1315	8	13	associative	associative	ADJ
cana-1315	8	14	ring	ring	NOUN
cana-1315	8	15	(	(	PUNCT
cana-1315	8	16	r	r	NOUN
cana-1315	8	17	,	,	PUNCT
cana-1315	8	18	+	+	NOUN
cana-1315	8	19	,	,	PUNCT
cana-1315	8	20	..	..	PUNCT
cana-1315	8	21	)	)	PUNCT
cana-1315	8	22	.	.	PUNCT
cana-1315	9	1	several	several	ADJ
cana-1315	9	2	near	near	ADJ
cana-1315	9	3	-	-	PUNCT
cana-1315	9	4	rings	ring	NOUN
cana-1315	9	5	and	and	CCONJ
cana-1315	9	6	semi	semi	ADJ
cana-1315	9	7	-	-	ADJ
cana-1315	9	8	ring	ring	ADJ
cana-1315	9	9	types	type	NOUN
cana-1315	9	10	,	,	PUNCT
cana-1315	9	11	in	in	ADP
cana-1315	9	12	particular	particular	ADJ
cana-1315	9	13	,	,	PUNCT
cana-1315	9	14	have	have	AUX
cana-1315	9	15	shown	show	VERB
cana-1315	9	16	to	to	PART
cana-1315	9	17	be	be	AUX
cana-1315	9	18	quite	quite	ADV
cana-1315	9	19	beneficial	beneficial	ADJ
cana-1315	9	20	.	.	PUNCT
cana-1315	10	1	if	if	SCONJ
cana-1315	10	2	both	both	PRON
cana-1315	10	3	(	(	PUNCT
cana-1315	10	4	t	t	PROPN
cana-1315	10	5	,	,	PUNCT
cana-1315	10	6	+	+	NOUN
cana-1315	10	7	)	)	PUNCT
cana-1315	10	8	and	and	CCONJ
cana-1315	10	9	(	(	PUNCT
cana-1315	10	10	t	t	PROPN
cana-1315	10	11	,	,	PUNCT
cana-1315	10	12	.	.	PUNCT
cana-1315	10	13	)	)	PUNCT
cana-1315	10	14	are	be	AUX
cana-1315	10	15	commutative	commutative	ADJ
cana-1315	10	16	semi	semi	ADJ
cana-1315	10	17	-	-	NOUN
cana-1315	10	18	groups	group	NOUN
cana-1315	10	19	with	with	ADP
cana-1315	10	20	+	+	CCONJ
cana-1315	10	21	being	be	AUX
cana-1315	10	22	a	a	DET
cana-1315	10	23	binary	binary	ADJ
cana-1315	10	24	operation	operation	NOUN
cana-1315	10	25	and	and	CCONJ
cana-1315	10	26	.	.	PUNCT
cana-1315	11	1	being	be	AUX
cana-1315	11	2	a	a	DET
cana-1315	11	3	ternary	ternary	ADJ
cana-1315	11	4	multiplication	multiplication	NOUN
cana-1315	11	5	fulfilling	fulfil	VERB
cana-1315	11	6	a(b+c)d	a(b+c)d	NOUN
cana-1315	11	7	=	=	SYM
cana-1315	11	8	abd+acd	abd+acd	PROPN
cana-1315	11	9	,	,	PUNCT
cana-1315	11	10	ab(c	ab(c	PUNCT
cana-1315	11	11	+	+	NUM
cana-1315	11	12	d)=	d)=	NOUN
cana-1315	11	13	abc	abc	PROPN
cana-1315	11	14	+	+	CCONJ
cana-1315	11	15	abd	abd	PROPN
cana-1315	11	16	,	,	PUNCT
cana-1315	11	17	(	(	PUNCT
cana-1315	11	18	a+b)cd	a+b)cd	NOUN
cana-1315	11	19	=	=	SYM
cana-1315	11	20	abd	abd	PROPN
cana-1315	11	21	+	+	CCONJ
cana-1315	11	22	bcd,	bcd,	PROPN
cana-1315	11	23	a	a	DET
cana-1315	11	24	,	,	PUNCT
cana-1315	11	25	b	b	NOUN
cana-1315	11	26	,	,	PUNCT
cana-1315	11	27	c	c	NOUN
cana-1315	11	28	,	,	PUNCT
cana-1315	11	29	d	d	PROPN
cana-1315	11	30	t	t	PROPN
cana-1315	11	31	,	,	PUNCT
cana-1315	11	32	then	then	ADV
cana-1315	11	33	an	an	DET
cana-1315	11	34	algebra	algebra	NOUN
cana-1315	11	35	(	(	PUNCT
cana-1315	11	36	t	t	PROPN
cana-1315	11	37	,	,	PUNCT
cana-1315	11	38	+	+	NOUN
cana-1315	11	39	,	,	PUNCT
cana-1315	11	40	.	.	PUNCT
cana-1315	11	41	)	)	PUNCT
cana-1315	11	42	is	be	AUX
cana-1315	11	43	considered	consider	VERB
cana-1315	11	44	a	a	DET
cana-1315	11	45	ter.semi	ter.semi	NOUN
cana-1315	11	46	-	-	PUNCT
cana-1315	11	47	ring	ring	NOUN
cana-1315	11	48	.	.	PUNCT
cana-1315	12	1	elaborately	elaborately	ADV
cana-1315	12	2	ternary	ternary	ADJ
cana-1315	12	3	semi	semi	ADJ
cana-1315	12	4	-	-	ADJ
cana-1315	12	5	ring	ring	NOUN
cana-1315	12	6	was	be	AUX
cana-1315	12	7	researched	research	VERB
cana-1315	12	8	by	by	ADP
cana-1315	12	9	g.	g.	PROPN
cana-1315	12	10	srinivasa	srinivasa	PROPN
cana-1315	12	11	rao	rao	PROPN
cana-1315	12	12	et	et	PROPN
cana-1315	12	13	al	al	PROPN
cana-1315	12	14	.	.	PUNCT
cana-1315	13	1	[	[	X
cana-1315	13	2	10–14	10–14	NUM
cana-1315	13	3	]	]	PUNCT
cana-1315	13	4	.	.	PUNCT
cana-1315	14	1	this	this	DET
cana-1315	14	2	paper	paper	NOUN
cana-1315	14	3	delves	delve	VERB
cana-1315	14	4	into	into	ADP
cana-1315	14	5	a	a	DET
cana-1315	14	6	few	few	ADJ
cana-1315	14	7	theorems	theorem	NOUN
cana-1315	14	8	related	relate	VERB
cana-1315	14	9	to	to	ADP
cana-1315	14	10	the	the	DET
cana-1315	14	11	anti	anti	ADJ
cana-1315	14	12	-	-	ADJ
cana-1315	14	13	fuzzy	fuzzy	ADJ
cana-1315	14	14	ter.sub	ter.sub	NUM
cana-1315	14	15	-	-	PUNCT
cana-1315	14	16	semi	semi	NOUN
cana-1315	14	17	-	-	NOUN
cana-1315	14	18	ring	ring	NOUN
cana-1315	14	19	of	of	ADP
cana-1315	14	20	a	a	DET
cana-1315	14	21	semi	semi	NOUN
cana-1315	14	22	-	-	NOUN
cana-1315	14	23	ring	ring	NOUN
cana-1315	14	24	.	.	PUNCT
cana-1315	15	1	2	2	X
cana-1315	15	2	.	.	X
cana-1315	15	3	preliminaries	preliminary	NOUN
cana-1315	15	4	def.2.1	def.2.1	PROPN
cana-1315	15	5	:	:	PUNCT
cana-1315	15	6	let	let	VERB
cana-1315	15	7	p	p	PRON
cana-1315	15	8	.	.	PUNCT
cana-1315	16	1	a	a	DET
cana-1315	16	2	fuzzy	fuzzy	ADJ
cana-1315	16	3	subset	subset	NOUN
cana-1315	16	4			NOUN
cana-1315	16	5	of	of	ADP
cana-1315	16	6	p	p	PROPN
cana-1315	16	7	is	be	AUX
cana-1315	16	8	a	a	DET
cana-1315	16	9	mapping	mapping	NOUN
cana-1315	16	10			NOUN
cana-1315	16	11	:	:	PUNCT
cana-1315	17	1	p	p	X
cana-1315	17	2	→	→	SYM
cana-1315	17	3	[	[	X
cana-1315	17	4	0	0	NUM
cana-1315	17	5	,	,	PUNCT
cana-1315	17	6	1	1	NUM
cana-1315	17	7	]	]	PUNCT
cana-1315	17	8	.	.	PUNCT
cana-1315	18	1	def.2.2	def.2.2	AUX
cana-1315	18	2	:	:	PUNCT
cana-1315	18	3	let	let	VERB
cana-1315	18	4	t	t	NOUN
cana-1315	18	5	be	be	AUX
cana-1315	18	6	a	a	DET
cana-1315	18	7	ter.semi	ter.semi	NOUN
cana-1315	18	8	-	-	PUNCT
cana-1315	18	9	ring	ring	NOUN
cana-1315	18	10	.	.	PUNCT
cana-1315	19	1	a	a	DET
cana-1315	19	2	fuzzy	fuzzy	ADJ
cana-1315	19	3	subset	subset	NOUN
cana-1315	19	4	s	s	PROPN
cana-1315	19	5	of	of	ADP
cana-1315	19	6	t	t	PROPN
cana-1315	19	7	is	be	AUX
cana-1315	19	8	said	say	VERB
cana-1315	19	9	to	to	PART
cana-1315	19	10	be	be	AUX
cana-1315	19	11	a	a	DET
cana-1315	19	12	fuzzy	fuzzy	ADJ
cana-1315	19	13	ter.sub	ter.sub	NUM
cana-1315	19	14	-	-	PUNCT
cana-1315	19	15	semi	semi	NOUN
cana-1315	19	16	-	-	ADJ
cana-1315	19	17	ring	ring	ADJ
cana-1315	19	18	(	(	PUNCT
cana-1315	19	19	ftssr	ftssr	ADJ
cana-1315	19	20	)	)	PUNCT
cana-1315	19	21	of	of	ADP
cana-1315	19	22	t	t	PROPN
cana-1315	19	23	if	if	SCONJ
cana-1315	19	24	(	(	PUNCT
cana-1315	19	25	i	i	NOUN
cana-1315	19	26	)	)	PUNCT
cana-1315	19	27	s	s	NOUN
cana-1315	19	28	(	(	PUNCT
cana-1315	19	29	a	a	DET
cana-1315	19	30	+	+	NUM
cana-1315	19	31	b	b	NOUN
cana-1315	19	32	)	)	PUNCT
cana-1315	19	33	≥	≥	NOUN
cana-1315	19	34	min	min	PROPN
cana-1315	19	35	{	{	PUNCT
cana-1315	19	36	s	s	NOUN
cana-1315	19	37	(	(	PUNCT
cana-1315	19	38	a	a	NOUN
cana-1315	19	39	)	)	PUNCT
cana-1315	19	40	,	,	PUNCT
cana-1315	19	41	s	s	INTJ
cana-1315	19	42	(	(	PUNCT
cana-1315	19	43	b)},(ii	b)},(ii	NOUN
cana-1315	19	44	)	)	PUNCT
cana-1315	19	45	s	s	NOUN
cana-1315	19	46	(	(	PUNCT
cana-1315	19	47	abc	abc	PROPN
cana-1315	19	48	)	)	PUNCT
cana-1315	19	49	≥	≥	PROPN
cana-1315	19	50	min	min	PROPN
cana-1315	19	51	{	{	PUNCT
cana-1315	19	52	s	s	NOUN
cana-1315	19	53	(	(	PUNCT
cana-1315	19	54	a	a	NOUN
cana-1315	19	55	)	)	PUNCT
cana-1315	19	56	,	,	PUNCT
cana-1315	19	57	s	s	NOUN
cana-1315	19	58	(	(	PUNCT
cana-1315	19	59	b	b	NOUN
cana-1315	19	60	)	)	PUNCT
cana-1315	19	61	,	,	PUNCT
cana-1315	19	62	s	s	INTJ
cana-1315	19	63	(	(	PUNCT
cana-1315	19	64	c	c	NOUN
cana-1315	19	65	)	)	PUNCT
cana-1315	19	66	}	}	PUNCT
cana-1315	19	67	,	,	PUNCT
cana-1315	19	68			NOUN
cana-1315	19	69	a	a	PRON
cana-1315	19	70	,	,	PUNCT
cana-1315	19	71	b	b	NOUN
cana-1315	19	72	,	,	PUNCT
cana-1315	19	73	ct	ct	PROPN
cana-1315	19	74	.	.	PUNCT
cana-1315	20	1	ex.:2.3	ex.:2.3	PROPN
cana-1315	20	2	:	:	PUNCT
cana-1315	20	3	let	let	VERB
cana-1315	20	4	z	z	PRON
cana-1315	20	5	be	be	AUX
cana-1315	20	6	a	a	DET
cana-1315	20	7	ring	ring	NOUN
cana-1315	20	8	of	of	ADP
cana-1315	20	9	integers	integer	NOUN
cana-1315	20	10	and	and	CCONJ
cana-1315	20	11	s	s	NOUN
cana-1315	20	12	=	=	PUNCT
cana-1315	20	13	(	(	PUNCT
cana-1315	20	14	z\n	z\n	NUM
cana-1315	20	15	)	)	PUNCT
cana-1315	20	16	z	z	NOUN
cana-1315	20	17	,	,	PUNCT
cana-1315	20	18	set	set	VERB
cana-1315	20	19	of	of	ADP
cana-1315	20	20	all	all	DET
cana-1315	20	21	negative	negative	ADJ
cana-1315	20	22	integers	integer	NOUN
cana-1315	20	23	with	with	ADP
cana-1315	20	24	zero	zero	NUM
cana-1315	20	25	.	.	PUNCT
cana-1315	21	1	then	then	ADV
cana-1315	21	2	(	(	PUNCT
cana-1315	21	3	z\n	z\n	NUM
cana-1315	21	4	,	,	PUNCT
cana-1315	21	5	+	+	NOUN
cana-1315	21	6	,	,	PUNCT
cana-1315	21	7	.	.	PUNCT
cana-1315	21	8	)	)	PUNCT
cana-1315	21	9	forms	form	VERB
cana-1315	21	10	a	a	DET
cana-1315	21	11	ternary	ternary	ADJ
cana-1315	21	12	semi	semi	ADJ
cana-1315	21	13	-	-	NOUN
cana-1315	21	14	ring	ring	ADJ
cana-1315	21	15	s	s	NOUN
cana-1315	21	16	with	with	ADP
cana-1315	21	17	zero	zero	NUM
cana-1315	21	18	with	with	ADP
cana-1315	21	19	respect	respect	NOUN
cana-1315	21	20	to	to	ADP
cana-1315	21	21	binary	binary	ADJ
cana-1315	21	22	addition	addition	NOUN
cana-1315	21	23	and	and	CCONJ
cana-1315	21	24	ternary	ternary	ADJ
cana-1315	21	25	multiplication	multiplication	NOUN
cana-1315	21	26	.	.	PUNCT
cana-1315	22	1	define	define	VERB
cana-1315	22	2	a	a	DET
cana-1315	22	3	fuzzy	fuzzy	ADJ
cana-1315	22	4	subset	subset	NOUN
cana-1315	22	5	a	a	X
cana-1315	22	6	:	:	PUNCT
cana-1315	22	7	z	z	NOUN
cana-1315	23	1	[	[	X
cana-1315	23	2	0	0	NUM
cana-1315	23	3	,	,	PUNCT
cana-1315	23	4	1	1	NUM
cana-1315	23	5	]	]	PUNCT
cana-1315	23	6	,	,	PUNCT
cana-1315	23	7	we	we	PRON
cana-1315	23	8	have	have	VERB
cana-1315	23	9	a	a	DET
cana-1315	23	10	(	(	PUNCT
cana-1315	23	11	x	x	NOUN
cana-1315	23	12	)	)	PUNCT
cana-1315	23	13	=	=	SYM
cana-1315	23	14	{	{	PUNCT
cana-1315	23	15	communications	communication	NOUN
cana-1315	23	16	on	on	ADP
cana-1315	23	17	applied	apply	VERB
cana-1315	23	18	nonlinear	nonlinear	ADJ
cana-1315	23	19	analysis	analysis	NOUN
cana-1315	23	20	issn	issn	NOUN
cana-1315	23	21	:	:	PUNCT
cana-1315	23	22	1074	1074	NUM
cana-1315	23	23	-	-	PUNCT
cana-1315	23	24	133x	133x	NUM
cana-1315	23	25	vol	vol	NOUN
cana-1315	23	26	31	31	NUM
cana-1315	23	27	no	no	NOUN
cana-1315	23	28	.	.	PUNCT
cana-1315	24	1	7s	7	NOUN
cana-1315	24	2	(	(	PUNCT
cana-1315	24	3	2024	2024	NUM
cana-1315	24	4	)	)	PUNCT
cana-1315	24	5	358	358	NUM
cana-1315	24	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1315	24	7	then	then	ADV
cana-1315	24	8	a(x	a(x	NOUN
cana-1315	24	9	)	)	PUNCT
cana-1315	24	10	is	be	AUX
cana-1315	24	11	a	a	DET
cana-1315	24	12	fuzzy	fuzzy	ADJ
cana-1315	24	13	ternary	ternary	ADJ
cana-1315	24	14	sub	sub	ADJ
cana-1315	24	15	-	-	ADJ
cana-1315	24	16	semi	semi	ADJ
cana-1315	24	17	-	-	NOUN
cana-1315	24	18	ring	ring	NOUN
cana-1315	24	19	of	of	ADP
cana-1315	24	20	s.	s.	PROPN
cana-1315	24	21	ex.2.4	ex.2.4	PROPN
cana-1315	24	22	:	:	PUNCT
cana-1315	24	23	consider	consider	VERB
cana-1315	24	24	the	the	DET
cana-1315	24	25	set	set	NOUN
cana-1315	24	26	of	of	ADP
cana-1315	24	27	integers	integer	NOUN
cana-1315	24	28	modulo	modulo	VERB
cana-1315	24	29	5	5	NUM
cana-1315	24	30	,	,	PUNCT
cana-1315	24	31	non	non	ADJ
cana-1315	24	32	-	-	ADJ
cana-1315	24	33	positive	positive	ADJ
cana-1315	24	34	integers	integer	NOUN
cana-1315	24	35	=	=	SYM
cana-1315	24	36	{	{	PUNCT
cana-1315	24	37	0	0	NUM
cana-1315	24	38	,	,	PUNCT
cana-1315	24	39	-1	-1	PRON
cana-1315	24	40	,	,	PUNCT
cana-1315	24	41	-2	-2	INTJ
cana-1315	24	42	,	,	PUNCT
cana-1315	24	43	-3	-3	PUNCT
cana-1315	24	44	,	,	PUNCT
cana-1315	24	45	-4}under	-4}under	PUNCT
cana-1315	24	46	the	the	DET
cana-1315	24	47	usual	usual	ADJ
cana-1315	24	48	addition	addition	NOUN
cana-1315	24	49	and	and	CCONJ
cana-1315	24	50	ternary	ternary	ADJ
cana-1315	24	51	multiplication	multiplication	NOUN
cana-1315	24	52	,	,	PUNCT
cana-1315	24	53	we	we	PRON
cana-1315	24	54	have	have	AUX
cana-1315	24	55	clearly	clearly	ADV
cana-1315	24	56	(	(	PUNCT
cana-1315	24	57	,	,	PUNCT
cana-1315	24	58	+	+	PROPN
cana-1315	24	59	,	,	PUNCT
cana-1315	24	60	.	.	PUNCT
cana-1315	24	61	)	)	PUNCT
cana-1315	24	62	is	be	AUX
cana-1315	24	63	a	a	DET
cana-1315	24	64	ternary	ternary	ADJ
cana-1315	24	65	semi	semi	ADJ
cana-1315	24	66	ring	ring	NOUN
cana-1315	24	67	.	.	PUNCT
cana-1315	25	1	let	let	VERB
cana-1315	25	2	a	a	DET
cana-1315	25	3	fuzzy	fuzzy	ADJ
cana-1315	25	4	set	set	NOUN
cana-1315	25	5	:	:	PUNCT
cana-1315	25	6	[	[	X
cana-1315	25	7	0	0	NUM
cana-1315	25	8	,	,	PUNCT
cana-1315	25	9	1	1	NUM
cana-1315	25	10	]	]	PUNCT
cana-1315	25	11	be	be	AUX
cana-1315	25	12	defined	define	VERB
cana-1315	25	13	as	as	ADP
cana-1315	25	14	(	(	PUNCT
cana-1315	25	15	0	0	NUM
cana-1315	25	16	)	)	PUNCT
cana-1315	25	17	=	=	SYM
cana-1315	25	18	1	1	NUM
cana-1315	25	19	,	,	PUNCT
cana-1315	25	20	(	(	PUNCT
cana-1315	25	21	−1	−1	NOUN
cana-1315	25	22	)	)	PUNCT
cana-1315	25	23	=	=	PUNCT
cana-1315	26	1	0.3	0.3	NUM
cana-1315	26	2	,	,	PUNCT
cana-1315	26	3	(	(	PUNCT
cana-1315	26	4	−2	−2	NOUN
cana-1315	26	5	)	)	PUNCT
cana-1315	26	6	=	=	SYM
cana-1315	26	7	1	1	NUM
cana-1315	26	8	,	,	PUNCT
cana-1315	26	9	(	(	PUNCT
cana-1315	26	10	−3	−3	NOUN
cana-1315	26	11	)	)	PUNCT
cana-1315	26	12	=	=	SYM
cana-1315	26	13	0.3	0.3	NUM
cana-1315	26	14	,	,	PUNCT
cana-1315	26	15	(	(	PUNCT
cana-1315	26	16	−4	−4	X
cana-1315	26	17	)	)	PUNCT
cana-1315	26	18	=	=	SYM
cana-1315	26	19	1	1	NUM
cana-1315	26	20	and	and	CCONJ
cana-1315	26	21	(	(	PUNCT
cana-1315	26	22	−5	−5	NOUN
cana-1315	26	23	)	)	PUNCT
cana-1315	26	24	=	=	SYM
cana-1315	26	25	0.3	0.3	NUM
cana-1315	26	26	.	.	PUNCT
cana-1315	27	1	thus	thus	ADV
cana-1315	27	2	(	(	PUNCT
cana-1315	27	3	,	,	PUNCT
cana-1315	27	4	+	+	PROPN
cana-1315	27	5	,	,	PUNCT
cana-1315	27	6	.	.	PUNCT
cana-1315	27	7	,	,	PUNCT
cana-1315	27	8	)	)	PUNCT
cana-1315	27	9	is	be	AUX
cana-1315	27	10	a	a	DET
cana-1315	27	11	fuzzy	fuzzy	ADJ
cana-1315	27	12	ternary	ternary	ADJ
cana-1315	27	13	semi	semi	NOUN
cana-1315	27	14	-	-	ADJ
cana-1315	27	15	ring	ring	ADJ
cana-1315	27	16	.	.	PUNCT
cana-1315	28	1	ex.2.5	ex.2.5	NOUN
cana-1315	28	2	:	:	PUNCT
cana-1315	28	3	let	let	VERB
cana-1315	28	4	r	r	NOUN
cana-1315	28	5	=	=	SYM
cana-1315	28	6	n	n	CCONJ
cana-1315	28	7	,	,	PUNCT
cana-1315	28	8	be	be	AUX
cana-1315	28	9	the	the	DET
cana-1315	28	10	set	set	NOUN
cana-1315	28	11	of	of	ADP
cana-1315	28	12	all	all	PRON
cana-1315	28	13	-	-	PUNCT
cana-1315	28	14	natural	natural	ADJ
cana-1315	28	15	numbers	number	NOUN
cana-1315	28	16	with	with	ADP
cana-1315	28	17	zero	zero	NUM
cana-1315	28	18	and	and	CCONJ
cana-1315	28	19	=	=	SYM
cana-1315	28	20	{	{	PUNCT
cana-1315	28	21	0	0	NUM
cana-1315	28	22	,	,	PUNCT
cana-1315	28	23	1	1	NUM
cana-1315	28	24	}	}	PUNCT
cana-1315	28	25	.	.	PUNCT
cana-1315	29	1	define	define	VERB
cana-1315	29	2	a	a	DET
cana-1315	29	3	mapping	mapping	NOUN
cana-1315	29	4	r	r	NOUN
cana-1315	29	5	×	×	NOUN
cana-1315	29	6	×	×	NOUN
cana-1315	29	7	r	r	NOUN
cana-1315	29	8	×	×	NOUN
cana-1315	29	9	×	×	NOUN
cana-1315	29	10	r	r	NOUN
cana-1315	29	11	r	r	NOUN
cana-1315	29	12	as	as	ADP
cana-1315	29	13	aαbβc	aαbβc	PROPN
cana-1315	29	14	by	by	ADP
cana-1315	29	15	ternary	ternary	ADJ
cana-1315	29	16	multiplication	multiplication	NOUN
cana-1315	29	17	of	of	ADP
cana-1315	29	18	a	a	DET
cana-1315	29	19	,	,	PUNCT
cana-1315	29	20	α	α	PROPN
cana-1315	29	21	,	,	PUNCT
cana-1315	29	22	b	b	PROPN
cana-1315	29	23	,	,	PUNCT
cana-1315	29	24	β	β	X
cana-1315	29	25	,	,	PUNCT
cana-1315	29	26	c	c	NOUN
cana-1315	29	27	for	for	ADP
cana-1315	29	28	all	all	DET
cana-1315	29	29	a	a	DET
cana-1315	29	30	,	,	PUNCT
cana-1315	29	31	b	b	NOUN
cana-1315	29	32	,	,	PUNCT
cana-1315	29	33	c	c	NOUN
cana-1315	29	34	r	r	NOUN
cana-1315	29	35	and	and	CCONJ
cana-1315	29	36	α	α	NOUN
cana-1315	29	37	,	,	PUNCT
cana-1315	29	38	β	β	X
cana-1315	29	39	.	.	PUNCT
cana-1315	30	1	clearly	clearly	ADV
cana-1315	30	2	r	r	NOUN
cana-1315	30	3	is	be	AUX
cana-1315	30	4	a	a	DET
cana-1315	30	5	ternary	ternary	ADJ
cana-1315	30	6	gamma	gamma	NOUN
cana-1315	30	7	semi	semi	ADJ
cana-1315	30	8	-	-	NOUN
cana-1315	30	9	ring	ring	NOUN
cana-1315	30	10	.	.	PUNCT
cana-1315	31	1	define	define	NOUN
cana-1315	31	2	:	:	PUNCT
cana-1315	31	3	r	r	NOUN
cana-1315	32	1	[	[	X
cana-1315	32	2	0	0	NUM
cana-1315	32	3	,	,	PUNCT
cana-1315	32	4	1	1	NUM
cana-1315	32	5	]	]	PUNCT
cana-1315	32	6	as	as	SCONJ
cana-1315	32	7	=	=	PRON
cana-1315	32	8	{	{	PUNCT
cana-1315	32	9	clearly	clearly	ADV
cana-1315	32	10	is	be	AUX
cana-1315	32	11	a	a	DET
cana-1315	32	12	fuzzy	fuzzy	ADJ
cana-1315	32	13	ternary	ternary	ADJ
cana-1315	32	14	gamma	gamma	NOUN
cana-1315	32	15	semi	semi	ADJ
cana-1315	32	16	-	-	ADJ
cana-1315	32	17	ring	ring	NOUN
cana-1315	32	18	.	.	PUNCT
cana-1315	33	1	ex.2.6	ex.2.6	NOUN
cana-1315	33	2	:	:	PUNCT
cana-1315	33	3	let	let	VERB
cana-1315	33	4	r	r	NOUN
cana-1315	33	5	=	=	PUNCT
cana-1315	34	1	[	[	X
cana-1315	34	2	0	0	NUM
cana-1315	34	3	,	,	PUNCT
cana-1315	34	4	1	1	NUM
cana-1315	34	5	]	]	PUNCT
cana-1315	34	6	,	,	PUNCT
cana-1315	34	7	=	=	PUNCT
cana-1315	34	8	n.	n.	NOUN
cana-1315	34	9	define	define	VERB
cana-1315	34	10	+	+	CCONJ
cana-1315	34	11	and	and	CCONJ
cana-1315	34	12	ternary	ternary	ADJ
cana-1315	34	13	multiplication	multiplication	NOUN
cana-1315	34	14	‘	'	PUNCT
cana-1315	34	15	.	.	PUNCT
cana-1315	35	1	‘	'	PUNCT
cana-1315	35	2	defined	define	VERB
cana-1315	35	3	as	as	ADP
cana-1315	35	4	a	a	DET
cana-1315	35	5	+	+	NOUN
cana-1315	35	6	b	b	NOUN
cana-1315	35	7	=	=	SYM
cana-1315	35	8	max	max	PROPN
cana-1315	35	9	{	{	PUNCT
cana-1315	35	10	a	a	PROPN
cana-1315	35	11	,	,	PUNCT
cana-1315	35	12	b	b	NOUN
cana-1315	35	13	}	}	PUNCT
cana-1315	35	14	and	and	CCONJ
cana-1315	35	15	aαbβc	aαbβc	PROPN
cana-1315	35	16	=	=	SYM
cana-1315	35	17	min	min	PROPN
cana-1315	35	18	{	{	PUNCT
cana-1315	35	19	aαbβc	aαbβc	PROPN
cana-1315	35	20	}	}	PUNCT
cana-1315	35	21	def.2.7	def.2.7	PROPN
cana-1315	35	22	:	:	PUNCT
cana-1315	35	23	let	let	VERB
cana-1315	35	24	t	t	NOUN
cana-1315	35	25	be	be	AUX
cana-1315	35	26	a	a	DET
cana-1315	35	27	ter.semi	ter.semi	NOUN
cana-1315	35	28	-	-	PUNCT
cana-1315	35	29	ring	ring	NOUN
cana-1315	35	30	.	.	PUNCT
cana-1315	36	1	a	a	DET
cana-1315	36	2	fuzzy	fuzzy	ADJ
cana-1315	36	3	subset	subset	NOUN
cana-1315	36	4	s	s	PROPN
cana-1315	36	5	of	of	ADP
cana-1315	36	6	t	t	PROPN
cana-1315	36	7	is	be	AUX
cana-1315	36	8	said	say	VERB
cana-1315	36	9	to	to	PART
cana-1315	36	10	be	be	AUX
cana-1315	36	11	an	an	DET
cana-1315	36	12	anti	anti	ADJ
cana-1315	36	13	-	-	ADJ
cana-1315	36	14	fuzzy	fuzzy	ADJ
cana-1315	36	15	ter.sub	ter.sub	NUM
cana-1315	36	16	-	-	PUNCT
cana-1315	36	17	semi	semi	NOUN
cana-1315	36	18	-	-	NOUN
cana-1315	36	19	ring	ring	ADJ
cana-1315	36	20	(	(	PUNCT
cana-1315	36	21	afssr	afssr	NOUN
cana-1315	36	22	)	)	PUNCT
cana-1315	36	23	of	of	ADP
cana-1315	36	24	t	t	PROPN
cana-1315	36	25	when	when	SCONJ
cana-1315	36	26	(	(	PUNCT
cana-1315	36	27	i	i	NOUN
cana-1315	36	28	)	)	PUNCT
cana-1315	36	29	s	s	NOUN
cana-1315	36	30	(	(	PUNCT
cana-1315	36	31	a	a	DET
cana-1315	36	32	+	+	NUM
cana-1315	36	33	b	b	NOUN
cana-1315	36	34	)	)	PUNCT
cana-1315	36	35	≤	≤	NUM
cana-1315	36	36	max	max	PROPN
cana-1315	36	37	{	{	PUNCT
cana-1315	36	38	s	s	NOUN
cana-1315	36	39	(	(	PUNCT
cana-1315	36	40	a	a	NOUN
cana-1315	36	41	)	)	PUNCT
cana-1315	36	42	,	,	PUNCT
cana-1315	36	43	s	s	INTJ
cana-1315	36	44	(	(	PUNCT
cana-1315	36	45	b)},(ii	b)},(ii	NOUN
cana-1315	36	46	)	)	PUNCT
cana-1315	36	47	s	s	NOUN
cana-1315	36	48	(	(	PUNCT
cana-1315	36	49	abc	abc	PROPN
cana-1315	36	50	)	)	PUNCT
cana-1315	36	51	≤	≤	NUM
cana-1315	36	52	max	max	PROPN
cana-1315	36	53	{	{	PUNCT
cana-1315	36	54	s	s	NOUN
cana-1315	36	55	(	(	PUNCT
cana-1315	36	56	a	a	NOUN
cana-1315	36	57	)	)	PUNCT
cana-1315	36	58	,	,	PUNCT
cana-1315	36	59	s	s	NOUN
cana-1315	36	60	(	(	PUNCT
cana-1315	36	61	b	b	NOUN
cana-1315	36	62	)	)	PUNCT
cana-1315	36	63	,	,	PUNCT
cana-1315	36	64	s	s	INTJ
cana-1315	36	65	(	(	PUNCT
cana-1315	36	66	c	c	NOUN
cana-1315	36	67	)	)	PUNCT
cana-1315	36	68	}	}	PUNCT
cana-1315	36	69	,	,	PUNCT
cana-1315	36	70			NOUN
cana-1315	36	71	a	a	PRON
cana-1315	36	72	,	,	PUNCT
cana-1315	36	73	b	b	NOUN
cana-1315	36	74	,	,	PUNCT
cana-1315	36	75	ct	ct	PROPN
cana-1315	36	76	.	.	PUNCT
cana-1315	37	1	def.2.8	def.2.8	NOUN
cana-1315	37	2	:	:	PUNCT
cana-1315	37	3	let	let	VERB
cana-1315	37	4	t	t	NOUN
cana-1315	37	5	be	be	AUX
cana-1315	37	6	a	a	DET
cana-1315	37	7	ter.semi	ter.semi	NOUN
cana-1315	37	8	-	-	PUNCT
cana-1315	37	9	ring	ring	NOUN
cana-1315	37	10	.	.	PUNCT
cana-1315	38	1	an	an	DET
cana-1315	38	2	anti	anti	ADJ
cana-1315	38	3	-	-	ADJ
cana-1315	38	4	fuzzy	fuzzy	ADJ
cana-1315	38	5	ter.sub	ter.sub	NUM
cana-1315	38	6	-	-	PUNCT
cana-1315	38	7	semi	semi	NOUN
cana-1315	38	8	-	-	ADJ
cana-1315	38	9	ring	ring	ADJ
cana-1315	38	10	(	(	PUNCT
cana-1315	38	11	aftssr	aftssr	NUM
cana-1315	38	12	)	)	PUNCT
cana-1315	38	13	s	s	PROPN
cana-1315	38	14	of	of	ADP
cana-1315	38	15	t	t	PROPN
cana-1315	38	16	is	be	AUX
cana-1315	38	17	said	say	VERB
cana-1315	38	18	to	to	PART
cana-1315	38	19	be	be	AUX
cana-1315	38	20	an	an	DET
cana-1315	38	21	anti	anti	ADJ
cana-1315	38	22	-	-	ADJ
cana-1315	38	23	fuzzy	fuzzy	ADJ
cana-1315	38	24	normal	normal	ADJ
cana-1315	38	25	ter.sub	ter.sub	NUM
cana-1315	38	26	-	-	PUNCT
cana-1315	38	27	semi	semi	NOUN
cana-1315	38	28	-	-	ADJ
cana-1315	38	29	ring	ring	ADJ
cana-1315	38	30	(	(	PUNCT
cana-1315	38	31	afnssr	afnssr	NOUN
cana-1315	38	32	)	)	PUNCT
cana-1315	38	33	of	of	ADP
cana-1315	38	34	t	t	PROPN
cana-1315	38	35	if	if	SCONJ
cana-1315	38	36	it	it	PRON
cana-1315	38	37	satisfies	satisfy	VERB
cana-1315	38	38	the	the	DET
cana-1315	38	39	following	follow	VERB
cana-1315	38	40	conditions	condition	NOUN
cana-1315	38	41	:	:	PUNCT
cana-1315	38	42	(	(	PUNCT
cana-1315	38	43	i	i	NOUN
cana-1315	38	44	)	)	PUNCT
cana-1315	38	45	s	s	NOUN
cana-1315	38	46	(	(	PUNCT
cana-1315	38	47	a	a	DET
cana-1315	38	48	+	+	NOUN
cana-1315	38	49	b	b	NOUN
cana-1315	38	50	)	)	PUNCT
cana-1315	38	51	=	=	SYM
cana-1315	38	52	s	s	NOUN
cana-1315	38	53	(	(	PUNCT
cana-1315	38	54	b+a	b+a	PROPN
cana-1315	38	55	)	)	PUNCT
cana-1315	38	56	,	,	PUNCT
cana-1315	38	57	(	(	PUNCT
cana-1315	38	58	ii	ii	NOUN
cana-1315	38	59	)	)	PUNCT
cana-1315	38	60	s	s	NOUN
cana-1315	38	61	(	(	PUNCT
cana-1315	38	62	abc	abc	PROPN
cana-1315	38	63	)	)	PUNCT
cana-1315	39	1	=	=	SYM
cana-1315	39	2	s	s	NOUN
cana-1315	39	3	(	(	PUNCT
cana-1315	39	4	cba	cba	PROPN
cana-1315	39	5	)	)	PUNCT
cana-1315	39	6	,	,	PUNCT
cana-1315	39	7			VERB
cana-1315	39	8	a	a	PRON
cana-1315	39	9	,	,	PUNCT
cana-1315	39	10	b	b	NOUN
cana-1315	39	11	,	,	PUNCT
cana-1315	39	12	ct	ct	PROPN
cana-1315	39	13	.	.	PUNCT
cana-1315	40	1	def.2.9	def.2.9	NOUN
cana-1315	40	2	:	:	PUNCT
cana-1315	40	3	let	let	VERB
cana-1315	40	4	(	(	PUNCT
cana-1315	40	5	t	t	PROPN
cana-1315	40	6	,	,	PUNCT
cana-1315	40	7	+	+	PROPN
cana-1315	40	8	,	,	PUNCT
cana-1315	40	9	.	.	PUNCT
cana-1315	40	10	)	)	PUNCT
cana-1315	41	1	and	and	CCONJ
cana-1315	41	2	(	(	PUNCT
cana-1315	41	3	t1	t1	NOUN
cana-1315	41	4	,	,	PUNCT
cana-1315	41	5	+	+	ADJ
cana-1315	41	6	,	,	PUNCT
cana-1315	41	7	.	.	PUNCT
cana-1315	41	8	)	)	PUNCT
cana-1315	41	9	be	be	AUX
cana-1315	41	10	any	any	DET
cana-1315	41	11	two	two	NUM
cana-1315	41	12	ter.semi	ter.semi	NUM
cana-1315	41	13	-	-	PUNCT
cana-1315	41	14	rings(tsr	rings(tsr	NOUN
cana-1315	41	15	)	)	PUNCT
cana-1315	41	16	.	.	PUNCT
cana-1315	42	1	let	let	VERB
cana-1315	42	2	h	h	NOUN
cana-1315	42	3	:	:	PUNCT
cana-1315	42	4	t	t	PROPN
cana-1315	42	5	→t1	→t1	NOUN
cana-1315	42	6	be	be	AUX
cana-1315	42	7	any	any	DET
cana-1315	42	8	function	function	NOUN
cana-1315	42	9	and	and	CCONJ
cana-1315	42	10	p	p	NOUN
cana-1315	42	11	be	be	AUX
cana-1315	42	12	an	an	DET
cana-1315	42	13	aftssr	aftssr	NOUN
cana-1315	42	14	in	in	ADP
cana-1315	42	15	t	t	PROPN
cana-1315	42	16	,	,	PUNCT
cana-1315	42	17	u	u	PRON
cana-1315	42	18	be	be	VERB
cana-1315	42	19	an	an	DET
cana-1315	42	20	aftssr	aftssr	NOUN
cana-1315	42	21	in	in	ADP
cana-1315	42	22	h(t	h(t	NUM
cana-1315	42	23	)	)	PUNCT
cana-1315	43	1	=	=	SYM
cana-1315	43	2	t1	t1	NOUN
cana-1315	43	3	,	,	PUNCT
cana-1315	43	4	defined	define	VERB
cana-1315	43	5	by	by	ADP
cana-1315	43	6	u	u	INTJ
cana-1315	43	7	(	(	PUNCT
cana-1315	43	8	b	b	NOUN
cana-1315	43	9	)	)	PUNCT
cana-1315	43	10	=	=	SYM
cana-1315	43	11			NOUN
cana-1315	43	12			SYM
cana-1315	43	13			PROPN
cana-1315	43	14	au	au	X
cana-1315	43	15	bha	bha	PROPN
cana-1315	43	16			PROPN
cana-1315	43	17	1	1	NUM
cana-1315	43	18	inf	inf	PROPN
cana-1315	43	19			PROPN
cana-1315	43	20	,	,	PUNCT
cana-1315	43	21	for	for	ADP
cana-1315	43	22	all	all	DET
cana-1315	43	23	a	a	PRON
cana-1315	43	24	in	in	ADP
cana-1315	43	25	t	t	PROPN
cana-1315	43	26	and	and	CCONJ
cana-1315	43	27	b	b	PROPN
cana-1315	43	28	in	in	ADP
cana-1315	43	29	t1	t1	PROPN
cana-1315	43	30	.	.	PUNCT
cana-1315	44	1	then	then	ADV
cana-1315	44	2	p	p	NOUN
cana-1315	44	3	is	be	AUX
cana-1315	44	4	called	call	VERB
cana-1315	44	5	a	a	DET
cana-1315	44	6	pre	pre	NOUN
cana-1315	44	7	-	-	NOUN
cana-1315	44	8	image	image	NOUN
cana-1315	44	9	of	of	ADP
cana-1315	44	10	u	u	NOUN
cana-1315	44	11	with	with	ADP
cana-1315	44	12	respect	respect	NOUN
cana-1315	44	13	to	to	ADP
cana-1315	44	14	h	h	NOUN
cana-1315	44	15	and	and	CCONJ
cana-1315	44	16	is	be	AUX
cana-1315	44	17	denoted	denote	VERB
cana-1315	44	18	by	by	ADP
cana-1315	44	19	h	h	PROPN
cana-1315	44	20	-1	-1	PUNCT
cana-1315	44	21	(	(	PUNCT
cana-1315	44	22	u	u	NOUN
cana-1315	44	23	)	)	PUNCT
cana-1315	44	24	.	.	PUNCT
cana-1315	45	1	def.2.10	def.2.10	ADV
cana-1315	45	2	:	:	PUNCT
cana-1315	45	3	let	let	VERB
cana-1315	45	4	(	(	PUNCT
cana-1315	45	5	t	t	NOUN
cana-1315	45	6	,	,	PUNCT
cana-1315	45	7	+	+	PROPN
cana-1315	45	8	,	,	PUNCT
cana-1315	45	9	.	.	PUNCT
cana-1315	45	10	)	)	PUNCT
cana-1315	46	1	and	and	CCONJ
cana-1315	46	2	(	(	PUNCT
cana-1315	46	3	t1	t1	NOUN
cana-1315	46	4	,	,	PUNCT
cana-1315	46	5	+	+	ADJ
cana-1315	46	6	,	,	PUNCT
cana-1315	46	7	.	.	PUNCT
cana-1315	46	8	)	)	PUNCT
cana-1315	46	9	be	be	AUX
cana-1315	46	10	any	any	DET
cana-1315	46	11	two	two	NUM
cana-1315	46	12	tsrs	tsr	NOUN
cana-1315	46	13	.	.	PUNCT
cana-1315	47	1	a	a	DET
cana-1315	47	2	mapping	mapping	NOUN
cana-1315	47	3	from	from	ADP
cana-1315	47	4	h	h	NOUN
cana-1315	47	5	:	:	PUNCT
cana-1315	47	6	t	t	PROPN
cana-1315	47	7	→t1is	→t1is	PUNCT
cana-1315	47	8	said	say	VERB
cana-1315	47	9	to	to	PART
cana-1315	47	10	be	be	AUX
cana-1315	47	11	a	a	DET
cana-1315	47	12	tsr	tsr	PROPN
cana-1315	47	13	homomorphism	homomorphism	NOUN
cana-1315	47	14	if	if	SCONJ
cana-1315	47	15	h(a	h(a	PROPN
cana-1315	47	16	+	+	PROPN
cana-1315	47	17	b	b	NOUN
cana-1315	47	18	)	)	PUNCT
cana-1315	47	19	=	=	SYM
cana-1315	47	20	h(a	h(a	PROPN
cana-1315	47	21	)	)	PUNCT
cana-1315	47	22	+	+	CCONJ
cana-1315	47	23	h(b	h(b	PROPN
cana-1315	47	24	)	)	PUNCT
cana-1315	47	25	,	,	PUNCT
cana-1315	47	26	h(abc	h(abc	PROPN
cana-1315	47	27	)	)	PUNCT
cana-1315	47	28	=	=	SYM
cana-1315	47	29	h(a	h(a	PROPN
cana-1315	47	30	)	)	PUNCT
cana-1315	47	31	h(b)h(c	h(b)h(c	PROPN
cana-1315	47	32	)	)	PUNCT
cana-1315	47	33	,	,	PUNCT
cana-1315	47	34			VERB
cana-1315	47	35	a	a	DET
cana-1315	47	36	,	,	PUNCT
cana-1315	47	37	b	b	NOUN
cana-1315	47	38	,	,	PUNCT
cana-1315	47	39	ct	ct	NOUN
cana-1315	47	40	.	.	PUNCT
cana-1315	48	1	def.2.11	def.2.11	NOUN
cana-1315	48	2	:	:	PUNCT
cana-1315	48	3	let	let	VERB
cana-1315	48	4	(	(	PUNCT
cana-1315	48	5	t	t	NOUN
cana-1315	48	6	,	,	PUNCT
cana-1315	48	7	+	+	NOUN
cana-1315	48	8	,	,	PUNCT
cana-1315	48	9	.	.	PUNCT
cana-1315	48	10	)	)	PUNCT
cana-1315	49	1	and	and	CCONJ
cana-1315	49	2	(	(	PUNCT
cana-1315	49	3	t1	t1	NOUN
cana-1315	49	4	,	,	PUNCT
cana-1315	49	5	+	+	ADJ
cana-1315	49	6	,	,	PUNCT
cana-1315	49	7	.	.	PUNCT
cana-1315	49	8	)	)	PUNCT
cana-1315	49	9	be	be	AUX
cana-1315	49	10	any	any	DET
cana-1315	49	11	two	two	NUM
cana-1315	49	12	tsrs	tsr	NOUN
cana-1315	49	13	.	.	PUNCT
cana-1315	50	1	a	a	DET
cana-1315	50	2	mapping	mapping	NOUN
cana-1315	50	3	from	from	ADP
cana-1315	50	4	h	h	NOUN
cana-1315	50	5	:	:	PUNCT
cana-1315	50	6	t	t	PROPN
cana-1315	50	7	→t1	→t1	NOUN
cana-1315	50	8	is	be	AUX
cana-1315	50	9	said	say	VERB
cana-1315	50	10	to	to	PART
cana-1315	50	11	be	be	AUX
cana-1315	50	12	a	a	DET
cana-1315	50	13	tsr	tsr	PROPN
cana-1315	50	14	anti	anti	NOUN
cana-1315	50	15	-	-	NOUN
cana-1315	50	16	homomorphism	homomorphism	ADJ
cana-1315	50	17	if	if	SCONJ
cana-1315	50	18	h(a	h(a	PROPN
cana-1315	50	19	+	+	PROPN
cana-1315	50	20	b	b	NOUN
cana-1315	50	21	)	)	PUNCT
cana-1315	50	22	=	=	SYM
cana-1315	50	23	h(a	h(a	PROPN
cana-1315	50	24	)	)	PUNCT
cana-1315	51	1	+	+	CCONJ
cana-1315	51	2	h(b	h(b	PROPN
cana-1315	51	3	)	)	PUNCT
cana-1315	51	4	,	,	PUNCT
cana-1315	51	5	h(abc	h(abc	PROPN
cana-1315	51	6	)	)	PUNCT
cana-1315	51	7	=	=	SYM
cana-1315	51	8	h(c	h(c	PROPN
cana-1315	51	9	)	)	PUNCT
cana-1315	51	10	h(b	h(b	PROPN
cana-1315	51	11	)	)	PUNCT
cana-1315	51	12	h(a	h(a	PROPN
cana-1315	51	13	)	)	PUNCT
cana-1315	51	14	,	,	PUNCT
cana-1315	51	15			VERB
cana-1315	51	16	a	a	DET
cana-1315	51	17	,	,	PUNCT
cana-1315	51	18	b	b	NOUN
cana-1315	51	19	,	,	PUNCT
cana-1315	51	20	c	c	NOUN
cana-1315	51	21	t.	t.	PROPN
cana-1315	52	1	+	+	CCONJ
cana-1315	52	2	0	0	NUM
cana-1315	53	1	-1	-1	NOUN
cana-1315	54	1	-2	-2	INTJ
cana-1315	54	2	-3	-3	INTJ
cana-1315	55	1	-4	-4	INTJ
cana-1315	55	2	0	0	NUM
cana-1315	55	3	0	0	NUM
cana-1315	56	1	-1	-1	NOUN
cana-1315	57	1	-2	-2	INTJ
cana-1315	57	2	-3	-3	INTJ
cana-1315	57	3	-4	-4	INTJ
cana-1315	58	1	-1	-1	INTJ
cana-1315	59	1	-1	-1	INTJ
cana-1315	59	2	-2	-2	INTJ
cana-1315	59	3	-3	-3	INTJ
cana-1315	60	1	-4	-4	INTJ
cana-1315	60	2	0	0	NUM
cana-1315	61	1	-2	-2	INTJ
cana-1315	62	1	-2	-2	INTJ
cana-1315	62	2	-3	-3	INTJ
cana-1315	63	1	-4	-4	INTJ
cana-1315	63	2	0	0	NUM
cana-1315	64	1	-4	-4	INTJ
cana-1315	64	2	-3	-3	INTJ
cana-1315	64	3	-3	-3	INTJ
cana-1315	64	4	-4	-4	INTJ
cana-1315	64	5	0	0	NUM
cana-1315	65	1	-1	-1	INTJ
cana-1315	66	1	-2	-2	INTJ
cana-1315	66	2	-4	-4	INTJ
cana-1315	67	1	-4	-4	INTJ
cana-1315	67	2	0	0	NUM
cana-1315	68	1	-1	-1	INTJ
cana-1315	68	2	-2	-2	INTJ
cana-1315	68	3	-3	-3	INTJ
cana-1315	68	4	.	.	PUNCT
cana-1315	68	5	0	0	PUNCT
cana-1315	69	1	-1	-1	CCONJ
cana-1315	70	1	-2	-2	INTJ
cana-1315	70	2	-3	-3	INTJ
cana-1315	70	3	-4	-4	INTJ
cana-1315	70	4	0	0	NUM
cana-1315	70	5	0	0	NUM
cana-1315	70	6	0	0	NUM
cana-1315	70	7	0	0	NUM
cana-1315	70	8	0	0	NUM
cana-1315	70	9	0	0	NUM
cana-1315	70	10	-1	-1	SYM
cana-1315	70	11	0	0	NUM
cana-1315	70	12	1	1	NUM
cana-1315	70	13	2	2	NUM
cana-1315	70	14	3	3	NUM
cana-1315	70	15	4	4	NUM
cana-1315	70	16	-2	-2	NOUN
cana-1315	70	17	0	0	NUM
cana-1315	70	18	2	2	NUM
cana-1315	70	19	4	4	NUM
cana-1315	70	20	1	1	NUM
cana-1315	70	21	3	3	NUM
cana-1315	70	22	-3	-3	SYM
cana-1315	70	23	0	0	NUM
cana-1315	70	24	3	3	NUM
cana-1315	70	25	1	1	NUM
cana-1315	70	26	4	4	NUM
cana-1315	70	27	2	2	NUM
cana-1315	70	28	-4	-4	SYM
cana-1315	70	29	0	0	NUM
cana-1315	70	30	4	4	NUM
cana-1315	70	31	3	3	NUM
cana-1315	70	32	2	2	NUM
cana-1315	70	33	1	1	NUM
cana-1315	70	34	communications	communication	NOUN
cana-1315	70	35	on	on	ADP
cana-1315	70	36	applied	apply	VERB
cana-1315	70	37	nonlinear	nonlinear	ADJ
cana-1315	70	38	analysis	analysis	NOUN
cana-1315	70	39	issn	issn	NOUN
cana-1315	70	40	:	:	PUNCT
cana-1315	70	41	1074	1074	NUM
cana-1315	70	42	-	-	PUNCT
cana-1315	70	43	133x	133x	NUM
cana-1315	70	44	vol	vol	NOUN
cana-1315	70	45	31	31	NUM
cana-1315	70	46	no	no	NOUN
cana-1315	70	47	.	.	PUNCT
cana-1315	71	1	7s	7	NOUN
cana-1315	71	2	(	(	PUNCT
cana-1315	71	3	2024	2024	NUM
cana-1315	71	4	)	)	PUNCT
cana-1315	71	5	359	359	NUM
cana-1315	72	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1315	72	2	def.2.12	def.2.12	NOUN
cana-1315	72	3	:	:	PUNCT
cana-1315	72	4	let	let	VERB
cana-1315	72	5	(	(	PUNCT
cana-1315	72	6	t	t	NOUN
cana-1315	72	7	,	,	PUNCT
cana-1315	72	8	+	+	NOUN
cana-1315	72	9	,	,	PUNCT
cana-1315	72	10	.	.	PUNCT
cana-1315	72	11	)	)	PUNCT
cana-1315	73	1	and	and	CCONJ
cana-1315	73	2	(	(	PUNCT
cana-1315	73	3	t1	t1	NOUN
cana-1315	73	4	,	,	PUNCT
cana-1315	73	5	+	+	ADJ
cana-1315	73	6	,	,	PUNCT
cana-1315	73	7	.	.	PUNCT
cana-1315	73	8	)	)	PUNCT
cana-1315	73	9	be	be	AUX
cana-1315	73	10	any	any	DET
cana-1315	73	11	two	two	NUM
cana-1315	73	12	tsrs	tsr	NOUN
cana-1315	73	13	.	.	PUNCT
cana-1315	74	1	function	function	VERB
cana-1315	75	1	f	f	NOUN
cana-1315	75	2	:	:	PUNCT
cana-1315	75	3	t	t	PROPN
cana-1315	75	4	→t1	→t1	NOUN
cana-1315	75	5	is	be	AUX
cana-1315	75	6	a	a	DET
cana-1315	75	7	tsr	tsr	PROPN
cana-1315	75	8	isomorphism	isomorphism	NOUN
cana-1315	75	9	,	,	PUNCT
cana-1315	75	10	if	if	SCONJ
cana-1315	75	11	f	f	PROPN
cana-1315	75	12	is	be	AUX
cana-1315	75	13	homomorphism	homomorphism	NOUN
cana-1315	75	14	,	,	PUNCT
cana-1315	75	15	one	one	NUM
cana-1315	75	16	-	-	PUNCT
cana-1315	75	17	to	to	ADP
cana-1315	75	18	-	-	PUNCT
cana-1315	75	19	one	one	NUM
cana-1315	75	20	and	and	CCONJ
cana-1315	75	21	onto	onto	ADP
cana-1315	75	22	.	.	PUNCT
cana-1315	76	1	def.2.13	def.2.13	NOUN
cana-1315	76	2	:	:	PUNCT
cana-1315	76	3	let	let	VERB
cana-1315	76	4	(	(	PUNCT
cana-1315	76	5	t	t	NOUN
cana-1315	76	6	,	,	PUNCT
cana-1315	76	7	+	+	NOUN
cana-1315	76	8	,	,	PUNCT
cana-1315	76	9	.	.	PUNCT
cana-1315	76	10	)	)	PUNCT
cana-1315	77	1	and	and	CCONJ
cana-1315	77	2	(	(	PUNCT
cana-1315	77	3	t1	t1	NOUN
cana-1315	77	4	,	,	PUNCT
cana-1315	77	5	+	+	ADJ
cana-1315	77	6	,	,	PUNCT
cana-1315	77	7	.	.	PUNCT
cana-1315	77	8	)	)	PUNCT
cana-1315	77	9	be	be	AUX
cana-1315	77	10	any	any	DET
cana-1315	77	11	two	two	NUM
cana-1315	77	12	tsrs	tsr	NOUN
cana-1315	77	13	.	.	PUNCT
cana-1315	78	1	then	then	ADV
cana-1315	78	2	the	the	DET
cana-1315	78	3	function	function	NOUN
cana-1315	78	4	f	f	X
cana-1315	78	5	:	:	PUNCT
cana-1315	78	6	t	t	PROPN
cana-1315	78	7	→t1	→t1	NOUN
cana-1315	78	8	is	be	AUX
cana-1315	78	9	a	a	DET
cana-1315	78	10	tsr	tsr	PROPN
cana-1315	78	11	is	be	AUX
cana-1315	78	12	said	say	VERB
cana-1315	78	13	to	to	PART
cana-1315	78	14	be	be	AUX
cana-1315	78	15	a	a	DET
cana-1315	78	16	ter.semi	ter.semi	NOUN
cana-1315	78	17	-	-	PUNCT
cana-1315	78	18	ring	ring	NOUN
cana-1315	78	19	anti	anti	ADJ
cana-1315	78	20	-	-	ADJ
cana-1315	78	21	isomorphism	isomorphism	ADJ
cana-1315	78	22	,	,	PUNCT
cana-1315	78	23	if	if	SCONJ
cana-1315	78	24	f	f	PROPN
cana-1315	78	25	is	be	AUX
cana-1315	78	26	anti	anti	ADJ
cana-1315	78	27	-	-	ADJ
cana-1315	78	28	homomorphism	homomorphism	ADJ
cana-1315	78	29	,	,	PUNCT
cana-1315	78	30	one	one	NUM
cana-1315	78	31	-	-	PUNCT
cana-1315	78	32	to	to	ADP
cana-1315	78	33	-	-	PUNCT
cana-1315	78	34	one	one	NUM
cana-1315	78	35	and	and	CCONJ
cana-1315	78	36	onto	onto	ADP
cana-1315	78	37	.	.	PUNCT
cana-1315	79	1	def.2.14	def.2.14	NOUN
cana-1315	79	2	:	:	PUNCT
cana-1315	79	3	let	let	VERB
cana-1315	79	4	p	p	PRON
cana-1315	79	5	be	be	AUX
cana-1315	79	6	an	an	DET
cana-1315	79	7	aftssr	aftssr	NOUN
cana-1315	79	8	of	of	ADP
cana-1315	79	9	a	a	DET
cana-1315	79	10	ter.semi	ter.semi	NOUN
cana-1315	79	11	-	-	PUNCT
cana-1315	79	12	ring	ring	NOUN
cana-1315	79	13	(	(	PUNCT
cana-1315	79	14	t	t	PROPN
cana-1315	79	15	,	,	PUNCT
cana-1315	79	16	+	+	PROPN
cana-1315	79	17	,	,	PUNCT
cana-1315	79	18	∙	∙	PROPN
cana-1315	79	19	)	)	PUNCT
cana-1315	79	20	and	and	CCONJ
cana-1315	79	21	x	x	X
cana-1315	79	22	in	in	ADP
cana-1315	79	23	t.	t.	PROPN
cana-1315	79	24	then	then	ADV
cana-1315	79	25	the	the	DET
cana-1315	79	26	pseudo	pseudo	NOUN
cana-1315	79	27	anti	anti	ADJ
cana-1315	79	28	-	-	ADJ
cana-1315	79	29	fuzzy	fuzzy	ADJ
cana-1315	79	30	coset	coset	NOUN
cana-1315	79	31	(	(	PUNCT
cana-1315	79	32	xp	xp	INTJ
cana-1315	79	33	)	)	PUNCT
cana-1315	79	34	p	p	NOUN
cana-1315	79	35	is	be	AUX
cana-1315	79	36	defined	define	VERB
cana-1315	79	37	by	by	ADP
cana-1315	79	38	(	(	PUNCT
cana-1315	79	39	(	(	PUNCT
cana-1315	79	40	x	x	X
cana-1315	79	41	p	p	NOUN
cana-1315	79	42	)	)	PUNCT
cana-1315	79	43	p)(u	p)(u	ADJ
cana-1315	79	44	)	)	PUNCT
cana-1315	79	45	=	=	PUNCT
cana-1315	79	46	p(x	p(x	NOUN
cana-1315	79	47	p	p	NOUN
cana-1315	79	48	(	(	PUNCT
cana-1315	79	49	u	u	NOUN
cana-1315	79	50	)	)	PUNCT
cana-1315	79	51	,	,	PUNCT
cana-1315	79	52	for	for	ADP
cana-1315	79	53	every	every	DET
cana-1315	79	54	u	u	NOUN
cana-1315	79	55	in	in	ADP
cana-1315	79	56	t	t	PROPN
cana-1315	79	57	and	and	CCONJ
cana-1315	79	58	for	for	ADP
cana-1315	79	59	some	some	DET
cana-1315	79	60	p	p	NOUN
cana-1315	79	61	in	in	ADP
cana-1315	79	62	p.	p.	NOUN
cana-1315	79	63	3	3	NUM
cana-1315	79	64	.	.	PUNCT
cana-1315	79	65	properties	property	NOUN
cana-1315	79	66	of	of	ADP
cana-1315	79	67	anti	anti	ADJ
cana-1315	79	68	-	-	ADJ
cana-1315	79	69	fuzzy	fuzzy	ADJ
cana-1315	79	70	ternary	ternary	ADJ
cana-1315	79	71	ter.subsemiring	ter.subsemiring	NOUN
cana-1315	79	72	of	of	ADP
cana-1315	79	73	a	a	DET
cana-1315	79	74	ternary	ternary	ADJ
cana-1315	79	75	semiring	semire	VERB
cana-1315	79	76	th.3.1	th.3.1	NOUN
cana-1315	79	77	:	:	PUNCT
cana-1315	79	78	union	union	NOUN
cana-1315	79	79	of	of	ADP
cana-1315	79	80	any	any	DET
cana-1315	79	81	two	two	NUM
cana-1315	79	82	aftssr	aftssr	NOUN
cana-1315	79	83	of	of	ADP
cana-1315	79	84	a	a	DET
cana-1315	79	85	ter.semi	ter.semi	NOUN
cana-1315	79	86	-	-	PUNCT
cana-1315	79	87	ring	ring	NOUN
cana-1315	79	88	t	t	NOUN
cana-1315	79	89	is	be	AUX
cana-1315	79	90	an	an	DET
cana-1315	79	91	aftssr	aftssr	NOUN
cana-1315	79	92	of	of	ADP
cana-1315	79	93	t.	t.	PROPN
cana-1315	79	94	pf	pf	PROPN
cana-1315	79	95	.	.	PUNCT
cana-1315	79	96	:	:	PUNCT
cana-1315	80	1	let	let	VERB
cana-1315	80	2	p	p	NOUN
cana-1315	80	3	and	and	CCONJ
cana-1315	80	4	q	q	NOUN
cana-1315	80	5	be	be	AUX
cana-1315	80	6	any	any	DET
cana-1315	80	7	two	two	NUM
cana-1315	80	8	aftssrs	aftssrs	NOUN
cana-1315	80	9	of	of	ADP
cana-1315	80	10	a	a	DET
cana-1315	80	11	ter.semi	ter.semi	NOUN
cana-1315	80	12	-	-	PUNCT
cana-1315	80	13	ring	ring	NOUN
cana-1315	80	14	t	t	NOUN
cana-1315	80	15	and	and	CCONJ
cana-1315	80	16	p	p	PROPN
cana-1315	80	17	and	and	CCONJ
cana-1315	80	18	q	q	NOUN
cana-1315	80	19	in	in	ADP
cana-1315	80	20	t.	t.	PROPN
cana-1315	80	21	let	let	VERB
cana-1315	80	22	p=	p=	VERB
cana-1315	80	23	{	{	PUNCT
cana-1315	80	24	(	(	PUNCT
cana-1315	80	25	p	p	X
cana-1315	80	26	,	,	PUNCT
cana-1315	80	27	p	p	X
cana-1315	80	28	(	(	PUNCT
cana-1315	80	29	α	α	NOUN
cana-1315	80	30	)	)	PUNCT
cana-1315	80	31	)	)	PUNCT
cana-1315	80	32	/α	/α	PUNCT
cana-1315	81	1	t}and	t}and	CCONJ
cana-1315	81	2	q={(q	q={(q	PROPN
cana-1315	81	3	,	,	PUNCT
cana-1315	81	4	q	q	VERB
cana-1315	81	5	(	(	PUNCT
cana-1315	81	6	α	α	NOUN
cana-1315	81	7	)	)	PUNCT
cana-1315	81	8	)	)	PUNCT
cana-1315	82	1	/αt}and	/αt}and	PUNCT
cana-1315	82	2	also	also	ADV
cana-1315	82	3	let	let	VERB
cana-1315	82	4	u	u	PRON
cana-1315	82	5	=	=	NOUN
cana-1315	82	6	pq	pq	PROPN
cana-1315	82	7	=	=	SYM
cana-1315	82	8	{	{	PUNCT
cana-1315	82	9	(	(	PUNCT
cana-1315	82	10	α	α	PROPN
cana-1315	82	11	,	,	PUNCT
cana-1315	82	12	u	u	INTJ
cana-1315	82	13	(	(	PUNCT
cana-1315	82	14	α	α	NOUN
cana-1315	82	15	)	)	PUNCT
cana-1315	82	16	)	)	PUNCT
cana-1315	82	17	/αt	/αt	PUNCT
cana-1315	82	18	}	}	PUNCT
cana-1315	82	19	,	,	PUNCT
cana-1315	82	20	where	where	SCONJ
cana-1315	82	21	max	max	PROPN
cana-1315	82	22	{	{	PUNCT
cana-1315	82	23	p	p	X
cana-1315	82	24	(	(	PUNCT
cana-1315	82	25	α	α	NOUN
cana-1315	82	26	)	)	PUNCT
cana-1315	82	27	,	,	PUNCT
cana-1315	82	28	q	q	VERB
cana-1315	82	29	(	(	PUNCT
cana-1315	82	30	α	α	NOUN
cana-1315	82	31	)	)	PUNCT
cana-1315	82	32	}	}	PUNCT
cana-1315	82	33	=	=	SYM
cana-1315	82	34	u	u	INTJ
cana-1315	82	35	(	(	PUNCT
cana-1315	82	36	α	α	NOUN
cana-1315	82	37	)	)	PUNCT
cana-1315	82	38	.	.	PUNCT
cana-1315	83	1	now	now	ADV
cana-1315	83	2	,	,	PUNCT
cana-1315	83	3	u	u	INTJ
cana-1315	83	4	(	(	PUNCT
cana-1315	83	5	α	α	NOUN
cana-1315	83	6	+	+	X
cana-1315	83	7	β	β	X
cana-1315	83	8	)	)	PUNCT
cana-1315	83	9	=	=	SYM
cana-1315	83	10	max	max	X
cana-1315	83	11	{	{	PUNCT
cana-1315	83	12	p	p	X
cana-1315	83	13	(	(	PUNCT
cana-1315	83	14	α	α	NOUN
cana-1315	83	15	+	+	X
cana-1315	83	16	β	β	NOUN
cana-1315	83	17	)	)	PUNCT
cana-1315	83	18	,	,	PUNCT
cana-1315	83	19	q	q	VERB
cana-1315	83	20	(	(	PUNCT
cana-1315	83	21	α	α	NOUN
cana-1315	83	22	+	+	X
cana-1315	83	23	β	β	X
cana-1315	83	24	)	)	PUNCT
cana-1315	83	25	}	}	PUNCT
cana-1315	83	26	≤	≤	NUM
cana-1315	83	27	max{max	max{max	X
cana-1315	83	28	{	{	PUNCT
cana-1315	83	29	p	p	X
cana-1315	83	30	(	(	PUNCT
cana-1315	83	31	α	α	NOUN
cana-1315	83	32	)	)	PUNCT
cana-1315	83	33	,	,	PUNCT
cana-1315	83	34	p	p	X
cana-1315	83	35	(	(	PUNCT
cana-1315	83	36	β	β	NOUN
cana-1315	83	37	)	)	PUNCT
cana-1315	83	38	}	}	PUNCT
cana-1315	83	39	,	,	PUNCT
cana-1315	83	40	max	max	PROPN
cana-1315	83	41	{	{	PUNCT
cana-1315	83	42	q	q	PROPN
cana-1315	83	43	(	(	PUNCT
cana-1315	83	44	α	α	NOUN
cana-1315	83	45	)	)	PUNCT
cana-1315	83	46	,	,	PUNCT
cana-1315	83	47	q	q	VERB
cana-1315	83	48	(	(	PUNCT
cana-1315	83	49	β	β	NOUN
cana-1315	83	50	)	)	PUNCT
cana-1315	83	51	}	}	PUNCT
cana-1315	83	52	}	}	PUNCT
cana-1315	83	53	=	=	SYM
cana-1315	83	54	max{max	max{max	X
cana-1315	83	55	{	{	PUNCT
cana-1315	83	56	p	p	X
cana-1315	83	57	(	(	PUNCT
cana-1315	83	58	α	α	NOUN
cana-1315	83	59	)	)	PUNCT
cana-1315	83	60	,	,	PUNCT
cana-1315	83	61	q	q	VERB
cana-1315	83	62	(	(	PUNCT
cana-1315	83	63	α	α	NOUN
cana-1315	83	64	)	)	PUNCT
cana-1315	83	65	}	}	PUNCT
cana-1315	83	66	,	,	PUNCT
cana-1315	83	67	max	max	PROPN
cana-1315	83	68	{	{	PUNCT
cana-1315	83	69	p	p	X
cana-1315	83	70	(	(	PUNCT
cana-1315	83	71	β	β	NOUN
cana-1315	83	72	)	)	PUNCT
cana-1315	83	73	,	,	PUNCT
cana-1315	83	74	q	q	X
cana-1315	83	75	(	(	PUNCT
cana-1315	83	76	β	β	NOUN
cana-1315	83	77	)	)	PUNCT
cana-1315	83	78	}	}	PUNCT
cana-1315	83	79	}	}	PUNCT
cana-1315	83	80	=	=	SYM
cana-1315	83	81	max	max	X
cana-1315	83	82	{	{	PUNCT
cana-1315	83	83	u	u	NOUN
cana-1315	83	84	(	(	PUNCT
cana-1315	83	85	α	α	NOUN
cana-1315	83	86	)	)	PUNCT
cana-1315	83	87	,	,	PUNCT
cana-1315	83	88	u	u	INTJ
cana-1315	83	89	(	(	PUNCT
cana-1315	83	90	β	β	NOUN
cana-1315	83	91	)	)	PUNCT
cana-1315	83	92	}	}	PUNCT
cana-1315	83	93	.	.	PUNCT
cana-1315	84	1	therefore	therefore	ADV
cana-1315	84	2	,	,	PUNCT
cana-1315	84	3	u	u	INTJ
cana-1315	84	4	(	(	PUNCT
cana-1315	84	5	α	α	NOUN
cana-1315	84	6	+	+	X
cana-1315	84	7	β	β	NOUN
cana-1315	84	8	)	)	PUNCT
cana-1315	84	9	≤max	≤max	NUM
cana-1315	84	10	{	{	PUNCT
cana-1315	84	11	u	u	INTJ
cana-1315	84	12	(	(	PUNCT
cana-1315	84	13	α	α	NOUN
cana-1315	84	14	)	)	PUNCT
cana-1315	84	15	,	,	PUNCT
cana-1315	84	16	u	u	INTJ
cana-1315	84	17	(	(	PUNCT
cana-1315	84	18	β	β	NOUN
cana-1315	84	19	)	)	PUNCT
cana-1315	84	20	}	}	PUNCT
cana-1315	84	21	,	,	PUNCT
cana-1315	84	22	.	.	PUNCT
cana-1315	85	1	and	and	CCONJ
cana-1315	85	2	,	,	PUNCT
cana-1315	85	3			PROPN
cana-1315	85	4	u	u	PUNCT
cana-1315	85	5	=	=	SYM
cana-1315	85	6	max	max	X
cana-1315	85	7	{	{	PUNCT
cana-1315	85	8			NOUN
cana-1315	85	9	p	p	PUNCT
cana-1315	85	10	,	,	PUNCT
cana-1315	85	11			NOUN
cana-1315	85	12	q	q	PUNCT
cana-1315	85	13	)	)	PUNCT
cana-1315	85	14	}	}	PUNCT
cana-1315	85	15	≤	≤	NUM
cana-1315	85	16	max{{max	max{{max	NOUN
cana-1315	85	17	p	p	NOUN
cana-1315	85	18	(	(	PUNCT
cana-1315	85	19	α	α	NOUN
cana-1315	85	20	)	)	PUNCT
cana-1315	85	21	,	,	PUNCT
cana-1315	85	22	p	p	X
cana-1315	85	23	(	(	PUNCT
cana-1315	85	24	β	β	NOUN
cana-1315	85	25	)	)	PUNCT
cana-1315	85	26	,	,	PUNCT
cana-1315	85	27			PROPN
cana-1315	85	28			VERB
cana-1315	85	29	p	p	NOUN
cana-1315	85	30	}	}	PUNCT
cana-1315	85	31	,	,	PUNCT
cana-1315	85	32	max{max	max{max	PROPN
cana-1315	85	33	q	q	VERB
cana-1315	85	34	(	(	PUNCT
cana-1315	85	35	α	α	NOUN
cana-1315	85	36	)	)	PUNCT
cana-1315	85	37	,	,	PUNCT
cana-1315	85	38	q	q	VERB
cana-1315	85	39	(	(	PUNCT
cana-1315	85	40	β	β	NOUN
cana-1315	85	41	)	)	PUNCT
cana-1315	85	42	,	,	PUNCT
cana-1315	85	43			NOUN
cana-1315	85	44	q	q	PUNCT
cana-1315	85	45	}	}	PUNCT
cana-1315	85	46	}	}	PUNCT
cana-1315	85	47	=	=	SYM
cana-1315	85	48	max{max	max{max	X
cana-1315	85	49	{	{	PUNCT
cana-1315	85	50	p	p	X
cana-1315	85	51	(	(	PUNCT
cana-1315	85	52	α	α	NOUN
cana-1315	85	53	)	)	PUNCT
cana-1315	85	54	,	,	PUNCT
cana-1315	85	55	q	q	X
cana-1315	85	56	(	(	PUNCT
cana-1315	85	57	α)},max	α)},max	NUM
cana-1315	85	58	{	{	PUNCT
cana-1315	85	59	p	p	X
cana-1315	85	60	(	(	PUNCT
cana-1315	85	61	β	β	NOUN
cana-1315	85	62	)	)	PUNCT
cana-1315	85	63	,	,	PUNCT
cana-1315	85	64	q	q	X
cana-1315	85	65	(	(	PUNCT
cana-1315	85	66	β	β	NOUN
cana-1315	85	67	)	)	PUNCT
cana-1315	85	68	}	}	PUNCT
cana-1315	85	69	,	,	PUNCT
cana-1315	85	70	max	max	PROPN
cana-1315	85	71	{	{	PUNCT
cana-1315	85	72	p	p	X
cana-1315	85	73	(	(	PUNCT
cana-1315	85	74	γ	γ	NOUN
cana-1315	85	75	)	)	PUNCT
cana-1315	85	76	,	,	PUNCT
cana-1315	85	77	q	q	VERB
cana-1315	85	78	(	(	PUNCT
cana-1315	85	79	γ)}}=	γ)}}=	PROPN
cana-1315	85	80	max	max	PROPN
cana-1315	85	81	{	{	PUNCT
cana-1315	85	82	u	u	NOUN
cana-1315	85	83	(	(	PUNCT
cana-1315	85	84	α	α	NOUN
cana-1315	85	85	)	)	PUNCT
cana-1315	85	86	,	,	PUNCT
cana-1315	85	87	u	u	INTJ
cana-1315	85	88	(	(	PUNCT
cana-1315	85	89	β	β	NOUN
cana-1315	85	90	)	)	PUNCT
cana-1315	85	91	,	,	PUNCT
cana-1315	85	92	u	u	INTJ
cana-1315	85	93	(	(	PUNCT
cana-1315	85	94	γ	γ	NOUN
cana-1315	85	95	)	)	PUNCT
cana-1315	85	96	}	}	PUNCT
cana-1315	85	97	.	.	PUNCT
cana-1315	86	1	therefore	therefore	ADV
cana-1315	86	2	,	,	PUNCT
cana-1315	86	3	u	u	INTJ
cana-1315	86	4	(	(	PUNCT
cana-1315	86	5	αβγ	αβγ	NOUN
cana-1315	86	6	)	)	PUNCT
cana-1315	86	7	≤	≤	NUM
cana-1315	86	8	max	max	PROPN
cana-1315	86	9	{	{	PUNCT
cana-1315	86	10	u	u	INTJ
cana-1315	86	11	(	(	PUNCT
cana-1315	86	12	α	α	NOUN
cana-1315	86	13	)	)	PUNCT
cana-1315	86	14	,	,	PUNCT
cana-1315	86	15	u	u	INTJ
cana-1315	86	16	(	(	PUNCT
cana-1315	86	17	β	β	NOUN
cana-1315	86	18	)	)	PUNCT
cana-1315	86	19	,	,	PUNCT
cana-1315	86	20	u	u	INTJ
cana-1315	86	21	(	(	PUNCT
cana-1315	86	22	γ	γ	NOUN
cana-1315	86	23	)	)	PUNCT
cana-1315	86	24	}	}	PUNCT
cana-1315	86	25	,	,	PUNCT
cana-1315	86	26			NOUN
cana-1315	86	27	α	α	NOUN
cana-1315	86	28	,	,	PUNCT
cana-1315	86	29	β	β	X
cana-1315	86	30	,	,	PUNCT
cana-1315	86	31	γt	γt	PROPN
cana-1315	86	32	.	.	PROPN
cana-1315	86	33	therefore	therefore	ADV
cana-1315	86	34	,	,	PUNCT
cana-1315	86	35	u	u	NOUN
cana-1315	86	36	is	be	AUX
cana-1315	86	37	an	an	DET
cana-1315	86	38	aftssr	aftssr	NOUN
cana-1315	86	39	of	of	ADP
cana-1315	86	40	a	a	DET
cana-1315	86	41	tsrt	tsrt	NOUN
cana-1315	86	42	.	.	PUNCT
cana-1315	87	1	hence	hence	ADV
cana-1315	87	2	the	the	DET
cana-1315	87	3	union	union	NOUN
cana-1315	87	4	of	of	ADP
cana-1315	87	5	any	any	DET
cana-1315	87	6	two	two	NUM
cana-1315	87	7	aftssrs	aftssrs	NOUN
cana-1315	87	8	of	of	ADP
cana-1315	87	9	a	a	DET
cana-1315	87	10	tsrt	tsrt	NOUN
cana-1315	87	11	is	be	AUX
cana-1315	87	12	an	an	DET
cana-1315	87	13	aftssr	aftssr	NOUN
cana-1315	87	14	of	of	ADP
cana-1315	87	15	t.	t.	PROPN
cana-1315	87	16	th.3.2	th.3.2	PROPN
cana-1315	87	17	:	:	PUNCT
cana-1315	87	18	the	the	DET
cana-1315	87	19	arbitrary	arbitrary	ADJ
cana-1315	87	20	union	union	NOUN
cana-1315	87	21	of	of	ADP
cana-1315	87	22	a	a	DET
cana-1315	87	23	family	family	NOUN
cana-1315	87	24	of	of	ADP
cana-1315	87	25	aftssrs	aftssrs	NOUN
cana-1315	87	26	of	of	ADP
cana-1315	87	27	tsrt	tsrt	NOUN
cana-1315	87	28	is	be	AUX
cana-1315	87	29	an	an	DET
cana-1315	87	30	aftssr	aftssr	NOUN
cana-1315	87	31	of	of	ADP
cana-1315	87	32	t.	t.	PROPN
cana-1315	87	33	pf	pf	PROPN
cana-1315	87	34	.	.	PUNCT
cana-1315	87	35	:	:	PUNCT
cana-1315	88	1	let	let	VERB
cana-1315	88	2	{	{	PUNCT
cana-1315	88	3	si	si	X
cana-1315	88	4	:	:	PUNCT
cana-1315	88	5	i	i	PROPN
cana-1315	88	6			NOUN
cana-1315	88	7	}	}	PUNCT
cana-1315	88	8	be	be	AUX
cana-1315	88	9	an	an	DET
cana-1315	88	10	arbitrary	arbitrary	ADJ
cana-1315	88	11	family	family	NOUN
cana-1315	88	12	of	of	ADP
cana-1315	88	13	aftssrs	aftssrs	NOUN
cana-1315	88	14	of	of	ADP
cana-1315	88	15	a	a	DET
cana-1315	88	16	tsrt	tsrt	NOUN
cana-1315	88	17	and	and	CCONJ
cana-1315	88	18	let	let	VERB
cana-1315	88	19	p	p	NOUN
cana-1315	88	20	=	=	PUNCT
cana-1315	89	1			ADJ
cana-1315	89	2	i	i	PROPN
cana-1315	89	3	is	be	AUX
cana-1315	89	4	.	.	PUNCT
cana-1315	90	1	let	let	VERB
cana-1315	90	2	α	α	PRON
cana-1315	90	3	,	,	PUNCT
cana-1315	90	4	β	β	X
cana-1315	90	5	and	and	CCONJ
cana-1315	90	6	γ	γ	X
cana-1315	90	7	in	in	ADP
cana-1315	90	8	t.	t.	PROPN
cana-1315	90	9	then	then	ADV
cana-1315	90	10	,	,	PUNCT
cana-1315	90	11	p	p	X
cana-1315	90	12	(	(	PUNCT
cana-1315	90	13	α	α	NOUN
cana-1315	90	14	+	+	NOUN
cana-1315	90	15	β	β	X
cana-1315	90	16	)	)	PUNCT
cana-1315	90	17	=	=	SYM
cana-1315	90	18			PROPN
cana-1315	90	19			X
cana-1315	90	20			ADJ
cana-1315	90	21			NUM
cana-1315	90	22	is	be	AUX
cana-1315	90	23	i	i	PRON
cana-1315	90	24	sup	sup	NOUN
cana-1315	90	25	≤	≤	ADV
cana-1315	91	1	i	i	PROPN
cana-1315	91	2	sup	sup	NUM
cana-1315	91	3	max	max	PROPN
cana-1315	91	4	{	{	PUNCT
cana-1315	91	5	is	is	X
cana-1315	91	6	(	(	PUNCT
cana-1315	91	7	α	α	NOUN
cana-1315	91	8	)	)	PUNCT
cana-1315	91	9	,	,	PUNCT
cana-1315	91	10	is	is	X
cana-1315	91	11	(	(	PUNCT
cana-1315	91	12	β	β	NOUN
cana-1315	91	13	)	)	PUNCT
cana-1315	91	14	}	}	PUNCT
cana-1315	92	1	=	=	X
cana-1315	92	2	max	max	X
cana-1315	92	3	{	{	PUNCT
cana-1315	92	4	i	i	PROPN
cana-1315	92	5	sup	sup	PROPN
cana-1315	92	6	{	{	PUNCT
cana-1315	92	7			PROPN
cana-1315	92	8			PROPN
cana-1315	92	9	is	be	AUX
cana-1315	92	10	,	,	PUNCT
cana-1315	92	11	i	i	PROPN
cana-1315	92	12	sup	sup	PROPN
cana-1315	92	13	{	{	PUNCT
cana-1315	92	14			NOUN
cana-1315	92	15			NUM
cana-1315	92	16	is	be	AUX
cana-1315	92	17	}	}	PUNCT
cana-1315	92	18	=	=	SYM
cana-1315	92	19	max	max	PROPN
cana-1315	92	20	{	{	PUNCT
cana-1315	92	21			PROPN
cana-1315	92	22			PROPN
cana-1315	92	23	p	p	PROPN
cana-1315	92	24	,	,	PUNCT
cana-1315	92	25			PROPN
cana-1315	92	26			PROPN
cana-1315	92	27	p	p	X
cana-1315	92	28	}	}	PUNCT
cana-1315	92	29	.	.	PUNCT
cana-1315	93	1	therefore	therefore	ADV
cana-1315	93	2	,	,	PUNCT
cana-1315	93	3	p	p	X
cana-1315	93	4	(	(	PUNCT
cana-1315	93	5	α	α	NOUN
cana-1315	93	6	+	+	NOUN
cana-1315	93	7	β	β	NOUN
cana-1315	93	8	)	)	PUNCT
cana-1315	93	9	≤	≤	NUM
cana-1315	93	10	max	max	PROPN
cana-1315	93	11	{	{	PUNCT
cana-1315	93	12			PROPN
cana-1315	93	13			PROPN
cana-1315	93	14	p	p	PROPN
cana-1315	93	15	,	,	PUNCT
cana-1315	93	16			PROPN
cana-1315	93	17			PROPN
cana-1315	93	18	p	p	X
cana-1315	93	19	}	}	PUNCT
cana-1315	93	20	,	,	PUNCT
cana-1315	93	21			NOUN
cana-1315	93	22	α	α	NOUN
cana-1315	93	23	,	,	PUNCT
cana-1315	93	24	β	β	X
cana-1315	93	25	,	,	PUNCT
cana-1315	93	26	γ	γ	NOUN
cana-1315	93	27	t.	t.	PROPN
cana-1315	93	28	and	and	CCONJ
cana-1315	93	29	,	,	PUNCT
cana-1315	93	30			PROPN
cana-1315	93	31	p	p	PUNCT
cana-1315	93	32	=	=	SYM
cana-1315	93	33			NOUN
cana-1315	93	34			ADJ
cana-1315	93	35	is	be	AUX
cana-1315	93	36	i	i	PRON
cana-1315	93	37	sup	sup	NOUN
cana-1315	93	38			PROPN
cana-1315	93	39	≤	≤	ADV
cana-1315	94	1	i	i	PROPN
cana-1315	94	2	sup	sup	NUM
cana-1315	94	3	max	max	PROPN
cana-1315	94	4	{	{	PUNCT
cana-1315	94	5	is	is	X
cana-1315	94	6	(	(	PUNCT
cana-1315	94	7	α	α	NOUN
cana-1315	94	8	)	)	PUNCT
cana-1315	94	9	,	,	PUNCT
cana-1315	94	10	is	is	X
cana-1315	94	11	(	(	PUNCT
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cana-1315	94	14	,	,	PUNCT
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cana-1315	94	16	(	(	PUNCT
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cana-1315	94	18	max	max	PROPN
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cana-1315	94	26	,	,	PUNCT
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cana-1315	94	28	sup	sup	PROPN
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cana-1315	94	30			NOUN
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cana-1315	94	43	=	=	SYM
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cana-1315	94	46			PROPN
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cana-1315	95	51	t1	t1	PROPN
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cana-1315	98	9	,	,	PUNCT
cana-1315	98	10	(	(	PUNCT
cana-1315	98	11	a2	a2	PROPN
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cana-1315	98	15	c2	c2	PROPN
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cana-1315	98	21	b3	b3	PROPN
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cana-1315	98	24	)	)	PUNCT
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cana-1315	99	4	)	)	PUNCT
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cana-1315	100	42			PROPN
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cana-1315	100	45	max{max	max{max	X
cana-1315	100	46	{	{	PUNCT
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cana-1315	100	56	,	,	PUNCT
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cana-1315	100	69	,	,	PUNCT
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cana-1315	100	93	,	,	PUNCT
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cana-1315	100	117	=	=	SYM
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cana-1315	101	2	,	,	PUNCT
cana-1315	101	3			NOUN
cana-1315	101	4			AUX
cana-1315	101	5	321321321	321321321	VERB
cana-1315	101	6	,	,	PUNCT
cana-1315	101	7	,	,	PUNCT
cana-1315	101	8	cccbbbaaarqp	cccbbbaaarqp	NOUN
cana-1315	101	9			VERB
cana-1315	101	10	≤	≤	NUM
cana-1315	101	11	max	max	PROPN
cana-1315	101	12	{	{	PUNCT
cana-1315	101	13			PROPN
cana-1315	101	14	111	111	NOUN
cana-1315	101	15	,	,	PUNCT
cana-1315	101	16	,	,	PUNCT
cana-1315	101	17	cbarqp	cbarqp	NOUN
cana-1315	101	18			ADJ
cana-1315	101	19	,	,	PUNCT
cana-1315	101	20			PROPN
cana-1315	101	21	222	222	NOUN
cana-1315	101	22	,	,	PUNCT
cana-1315	101	23	,	,	PUNCT
cana-1315	101	24	cbarqp	cbarqp	NOUN
cana-1315	101	25			X
cana-1315	101	26	,	,	PUNCT
cana-1315	101	27			PROPN
cana-1315	101	28	333	333	PROPN
cana-1315	101	29	,	,	PUNCT
cana-1315	101	30	,	,	PUNCT
cana-1315	101	31	cbarqp	cbarqp	NOUN
cana-1315	101	32			ADJ
cana-1315	101	33	}	}	PUNCT
cana-1315	101	34	.	.	PUNCT
cana-1315	102	1	also	also	ADV
cana-1315	102	2	,	,	PUNCT
cana-1315	102	3			PROPN
cana-1315	102	4			PROPN
cana-1315	102	5			PROPN
cana-1315	102	6			INTJ
cana-1315	102	7	333222111	333222111	NOUN
cana-1315	102	8	,	,	PUNCT
cana-1315	102	9	,	,	PUNCT
cana-1315	102	10	,	,	PUNCT
cana-1315	102	11	,	,	PUNCT
cana-1315	102	12	,	,	PUNCT
cana-1315	102	13	,	,	PUNCT
cana-1315	102	14	cbacbacbarqp	cbacbacbarqp	NOUN
cana-1315	102	15			NOUN
cana-1315	103	1	=	=	PUNCT
cana-1315	103	2			NOUN
cana-1315	103	3	321321321	321321321	PUNCT
cana-1315	103	4	,	,	PUNCT
cana-1315	103	5	,	,	PUNCT
cana-1315	103	6	cccbbbaaarqp	cccbbbaaarqp	NOUN
cana-1315	103	7			ADJ
cana-1315	103	8	=	=	SYM
cana-1315	103	9	max	max	PROPN
cana-1315	103	10	{	{	PUNCT
cana-1315	103	11			NOUN
cana-1315	103	12	321	321	ADP
cana-1315	104	1	aaap	aaap	PROPN
cana-1315	104	2	,	,	PUNCT
cana-1315	104	3			NOUN
cana-1315	104	4	321	321	ADP
cana-1315	104	5	bbbq	bbbq	NOUN
cana-1315	104	6	,	,	PUNCT
cana-1315	104	7			PROPN
cana-1315	104	8	321	321	ADP
cana-1315	104	9	cccr	cccr	PROPN
cana-1315	104	10	}	}	PUNCT
cana-1315	104	11	≤	≤	NUM
cana-1315	104	12	max{max	max{max	X
cana-1315	104	13	{	{	PUNCT
cana-1315	104	14			PROPN
cana-1315	104	15	1ap	1ap	ADJ
cana-1315	104	16	,	,	PUNCT
cana-1315	104	17			PROPN
cana-1315	104	18	2ap	2ap	PROPN
cana-1315	104	19	,	,	PUNCT
cana-1315	104	20			PROPN
cana-1315	104	21	3ap	3ap	NUM
cana-1315	104	22	}	}	PUNCT
cana-1315	104	23	,	,	PUNCT
cana-1315	104	24	max	max	PROPN
cana-1315	104	25	{	{	PUNCT
cana-1315	104	26			PROPN
cana-1315	104	27	1bq	1bq	NOUN
cana-1315	104	28	,	,	PUNCT
cana-1315	104	29			PROPN
cana-1315	104	30	2bq	2bq	NOUN
cana-1315	104	31	,	,	PUNCT
cana-1315	104	32			NOUN
cana-1315	104	33	3bq	3bq	NOUN
cana-1315	104	34	)	)	PUNCT
cana-1315	104	35	}	}	PUNCT
cana-1315	104	36	,	,	PUNCT
cana-1315	104	37	max	max	PROPN
cana-1315	104	38	{	{	PUNCT
cana-1315	104	39			PROPN
cana-1315	104	40	1cr	1cr	PROPN
cana-1315	104	41	,	,	PUNCT
cana-1315	104	42			PROPN
cana-1315	104	43	2cr	2cr	PROPN
cana-1315	104	44	,	,	PUNCT
cana-1315	104	45			NOUN
cana-1315	104	46	3cr	3cr	PUNCT
cana-1315	104	47	}	}	PUNCT
cana-1315	104	48	}	}	PUNCT
cana-1315	104	49	=	=	SYM
cana-1315	104	50	max{max	max{max	ADJ
cana-1315	104	51	{	{	PUNCT
cana-1315	104	52			PROPN
cana-1315	104	53	1ap	1ap	ADJ
cana-1315	104	54	,	,	PUNCT
cana-1315	104	55			PROPN
cana-1315	104	56	1bq	1bq	NOUN
cana-1315	104	57	,	,	PUNCT
cana-1315	104	58			PROPN
cana-1315	104	59	1cr	1cr	PROPN
cana-1315	104	60	}	}	PUNCT
cana-1315	104	61	,	,	PUNCT
cana-1315	104	62	max	max	PROPN
cana-1315	104	63	{	{	PUNCT
cana-1315	104	64	max	max	PROPN
cana-1315	104	65	{	{	PUNCT
cana-1315	104	66			PROPN
cana-1315	104	67	2ap	2ap	PROPN
cana-1315	104	68	,	,	PUNCT
cana-1315	104	69			PROPN
cana-1315	104	70	2bq	2bq	NOUN
cana-1315	104	71	,	,	PUNCT
cana-1315	104	72			NOUN
cana-1315	104	73	2cr	2cr	PUNCT
cana-1315	104	74	}	}	PUNCT
cana-1315	104	75	,	,	PUNCT
cana-1315	104	76	max	max	PROPN
cana-1315	104	77	{	{	PUNCT
cana-1315	104	78			PROPN
cana-1315	104	79	3ap	3ap	PROPN
cana-1315	104	80	,	,	PUNCT
cana-1315	104	81			NOUN
cana-1315	104	82	3bq	3bq	NOUN
cana-1315	104	83	,	,	PUNCT
cana-1315	104	84			NOUN
cana-1315	104	85	3cr	3cr	PUNCT
cana-1315	104	86	}	}	PUNCT
cana-1315	104	87	}	}	PUNCT
cana-1315	104	88	=	=	SYM
cana-1315	104	89	max	max	PROPN
cana-1315	104	90	{	{	PUNCT
cana-1315	104	91			PROPN
cana-1315	104	92	111	111	NOUN
cana-1315	104	93	,	,	PUNCT
cana-1315	104	94	,	,	PUNCT
cana-1315	104	95	cbarqp	cbarqp	NOUN
cana-1315	104	96			ADJ
cana-1315	104	97	,	,	PUNCT
cana-1315	104	98			PROPN
cana-1315	104	99	222	222	NOUN
cana-1315	104	100	,	,	PUNCT
cana-1315	104	101	,	,	PUNCT
cana-1315	104	102	cbarqp	cbarqp	NOUN
cana-1315	104	103			X
cana-1315	104	104	,	,	PUNCT
cana-1315	104	105			PROPN
cana-1315	104	106	333	333	PROPN
cana-1315	104	107	,	,	PUNCT
cana-1315	104	108	,	,	PUNCT
cana-1315	104	109	cbarqp	cbarqp	NOUN
cana-1315	104	110			ADJ
cana-1315	104	111	}	}	PUNCT
cana-1315	104	112	.	.	PUNCT
cana-1315	105	1	therefore	therefore	ADV
cana-1315	105	2	,	,	PUNCT
cana-1315	105	3			PROPN
cana-1315	105	4			PROPN
cana-1315	105	5			PROPN
cana-1315	105	6			INTJ
cana-1315	105	7	333222111	333222111	NOUN
cana-1315	105	8	,	,	PUNCT
cana-1315	105	9	,	,	PUNCT
cana-1315	105	10	,	,	PUNCT
cana-1315	105	11	,	,	PUNCT
cana-1315	105	12	,	,	PUNCT
cana-1315	105	13	,	,	PUNCT
cana-1315	105	14	cbacbacbarqp	cbacbacbarqp	NOUN
cana-1315	105	15			ADJ
cana-1315	105	16	≤	≤	NUM
cana-1315	105	17	max	max	PROPN
cana-1315	105	18	{	{	PUNCT
cana-1315	105	19			PROPN
cana-1315	105	20	111	111	NOUN
cana-1315	105	21	,	,	PUNCT
cana-1315	105	22	,	,	PUNCT
cana-1315	105	23	cbarqp	cbarqp	NOUN
cana-1315	105	24			ADJ
cana-1315	105	25	,	,	PUNCT
cana-1315	105	26			PROPN
cana-1315	105	27	222	222	NOUN
cana-1315	105	28	,	,	PUNCT
cana-1315	105	29	,	,	PUNCT
cana-1315	105	30	cbarqp	cbarqp	NOUN
cana-1315	105	31			X
cana-1315	105	32	,	,	PUNCT
cana-1315	105	33			PROPN
cana-1315	105	34	333	333	PROPN
cana-1315	105	35	,	,	PUNCT
cana-1315	105	36	,	,	PUNCT
cana-1315	105	37	cbarqp	cbarqp	NOUN
cana-1315	105	38			ADJ
cana-1315	105	39	}	}	PUNCT
cana-1315	105	40	.	.	PUNCT
cana-1315	106	1	hence	hence	ADV
cana-1315	106	2	p	p	X
cana-1315	106	3	×	×	NOUN
cana-1315	106	4	q	q	X
cana-1315	106	5	×	×	NOUN
cana-1315	106	6	r	r	NOUN
cana-1315	106	7	is	be	AUX
cana-1315	106	8	an	an	DET
cana-1315	106	9	aftssr	aftssr	NOUN
cana-1315	106	10	of	of	ADP
cana-1315	106	11	tsr	tsr	PROPN
cana-1315	106	12	of	of	ADP
cana-1315	106	13	t1	t1	PROPN
cana-1315	106	14	x	x	PUNCT
cana-1315	106	15	t2	t2	PROPN
cana-1315	106	16	x	x	SYM
cana-1315	106	17	t3	t3	PROPN
cana-1315	106	18	.	.	PUNCT
cana-1315	107	1	th.3.4	th.3.4	NOUN
cana-1315	107	2	:	:	PUNCT
cana-1315	107	3	p	p	PRON
cana-1315	107	4	is	be	AUX
cana-1315	107	5	an	an	DET
cana-1315	107	6	aftssr	aftssr	NOUN
cana-1315	107	7	of	of	ADP
cana-1315	107	8	t	t	PROPN
cana-1315	107	9	if	if	SCONJ
cana-1315	108	1	and	and	CCONJ
cana-1315	108	2	only	only	ADV
cana-1315	108	3	if	if	SCONJ
cana-1315	108	4	u	u	NOUN
cana-1315	108	5	is	be	AUX
cana-1315	108	6	an	an	DET
cana-1315	108	7	aftssr	aftssr	NOUN
cana-1315	108	8	of	of	ADP
cana-1315	108	9	t×t×t	t×t×t	NOUN
cana-1315	108	10	,	,	PUNCT
cana-1315	108	11	when	when	SCONJ
cana-1315	108	12	p	p	NOUN
cana-1315	108	13	is	be	AUX
cana-1315	108	14	a	a	DET
cana-1315	108	15	fuzzy	fuzzy	ADJ
cana-1315	108	16	subset	subset	NOUN
cana-1315	108	17	of	of	ADP
cana-1315	108	18	a	a	DET
cana-1315	108	19	tsrt	tsrt	NOUN
cana-1315	108	20	and	and	CCONJ
cana-1315	108	21	u	u	NOUN
cana-1315	108	22	is	be	AUX
cana-1315	108	23	a	a	DET
cana-1315	108	24	strongest	strong	ADJ
cana-1315	108	25	anti	anti	ADJ
cana-1315	108	26	-	-	ADJ
cana-1315	108	27	fuzzy	fuzzy	ADJ
cana-1315	108	28	relation	relation	NOUN
cana-1315	108	29	of	of	ADP
cana-1315	108	30	t.	t.	PROPN
cana-1315	108	31	pf	pf	PROPN
cana-1315	108	32	.	.	PROPN
cana-1315	108	33	:	:	PUNCT
cana-1315	109	1	given	give	VERB
cana-1315	109	2	that	that	SCONJ
cana-1315	109	3	p	p	NOUN
cana-1315	109	4	is	be	AUX
cana-1315	109	5	an	an	DET
cana-1315	109	6	aftssr	aftssr	NOUN
cana-1315	109	7	of	of	ADP
cana-1315	109	8	a	a	DET
cana-1315	109	9	tsr	tsr	PROPN
cana-1315	109	10	t.	t.	NOUN
cana-1315	109	11	then	then	ADV
cana-1315	109	12	for	for	ADP
cana-1315	109	13	any	any	DET
cana-1315	109	14	a	a	DET
cana-1315	109	15	=	=	SYM
cana-1315	109	16	(	(	PUNCT
cana-1315	109	17	a1	a1	PROPN
cana-1315	109	18	,	,	PUNCT
cana-1315	109	19	b1	b1	NOUN
cana-1315	109	20	,	,	PUNCT
cana-1315	109	21	c1	c1	PROPN
cana-1315	109	22	)	)	PUNCT
cana-1315	109	23	,	,	PUNCT
cana-1315	109	24	b	b	X
cana-1315	109	25	=	=	SYM
cana-1315	109	26	(	(	PUNCT
cana-1315	109	27	a2	a2	PROPN
cana-1315	109	28	,	,	PUNCT
cana-1315	109	29	b2	b2	NOUN
cana-1315	109	30	,	,	PUNCT
cana-1315	109	31	c2	c2	PROPN
cana-1315	109	32	)	)	PUNCT
cana-1315	109	33	and	and	CCONJ
cana-1315	109	34	c=(a3	c=(a3	NOUN
cana-1315	109	35	,	,	PUNCT
cana-1315	109	36	b3	b3	PROPN
cana-1315	109	37	,	,	PUNCT
cana-1315	109	38	c3	c3	PROPN
cana-1315	109	39	)	)	PUNCT
cana-1315	109	40	,	,	PUNCT
cana-1315	109	41	are	be	AUX
cana-1315	109	42	in	in	ADP
cana-1315	109	43	t	t	PROPN
cana-1315	109	44	x	x	SYM
cana-1315	109	45	t	t	NOUN
cana-1315	109	46	x	x	PROPN
cana-1315	109	47	t.	t.	NOUN
cana-1315	109	48	we	we	PRON
cana-1315	109	49	have	have	VERB
cana-1315	109	50	,	,	PUNCT
cana-1315	109	51			PROPN
cana-1315	109	52	bau	bau	X
cana-1315	109	53			NUM
cana-1315	109	54	=	=	SYM
cana-1315	109	55	u	u	NOUN
cana-1315	109	56	[	[	X
cana-1315	109	57	(	(	PUNCT
cana-1315	109	58	a1	a1	PROPN
cana-1315	109	59	,	,	PUNCT
cana-1315	109	60	b1	b1	NOUN
cana-1315	109	61	,	,	PUNCT
cana-1315	109	62	c1)+(a2	c1)+(a2	PROPN
cana-1315	109	63	,	,	PUNCT
cana-1315	109	64	b2	b2	NOUN
cana-1315	109	65	,	,	PUNCT
cana-1315	109	66	c2	c2	PROPN
cana-1315	109	67	)	)	PUNCT
cana-1315	109	68	]	]	PUNCT
cana-1315	110	1	=	=	PUNCT
cana-1315	110	2			NOUN
cana-1315	110	3	212121	212121	VERB
cana-1315	110	4	,	,	PUNCT
cana-1315	110	5	,	,	PUNCT
cana-1315	110	6	ccbbaau	ccbbaau	NOUN
cana-1315	110	7			NOUN
cana-1315	110	8	=	=	SYM
cana-1315	110	9	max	max	PROPN
cana-1315	110	10			PROPN
cana-1315	110	11	212121	212121	PUNCT
cana-1315	110	12	,	,	PUNCT
cana-1315	110	13	,	,	PUNCT
cana-1315	110	14	ccbbaau	ccbbaau	PROPN
cana-1315	110	15			NOUN
cana-1315	110	16	)	)	PUNCT
cana-1315	110	17	}	}	PUNCT
cana-1315	110	18	≤	≤	NUM
cana-1315	110	19	max{max	max{max	X
cana-1315	110	20	{	{	PUNCT
cana-1315	110	21			PROPN
cana-1315	110	22	1au	1au	PROPN
cana-1315	110	23	,	,	PUNCT
cana-1315	110	24			PROPN
cana-1315	110	25	2au	2au	PUNCT
cana-1315	110	26	}	}	PUNCT
cana-1315	110	27	,	,	PUNCT
cana-1315	110	28	max	max	PROPN
cana-1315	110	29	{	{	PUNCT
cana-1315	110	30			PROPN
cana-1315	110	31	1bu	1bu	PROPN
cana-1315	110	32	,	,	PUNCT
cana-1315	110	33			PROPN
cana-1315	110	34	2bu	2bu	PROPN
cana-1315	110	35	)	)	PUNCT
cana-1315	110	36	}	}	PUNCT
cana-1315	110	37	max	max	PROPN
cana-1315	110	38	{	{	PUNCT
cana-1315	110	39			PROPN
cana-1315	110	40	1cu	1cu	ADJ
cana-1315	110	41	,	,	PUNCT
cana-1315	110	42			PROPN
cana-1315	110	43	2cu	2cu	NOUN
cana-1315	110	44	}	}	PUNCT
cana-1315	110	45	}	}	PUNCT
cana-1315	110	46	=	=	SYM
cana-1315	110	47	max{max	max{max	ADJ
cana-1315	110	48	{	{	PUNCT
cana-1315	110	49			PROPN
cana-1315	110	50	1au	1au	PROPN
cana-1315	110	51	,	,	PUNCT
cana-1315	110	52			PROPN
cana-1315	110	53	2au	2au	PUNCT
cana-1315	110	54	}	}	PUNCT
cana-1315	110	55	,	,	PUNCT
cana-1315	110	56	max	max	PROPN
cana-1315	110	57	{	{	PUNCT
cana-1315	110	58			PROPN
cana-1315	110	59	1bu	1bu	PROPN
cana-1315	110	60	,	,	PUNCT
cana-1315	110	61			PROPN
cana-1315	110	62	2bu	2bu	PROPN
cana-1315	110	63	)	)	PUNCT
cana-1315	110	64	}	}	PUNCT
cana-1315	110	65	,	,	PUNCT
cana-1315	110	66	max	max	PROPN
cana-1315	110	67	{	{	PUNCT
cana-1315	110	68			PROPN
cana-1315	110	69	1cu	1cu	ADJ
cana-1315	110	70	,	,	PUNCT
cana-1315	110	71			PROPN
cana-1315	110	72	2cu	2cu	NOUN
cana-1315	110	73	}	}	PUNCT
cana-1315	110	74	}	}	PUNCT
cana-1315	110	75	=	=	SYM
cana-1315	110	76	max	max	X
cana-1315	110	77	{	{	PUNCT
cana-1315	110	78			PROPN
cana-1315	110	79	111	111	NOUN
cana-1315	110	80	,	,	PUNCT
cana-1315	110	81	,	,	PUNCT
cana-1315	110	82	cbau	cbau	PROPN
cana-1315	110	83	,	,	PUNCT
cana-1315	110	84			PROPN
cana-1315	110	85	222	222	NOUN
cana-1315	110	86	,	,	PUNCT
cana-1315	110	87	,	,	PUNCT
cana-1315	110	88	cbau	cbau	PROPN
cana-1315	110	89	)	)	PUNCT
cana-1315	110	90	}	}	PUNCT
cana-1315	110	91	=	=	SYM
cana-1315	110	92	max	max	PROPN
cana-1315	110	93	{	{	PUNCT
cana-1315	110	94			PROPN
cana-1315	110	95	au	au	PROPN
cana-1315	110	96	,	,	PUNCT
cana-1315	110	97			PROPN
cana-1315	110	98	bu	bu	PROPN
cana-1315	110	99	}	}	PUNCT
cana-1315	110	100	.	.	PUNCT
cana-1315	111	1	therefore	therefore	ADV
cana-1315	111	2	,	,	PUNCT
cana-1315	111	3			PROPN
cana-1315	111	4	bau	bau	X
cana-1315	111	5			NUM
cana-1315	111	6	≤	≤	NUM
cana-1315	111	7	max	max	PROPN
cana-1315	111	8	{	{	PUNCT
cana-1315	111	9			PROPN
cana-1315	111	10	au	au	PROPN
cana-1315	111	11	,	,	PUNCT
cana-1315	111	12			PROPN
cana-1315	111	13	bu	bu	PROPN
cana-1315	111	14	}	}	PUNCT
cana-1315	111	15	,	,	PUNCT
cana-1315	111	16			VERB
cana-1315	111	17	a	a	PRON
cana-1315	111	18	,	,	PUNCT
cana-1315	111	19	b	b	NOUN
cana-1315	111	20	,	,	PUNCT
cana-1315	111	21	c	c	PROPN
cana-1315	111	22			PROPN
cana-1315	111	23	t	t	PROPN
cana-1315	111	24	×	×	NOUN
cana-1315	111	25	t	t	PROPN
cana-1315	111	26	×	×	NOUN
cana-1315	111	27	t.	t.	PROPN
cana-1315	111	28	and	and	CCONJ
cana-1315	111	29	,	,	PUNCT
cana-1315	111	30			PROPN
cana-1315	111	31	abcu	abcu	PROPN
cana-1315	111	32	=	=	SYM
cana-1315	111	33			PROPN
cana-1315	111	34			NOUN
cana-1315	111	35			PROPN
cana-1315	111	36			PUNCT
cana-1315	111	37	333222111	333222111	NOUN
cana-1315	111	38	,	,	PUNCT
cana-1315	111	39	,	,	PUNCT
cana-1315	111	40	,	,	PUNCT
cana-1315	111	41	,	,	PUNCT
cana-1315	111	42	,	,	PUNCT
cana-1315	111	43	,	,	PUNCT
cana-1315	111	44	cbacbacbau	cbacbacbau	PROPN
cana-1315	111	45	=	=	SYM
cana-1315	111	46			PROPN
cana-1315	111	47	321321321	321321321	PUNCT
cana-1315	111	48	,	,	PUNCT
cana-1315	111	49	,	,	PUNCT
cana-1315	111	50	cccbbbaaau	cccbbbaaau	PROPN
cana-1315	111	51	=	=	SYM
cana-1315	111	52	max	max	PROPN
cana-1315	111	53	{	{	PUNCT
cana-1315	111	54			NOUN
cana-1315	111	55	321	321	ADP
cana-1315	111	56	aaau	aaau	PROPN
cana-1315	111	57	,	,	PUNCT
cana-1315	111	58			PROPN
cana-1315	111	59	321	321	ADP
cana-1315	111	60	bbbu	bbbu	PROPN
cana-1315	111	61	,	,	PUNCT
cana-1315	111	62			PROPN
cana-1315	111	63	321	321	ADP
cana-1315	111	64	cccu	cccu	PROPN
cana-1315	111	65	}	}	PUNCT
cana-1315	111	66	≤	≤	PROPN
cana-1315	111	67	max	max	PROPN
cana-1315	111	68	{	{	PUNCT
cana-1315	111	69	max	max	PROPN
cana-1315	111	70	{	{	PUNCT
cana-1315	111	71			PROPN
cana-1315	111	72	1au	1au	PROPN
cana-1315	111	73	,	,	PUNCT
cana-1315	111	74			PROPN
cana-1315	111	75	2au	2au	NOUN
cana-1315	111	76	,	,	PUNCT
cana-1315	111	77			PROPN
cana-1315	111	78	3au	3au	PROPN
cana-1315	111	79	}	}	PUNCT
cana-1315	111	80	,	,	PUNCT
cana-1315	111	81	max	max	PROPN
cana-1315	111	82	{	{	PUNCT
cana-1315	111	83			PROPN
cana-1315	111	84	1bu	1bu	PROPN
cana-1315	111	85	,	,	PUNCT
cana-1315	111	86			PROPN
cana-1315	111	87	2bu	2bu	PROPN
cana-1315	111	88	,	,	PUNCT
cana-1315	111	89			PROPN
cana-1315	111	90	3bu	3bu	PROPN
cana-1315	111	91	}	}	PUNCT
cana-1315	111	92	,	,	PUNCT
cana-1315	111	93	max	max	PROPN
cana-1315	111	94	{	{	PUNCT
cana-1315	111	95			PROPN
cana-1315	111	96	1cu	1cu	ADJ
cana-1315	111	97	,	,	PUNCT
cana-1315	111	98			PROPN
cana-1315	111	99	2cu	2cu	ADJ
cana-1315	111	100	,	,	PUNCT
cana-1315	111	101			NOUN
cana-1315	111	102	3cu	3cu	NOUN
cana-1315	111	103	}	}	PUNCT
cana-1315	111	104	}	}	PUNCT
cana-1315	111	105	=	=	SYM
cana-1315	111	106	max{{max	max{{max	NUM
cana-1315	111	107	{	{	PUNCT
cana-1315	111	108			PROPN
cana-1315	111	109	1au	1au	PROPN
cana-1315	111	110	,	,	PUNCT
cana-1315	111	111			PROPN
cana-1315	111	112	2au	2au	NOUN
cana-1315	111	113	,	,	PUNCT
cana-1315	111	114			PROPN
cana-1315	111	115	3au	3au	PROPN
cana-1315	111	116	}	}	PUNCT
cana-1315	111	117	,	,	PUNCT
cana-1315	111	118	max	max	PROPN
cana-1315	111	119	{	{	PUNCT
cana-1315	111	120			PROPN
cana-1315	111	121	1bu	1bu	PROPN
cana-1315	111	122	,	,	PUNCT
cana-1315	111	123			PROPN
cana-1315	111	124	2bu	2bu	PROPN
cana-1315	111	125	,	,	PUNCT
cana-1315	111	126			PROPN
cana-1315	111	127	3bu	3bu	PROPN
cana-1315	111	128	}	}	PUNCT
cana-1315	111	129	,	,	PUNCT
cana-1315	111	130	max	max	PROPN
cana-1315	111	131	{	{	PUNCT
cana-1315	111	132			PROPN
cana-1315	111	133	1cu	1cu	ADJ
cana-1315	111	134	,	,	PUNCT
cana-1315	111	135			PROPN
cana-1315	111	136	2cu	2cu	ADJ
cana-1315	111	137	,	,	PUNCT
cana-1315	111	138			NOUN
cana-1315	111	139	3cu	3cu	NOUN
cana-1315	111	140	}	}	PUNCT
cana-1315	111	141	}	}	PUNCT
cana-1315	111	142	=	=	SYM
cana-1315	111	143	max	max	X
cana-1315	111	144	{	{	PUNCT
cana-1315	111	145			PROPN
cana-1315	111	146	111	111	NOUN
cana-1315	111	147	,	,	PUNCT
cana-1315	111	148	,	,	PUNCT
cana-1315	111	149	cbau	cbau	PROPN
cana-1315	111	150	,	,	PUNCT
cana-1315	111	151			PROPN
cana-1315	111	152	222	222	NOUN
cana-1315	111	153	,	,	PUNCT
cana-1315	111	154	,	,	PUNCT
cana-1315	111	155	cbau	cbau	PROPN
cana-1315	111	156	,	,	PUNCT
cana-1315	111	157			PROPN
cana-1315	111	158	333	333	PROPN
cana-1315	111	159	,	,	PUNCT
cana-1315	111	160	,	,	PUNCT
cana-1315	111	161	cbau	cbau	PROPN
cana-1315	111	162	}	}	PUNCT
cana-1315	111	163	=	=	SYM
cana-1315	111	164	max	max	PROPN
cana-1315	111	165	{	{	PUNCT
cana-1315	111	166			PROPN
cana-1315	111	167	au	au	PROPN
cana-1315	111	168	,	,	PUNCT
cana-1315	111	169			PROPN
cana-1315	111	170	bu	bu	PROPN
cana-1315	111	171	,	,	PUNCT
cana-1315	111	172			PROPN
cana-1315	111	173	cu	cu	PROPN
cana-1315	111	174	}	}	PUNCT
cana-1315	111	175	.	.	PUNCT
cana-1315	112	1	therefore	therefore	ADV
cana-1315	112	2	,	,	PUNCT
cana-1315	112	3			PROPN
cana-1315	112	4	abcu	abcu	PROPN
cana-1315	112	5	≤	≤	NUM
cana-1315	112	6	max	max	PROPN
cana-1315	112	7	{	{	PUNCT
cana-1315	112	8			PROPN
cana-1315	112	9	au	au	PROPN
cana-1315	112	10	,	,	PUNCT
cana-1315	112	11			PROPN
cana-1315	112	12	bu	bu	PROPN
cana-1315	112	13	,	,	PUNCT
cana-1315	112	14			PROPN
cana-1315	112	15	cu	cu	PROPN
cana-1315	112	16	}	}	PUNCT
cana-1315	112	17	,	,	PUNCT
cana-1315	112	18			NOUN
cana-1315	112	19	a	a	DET
cana-1315	112	20	,	,	PUNCT
cana-1315	112	21	b	b	NOUN
cana-1315	112	22	,	,	PUNCT
cana-1315	112	23	ct×t×t	ct×t×t	NOUN
cana-1315	112	24	.	.	PUNCT
cana-1315	113	1	this	this	PRON
cana-1315	113	2	proves	prove	VERB
cana-1315	113	3	that	that	SCONJ
cana-1315	113	4	p	p	NOUN
cana-1315	113	5	is	be	AUX
cana-1315	113	6	an	an	DET
cana-1315	113	7	aftssr	aftssr	NOUN
cana-1315	113	8	of	of	ADP
cana-1315	113	9	t×t×t	t×t×t	PROPN
cana-1315	113	10	.	.	PUNCT
cana-1315	114	1	conversely	conversely	ADV
cana-1315	114	2	assume	assume	VERB
cana-1315	114	3	that	that	SCONJ
cana-1315	114	4	u	u	PRON
cana-1315	114	5	is	be	AUX
cana-1315	114	6	an	an	DET
cana-1315	114	7	aftssr	aftssr	NOUN
cana-1315	114	8	of	of	ADP
cana-1315	114	9	t×t×t	t×t×t	NOUN
cana-1315	114	10	,	,	PUNCT
cana-1315	114	11	then	then	ADV
cana-1315	114	12	for	for	ADP
cana-1315	114	13	any	any	DET
cana-1315	114	14	a	a	PRON
cana-1315	114	15	=	=	SYM
cana-1315	114	16	(	(	PUNCT
cana-1315	114	17	a1	a1	PROPN
cana-1315	114	18	,	,	PUNCT
cana-1315	114	19	b1	b1	NOUN
cana-1315	114	20	,	,	PUNCT
cana-1315	114	21	c1	c1	PROPN
cana-1315	114	22	)	)	PUNCT
cana-1315	114	23	,	,	PUNCT
cana-1315	114	24	b=(a2	b=(a2	NOUN
cana-1315	114	25	,	,	PUNCT
cana-1315	114	26	b2	b2	NOUN
cana-1315	114	27	,	,	PUNCT
cana-1315	114	28	c2	c2	PROPN
cana-1315	114	29	)	)	PUNCT
cana-1315	114	30	and	and	CCONJ
cana-1315	114	31	c=(a3	c=(a3	NOUN
cana-1315	114	32	,	,	PUNCT
cana-1315	114	33	b3	b3	PROPN
cana-1315	114	34	,	,	PUNCT
cana-1315	114	35	c3),are	c3),are	VERB
cana-1315	114	36	in	in	ADP
cana-1315	114	37	t	t	PROPN
cana-1315	114	38	x	x	SYM
cana-1315	114	39	t	t	PROPN
cana-1315	114	40	x	x	SYM
cana-1315	114	41	t	t	PROPN
cana-1315	114	42	,	,	PUNCT
cana-1315	114	43	we	we	PRON
cana-1315	114	44	have	have	VERB
cana-1315	114	45	max	max	PROPN
cana-1315	114	46	{	{	PUNCT
cana-1315	114	47			PROPN
cana-1315	114	48	21	21	PROPN
cana-1315	114	49	aau	aau	PROPN
cana-1315	114	50			NUM
cana-1315	114	51	,	,	PUNCT
cana-1315	114	52			PROPN
cana-1315	114	53	21	21	NOUN
cana-1315	115	1	bbu	bbu	PROPN
cana-1315	115	2			PROPN
cana-1315	115	3	,	,	PUNCT
cana-1315	115	4			PROPN
cana-1315	115	5	21	21	PUNCT
cana-1315	116	1	ccu	ccu	PROPN
cana-1315	116	2			NUM
cana-1315	116	3	}	}	PUNCT
cana-1315	116	4	=	=	SYM
cana-1315	116	5			NOUN
cana-1315	116	6			NOUN
cana-1315	116	7	222111	222111	NOUN
cana-1315	116	8	,	,	PUNCT
cana-1315	116	9	cbacbau	cbacbau	VERB
cana-1315	116	10			NOUN
cana-1315	116	11	=	=	SYM
cana-1315	116	12	u	u	NOUN
cana-1315	116	13	[	[	X
cana-1315	116	14	(	(	PUNCT
cana-1315	116	15	a1	a1	PROPN
cana-1315	116	16	,	,	PUNCT
cana-1315	116	17	b1	b1	NOUN
cana-1315	116	18	,	,	PUNCT
cana-1315	116	19	c1)+	c1)+	PROPN
cana-1315	116	20	(	(	PUNCT
cana-1315	116	21	a2	a2	PROPN
cana-1315	116	22	,	,	PUNCT
cana-1315	116	23	b2	b2	NOUN
cana-1315	116	24	,	,	PUNCT
cana-1315	116	25	c2	c2	PROPN
cana-1315	116	26	)	)	PUNCT
cana-1315	116	27	]	]	PUNCT
cana-1315	117	1	=	=	PUNCT
cana-1315	117	2			NOUN
cana-1315	117	3	bau	bau	NOUN
cana-1315	117	4			NUM
cana-1315	117	5	≤	≤	PROPN
cana-1315	117	6	{	{	PUNCT
cana-1315	117	7			PROPN
cana-1315	117	8	au	au	PROPN
cana-1315	117	9	,	,	PUNCT
cana-1315	117	10			NOUN
cana-1315	117	11	bu	bu	PROPN
cana-1315	117	12	}	}	PUNCT
cana-1315	117	13	=	=	SYM
cana-1315	117	14	max	max	PROPN
cana-1315	117	15	{	{	PUNCT
cana-1315	117	16			PROPN
cana-1315	117	17	111	111	NOUN
cana-1315	117	18	,	,	PUNCT
cana-1315	117	19	,	,	PUNCT
cana-1315	117	20	cbau	cbau	PROPN
cana-1315	117	21	,	,	PUNCT
cana-1315	117	22			PROPN
cana-1315	117	23	222	222	NOUN
cana-1315	117	24	,	,	PUNCT
cana-1315	117	25	,	,	PUNCT
cana-1315	117	26	cbau	cbau	PROPN
cana-1315	117	27	)	)	PUNCT
cana-1315	117	28	}	}	PUNCT
cana-1315	117	29	=	=	SYM
cana-1315	117	30	max{max	max{max	PROPN
cana-1315	117	31	{	{	PUNCT
cana-1315	117	32			PROPN
cana-1315	117	33	1au	1au	PROPN
cana-1315	117	34	,	,	PUNCT
cana-1315	117	35			PROPN
cana-1315	117	36	1bu	1bu	PROPN
cana-1315	117	37	,	,	PUNCT
cana-1315	117	38			PROPN
cana-1315	117	39	1cu	1cu	PROPN
cana-1315	117	40	}	}	PUNCT
cana-1315	117	41	,	,	PUNCT
cana-1315	117	42	max	max	PROPN
cana-1315	117	43	{	{	PUNCT
cana-1315	117	44			PROPN
cana-1315	117	45	2au	2au	NOUN
cana-1315	117	46	,	,	PUNCT
cana-1315	117	47			PROPN
cana-1315	117	48	2bu	2bu	PROPN
cana-1315	117	49	,	,	PUNCT
cana-1315	117	50			PROPN
cana-1315	117	51	2cu	2cu	PROPN
cana-1315	117	52	}	}	PUNCT
cana-1315	117	53	.	.	PUNCT
cana-1315	118	1	if	if	SCONJ
cana-1315	118	2			PROPN
cana-1315	118	3	21	21	PROPN
cana-1315	118	4	aau	aau	PROPN
cana-1315	118	5			NUM
cana-1315	118	6	≥	≥	PROPN
cana-1315	118	7			PROPN
cana-1315	118	8	21	21	PROPN
cana-1315	118	9	bbu	bbu	PROPN
cana-1315	118	10			PROPN
cana-1315	118	11	,	,	PUNCT
cana-1315	118	12			PROPN
cana-1315	118	13			PROPN
cana-1315	118	14	1au	1au	PROPN
cana-1315	118	15	≥	≥	PROPN
cana-1315	118	16			PROPN
cana-1315	118	17	1bu	1bu	PROPN
cana-1315	118	18	,	,	PUNCT
cana-1315	118	19			PROPN
cana-1315	118	20	2au	2au	PROPN
cana-1315	118	21	≥	≥	NOUN
cana-1315	118	22			PROPN
cana-1315	118	23	2bu	2bu	PROPN
cana-1315	118	24	,	,	PUNCT
cana-1315	118	25	we	we	PRON
cana-1315	118	26	get	get	VERB
cana-1315	118	27	,	,	PUNCT
cana-1315	118	28			PROPN
cana-1315	118	29	21	21	NOUN
cana-1315	118	30	aau	aau	PROPN
cana-1315	118	31			NUM
cana-1315	118	32	≤	≤	PROPN
cana-1315	118	33	max	max	PROPN
cana-1315	118	34	{	{	PUNCT
cana-1315	118	35			PROPN
cana-1315	118	36	1au	1au	PROPN
cana-1315	118	37	,	,	PUNCT
cana-1315	118	38			PROPN
cana-1315	118	39	2au	2au	PUNCT
cana-1315	118	40	}	}	PUNCT
cana-1315	118	41	,	,	PUNCT
cana-1315	118	42			NOUN
cana-1315	118	43	a1	a1	NOUN
cana-1315	118	44	and	and	CCONJ
cana-1315	118	45	a2	a2	PROPN
cana-1315	118	46	in	in	ADP
cana-1315	118	47	t.	t.	PROPN
cana-1315	118	48	and	and	CCONJ
cana-1315	118	49	,	,	PUNCT
cana-1315	118	50	max	max	PROPN
cana-1315	118	51	{	{	PUNCT
cana-1315	118	52			PROPN
cana-1315	118	53	321	321	ADP
cana-1315	118	54	aaau	aaau	PROPN
cana-1315	118	55	,	,	PUNCT
cana-1315	118	56			PROPN
cana-1315	118	57	321	321	ADP
cana-1315	118	58	bbbu	bbbu	PROPN
cana-1315	118	59	,	,	PUNCT
cana-1315	118	60			PROPN
cana-1315	118	61	321	321	ADP
cana-1315	118	62	cccu	cccu	NOUN
cana-1315	118	63	}	}	PUNCT
cana-1315	118	64	=	=	SYM
cana-1315	118	65			NOUN
cana-1315	118	66	333222111	333222111	PUNCT
cana-1315	118	67	,	,	PUNCT
cana-1315	118	68	,	,	PUNCT
cana-1315	118	69	cbacbacbau	cbacbacbau	PROPN
cana-1315	118	70	=	=	PUNCT
cana-1315	118	71	communications	communication	NOUN
cana-1315	118	72	on	on	ADP
cana-1315	118	73	applied	apply	VERB
cana-1315	118	74	nonlinear	nonlinear	ADJ
cana-1315	118	75	analysis	analysis	NOUN
cana-1315	118	76	issn	issn	NOUN
cana-1315	118	77	:	:	PUNCT
cana-1315	118	78	1074	1074	NUM
cana-1315	118	79	-	-	PUNCT
cana-1315	118	80	133x	133x	NUM
cana-1315	118	81	vol	vol	NOUN
cana-1315	118	82	31	31	NUM
cana-1315	118	83	no	no	NOUN
cana-1315	118	84	.	.	PUNCT
cana-1315	119	1	7s	7	NOUN
cana-1315	119	2	(	(	PUNCT
cana-1315	119	3	2024	2024	NUM
cana-1315	119	4	)	)	PUNCT
cana-1315	119	5	361	361	NUM
cana-1315	120	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1315	120	2			PROPN
cana-1315	120	3			NOUN
cana-1315	120	4			PROPN
cana-1315	120	5			PUNCT
cana-1315	120	6	333222111	333222111	NOUN
cana-1315	120	7	,	,	PUNCT
cana-1315	120	8	,	,	PUNCT
cana-1315	120	9	,	,	PUNCT
cana-1315	120	10	,	,	PUNCT
cana-1315	120	11	,	,	PUNCT
cana-1315	120	12	,	,	PUNCT
cana-1315	120	13	cbacbacbau	cbacbacbau	PROPN
cana-1315	120	14	=	=	SYM
cana-1315	120	15			PROPN
cana-1315	120	16	abcu	abcu	PROPN
cana-1315	120	17	≤	≤	NUM
cana-1315	120	18	max	max	PROPN
cana-1315	120	19	{	{	PUNCT
cana-1315	120	20			PROPN
cana-1315	120	21	au	au	PROPN
cana-1315	120	22	,	,	PUNCT
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cana-1315	120	25	,	,	PUNCT
cana-1315	120	26			PROPN
cana-1315	120	27	cu	cu	ADJ
cana-1315	120	28	}	}	PUNCT
cana-1315	120	29	=	=	SYM
cana-1315	120	30	max	max	PROPN
cana-1315	120	31	{	{	PUNCT
cana-1315	120	32			PROPN
cana-1315	120	33	111	111	NOUN
cana-1315	120	34	,	,	PUNCT
cana-1315	120	35	,	,	PUNCT
cana-1315	120	36	cbau	cbau	PROPN
cana-1315	120	37	,	,	PUNCT
cana-1315	120	38			PROPN
cana-1315	120	39	222	222	NOUN
cana-1315	120	40	,	,	PUNCT
cana-1315	120	41	,	,	PUNCT
cana-1315	120	42	cbau	cbau	PROPN
cana-1315	120	43	,	,	PUNCT
cana-1315	120	44			PROPN
cana-1315	120	45	333	333	PROPN
cana-1315	120	46	,	,	PUNCT
cana-1315	120	47	,	,	PUNCT
cana-1315	120	48	cbau	cbau	PROPN
cana-1315	120	49	}	}	PUNCT
cana-1315	120	50	=	=	SYM
cana-1315	120	51	max	max	X
cana-1315	120	52	{	{	PUNCT
cana-1315	120	53	max	max	PROPN
cana-1315	120	54	{	{	PUNCT
cana-1315	120	55			PROPN
cana-1315	120	56	1au	1au	PROPN
cana-1315	120	57	,	,	PUNCT
cana-1315	120	58			PROPN
cana-1315	120	59	2au	2au	NOUN
cana-1315	120	60	,	,	PUNCT
cana-1315	120	61			PROPN
cana-1315	120	62	3au	3au	PROPN
cana-1315	120	63	}	}	PUNCT
cana-1315	120	64	,	,	PUNCT
cana-1315	120	65	max	max	PROPN
cana-1315	120	66	{	{	PUNCT
cana-1315	120	67			PROPN
cana-1315	120	68	1bu	1bu	PROPN
cana-1315	120	69	,	,	PUNCT
cana-1315	120	70			PROPN
cana-1315	120	71	2bu	2bu	PROPN
cana-1315	120	72	,	,	PUNCT
cana-1315	120	73			PROPN
cana-1315	120	74	3bu	3bu	PROPN
cana-1315	120	75	}	}	PUNCT
cana-1315	120	76	,	,	PUNCT
cana-1315	120	77	max	max	PROPN
cana-1315	120	78	{	{	PUNCT
cana-1315	120	79			PROPN
cana-1315	120	80	1cu	1cu	ADJ
cana-1315	120	81	,	,	PUNCT
cana-1315	120	82			PROPN
cana-1315	120	83	2cu	2cu	ADJ
cana-1315	120	84	,	,	PUNCT
cana-1315	120	85			NOUN
cana-1315	120	86	3cu	3cu	NOUN
cana-1315	120	87	}	}	PUNCT
cana-1315	120	88	}	}	PUNCT
cana-1315	120	89	.if	.if	PUNCT
cana-1315	121	1			NOUN
cana-1315	121	2	321	321	ADP
cana-1315	121	3	aaau	aaau	PROPN
cana-1315	121	4	≥	≥	PRON
cana-1315	121	5			NOUN
cana-1315	121	6	321	321	ADP
cana-1315	121	7	bbbu	bbbu	PROPN
cana-1315	121	8	,	,	PUNCT
cana-1315	121	9			PROPN
cana-1315	121	10	1au	1au	PROPN
cana-1315	121	11	≥	≥	PROPN
cana-1315	121	12			PROPN
cana-1315	121	13	1bu	1bu	PROPN
cana-1315	121	14	,	,	PUNCT
cana-1315	121	15			PROPN
cana-1315	121	16	2au	2au	PROPN
cana-1315	121	17	≥	≥	NOUN
cana-1315	121	18			PROPN
cana-1315	121	19	2bu	2bu	PROPN
cana-1315	121	20	,	,	PUNCT
cana-1315	121	21			PROPN
cana-1315	121	22	3au	3au	PROPN
cana-1315	121	23	≥	≥	PROPN
cana-1315	121	24			PROPN
cana-1315	121	25	3bu	3bu	PROPN
cana-1315	121	26	,	,	PUNCT
cana-1315	121	27	we	we	PRON
cana-1315	121	28	get	get	VERB
cana-1315	121	29			NOUN
cana-1315	121	30	321	321	ADP
cana-1315	121	31	aaau	aaau	PROPN
cana-1315	121	32	≤	≤	ADJ
cana-1315	121	33	max	max	PROPN
cana-1315	121	34	{	{	PUNCT
cana-1315	121	35			PROPN
cana-1315	121	36	1au	1au	PROPN
cana-1315	121	37	,	,	PUNCT
cana-1315	121	38			PROPN
cana-1315	121	39	2au	2au	NOUN
cana-1315	121	40	,	,	PUNCT
cana-1315	121	41			PROPN
cana-1315	121	42	3au	3au	PROPN
cana-1315	121	43	}	}	PUNCT
cana-1315	121	44	,	,	PUNCT
cana-1315	121	45			NOUN
cana-1315	121	46	a1	a1	PROPN
cana-1315	121	47	,	,	PUNCT
cana-1315	121	48	a2	a2	PROPN
cana-1315	121	49	,	,	PUNCT
cana-1315	121	50	a3	a3	NOUN
cana-1315	121	51	in	in	ADP
cana-1315	121	52	t.	t.	PROPN
cana-1315	121	53	therefore	therefore	ADV
cana-1315	121	54	,	,	PUNCT
cana-1315	121	55	p	p	PROPN
cana-1315	121	56	is	be	AUX
cana-1315	121	57	an	an	DET
cana-1315	121	58	aftssr	aftssr	NOUN
cana-1315	121	59	of	of	ADP
cana-1315	121	60	t.	t.	PROPN
cana-1315	121	61	th.3.5	th.3.5	PROPN
cana-1315	121	62	:	:	PUNCT
cana-1315	121	63	p	p	PRON
cana-1315	121	64	is	be	AUX
cana-1315	121	65	an	an	DET
cana-1315	121	66	aftssr	aftssr	NOUN
cana-1315	121	67	of	of	ADP
cana-1315	121	68	a	a	DET
cana-1315	121	69	tsr	tsr	PROPN
cana-1315	121	70	(	(	PUNCT
cana-1315	121	71	t	t	PROPN
cana-1315	121	72	,	,	PUNCT
cana-1315	121	73	+	+	PROPN
cana-1315	121	74	,	,	PUNCT
cana-1315	121	75	∙	∙	PROPN
cana-1315	121	76	)	)	PUNCT
cana-1315	122	1	if	if	SCONJ
cana-1315	122	2	and	and	CCONJ
cana-1315	122	3	only	only	ADV
cana-1315	122	4	if	if	SCONJ
cana-1315	122	5			NOUN
cana-1315	122	6			PUNCT
cana-1315	122	7	u	u	ADJ
cana-1315	122	8	≤	≤	NUM
cana-1315	122	9	max	max	PROPN
cana-1315	122	10	{	{	PUNCT
cana-1315	122	11			PROPN
cana-1315	122	12	u	u	PROPN
cana-1315	122	13	,	,	PUNCT
cana-1315	122	14			PROPN
cana-1315	122	15	u	u	PROPN
cana-1315	122	16	}	}	PUNCT
cana-1315	122	17	,	,	PUNCT
cana-1315	122	18			PROPN
cana-1315	122	19	u	u	PUNCT
cana-1315	122	20	≤	≤	NUM
cana-1315	122	21	max	max	PROPN
cana-1315	122	22	{	{	PUNCT
cana-1315	122	23			PROPN
cana-1315	122	24	u	u	PROPN
cana-1315	122	25	,	,	PUNCT
cana-1315	122	26			PROPN
cana-1315	122	27	u	u	PROPN
cana-1315	122	28	,	,	PUNCT
cana-1315	122	29			PROPN
cana-1315	122	30	u	u	PUNCT
cana-1315	122	31	}	}	PUNCT
cana-1315	122	32	,	,	PUNCT
cana-1315	122	33			NOUN
cana-1315	122	34	α	α	NOUN
cana-1315	122	35	,	,	PUNCT
cana-1315	122	36	β	β	X
cana-1315	122	37	and	and	CCONJ
cana-1315	122	38	γ	γ	X
cana-1315	122	39	in	in	ADP
cana-1315	122	40	t.	t.	NOUN
cana-1315	122	41	proof	proof	NOUN
cana-1315	122	42	:	:	PUNCT
cana-1315	122	43	it	it	PRON
cana-1315	122	44	is	be	AUX
cana-1315	122	45	trivial	trivial	ADJ
cana-1315	122	46	.	.	PUNCT
cana-1315	123	1	th.3.6	th.3.6	PROPN
cana-1315	123	2	:	:	PUNCT
cana-1315	123	3	if	if	SCONJ
cana-1315	123	4	p	p	NOUN
cana-1315	123	5	is	be	AUX
cana-1315	123	6	an	an	DET
cana-1315	123	7	aftssr	aftssr	NOUN
cana-1315	123	8	of	of	ADP
cana-1315	123	9	a	a	DET
cana-1315	123	10	tsr	tsr	PROPN
cana-1315	123	11	(	(	PUNCT
cana-1315	123	12	t	t	PROPN
cana-1315	123	13	,	,	PUNCT
cana-1315	123	14	+	+	PROPN
cana-1315	123	15	,	,	PUNCT
cana-1315	123	16	∙	∙	PROPN
cana-1315	123	17	)	)	PUNCT
cana-1315	123	18	,	,	PUNCT
cana-1315	123	19	then	then	ADV
cana-1315	123	20	h	h	NOUN
cana-1315	123	21	=	=	NOUN
cana-1315	123	22	{	{	PUNCT
cana-1315	123	23	α/	α/	X
cana-1315	123	24	αt	αt	NOUN
cana-1315	123	25	:	:	PUNCT
cana-1315	123	26			NOUN
cana-1315	123	27	p	p	PUNCT
cana-1315	124	1	=	=	NOUN
cana-1315	124	2	0	0	NUM
cana-1315	124	3	}	}	PUNCT
cana-1315	124	4	is	be	AUX
cana-1315	124	5	either	either	CCONJ
cana-1315	124	6	h=	h=	NOUN
cana-1315	124	7	or	or	CCONJ
cana-1315	124	8	a	a	DET
cana-1315	124	9	ter.sub	ter.sub	NUM
cana-1315	124	10	-	-	PUNCT
cana-1315	124	11	semi	semi	NOUN
cana-1315	124	12	-	-	ADJ
cana-1315	124	13	ring(tssr	ring(tssr	ADJ
cana-1315	124	14	)	)	PUNCT
cana-1315	124	15	of	of	ADP
cana-1315	124	16	t.	t.	PROPN
cana-1315	124	17	pf	pf	PROPN
cana-1315	124	18	.	.	PUNCT
cana-1315	124	19	:	:	PUNCT
cana-1315	124	20	if	if	SCONJ
cana-1315	124	21	each	each	DET
cana-1315	124	22	element	element	NOUN
cana-1315	124	23	does	do	AUX
cana-1315	124	24	n’t	not	PART
cana-1315	124	25	satisfies	satisfie	NOUN
cana-1315	124	26	this	this	DET
cana-1315	124	27	condition	condition	NOUN
cana-1315	124	28	,	,	PUNCT
cana-1315	124	29	then	then	ADV
cana-1315	124	30	h	h	NOUN
cana-1315	124	31	=	=	X
cana-1315	124	32	.	.	PUNCT
cana-1315	125	1	if	if	SCONJ
cana-1315	125	2	α	α	X
cana-1315	125	3	,	,	PUNCT
cana-1315	125	4	β	β	PROPN
cana-1315	125	5	h	h	NOUN
cana-1315	125	6	,	,	PUNCT
cana-1315	125	7	then	then	ADV
cana-1315	125	8			PROPN
cana-1315	125	9			PRON
cana-1315	125	10	u	u	ADJ
cana-1315	125	11	≤	≤	ADJ
cana-1315	125	12	max	max	PROPN
cana-1315	125	13	{	{	PUNCT
cana-1315	125	14			PROPN
cana-1315	125	15	u	u	PROPN
cana-1315	125	16	,	,	PUNCT
cana-1315	125	17			PROPN
cana-1315	125	18	u	u	NOUN
cana-1315	125	19	}	}	PUNCT
cana-1315	125	20	=	=	SYM
cana-1315	125	21	maximum{0	maximum{0	NOUN
cana-1315	125	22	,	,	PUNCT
cana-1315	125	23	0}=0	0}=0	NUM
cana-1315	125	24	.	.	PUNCT
cana-1315	126	1			PROPN
cana-1315	126	2			NOUN
cana-1315	126	3			PUNCT
cana-1315	126	4	u	u	NOUN
cana-1315	126	5	=	=	SYM
cana-1315	126	6	0	0	PROPN
cana-1315	126	7	.	.	PUNCT
cana-1315	127	1	and	and	CCONJ
cana-1315	127	2	,	,	PUNCT
cana-1315	127	3			PROPN
cana-1315	127	4	u	u	PUNCT
cana-1315	127	5	≤	≤	NUM
cana-1315	127	6	maximum	maximum	ADJ
cana-1315	127	7	{	{	PUNCT
cana-1315	127	8			PROPN
cana-1315	127	9	u	u	PROPN
cana-1315	127	10	,	,	PUNCT
cana-1315	127	11			PROPN
cana-1315	127	12	u	u	PROPN
cana-1315	127	13	,	,	PUNCT
cana-1315	127	14			PROPN
cana-1315	127	15	u	u	PUNCT
cana-1315	127	16	}	}	PUNCT
cana-1315	127	17	=	=	PUNCT
cana-1315	127	18	maximum{0,0,0	maximum{0,0,0	PROPN
cana-1315	127	19	}	}	PUNCT
cana-1315	127	20	=	=	SYM
cana-1315	127	21	0	0	X
cana-1315	127	22	.	.	PUNCT
cana-1315	128	1			NOUN
cana-1315	128	2			NOUN
cana-1315	128	3	u	u	PUNCT
cana-1315	129	1	=	=	NOUN
cana-1315	129	2	0	0	NUM
cana-1315	129	3			NOUN
cana-1315	129	4	α	α	NOUN
cana-1315	129	5	+	+	X
cana-1315	129	6	β	β	X
cana-1315	129	7	,	,	PUNCT
cana-1315	129	8	αβγ	αβγ	PROPN
cana-1315	129	9	h.	h.	NOUN
cana-1315	129	10	therefore	therefore	ADV
cana-1315	129	11	,	,	PUNCT
cana-1315	129	12	h	h	NOUN
cana-1315	129	13	is	be	AUX
cana-1315	129	14	a	a	DET
cana-1315	129	15	tssr	tssr	NOUN
cana-1315	129	16	of	of	ADP
cana-1315	129	17	t.	t.	PROPN
cana-1315	129	18	hence	hence	ADV
cana-1315	129	19	h=	h=	NOUN
cana-1315	129	20	or	or	CCONJ
cana-1315	129	21	a	a	DET
cana-1315	129	22	tssr	tssr	NOUN
cana-1315	129	23	of	of	ADP
cana-1315	129	24	t.	t.	NOUN
cana-1315	129	25	th.3.7	th.3.7	NOUN
cana-1315	129	26	:	:	PUNCT
cana-1315	129	27	if	if	SCONJ
cana-1315	129	28	p	p	PRON
cana-1315	129	29	be	be	VERB
cana-1315	129	30	an	an	DET
cana-1315	129	31	aftssr	aftssr	NOUN
cana-1315	129	32	of	of	ADP
cana-1315	129	33	a	a	DET
cana-1315	129	34	tsr	tsr	PROPN
cana-1315	129	35	(	(	PUNCT
cana-1315	129	36	t	t	PROPN
cana-1315	129	37	,	,	PUNCT
cana-1315	129	38	+	+	PROPN
cana-1315	129	39	,	,	PUNCT
cana-1315	129	40	∙	∙	PROPN
cana-1315	129	41	)	)	PUNCT
cana-1315	129	42	,	,	PUNCT
cana-1315	129	43	then	then	ADV
cana-1315	129	44	if	if	SCONJ
cana-1315	129	45			NOUN
cana-1315	129	46			PUNCT
cana-1315	129	47	u	u	NOUN
cana-1315	129	48	=	=	SYM
cana-1315	129	49	1	1	NUM
cana-1315	129	50	,	,	PUNCT
cana-1315	129	51	then	then	ADV
cana-1315	129	52	either	either	CCONJ
cana-1315	129	53			NOUN
cana-1315	129	54	u	u	NUM
cana-1315	130	1	=	=	SYM
cana-1315	130	2	1	1	NUM
cana-1315	130	3	or	or	CCONJ
cana-1315	130	4			NOUN
cana-1315	130	5	u	u	NOUN
cana-1315	130	6	=	=	SYM
cana-1315	130	7	1	1	NUM
cana-1315	130	8	,	,	PUNCT
cana-1315	130	9			NOUN
cana-1315	130	10	α	α	NOUN
cana-1315	130	11	,	,	PUNCT
cana-1315	130	12	β	β	X
cana-1315	130	13	in	in	ADP
cana-1315	130	14	t.	t.	PROPN
cana-1315	130	15	pf	pf	PROPN
cana-1315	130	16	.	.	PUNCT
cana-1315	130	17	:	:	PUNCT
cana-1315	131	1	let	let	VERB
cana-1315	131	2	α	α	PRON
cana-1315	131	3	and	and	CCONJ
cana-1315	131	4	β	β	X
cana-1315	131	5	in	in	ADP
cana-1315	131	6	t.	t.	PROPN
cana-1315	131	7	by	by	ADP
cana-1315	131	8	the	the	DET
cana-1315	131	9	definition	definition	NOUN
cana-1315	131	10			NOUN
cana-1315	131	11			PUNCT
cana-1315	131	12	u	u	ADV
cana-1315	131	13	≤	≤	ADJ
cana-1315	131	14	max	max	PROPN
cana-1315	131	15	{	{	PUNCT
cana-1315	131	16			PROPN
cana-1315	131	17	u	u	PROPN
cana-1315	131	18	,	,	PUNCT
cana-1315	131	19			PROPN
cana-1315	131	20	u	u	PROPN
cana-1315	131	21	}	}	PUNCT
cana-1315	131	22	,	,	PUNCT
cana-1315	131	23			NOUN
cana-1315	131	24	1	1	NUM
cana-1315	131	25	≤	≤	NUM
cana-1315	131	26	max	max	PROPN
cana-1315	131	27	{	{	PUNCT
cana-1315	131	28			PROPN
cana-1315	131	29	u	u	PROPN
cana-1315	131	30	,	,	PUNCT
cana-1315	131	31			PROPN
cana-1315	131	32	u	u	PROPN
cana-1315	131	33	}	}	PUNCT
cana-1315	131	34	.	.	PUNCT
cana-1315	132	1	therefore	therefore	ADV
cana-1315	132	2	,	,	PUNCT
cana-1315	132	3	either	either	CCONJ
cana-1315	132	4			NOUN
cana-1315	132	5	u	u	NUM
cana-1315	132	6	=	=	SYM
cana-1315	132	7	1	1	NUM
cana-1315	132	8	or	or	CCONJ
cana-1315	132	9			NOUN
cana-1315	132	10	u	u	NOUN
cana-1315	132	11	=	=	PUNCT
cana-1315	132	12	1	1	X
cana-1315	132	13	.	.	PUNCT
cana-1315	132	14	th.3.8	th.3.8	VERB
cana-1315	132	15	:	:	PUNCT
cana-1315	132	16	let	let	VERB
cana-1315	132	17	p	p	PRON
cana-1315	132	18	be	be	AUX
cana-1315	132	19	an	an	DET
cana-1315	132	20	aftssr	aftssr	NOUN
cana-1315	132	21	of	of	ADP
cana-1315	132	22	a	a	DET
cana-1315	132	23	tsr	tsr	PROPN
cana-1315	132	24	t	t	PROPN
cana-1315	132	25	and	and	CCONJ
cana-1315	132	26	f	f	PROPN
cana-1315	132	27	,	,	PUNCT
cana-1315	132	28	an	an	DET
cana-1315	132	29	isomorphism	isomorphism	NOUN
cana-1315	132	30	from	from	ADP
cana-1315	132	31	a	a	DET
cana-1315	132	32	tsrt	tsrt	NOUN
cana-1315	132	33	onto	onto	ADP
cana-1315	132	34	s.	s.	PROPN
cana-1315	132	35	then	then	ADV
cana-1315	132	36	p	p	X
cana-1315	132	37	◦	◦	NOUN
cana-1315	132	38	f	f	X
cana-1315	132	39	is	be	AUX
cana-1315	132	40	an	an	DET
cana-1315	132	41	aftssr	aftssr	NOUN
cana-1315	132	42	of	of	ADP
cana-1315	132	43	t.	t.	PROPN
cana-1315	132	44	pf	pf	PROPN
cana-1315	132	45	.	.	PUNCT
cana-1315	132	46	:	:	PUNCT
cana-1315	132	47	let	let	VERB
cana-1315	132	48	α	α	PRON
cana-1315	132	49	,	,	PUNCT
cana-1315	132	50	β	β	X
cana-1315	132	51	and	and	CCONJ
cana-1315	132	52	γ	γ	PROPN
cana-1315	132	53	in	in	ADP
cana-1315	132	54	t	t	PROPN
cana-1315	132	55	and	and	CCONJ
cana-1315	132	56	p	p	NOUN
cana-1315	132	57	be	be	AUX
cana-1315	132	58	an	an	DET
cana-1315	132	59	aftssr	aftssr	NOUN
cana-1315	132	60	of	of	ADP
cana-1315	132	61	a	a	DET
cana-1315	132	62	tsrt	tsrt	NOUN
cana-1315	132	63	.	.	PUNCT
cana-1315	133	1	then	then	ADV
cana-1315	133	2	we	we	PRON
cana-1315	133	3	have	have	VERB
cana-1315	133	4	,	,	PUNCT
cana-1315	133	5	(	(	PUNCT
cana-1315	133	6	fp	fp	INTJ
cana-1315	133	7			PROPN
cana-1315	133	8	)	)	PUNCT
cana-1315	133	9	(	(	PUNCT
cana-1315	133	10	α	α	NOUN
cana-1315	133	11	+	+	NOUN
cana-1315	133	12	β	β	X
cana-1315	133	13	)	)	PUNCT
cana-1315	133	14	=	=	SYM
cana-1315	133	15	p	p	NOUN
cana-1315	133	16	(	(	PUNCT
cana-1315	133	17	f(α	f(α	NOUN
cana-1315	133	18	+	+	CCONJ
cana-1315	133	19	β	β	NOUN
cana-1315	133	20	)	)	PUNCT
cana-1315	133	21	)	)	PUNCT
cana-1315	134	1	=	=	SYM
cana-1315	134	2	p	p	NOUN
cana-1315	134	3	(	(	PUNCT
cana-1315	134	4	f(α)+	f(α)+	PROPN
cana-1315	134	5	f(β	f(β	PROPN
cana-1315	134	6	)	)	PUNCT
cana-1315	134	7	)	)	PUNCT
cana-1315	135	1	≤	≤	NUM
cana-1315	135	2	max	max	PROPN
cana-1315	135	3	{	{	PUNCT
cana-1315	135	4	p	p	X
cana-1315	135	5	(	(	PUNCT
cana-1315	135	6	f(α	f(α	NOUN
cana-1315	135	7	)	)	PUNCT
cana-1315	135	8	)	)	PUNCT
cana-1315	135	9	,	,	PUNCT
cana-1315	135	10	p	p	X
cana-1315	135	11	(	(	PUNCT
cana-1315	135	12	f(β	f(β	NOUN
cana-1315	135	13	)	)	PUNCT
cana-1315	135	14	)	)	PUNCT
cana-1315	135	15	}	}	PUNCT
cana-1315	135	16	≤	≤	NUM
cana-1315	135	17	max	max	PROPN
cana-1315	135	18	{	{	PUNCT
cana-1315	135	19	(	(	PUNCT
cana-1315	135	20	fp	fp	INTJ
cana-1315	135	21			PROPN
cana-1315	135	22	)	)	PUNCT
cana-1315	135	23	(	(	PUNCT
cana-1315	135	24	α	α	NOUN
cana-1315	135	25	)	)	PUNCT
cana-1315	135	26	,	,	PUNCT
cana-1315	135	27	(	(	PUNCT
cana-1315	135	28	fp	fp	INTJ
cana-1315	135	29			PROPN
cana-1315	135	30	)	)	PUNCT
cana-1315	135	31	(	(	PUNCT
cana-1315	135	32	β	β	NOUN
cana-1315	135	33	)	)	PUNCT
cana-1315	135	34	}	}	PUNCT
cana-1315	135	35	,	,	PUNCT
cana-1315	135	36			NOUN
cana-1315	135	37	(	(	PUNCT
cana-1315	135	38	fp	fp	INTJ
cana-1315	135	39			PROPN
cana-1315	135	40	)	)	PUNCT
cana-1315	135	41	(	(	PUNCT
cana-1315	135	42	α	α	NOUN
cana-1315	135	43	+	+	NOUN
cana-1315	135	44	β	β	X
cana-1315	135	45	)	)	PUNCT
cana-1315	135	46	≤	≤	NOUN
cana-1315	135	47	max	max	PROPN
cana-1315	135	48	{	{	PUNCT
cana-1315	135	49	(	(	PUNCT
cana-1315	135	50	fp	fp	INTJ
cana-1315	135	51			PROPN
cana-1315	135	52	)	)	PUNCT
cana-1315	135	53	(	(	PUNCT
cana-1315	135	54	α	α	NOUN
cana-1315	135	55	)	)	PUNCT
cana-1315	135	56	,	,	PUNCT
cana-1315	135	57	(	(	PUNCT
cana-1315	135	58	fp	fp	INTJ
cana-1315	135	59			PROPN
cana-1315	135	60	)	)	PUNCT
cana-1315	135	61	(	(	PUNCT
cana-1315	135	62	β	β	NOUN
cana-1315	135	63	)	)	PUNCT
cana-1315	135	64	}	}	PUNCT
cana-1315	135	65	.	.	PUNCT
cana-1315	136	1	and	and	CCONJ
cana-1315	136	2	(	(	PUNCT
cana-1315	136	3	fp	fp	INTJ
cana-1315	136	4			PROPN
cana-1315	136	5	)	)	PUNCT
cana-1315	136	6	(	(	PUNCT
cana-1315	136	7	αβγ	αβγ	NOUN
cana-1315	136	8	)	)	PUNCT
cana-1315	136	9	=	=	SYM
cana-1315	136	10	p	p	X
cana-1315	136	11	(	(	PUNCT
cana-1315	136	12	f(αβγ	f(αβγ	NOUN
cana-1315	136	13	)	)	PUNCT
cana-1315	136	14	)	)	PUNCT
cana-1315	137	1	=	=	SYM
cana-1315	137	2	p	p	X
cana-1315	137	3	(	(	PUNCT
cana-1315	137	4	f(α)f(β)f(γ	f(α)f(β)f(γ	NUM
cana-1315	137	5	)	)	PUNCT
cana-1315	137	6	)	)	PUNCT
cana-1315	138	1	≤	≤	NUM
cana-1315	138	2	max	max	PROPN
cana-1315	138	3	{	{	PUNCT
cana-1315	138	4	p	p	X
cana-1315	138	5	(	(	PUNCT
cana-1315	138	6	f(α	f(α	NOUN
cana-1315	138	7	)	)	PUNCT
cana-1315	138	8	)	)	PUNCT
cana-1315	138	9	,	,	PUNCT
cana-1315	138	10	p	p	X
cana-1315	138	11	(	(	PUNCT
cana-1315	138	12	f(β	f(β	NOUN
cana-1315	138	13	)	)	PUNCT
cana-1315	138	14	)	)	PUNCT
cana-1315	138	15	,	,	PUNCT
cana-1315	138	16	p	p	NOUN
cana-1315	138	17	(	(	PUNCT
cana-1315	138	18	f(γ))}≤	f(γ))}≤	PROPN
cana-1315	138	19	max	max	NOUN
cana-1315	138	20	{	{	PUNCT
cana-1315	138	21	(	(	PUNCT
cana-1315	138	22	fp	fp	INTJ
cana-1315	138	23			PROPN
cana-1315	138	24	)	)	PUNCT
cana-1315	138	25	(	(	PUNCT
cana-1315	138	26	α	α	NOUN
cana-1315	138	27	)	)	PUNCT
cana-1315	138	28	,	,	PUNCT
cana-1315	138	29	(	(	PUNCT
cana-1315	138	30	fp	fp	INTJ
cana-1315	138	31			PROPN
cana-1315	138	32	)	)	PUNCT
cana-1315	138	33	(	(	PUNCT
cana-1315	138	34	β	β	NOUN
cana-1315	138	35	)	)	PUNCT
cana-1315	138	36	,	,	PUNCT
cana-1315	138	37	(	(	PUNCT
cana-1315	138	38	fp	fp	INTJ
cana-1315	138	39			PROPN
cana-1315	138	40	)	)	PUNCT
cana-1315	138	41	(	(	PUNCT
cana-1315	138	42	γ)}	γ)}	X
cana-1315	138	43	(	(	PUNCT
cana-1315	138	44	fp	fp	INTJ
cana-1315	138	45			PROPN
cana-1315	138	46	)	)	PUNCT
cana-1315	138	47	(	(	PUNCT
cana-1315	138	48	αβγ	αβγ	NOUN
cana-1315	138	49	)	)	PUNCT
cana-1315	138	50	≤	≤	NUM
cana-1315	138	51	max	max	PROPN
cana-1315	138	52	{	{	PUNCT
cana-1315	138	53	(	(	PUNCT
cana-1315	138	54	fp	fp	INTJ
cana-1315	138	55			PROPN
cana-1315	138	56	)	)	PUNCT
cana-1315	138	57	(	(	PUNCT
cana-1315	138	58	α	α	NOUN
cana-1315	138	59	)	)	PUNCT
cana-1315	138	60	,	,	PUNCT
cana-1315	138	61	(	(	PUNCT
cana-1315	138	62	fp	fp	INTJ
cana-1315	138	63			PROPN
cana-1315	138	64	)	)	PUNCT
cana-1315	138	65	(	(	PUNCT
cana-1315	138	66	β	β	NOUN
cana-1315	138	67	)	)	PUNCT
cana-1315	138	68	,	,	PUNCT
cana-1315	138	69	(	(	PUNCT
cana-1315	138	70	fp	fp	INTJ
cana-1315	138	71			PROPN
cana-1315	138	72	)	)	PUNCT
cana-1315	138	73	(	(	PUNCT
cana-1315	138	74	γ	γ	X
cana-1315	138	75	)	)	PUNCT
cana-1315	138	76	}	}	PUNCT
cana-1315	138	77	.	.	PUNCT
cana-1315	139	1	thus	thus	ADV
cana-1315	139	2	(	(	PUNCT
cana-1315	139	3	fp	fp	INTJ
cana-1315	139	4			PROPN
cana-1315	139	5	)	)	PUNCT
cana-1315	139	6	is	be	AUX
cana-1315	139	7	an	an	DET
cana-1315	139	8	aftssr	aftssr	NOUN
cana-1315	139	9	of	of	ADP
cana-1315	139	10	a	a	DET
cana-1315	139	11	tsrt	tsrt	NOUN
cana-1315	139	12	.	.	PUNCT
cana-1315	140	1	th.3.9	th.3.9	NOUN
cana-1315	140	2	:	:	PUNCT
cana-1315	140	3	let	let	VERB
cana-1315	140	4	p	p	PRON
cana-1315	140	5	be	be	AUX
cana-1315	140	6	an	an	DET
cana-1315	140	7	aftssr	aftssr	NOUN
cana-1315	140	8	of	of	ADP
cana-1315	140	9	a	a	DET
cana-1315	140	10	tsrt	tsrt	NOUN
cana-1315	140	11	and	and	CCONJ
cana-1315	140	12	h	h	NOUN
cana-1315	140	13	be	be	AUX
cana-1315	140	14	an	an	DET
cana-1315	140	15	anti	anti	ADJ
cana-1315	140	16	-	-	NOUN
cana-1315	140	17	isomorphism	isomorphism	NOUN
cana-1315	140	18	from	from	ADP
cana-1315	140	19	a	a	DET
cana-1315	140	20	tsrt	tsrt	NOUN
cana-1315	140	21	onto	onto	ADP
cana-1315	140	22	s.	s.	PROPN
cana-1315	140	23	then	then	ADV
cana-1315	140	24	hp	hp	X
cana-1315	140	25			PROPN
cana-1315	140	26	is	be	AUX
cana-1315	140	27	an	an	DET
cana-1315	140	28	aftssr	aftssr	NOUN
cana-1315	140	29	of	of	ADP
cana-1315	140	30	t.	t.	PROPN
cana-1315	140	31	pf	pf	PROPN
cana-1315	140	32	.	.	PUNCT
cana-1315	140	33	:	:	PUNCT
cana-1315	140	34	let	let	VERB
cana-1315	140	35	a	a	DET
cana-1315	140	36	,	,	PUNCT
cana-1315	140	37	b	b	NOUN
cana-1315	140	38	and	and	CCONJ
cana-1315	140	39	c	c	PROPN
cana-1315	140	40	in	in	ADP
cana-1315	140	41	t	t	PROPN
cana-1315	140	42	and	and	CCONJ
cana-1315	140	43	p	p	NOUN
cana-1315	140	44	be	be	AUX
cana-1315	140	45	an	an	DET
cana-1315	140	46	aftssr	aftssr	NOUN
cana-1315	140	47	of	of	ADP
cana-1315	140	48	a	a	DET
cana-1315	140	49	tsrt	tsrt	NOUN
cana-1315	140	50	.	.	PUNCT
cana-1315	141	1	then	then	ADV
cana-1315	141	2	we	we	PRON
cana-1315	141	3	have	have	AUX
cana-1315	141	4	,	,	PUNCT
cana-1315	141	5	(	(	PUNCT
cana-1315	141	6	hp	hp	X
cana-1315	141	7			PROPN
cana-1315	141	8	)	)	PUNCT
cana-1315	141	9	(	(	PUNCT
cana-1315	141	10	α	α	NOUN
cana-1315	141	11	+	+	X
cana-1315	141	12	β)=	β)=	X
cana-1315	141	13	p	p	NOUN
cana-1315	141	14	(	(	PUNCT
cana-1315	141	15	h(α	h(α	PROPN
cana-1315	141	16	+	+	CCONJ
cana-1315	141	17	β	β	NOUN
cana-1315	141	18	)	)	PUNCT
cana-1315	141	19	)	)	PUNCT
cana-1315	142	1	=	=	SYM
cana-1315	142	2	p	p	X
cana-1315	142	3	(	(	PUNCT
cana-1315	142	4	h(α	h(α	ADJ
cana-1315	142	5	)	)	PUNCT
cana-1315	142	6	+	+	CCONJ
cana-1315	142	7	h(β	h(β	NOUN
cana-1315	142	8	)	)	PUNCT
cana-1315	142	9	)	)	PUNCT
cana-1315	143	1	≤	≤	NUM
cana-1315	143	2	max	max	PROPN
cana-1315	143	3	{	{	PUNCT
cana-1315	143	4	p	p	X
cana-1315	143	5	(	(	PUNCT
cana-1315	143	6	h(α	h(α	ADJ
cana-1315	143	7	)	)	PUNCT
cana-1315	143	8	)	)	PUNCT
cana-1315	143	9	,	,	PUNCT
cana-1315	143	10	p	p	X
cana-1315	143	11	(	(	PUNCT
cana-1315	143	12	h(β	h(β	PROPN
cana-1315	143	13	)	)	PUNCT
cana-1315	143	14	)	)	PUNCT
cana-1315	143	15	}	}	PUNCT
cana-1315	143	16	≤	≤	NUM
cana-1315	143	17	max	max	PROPN
cana-1315	143	18	{	{	PUNCT
cana-1315	143	19	(	(	PUNCT
cana-1315	143	20	hp	hp	PROPN
cana-1315	143	21			PROPN
cana-1315	143	22	)	)	PUNCT
cana-1315	143	23	(	(	PUNCT
cana-1315	143	24	α	α	NOUN
cana-1315	143	25	)	)	PUNCT
cana-1315	143	26	,	,	PUNCT
cana-1315	143	27	(	(	PUNCT
cana-1315	143	28	hp	hp	PROPN
cana-1315	143	29			PROPN
cana-1315	143	30	)	)	PUNCT
cana-1315	143	31	(	(	PUNCT
cana-1315	143	32	β	β	NOUN
cana-1315	143	33	)	)	PUNCT
cana-1315	143	34	}	}	PUNCT
cana-1315	143	35	,	,	PUNCT
cana-1315	143	36			NOUN
cana-1315	143	37	(	(	PUNCT
cana-1315	143	38	hp	hp	NOUN
cana-1315	143	39			PROPN
cana-1315	143	40	)	)	PUNCT
cana-1315	143	41	(	(	PUNCT
cana-1315	143	42	α	α	NOUN
cana-1315	143	43	+	+	NOUN
cana-1315	143	44	β	β	X
cana-1315	143	45	)	)	PUNCT
cana-1315	143	46	≤	≤	NUM
cana-1315	143	47	max	max	PROPN
cana-1315	143	48	{	{	PUNCT
cana-1315	143	49	(	(	PUNCT
cana-1315	143	50	hp	hp	PROPN
cana-1315	143	51			PROPN
cana-1315	143	52	)	)	PUNCT
cana-1315	143	53	(	(	PUNCT
cana-1315	143	54	α	α	NOUN
cana-1315	143	55	)	)	PUNCT
cana-1315	143	56	,	,	PUNCT
cana-1315	143	57	(	(	PUNCT
cana-1315	143	58	hp	hp	PROPN
cana-1315	143	59			PROPN
cana-1315	143	60	)	)	PUNCT
cana-1315	143	61	(	(	PUNCT
cana-1315	143	62	β	β	NOUN
cana-1315	143	63	)	)	PUNCT
cana-1315	143	64	}	}	PUNCT
cana-1315	143	65	.	.	PUNCT
cana-1315	144	1	and	and	CCONJ
cana-1315	144	2	(	(	PUNCT
cana-1315	144	3	hp	hp	PROPN
cana-1315	144	4			PROPN
cana-1315	144	5	)	)	PUNCT
cana-1315	144	6	(	(	PUNCT
cana-1315	144	7	αβγ)=	αβγ)=	PROPN
cana-1315	144	8	p	p	PROPN
cana-1315	144	9	(	(	PUNCT
cana-1315	144	10	h(αβγ))=	h(αβγ))=	NOUN
cana-1315	144	11	p	p	NOUN
cana-1315	144	12	(	(	PUNCT
cana-1315	144	13	h(γ)h(β)h(α	h(γ)h(β)h(α	NOUN
cana-1315	144	14	)	)	PUNCT
cana-1315	144	15	)	)	PUNCT
cana-1315	144	16	communications	communication	NOUN
cana-1315	144	17	on	on	ADP
cana-1315	144	18	applied	apply	VERB
cana-1315	144	19	nonlinear	nonlinear	ADJ
cana-1315	144	20	analysis	analysis	NOUN
cana-1315	144	21	issn	issn	NOUN
cana-1315	144	22	:	:	PUNCT
cana-1315	144	23	1074	1074	NUM
cana-1315	144	24	-	-	PUNCT
cana-1315	144	25	133x	133x	NUM
cana-1315	144	26	vol	vol	NOUN
cana-1315	144	27	31	31	NUM
cana-1315	144	28	no	no	NOUN
cana-1315	144	29	.	.	PUNCT
cana-1315	145	1	7s	7	NOUN
cana-1315	145	2	(	(	PUNCT
cana-1315	145	3	2024	2024	NUM
cana-1315	145	4	)	)	PUNCT
cana-1315	146	1	362	362	NUM
cana-1315	146	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1315	146	3	≤	≤	NUM
cana-1315	146	4	max	max	PROPN
cana-1315	146	5	{	{	PUNCT
cana-1315	146	6	p	p	X
cana-1315	146	7	(	(	PUNCT
cana-1315	146	8	h(α	h(α	ADJ
cana-1315	146	9	)	)	PUNCT
cana-1315	146	10	)	)	PUNCT
cana-1315	146	11	,	,	PUNCT
cana-1315	146	12	p	p	X
cana-1315	146	13	(	(	PUNCT
cana-1315	146	14	h(β	h(β	PROPN
cana-1315	146	15	)	)	PUNCT
cana-1315	146	16	,	,	PUNCT
cana-1315	146	17	p	p	X
cana-1315	146	18	(	(	PUNCT
cana-1315	146	19	h(γ	h(γ	PROPN
cana-1315	146	20	)	)	PUNCT
cana-1315	146	21	)	)	PUNCT
cana-1315	146	22	}	}	PUNCT
cana-1315	146	23	≤	≤	NUM
cana-1315	146	24	max	max	PROPN
cana-1315	146	25	{	{	PUNCT
cana-1315	146	26	(	(	PUNCT
cana-1315	146	27	hp	hp	PROPN
cana-1315	146	28			PROPN
cana-1315	146	29	)	)	PUNCT
cana-1315	146	30	(	(	PUNCT
cana-1315	146	31	α	α	NOUN
cana-1315	146	32	)	)	PUNCT
cana-1315	146	33	,	,	PUNCT
cana-1315	146	34	(	(	PUNCT
cana-1315	146	35	hp	hp	PROPN
cana-1315	146	36			PROPN
cana-1315	146	37	)	)	PUNCT
cana-1315	146	38	(	(	PUNCT
cana-1315	146	39	β	β	NOUN
cana-1315	146	40	)	)	PUNCT
cana-1315	146	41	,	,	PUNCT
cana-1315	146	42	(	(	PUNCT
cana-1315	146	43	hp	hp	PROPN
cana-1315	146	44			PROPN
cana-1315	146	45	)	)	PUNCT
cana-1315	146	46	(	(	PUNCT
cana-1315	146	47	γ	γ	NOUN
cana-1315	146	48	)	)	PUNCT
cana-1315	146	49	}	}	PUNCT
cana-1315	146	50	,	,	PUNCT
cana-1315	146	51			NOUN
cana-1315	146	52	(	(	PUNCT
cana-1315	146	53	hp	hp	NOUN
cana-1315	146	54			PROPN
cana-1315	146	55	)	)	PUNCT
cana-1315	146	56	(	(	PUNCT
cana-1315	146	57	αβγ	αβγ	NOUN
cana-1315	146	58	)	)	PUNCT
cana-1315	146	59	≤	≤	NUM
cana-1315	146	60	max	max	PROPN
cana-1315	146	61	{	{	PUNCT
cana-1315	146	62	(	(	PUNCT
cana-1315	146	63	hp	hp	PROPN
cana-1315	146	64			PROPN
cana-1315	146	65	)	)	PUNCT
cana-1315	146	66	(	(	PUNCT
cana-1315	146	67	α	α	NOUN
cana-1315	146	68	)	)	PUNCT
cana-1315	146	69	,	,	PUNCT
cana-1315	146	70	(	(	PUNCT
cana-1315	146	71	hp	hp	PROPN
cana-1315	146	72			PROPN
cana-1315	146	73	)	)	PUNCT
cana-1315	146	74	(	(	PUNCT
cana-1315	146	75	β	β	NOUN
cana-1315	146	76	)	)	PUNCT
cana-1315	146	77	,	,	PUNCT
cana-1315	146	78	(	(	PUNCT
cana-1315	146	79	hp	hp	PROPN
cana-1315	146	80			PROPN
cana-1315	146	81	)	)	PUNCT
cana-1315	146	82	(	(	PUNCT
cana-1315	146	83	γ	γ	NOUN
cana-1315	146	84	)	)	PUNCT
cana-1315	146	85	}	}	PUNCT
cana-1315	146	86	.	.	PUNCT
cana-1315	147	1	therefore	therefore	ADV
cana-1315	147	2	,	,	PUNCT
cana-1315	147	3	hp	hp	PROPN
cana-1315	147	4			PROPN
cana-1315	147	5	is	be	AUX
cana-1315	147	6	aftssr	aftssr	NUM
cana-1315	147	7	of	of	ADP
cana-1315	147	8	a	a	DET
cana-1315	147	9	tsrt	tsrt	NOUN
cana-1315	147	10	.	.	PUNCT
cana-1315	147	11	th.3.10	th.3.10	PROPN
cana-1315	147	12	:	:	PUNCT
cana-1315	147	13	suppose	suppose	VERB
cana-1315	147	14	p	p	X
cana-1315	147	15	be	be	AUX
cana-1315	147	16	an	an	DET
cana-1315	147	17	aftssr	aftssr	NOUN
cana-1315	147	18	of	of	ADP
cana-1315	147	19	a	a	DET
cana-1315	147	20	tsr	tsr	PROPN
cana-1315	147	21	(	(	PUNCT
cana-1315	147	22	t	t	PROPN
cana-1315	147	23	,	,	PUNCT
cana-1315	147	24	+	+	PROPN
cana-1315	147	25	,	,	PUNCT
cana-1315	147	26	.	.	PUNCT
cana-1315	147	27	)	)	PUNCT
cana-1315	147	28	.	.	PUNCT
cana-1315	148	1	the	the	DET
cana-1315	148	2	pseudo	pseudo	NOUN
cana-1315	148	3	anti	anti	ADJ
cana-1315	148	4	-	-	ADJ
cana-1315	148	5	fuzzy	fuzzy	ADJ
cana-1315	148	6	coset	coset	NOUN
cana-1315	148	7	(	(	PUNCT
cana-1315	148	8	p	p	NOUN
cana-1315	148	9	)	)	PUNCT
cana-1315	148	10	p	p	NOUN
cana-1315	148	11	is	be	AUX
cana-1315	148	12	an	an	DET
cana-1315	148	13	aftssr	aftssr	NOUN
cana-1315	148	14	of	of	ADP
cana-1315	148	15	a	a	DET
cana-1315	148	16	tsrt	tsrt	NOUN
cana-1315	148	17	,	,	PUNCT
cana-1315	148	18	for	for	ADP
cana-1315	148	19	a	a	DET
cana-1315	148	20	in	in	ADP
cana-1315	148	21	t.	t.	PROPN
cana-1315	148	22	pf	pf	PROPN
cana-1315	148	23	.	.	PUNCT
cana-1315	148	24	:	:	PUNCT
cana-1315	149	1	let	let	VERB
cana-1315	149	2	p	p	PRON
cana-1315	149	3	be	be	AUX
cana-1315	149	4	an	an	DET
cana-1315	149	5	aftssr	aftssr	NOUN
cana-1315	149	6	of	of	ADP
cana-1315	149	7	a	a	DET
cana-1315	149	8	tsr	tsr	PROPN
cana-1315	149	9	t.	t.	NOUN
cana-1315	149	10	for	for	ADP
cana-1315	149	11	every	every	DET
cana-1315	149	12	α	α	NOUN
cana-1315	149	13	,	,	PUNCT
cana-1315	149	14	β	β	X
cana-1315	149	15	and	and	CCONJ
cana-1315	149	16	γ	γ	PROPN
cana-1315	149	17	in	in	ADP
cana-1315	149	18	t	t	PROPN
cana-1315	149	19	,	,	PUNCT
cana-1315	149	20	we	we	PRON
cana-1315	149	21	have,((x	have,((x	VERB
cana-1315	149	22	p	p	NOUN
cana-1315	149	23	)	)	PUNCT
cana-1315	150	1	p	p	NOUN
cana-1315	150	2	)	)	PUNCT
cana-1315	150	3	(	(	PUNCT
cana-1315	150	4	α	α	NOUN
cana-1315	150	5	+	+	NOUN
cana-1315	150	6	β	β	X
cana-1315	150	7	)	)	PUNCT
cana-1315	150	8	=	=	SYM
cana-1315	150	9	p(x	p(x	NOUN
cana-1315	150	10	)	)	PUNCT
cana-1315	150	11	p	p	NOUN
cana-1315	150	12	(	(	PUNCT
cana-1315	150	13	α	α	NOUN
cana-1315	150	14	+	+	NOUN
cana-1315	150	15	β	β	X
cana-1315	150	16	)	)	PUNCT
cana-1315	150	17	≤	≤	NUM
cana-1315	150	18	p(x)max	p(x)max	PROPN
cana-1315	150	19	{	{	PUNCT
cana-1315	150	20	p	p	X
cana-1315	150	21	(	(	PUNCT
cana-1315	150	22	α	α	NOUN
cana-1315	150	23	)	)	PUNCT
cana-1315	150	24	,	,	PUNCT
cana-1315	150	25	p	p	X
cana-1315	150	26	(	(	PUNCT
cana-1315	150	27	β	β	NOUN
cana-1315	150	28	)	)	PUNCT
cana-1315	150	29	}	}	PUNCT
cana-1315	150	30	=	=	SYM
cana-1315	150	31	max{p(x	max{p(x	PROPN
cana-1315	150	32	)	)	PUNCT
cana-1315	150	33	p	p	NOUN
cana-1315	150	34	(	(	PUNCT
cana-1315	150	35	α	α	NOUN
cana-1315	150	36	)	)	PUNCT
cana-1315	150	37	,	,	PUNCT
cana-1315	150	38	p(x	p(x	PROPN
cana-1315	150	39	)	)	PUNCT
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cana-1315	150	42	β	β	NOUN
cana-1315	150	43	)	)	PUNCT
cana-1315	150	44	}	}	PUNCT
cana-1315	150	45	=	=	SYM
cana-1315	150	46	max	max	X
cana-1315	150	47	{	{	PUNCT
cana-1315	150	48	(	(	PUNCT
cana-1315	150	49	(	(	PUNCT
cana-1315	150	50	x	x	SYM
cana-1315	150	51	p	p	X
cana-1315	150	52	)	)	PUNCT
cana-1315	150	53	p	p	NOUN
cana-1315	150	54	)	)	PUNCT
cana-1315	150	55	(	(	PUNCT
cana-1315	150	56	α	α	NOUN
cana-1315	150	57	)	)	PUNCT
cana-1315	150	58	,	,	PUNCT
cana-1315	150	59	(	(	PUNCT
cana-1315	150	60	(	(	PUNCT
cana-1315	150	61	x	x	X
cana-1315	150	62	p	p	X
cana-1315	150	63	)	)	PUNCT
cana-1315	150	64	p	p	NOUN
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cana-1315	150	66	(	(	PUNCT
cana-1315	150	67	β	β	NOUN
cana-1315	150	68	)	)	PUNCT
cana-1315	150	69	}	}	PUNCT
cana-1315	150	70	.	.	PUNCT
cana-1315	151	1	((x	((x	VERB
cana-1315	151	2	p	p	NOUN
cana-1315	151	3	)	)	PUNCT
cana-1315	152	1	p	p	NOUN
cana-1315	152	2	)	)	PUNCT
cana-1315	152	3	(	(	PUNCT
cana-1315	152	4	α	α	NOUN
cana-1315	152	5	+	+	NOUN
cana-1315	152	6	β	β	X
cana-1315	152	7	)	)	PUNCT
cana-1315	152	8	≤	≤	NOUN
cana-1315	152	9	max	max	PROPN
cana-1315	152	10	{	{	PUNCT
cana-1315	152	11	(	(	PUNCT
cana-1315	152	12	(	(	PUNCT
cana-1315	152	13	x	x	SYM
cana-1315	152	14	p	p	X
cana-1315	152	15	)	)	PUNCT
cana-1315	152	16	p	p	NOUN
cana-1315	152	17	)	)	PUNCT
cana-1315	152	18	(	(	PUNCT
cana-1315	152	19	α	α	NOUN
cana-1315	152	20	)	)	PUNCT
cana-1315	152	21	,	,	PUNCT
cana-1315	152	22	(	(	PUNCT
cana-1315	152	23	(	(	PUNCT
cana-1315	152	24	x	x	X
cana-1315	152	25	p	p	X
cana-1315	152	26	)	)	PUNCT
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cana-1315	152	29	(	(	PUNCT
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cana-1315	152	31	)	)	PUNCT
cana-1315	152	32	}	}	PUNCT
cana-1315	152	33	.	.	PUNCT
cana-1315	153	1	now	now	ADV
cana-1315	153	2	,	,	PUNCT
cana-1315	153	3	(	(	PUNCT
cana-1315	153	4	(	(	PUNCT
cana-1315	153	5	x	x	X
cana-1315	153	6	p	p	X
cana-1315	153	7	)	)	PUNCT
cana-1315	153	8	p	p	NOUN
cana-1315	153	9	)	)	PUNCT
cana-1315	153	10	(	(	PUNCT
cana-1315	153	11	αβγ	αβγ	NOUN
cana-1315	153	12	)	)	PUNCT
cana-1315	153	13	=	=	SYM
cana-1315	153	14	p(α	p(α	PROPN
cana-1315	153	15	)	)	PUNCT
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cana-1315	153	17	(	(	PUNCT
cana-1315	153	18	αβγ	αβγ	NOUN
cana-1315	153	19	)	)	PUNCT
cana-1315	153	20	≤	≤	NOUN
cana-1315	153	21	p(x	p(x	PROPN
cana-1315	153	22	)	)	PUNCT
cana-1315	153	23	max	max	PROPN
cana-1315	153	24	{	{	PUNCT
cana-1315	153	25	p	p	X
cana-1315	153	26	(	(	PUNCT
cana-1315	153	27	α	α	NOUN
cana-1315	153	28	)	)	PUNCT
cana-1315	153	29	,	,	PUNCT
cana-1315	153	30	p	p	X
cana-1315	153	31	(	(	PUNCT
cana-1315	153	32	β	β	NOUN
cana-1315	153	33	)	)	PUNCT
cana-1315	153	34	,	,	PUNCT
cana-1315	153	35	p	p	NOUN
cana-1315	153	36	(	(	PUNCT
cana-1315	153	37	γ)}=	γ)}=	PROPN
cana-1315	153	38	max	max	PROPN
cana-1315	153	39	{	{	PUNCT
cana-1315	153	40	p(x	p(x	PROPN
cana-1315	153	41	)	)	PUNCT
cana-1315	153	42	p	p	NOUN
cana-1315	153	43	(	(	PUNCT
cana-1315	153	44	α	α	NOUN
cana-1315	153	45	)	)	PUNCT
cana-1315	153	46	)	)	PUNCT
cana-1315	153	47	,	,	PUNCT
cana-1315	153	48	p(x	p(x	NOUN
cana-1315	153	49	)	)	PUNCT
cana-1315	153	50	p	p	NOUN
cana-1315	153	51	(	(	PUNCT
cana-1315	153	52	β	β	NOUN
cana-1315	153	53	)	)	PUNCT
cana-1315	153	54	}	}	PUNCT
cana-1315	153	55	=	=	SYM
cana-1315	153	56	max	max	X
cana-1315	153	57	{	{	PUNCT
cana-1315	153	58	(	(	PUNCT
cana-1315	153	59	(	(	PUNCT
cana-1315	153	60	x	x	SYM
cana-1315	153	61	p	p	X
cana-1315	153	62	)	)	PUNCT
cana-1315	153	63	p	p	NOUN
cana-1315	153	64	)	)	PUNCT
cana-1315	153	65	(	(	PUNCT
cana-1315	153	66	α	α	NOUN
cana-1315	153	67	)	)	PUNCT
cana-1315	153	68	,	,	PUNCT
cana-1315	153	69	(	(	PUNCT
cana-1315	153	70	(	(	PUNCT
cana-1315	153	71	x	x	X
cana-1315	153	72	p	p	X
cana-1315	153	73	)	)	PUNCT
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cana-1315	153	75	)	)	PUNCT
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cana-1315	153	77	β	β	NOUN
cana-1315	153	78	)	)	PUNCT
cana-1315	153	79	,	,	PUNCT
cana-1315	153	80	(	(	PUNCT
cana-1315	153	81	(	(	PUNCT
cana-1315	153	82	x	x	X
cana-1315	153	83	p	p	X
cana-1315	153	84	)	)	PUNCT
cana-1315	153	85	p	p	NOUN
cana-1315	153	86	)	)	PUNCT
cana-1315	153	87	(	(	PUNCT
cana-1315	153	88	γ	γ	NOUN
cana-1315	153	89	)	)	PUNCT
cana-1315	153	90	}	}	PUNCT
cana-1315	153	91	.	.	PUNCT
cana-1315	154	1			NOUN
cana-1315	154	2	(	(	PUNCT
cana-1315	154	3	(	(	PUNCT
cana-1315	154	4	x	x	X
cana-1315	154	5	p	p	X
cana-1315	154	6	)	)	PUNCT
cana-1315	154	7	p	p	NOUN
cana-1315	154	8	)	)	PUNCT
cana-1315	154	9	(	(	PUNCT
cana-1315	154	10	αβγ	αβγ	NOUN
cana-1315	154	11	)	)	PUNCT
cana-1315	154	12	≤	≤	NUM
cana-1315	154	13	max	max	NOUN
cana-1315	154	14	{	{	PUNCT
cana-1315	154	15	(	(	PUNCT
cana-1315	154	16	(	(	PUNCT
cana-1315	154	17	x	x	SYM
cana-1315	154	18	p	p	X
cana-1315	154	19	)	)	PUNCT
cana-1315	154	20	p	p	NOUN
cana-1315	154	21	)	)	PUNCT
cana-1315	154	22	)	)	PUNCT
cana-1315	154	23	(	(	PUNCT
cana-1315	154	24	α	α	NOUN
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cana-1315	154	26	,	,	PUNCT
cana-1315	154	27	(	(	PUNCT
cana-1315	154	28	(	(	PUNCT
cana-1315	154	29	x	x	X
cana-1315	154	30	p	p	X
cana-1315	154	31	)	)	PUNCT
cana-1315	154	32	p	p	NOUN
cana-1315	154	33	)	)	PUNCT
cana-1315	154	34	(	(	PUNCT
cana-1315	154	35	β	β	NOUN
cana-1315	154	36	)	)	PUNCT
cana-1315	154	37	,	,	PUNCT
cana-1315	154	38	(	(	PUNCT
cana-1315	154	39	(	(	PUNCT
cana-1315	154	40	(	(	PUNCT
cana-1315	154	41	x	x	X
cana-1315	154	42	p	p	X
cana-1315	154	43	)	)	PUNCT
cana-1315	154	44	p	p	NOUN
cana-1315	154	45	)	)	PUNCT
cana-1315	154	46	(	(	PUNCT
cana-1315	154	47	γ	γ	NOUN
cana-1315	154	48	)	)	PUNCT
cana-1315	154	49	}	}	PUNCT
cana-1315	154	50	.	.	PUNCT
cana-1315	155	1	hence	hence	ADV
cana-1315	155	2	(	(	PUNCT
cana-1315	155	3	(	(	PUNCT
cana-1315	155	4	x	x	X
cana-1315	155	5	p	p	X
cana-1315	155	6	)	)	PUNCT
cana-1315	155	7	p	p	NOUN
cana-1315	155	8	)	)	PUNCT
cana-1315	155	9	is	be	AUX
cana-1315	155	10	an	an	DET
cana-1315	155	11	aftssr	aftssr	NOUN
cana-1315	155	12	of	of	ADP
cana-1315	155	13	a	a	DET
cana-1315	155	14	tsrt	tsrt	NOUN
cana-1315	155	15	.	.	PUNCT
cana-1315	155	16	th.3.11	th.3.11	NOUN
cana-1315	155	17	:	:	PUNCT
cana-1315	156	1	let	let	VERB
cana-1315	156	2	(	(	PUNCT
cana-1315	156	3	t	t	NOUN
cana-1315	156	4	,	,	PUNCT
cana-1315	156	5	+	+	PROPN
cana-1315	156	6	,	,	PUNCT
cana-1315	156	7	.	.	PUNCT
cana-1315	156	8	)	)	PUNCT
cana-1315	157	1	and	and	CCONJ
cana-1315	157	2	(	(	PUNCT
cana-1315	157	3	t1	t1	NOUN
cana-1315	157	4	,	,	PUNCT
cana-1315	157	5	+	+	ADJ
cana-1315	157	6	,	,	PUNCT
cana-1315	157	7	.	.	PUNCT
cana-1315	157	8	)	)	PUNCT
cana-1315	157	9	be	be	AUX
cana-1315	157	10	any	any	DET
cana-1315	157	11	two	two	NUM
cana-1315	157	12	tsrs	tsr	NOUN
cana-1315	157	13	.	.	PUNCT
cana-1315	158	1	the	the	DET
cana-1315	158	2	homomorphic	homomorphic	ADJ
cana-1315	158	3	image	image	NOUN
cana-1315	158	4	of	of	ADP
cana-1315	158	5	an	an	DET
cana-1315	158	6	aftssr	aftssr	NOUN
cana-1315	158	7	of	of	ADP
cana-1315	158	8	t	t	PROPN
cana-1315	158	9	is	be	AUX
cana-1315	158	10	an	an	DET
cana-1315	158	11	aftssr	aftssr	NOUN
cana-1315	158	12	of	of	ADP
cana-1315	158	13	t1	t1	PROPN
cana-1315	158	14	.	.	PUNCT
cana-1315	159	1	pf	pf	PROPN
cana-1315	159	2	.	.	PUNCT
cana-1315	159	3	:	:	PUNCT
cana-1315	160	1	given	give	VERB
cana-1315	160	2	(	(	PUNCT
cana-1315	160	3	t	t	PROPN
cana-1315	160	4	,	,	PUNCT
cana-1315	160	5	+	+	NOUN
cana-1315	160	6	,	,	PUNCT
cana-1315	160	7	.	.	PUNCT
cana-1315	160	8	)	)	PUNCT
cana-1315	161	1	and	and	CCONJ
cana-1315	161	2	(	(	PUNCT
cana-1315	161	3	t1	t1	NOUN
cana-1315	161	4	,	,	PUNCT
cana-1315	161	5	+	+	ADJ
cana-1315	161	6	,	,	PUNCT
cana-1315	161	7	.	.	PUNCT
cana-1315	161	8	)	)	PUNCT
cana-1315	161	9	are	be	AUX
cana-1315	161	10	two	two	NUM
cana-1315	161	11	tsrs	tsr	NOUN
cana-1315	161	12	.	.	PUNCT
cana-1315	162	1	let	let	VERB
cana-1315	162	2	f	f	NOUN
cana-1315	162	3	:	:	PUNCT
cana-1315	162	4	tt1	tt1	ADV
cana-1315	162	5	be	be	AUX
cana-1315	162	6	a	a	DET
cana-1315	162	7	homomorphism	homomorphism	NOUN
cana-1315	162	8	.	.	PUNCT
cana-1315	163	1	then	then	ADV
cana-1315	163	2	,	,	PUNCT
cana-1315	163	3	f(α	f(α	PROPN
cana-1315	163	4	+	+	NOUN
cana-1315	163	5	β	β	X
cana-1315	163	6	)	)	PUNCT
cana-1315	163	7	=	=	SYM
cana-1315	163	8	f(α	f(α	NOUN
cana-1315	163	9	)	)	PUNCT
cana-1315	163	10	+	+	X
cana-1315	163	11	f(β	f(β	NOUN
cana-1315	163	12	)	)	PUNCT
cana-1315	163	13	and	and	CCONJ
cana-1315	163	14	f(αβγ	f(αβγ	NOUN
cana-1315	163	15	)	)	PUNCT
cana-1315	163	16	=	=	PUNCT
cana-1315	164	1	f(α)f(β)f(γ	f(α)f(β)f(γ	PROPN
cana-1315	164	2	)	)	PUNCT
cana-1315	164	3	,	,	PUNCT
cana-1315	164	4			NOUN
cana-1315	164	5	α	α	NOUN
cana-1315	164	6	,	,	PUNCT
cana-1315	164	7	β	β	X
cana-1315	164	8	and	and	CCONJ
cana-1315	164	9	γ	γ	PROPN
cana-1315	164	10	in	in	ADP
cana-1315	164	11	t.	t.	PROPN
cana-1315	164	12	let	let	VERB
cana-1315	164	13	q	q	PROPN
cana-1315	164	14	=	=	SYM
cana-1315	164	15	f(p	f(p	NOUN
cana-1315	164	16	)	)	PUNCT
cana-1315	164	17	,	,	PUNCT
cana-1315	164	18	where	where	SCONJ
cana-1315	164	19	p	p	NOUN
cana-1315	164	20	is	be	AUX
cana-1315	164	21	an	an	DET
cana-1315	164	22	aftssr	aftssr	NOUN
cana-1315	164	23	of	of	ADP
cana-1315	164	24	t.	t.	PROPN
cana-1315	164	25	to	to	PART
cana-1315	164	26	prove	prove	VERB
cana-1315	164	27	,	,	PUNCT
cana-1315	164	28	q	q	X
cana-1315	164	29	is	be	AUX
cana-1315	164	30	an	an	DET
cana-1315	164	31	aftssr	aftssr	NOUN
cana-1315	164	32	of	of	ADP
cana-1315	164	33	t1	t1	PROPN
cana-1315	164	34	.	.	PUNCT
cana-1315	165	1	now	now	ADV
cana-1315	165	2	,	,	PUNCT
cana-1315	165	3	for	for	ADP
cana-1315	165	4	f(α	f(α	NOUN
cana-1315	165	5	)	)	PUNCT
cana-1315	165	6	,	,	PUNCT
cana-1315	165	7	f(β	f(β	NOUN
cana-1315	165	8	)	)	PUNCT
cana-1315	165	9	,	,	PUNCT
cana-1315	165	10	f(γ	f(γ	NOUN
cana-1315	165	11	)	)	PUNCT
cana-1315	165	12	in	in	ADP
cana-1315	165	13	t1	t1	NOUN
cana-1315	165	14	,	,	PUNCT
cana-1315	165	15	q	q	VERB
cana-1315	165	16	(	(	PUNCT
cana-1315	165	17	f(α	f(α	NOUN
cana-1315	165	18	)	)	PUNCT
cana-1315	165	19	+	+	X
cana-1315	165	20	f(β	f(β	NOUN
cana-1315	165	21	)	)	PUNCT
cana-1315	165	22	)	)	PUNCT
cana-1315	166	1	=	=	PRON
cana-1315	166	2	q	q	VERB
cana-1315	166	3	(	(	PUNCT
cana-1315	166	4	f(α	f(α	NOUN
cana-1315	166	5	+	+	CCONJ
cana-1315	166	6	β	β	NOUN
cana-1315	166	7	)	)	PUNCT
cana-1315	166	8	)	)	PUNCT
cana-1315	166	9	≤	≤	NUM
cana-1315	166	10	p	p	NOUN
cana-1315	166	11	(	(	PUNCT
cana-1315	166	12	α	α	NOUN
cana-1315	166	13	+	+	NOUN
cana-1315	166	14	β	β	NOUN
cana-1315	166	15	)	)	PUNCT
cana-1315	166	16	≤	≤	NUM
cana-1315	166	17	max	max	PROPN
cana-1315	166	18	{	{	PUNCT
cana-1315	166	19	p	p	X
cana-1315	166	20	(	(	PUNCT
cana-1315	166	21	α	α	NOUN
cana-1315	166	22	)	)	PUNCT
cana-1315	166	23	,	,	PUNCT
cana-1315	166	24	p	p	X
cana-1315	166	25	(	(	PUNCT
cana-1315	166	26	β)}	β)}	ADJ
cana-1315	166	27	q	q	VERB
cana-1315	166	28	(	(	PUNCT
cana-1315	166	29	f(α	f(α	NOUN
cana-1315	166	30	)	)	PUNCT
cana-1315	166	31	+	+	NOUN
cana-1315	166	32	f(β	f(β	NOUN
cana-1315	166	33	)	)	PUNCT
cana-1315	166	34	)	)	PUNCT
cana-1315	166	35	≤	≤	NUM
cana-1315	166	36	max	max	PROPN
cana-1315	166	37	{	{	PUNCT
cana-1315	166	38	q	q	PROPN
cana-1315	166	39	(	(	PUNCT
cana-1315	166	40	f(α	f(α	NOUN
cana-1315	166	41	)	)	PUNCT
cana-1315	166	42	)	)	PUNCT
cana-1315	166	43	,	,	PUNCT
cana-1315	166	44	q	q	VERB
cana-1315	166	45	(	(	PUNCT
cana-1315	166	46	f(β	f(β	PROPN
cana-1315	166	47	)	)	PUNCT
cana-1315	166	48	)	)	PUNCT
cana-1315	166	49	}	}	PUNCT
cana-1315	166	50	.	.	PUNCT
cana-1315	167	1	again	again	ADV
cana-1315	167	2	,	,	PUNCT
cana-1315	167	3	q	q	X
cana-1315	167	4	(	(	PUNCT
cana-1315	167	5	f(α)f(β)f(γ	f(α)f(β)f(γ	NOUN
cana-1315	167	6	)	)	PUNCT
cana-1315	167	7	)	)	PUNCT
cana-1315	168	1	=	=	PRON
cana-1315	168	2	q	q	VERB
cana-1315	168	3	(	(	PUNCT
cana-1315	168	4	f(αβγ	f(αβγ	NOUN
cana-1315	168	5	)	)	PUNCT
cana-1315	168	6	)	)	PUNCT
cana-1315	168	7	≤	≤	NUM
cana-1315	168	8	q	q	VERB
cana-1315	168	9	(	(	PUNCT
cana-1315	168	10	αβγ	αβγ	NOUN
cana-1315	168	11	)	)	PUNCT
cana-1315	168	12	≤	≤	NUM
cana-1315	168	13	max	max	PROPN
cana-1315	168	14	{	{	PUNCT
cana-1315	168	15	q	q	PROPN
cana-1315	168	16	(	(	PUNCT
cana-1315	168	17	α	α	NOUN
cana-1315	168	18	)	)	PUNCT
cana-1315	168	19	,	,	PUNCT
cana-1315	168	20	q	q	VERB
cana-1315	168	21	(	(	PUNCT
cana-1315	168	22	β	β	NOUN
cana-1315	168	23	)	)	PUNCT
cana-1315	168	24	,	,	PUNCT
cana-1315	168	25	q	q	VERB
cana-1315	168	26	(	(	PUNCT
cana-1315	168	27	γ	γ	NOUN
cana-1315	168	28	)	)	PUNCT
cana-1315	168	29	}	}	PUNCT
cana-1315	168	30			NOUN
cana-1315	168	31	q	q	VERB
cana-1315	168	32	(	(	PUNCT
cana-1315	168	33	f(α)f(β)f(γ	f(α)f(β)f(γ	NUM
cana-1315	168	34	)	)	PUNCT
cana-1315	168	35	)	)	PUNCT
cana-1315	168	36	≤	≤	NUM
cana-1315	168	37	max	max	PROPN
cana-1315	168	38	{	{	PUNCT
cana-1315	168	39	q	q	PROPN
cana-1315	168	40	(	(	PUNCT
cana-1315	168	41	α	α	NOUN
cana-1315	168	42	)	)	PUNCT
cana-1315	168	43	,	,	PUNCT
cana-1315	168	44	q	q	VERB
cana-1315	168	45	(	(	PUNCT
cana-1315	168	46	β	β	NOUN
cana-1315	168	47	)	)	PUNCT
cana-1315	168	48	,	,	PUNCT
cana-1315	168	49	q	q	VERB
cana-1315	168	50	(	(	PUNCT
cana-1315	168	51	γ	γ	NOUN
cana-1315	168	52	)	)	PUNCT
cana-1315	168	53	}	}	PUNCT
cana-1315	168	54	.	.	PUNCT
cana-1315	169	1	hence	hence	ADV
cana-1315	169	2	q	q	X
cana-1315	169	3	is	be	AUX
cana-1315	169	4	an	an	DET
cana-1315	169	5	aftssr	aftssr	NOUN
cana-1315	169	6	of	of	ADP
cana-1315	169	7	t1	t1	PROPN
cana-1315	169	8	.	.	PUNCT
cana-1315	170	1	th.3.12	th.3.12	PROPN
cana-1315	170	2	:	:	PUNCT
cana-1315	170	3	let	let	VERB
cana-1315	170	4	(	(	PUNCT
cana-1315	170	5	t	t	PROPN
cana-1315	170	6	,	,	PUNCT
cana-1315	170	7	+	+	PROPN
cana-1315	170	8	,	,	PUNCT
cana-1315	170	9	.	.	PUNCT
cana-1315	170	10	)	)	PUNCT
cana-1315	171	1	and	and	CCONJ
cana-1315	171	2	(	(	PUNCT
cana-1315	171	3	t1	t1	NOUN
cana-1315	171	4	,	,	PUNCT
cana-1315	171	5	+	+	ADJ
cana-1315	171	6	,	,	PUNCT
cana-1315	171	7	.	.	PUNCT
cana-1315	171	8	)	)	PUNCT
cana-1315	171	9	be	be	AUX
cana-1315	171	10	any	any	DET
cana-1315	171	11	two	two	NUM
cana-1315	171	12	tsrs	tsr	NOUN
cana-1315	171	13	.	.	PUNCT
cana-1315	172	1	the	the	DET
cana-1315	172	2	homomorphic	homomorphic	ADJ
cana-1315	172	3	pre	pre	NOUN
cana-1315	172	4	-	-	NOUN
cana-1315	172	5	image	image	NOUN
cana-1315	172	6	of	of	ADP
cana-1315	172	7	an	an	DET
cana-1315	172	8	aftssr	aftssr	NOUN
cana-1315	172	9	of	of	ADP
cana-1315	172	10	t1	t1	PROPN
cana-1315	172	11	is	be	AUX
cana-1315	172	12	an	an	DET
cana-1315	172	13	aftssr	aftssr	NOUN
cana-1315	172	14	of	of	ADP
cana-1315	172	15	t.	t.	PROPN
cana-1315	172	16	pf	pf	PROPN
cana-1315	172	17	.	.	PROPN
cana-1315	172	18	:	:	PUNCT
cana-1315	173	1	given	give	VERB
cana-1315	173	2	(	(	PUNCT
cana-1315	173	3	t	t	PROPN
cana-1315	173	4	,	,	PUNCT
cana-1315	173	5	+	+	NOUN
cana-1315	173	6	,	,	PUNCT
cana-1315	173	7	.	.	PUNCT
cana-1315	173	8	)	)	PUNCT
cana-1315	174	1	and	and	CCONJ
cana-1315	174	2	(	(	PUNCT
cana-1315	174	3	t1	t1	NOUN
cana-1315	174	4	,	,	PUNCT
cana-1315	174	5	+	+	ADJ
cana-1315	174	6	,	,	PUNCT
cana-1315	174	7	.	.	PUNCT
cana-1315	174	8	)	)	PUNCT
cana-1315	174	9	are	be	AUX
cana-1315	174	10	two	two	NUM
cana-1315	174	11	tsrs	tsr	NOUN
cana-1315	174	12	.	.	PUNCT
cana-1315	175	1	let	let	VERB
cana-1315	175	2	f	f	X
cana-1315	175	3	:	:	PUNCT
cana-1315	175	4	tt1	tt1	ADV
cana-1315	175	5	be	be	AUX
cana-1315	175	6	a	a	DET
cana-1315	175	7	homomorphism	homomorphism	NOUN
cana-1315	175	8	.	.	PUNCT
cana-1315	176	1	then	then	ADV
cana-1315	176	2	,	,	PUNCT
cana-1315	176	3	f(α	f(α	PROPN
cana-1315	176	4	+	+	NOUN
cana-1315	176	5	β	β	X
cana-1315	176	6	)	)	PUNCT
cana-1315	176	7	=	=	SYM
cana-1315	176	8	f(α	f(α	NOUN
cana-1315	176	9	)	)	PUNCT
cana-1315	176	10	+	+	X
cana-1315	176	11	f(β	f(β	NOUN
cana-1315	176	12	)	)	PUNCT
cana-1315	176	13	and	and	CCONJ
cana-1315	176	14	f(αβγ	f(αβγ	NOUN
cana-1315	176	15	)	)	PUNCT
cana-1315	176	16	=	=	PUNCT
cana-1315	177	1	f(α)f(β)f(γ	f(α)f(β)f(γ	NOUN
cana-1315	177	2	)	)	PUNCT
cana-1315	177	3	,	,	PUNCT
cana-1315	177	4	.	.	PUNCT
cana-1315	178	1	let	let	VERB
cana-1315	178	2	q	q	NOUN
cana-1315	178	3	=	=	SYM
cana-1315	178	4	f(p	f(p	NOUN
cana-1315	178	5	)	)	PUNCT
cana-1315	178	6	,	,	PUNCT
cana-1315	178	7	where	where	SCONJ
cana-1315	178	8	p	p	NOUN
cana-1315	178	9	is	be	AUX
cana-1315	178	10	an	an	DET
cana-1315	178	11	aftssr	aftssr	NOUN
cana-1315	178	12	of	of	ADP
cana-1315	178	13	t.	t.	PROPN
cana-1315	178	14	we	we	PRON
cana-1315	178	15	have	have	VERB
cana-1315	178	16	to	to	PART
cana-1315	178	17	prove	prove	VERB
cana-1315	178	18	that	that	SCONJ
cana-1315	178	19	p	p	PROPN
cana-1315	178	20	is	be	AUX
cana-1315	178	21	aftssr	aftssr	NUM
cana-1315	178	22	of	of	ADP
cana-1315	178	23	t.	t.	PROPN
cana-1315	178	24	let	let	VERB
cana-1315	178	25	α	α	PRON
cana-1315	178	26	,	,	PUNCT
cana-1315	178	27	β	β	X
cana-1315	178	28	and	and	CCONJ
cana-1315	178	29	γ	γ	X
cana-1315	178	30	in	in	ADP
cana-1315	178	31	t.	t.	PROPN
cana-1315	178	32	then	then	ADV
cana-1315	178	33	,	,	PUNCT
cana-1315	178	34	p	p	X
cana-1315	178	35	(	(	PUNCT
cana-1315	178	36	α	α	NOUN
cana-1315	178	37	+	+	X
cana-1315	178	38	β)=	β)=	ADV
cana-1315	178	39	q	q	NOUN
cana-1315	178	40	(	(	PUNCT
cana-1315	178	41	f(α	f(α	PROPN
cana-1315	178	42	+	+	CCONJ
cana-1315	178	43	β))=	β))=	PROPN
cana-1315	178	44	q	q	VERB
cana-1315	178	45	(	(	PUNCT
cana-1315	178	46	f(α	f(α	PROPN
cana-1315	178	47	)	)	PUNCT
cana-1315	178	48	+	+	CCONJ
cana-1315	178	49	f(β	f(β	NOUN
cana-1315	178	50	)	)	PUNCT
cana-1315	178	51	)	)	PUNCT
cana-1315	179	1	≤	≤	NUM
cana-1315	179	2	max	max	PROPN
cana-1315	179	3	{	{	PUNCT
cana-1315	179	4	q	q	PROPN
cana-1315	179	5	(	(	PUNCT
cana-1315	179	6	f(α	f(α	NOUN
cana-1315	179	7	)	)	PUNCT
cana-1315	179	8	)	)	PUNCT
cana-1315	179	9	,	,	PUNCT
cana-1315	179	10	q	q	VERB
cana-1315	179	11	(	(	PUNCT
cana-1315	179	12	f(β	f(β	PROPN
cana-1315	179	13	)	)	PUNCT
cana-1315	179	14	)	)	PUNCT
cana-1315	179	15	}	}	PUNCT
cana-1315	180	1	=	=	SYM
cana-1315	180	2	max	max	X
cana-1315	180	3	{	{	PUNCT
cana-1315	180	4	p	p	X
cana-1315	180	5	(	(	PUNCT
cana-1315	180	6	α	α	NOUN
cana-1315	180	7	)	)	PUNCT
cana-1315	180	8	,	,	PUNCT
cana-1315	180	9	p	p	X
cana-1315	180	10	(	(	PUNCT
cana-1315	180	11	β	β	NOUN
cana-1315	180	12	)	)	PUNCT
cana-1315	180	13	}	}	PUNCT
cana-1315	180	14			NOUN
cana-1315	180	15	p	p	NOUN
cana-1315	180	16	(	(	PUNCT
cana-1315	180	17	α	α	NOUN
cana-1315	180	18	+	+	NOUN
cana-1315	180	19	β	β	NOUN
cana-1315	180	20	)	)	PUNCT
cana-1315	180	21	≤	≤	NOUN
cana-1315	180	22	max	max	PROPN
cana-1315	180	23	{	{	PUNCT
cana-1315	180	24	p	p	X
cana-1315	180	25	(	(	PUNCT
cana-1315	180	26	α	α	NOUN
cana-1315	180	27	)	)	PUNCT
cana-1315	180	28	,	,	PUNCT
cana-1315	180	29	p	p	X
cana-1315	180	30	(	(	PUNCT
cana-1315	180	31	β	β	NOUN
cana-1315	180	32	)	)	PUNCT
cana-1315	180	33	}	}	PUNCT
cana-1315	180	34	.	.	PUNCT
cana-1315	181	1	again	again	ADV
cana-1315	181	2	,	,	PUNCT
cana-1315	181	3	p	p	X
cana-1315	181	4	(	(	PUNCT
cana-1315	181	5	f(αβγ	f(αβγ	NOUN
cana-1315	181	6	)	)	PUNCT
cana-1315	181	7	)	)	PUNCT
cana-1315	182	1	=	=	PRON
cana-1315	182	2	q	q	VERB
cana-1315	182	3	(	(	PUNCT
cana-1315	182	4	f(αβγ	f(αβγ	NOUN
cana-1315	182	5	)	)	PUNCT
cana-1315	182	6	)	)	PUNCT
cana-1315	183	1	=	=	PRON
cana-1315	183	2	q	q	X
cana-1315	183	3	(	(	PUNCT
cana-1315	183	4	f(α)f(β)f(γ	f(α)f(β)f(γ	NOUN
cana-1315	183	5	)	)	PUNCT
cana-1315	183	6	)	)	PUNCT
cana-1315	183	7	≤	≤	NUM
cana-1315	183	8	max	max	PROPN
cana-1315	183	9	{	{	PUNCT
cana-1315	183	10	q	q	PROPN
cana-1315	183	11	(	(	PUNCT
cana-1315	183	12	α	α	NOUN
cana-1315	183	13	)	)	PUNCT
cana-1315	183	14	,	,	PUNCT
cana-1315	183	15	q	q	VERB
cana-1315	183	16	(	(	PUNCT
cana-1315	183	17	β	β	NOUN
cana-1315	183	18	)	)	PUNCT
cana-1315	183	19	,	,	PUNCT
cana-1315	183	20	q	q	VERB
cana-1315	183	21	(	(	PUNCT
cana-1315	183	22	γ)}}=	γ)}}=	PROPN
cana-1315	183	23	max	max	PROPN
cana-1315	183	24	{	{	PUNCT
cana-1315	183	25	p	p	X
cana-1315	183	26	(	(	PUNCT
cana-1315	183	27	α	α	NOUN
cana-1315	183	28	)	)	PUNCT
cana-1315	183	29	,	,	PUNCT
cana-1315	183	30	p	p	X
cana-1315	183	31	(	(	PUNCT
cana-1315	183	32	β	β	NOUN
cana-1315	183	33	)	)	PUNCT
cana-1315	183	34	,	,	PUNCT
cana-1315	183	35	p	p	NOUN
cana-1315	183	36	(	(	PUNCT
cana-1315	183	37	γ)}	γ)}	X
cana-1315	183	38	p	p	X
cana-1315	183	39	(	(	PUNCT
cana-1315	183	40	f(αβγ	f(αβγ	NOUN
cana-1315	183	41	)	)	PUNCT
cana-1315	183	42	)	)	PUNCT
cana-1315	183	43	≤	≤	NUM
cana-1315	183	44	max	max	PROPN
cana-1315	183	45	{	{	PUNCT
cana-1315	183	46	p	p	X
cana-1315	183	47	(	(	PUNCT
cana-1315	183	48	α	α	NOUN
cana-1315	183	49	)	)	PUNCT
cana-1315	183	50	,	,	PUNCT
cana-1315	183	51	p	p	X
cana-1315	183	52	(	(	PUNCT
cana-1315	183	53	β	β	NOUN
cana-1315	183	54	)	)	PUNCT
cana-1315	183	55	,	,	PUNCT
cana-1315	183	56	p	p	X
cana-1315	183	57	(	(	PUNCT
cana-1315	183	58	γ	γ	NOUN
cana-1315	183	59	)	)	PUNCT
cana-1315	183	60	}	}	PUNCT
cana-1315	183	61	.	.	PUNCT
cana-1315	184	1	hence	hence	ADV
cana-1315	184	2	p	p	PROPN
cana-1315	184	3	is	be	AUX
cana-1315	184	4	an	an	DET
cana-1315	184	5	aftssr	aftssr	NOUN
cana-1315	184	6	of	of	ADP
cana-1315	184	7	t.	t.	PROPN
cana-1315	184	8	th.3.13	th.3.13	PROPN
cana-1315	184	9	:	:	PUNCT
cana-1315	184	10	if	if	SCONJ
cana-1315	184	11	(	(	PUNCT
cana-1315	184	12	t	t	PROPN
cana-1315	184	13	,	,	PUNCT
cana-1315	184	14	+	+	NOUN
cana-1315	184	15	,	,	PUNCT
cana-1315	184	16	.	.	PUNCT
cana-1315	184	17	)	)	PUNCT
cana-1315	185	1	and	and	CCONJ
cana-1315	185	2	(	(	PUNCT
cana-1315	185	3	t1	t1	NOUN
cana-1315	185	4	,	,	PUNCT
cana-1315	185	5	+	+	ADJ
cana-1315	185	6	,	,	PUNCT
cana-1315	185	7	.	.	PUNCT
cana-1315	185	8	)	)	PUNCT
cana-1315	185	9	are	be	AUX
cana-1315	185	10	two	two	NUM
cana-1315	185	11	tsrs	tsr	NOUN
cana-1315	185	12	,	,	PUNCT
cana-1315	185	13	then	then	ADV
cana-1315	185	14	anti	anti	ADJ
cana-1315	185	15	-	-	ADJ
cana-1315	185	16	homomorphic	homomorphic	ADJ
cana-1315	185	17	image	image	NOUN
cana-1315	185	18	of	of	ADP
cana-1315	185	19	an	an	DET
cana-1315	185	20	aftssr	aftssr	NOUN
cana-1315	185	21	of	of	ADP
cana-1315	185	22	t	t	PROPN
cana-1315	185	23	is	be	AUX
cana-1315	185	24	an	an	DET
cana-1315	185	25	aftssr	aftssr	NOUN
cana-1315	185	26	of	of	ADP
cana-1315	185	27	t1	t1	PROPN
cana-1315	185	28	.	.	PUNCT
cana-1315	186	1	pf	pf	PROPN
cana-1315	186	2	.	.	PUNCT
cana-1315	186	3	:	:	PUNCT
cana-1315	187	1	given	give	VERB
cana-1315	187	2	(	(	PUNCT
cana-1315	187	3	t	t	PROPN
cana-1315	187	4	,	,	PUNCT
cana-1315	187	5	+	+	NOUN
cana-1315	187	6	,	,	PUNCT
cana-1315	187	7	.	.	PUNCT
cana-1315	187	8	)	)	PUNCT
cana-1315	188	1	and	and	CCONJ
cana-1315	188	2	(	(	PUNCT
cana-1315	188	3	t1	t1	NOUN
cana-1315	188	4	,	,	PUNCT
cana-1315	188	5	+	+	ADJ
cana-1315	188	6	,	,	PUNCT
cana-1315	188	7	.	.	PUNCT
cana-1315	188	8	)	)	PUNCT
cana-1315	188	9	are	be	AUX
cana-1315	188	10	two	two	NUM
cana-1315	188	11	tsrs	tsr	NOUN
cana-1315	188	12	.	.	PUNCT
cana-1315	189	1	let	let	VERB
cana-1315	189	2	f	f	X
cana-1315	189	3	:	:	PUNCT
cana-1315	189	4	tt1	tt1	ADP
cana-1315	189	5	a	a	DET
cana-1315	189	6	homomorphism	homomorphism	NOUN
cana-1315	189	7	.	.	PUNCT
cana-1315	190	1	then	then	ADV
cana-1315	190	2	,	,	PUNCT
cana-1315	190	3	f(α	f(α	PROPN
cana-1315	190	4	+	+	NOUN
cana-1315	190	5	β	β	X
cana-1315	190	6	)	)	PUNCT
cana-1315	190	7	=	=	SYM
cana-1315	190	8	f(β	f(β	NOUN
cana-1315	190	9	)	)	PUNCT
cana-1315	191	1	+	+	NUM
cana-1315	191	2	f(α	f(α	NOUN
cana-1315	191	3	)	)	PUNCT
cana-1315	191	4	and	and	CCONJ
cana-1315	191	5	f(αβγ	f(αβγ	NOUN
cana-1315	191	6	)	)	PUNCT
cana-1315	191	7	=	=	SYM
cana-1315	191	8	f(γ)f(β)f(α	f(γ)f(β)f(α	PROPN
cana-1315	191	9	)	)	PUNCT
cana-1315	191	10	,	,	PUNCT
cana-1315	191	11	.	.	PUNCT
cana-1315	192	1	let	let	VERB
cana-1315	192	2	q	q	NOUN
cana-1315	192	3	=	=	SYM
cana-1315	192	4	f(p	f(p	NOUN
cana-1315	192	5	)	)	PUNCT
cana-1315	192	6	,	,	PUNCT
cana-1315	192	7	where	where	SCONJ
cana-1315	192	8	p	p	NOUN
cana-1315	192	9	is	be	AUX
cana-1315	192	10	an	an	DET
cana-1315	192	11	aftssr	aftssr	NOUN
cana-1315	192	12	of	of	ADP
cana-1315	192	13	t.	t.	PROPN
cana-1315	192	14	we	we	PRON
cana-1315	192	15	prove	prove	VERB
cana-1315	192	16	that	that	SCONJ
cana-1315	192	17	q	q	NOUN
cana-1315	192	18	is	be	AUX
cana-1315	192	19	an	an	DET
cana-1315	192	20	aftssr	aftssr	NOUN
cana-1315	192	21	of	of	ADP
cana-1315	192	22	t1	t1	PROPN
cana-1315	192	23	.	.	PUNCT
cana-1315	193	1	now	now	ADV
cana-1315	193	2	,	,	PUNCT
cana-1315	193	3	for	for	ADP
cana-1315	193	4	f(α	f(α	NOUN
cana-1315	193	5	)	)	PUNCT
cana-1315	193	6	,	,	PUNCT
cana-1315	193	7	f(β	f(β	NOUN
cana-1315	193	8	)	)	PUNCT
cana-1315	193	9	,	,	PUNCT
cana-1315	193	10	f(γ)in	f(γ)in	PROPN
cana-1315	193	11	t1	t1	NOUN
cana-1315	193	12	,	,	PUNCT
cana-1315	193	13	q	q	VERB
cana-1315	193	14	(	(	PUNCT
cana-1315	193	15	f(α	f(α	NOUN
cana-1315	193	16	)	)	PUNCT
cana-1315	193	17	+	+	CCONJ
cana-1315	193	18	f(β))=	f(β))=	PUNCT
cana-1315	193	19	q	q	VERB
cana-1315	193	20	(	(	PUNCT
cana-1315	193	21	f(α	f(α	NOUN
cana-1315	193	22	+	+	CCONJ
cana-1315	193	23	β))≤	β))≤	ADJ
cana-1315	193	24	p	p	NOUN
cana-1315	193	25	(	(	PUNCT
cana-1315	193	26	β	β	X
cana-1315	193	27	+	+	CCONJ
cana-1315	193	28	α	α	X
cana-1315	193	29	)	)	PUNCT
cana-1315	193	30	communications	communication	NOUN
cana-1315	193	31	on	on	ADP
cana-1315	193	32	applied	apply	VERB
cana-1315	193	33	nonlinear	nonlinear	ADJ
cana-1315	193	34	analysis	analysis	NOUN
cana-1315	193	35	issn	issn	NOUN
cana-1315	193	36	:	:	PUNCT
cana-1315	193	37	1074	1074	NUM
cana-1315	193	38	-	-	PUNCT
cana-1315	193	39	133x	133x	NUM
cana-1315	193	40	vol	vol	NOUN
cana-1315	193	41	31	31	NUM
cana-1315	193	42	no	no	NOUN
cana-1315	193	43	.	.	PUNCT
cana-1315	194	1	7s	7	NOUN
cana-1315	194	2	(	(	PUNCT
cana-1315	194	3	2024	2024	NUM
cana-1315	194	4	)	)	PUNCT
cana-1315	194	5	363	363	NUM
cana-1315	194	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-1315	194	7	≤	≤	NUM
cana-1315	194	8	max	max	PROPN
cana-1315	194	9	{	{	PUNCT
cana-1315	194	10	p	p	X
cana-1315	194	11	(	(	PUNCT
cana-1315	194	12	β	β	NOUN
cana-1315	194	13	)	)	PUNCT
cana-1315	194	14	,	,	PUNCT
cana-1315	194	15	p	p	X
cana-1315	194	16	(	(	PUNCT
cana-1315	194	17	α)}=	α)}=	NUM
cana-1315	194	18	max	max	PROPN
cana-1315	194	19	{	{	PUNCT
cana-1315	194	20	p	p	X
cana-1315	194	21	(	(	PUNCT
cana-1315	194	22	α	α	NOUN
cana-1315	194	23	)	)	PUNCT
cana-1315	194	24	,	,	PUNCT
cana-1315	194	25	p	p	X
cana-1315	194	26	(	(	PUNCT
cana-1315	194	27	β	β	NOUN
cana-1315	194	28	)	)	PUNCT
cana-1315	194	29	}	}	PUNCT
cana-1315	194	30			NOUN
cana-1315	194	31	q	q	VERB
cana-1315	194	32	(	(	PUNCT
cana-1315	194	33	f(α	f(α	NOUN
cana-1315	194	34	)	)	PUNCT
cana-1315	195	1	+	+	CCONJ
cana-1315	195	2	f(β))≤	f(β))≤	PROPN
cana-1315	195	3	max	max	PROPN
cana-1315	195	4	{	{	PUNCT
cana-1315	195	5	p	p	X
cana-1315	195	6	(	(	PUNCT
cana-1315	195	7	α	α	NOUN
cana-1315	195	8	)	)	PUNCT
cana-1315	195	9	,	,	PUNCT
cana-1315	195	10	p	p	X
cana-1315	195	11	(	(	PUNCT
cana-1315	195	12	β	β	NOUN
cana-1315	195	13	)	)	PUNCT
cana-1315	195	14	}	}	PUNCT
cana-1315	195	15	.	.	PUNCT
cana-1315	196	1	again	again	ADV
cana-1315	196	2	,	,	PUNCT
cana-1315	196	3	q	q	VERB
cana-1315	196	4	(	(	PUNCT
cana-1315	196	5	f(α)f(β)f(γ))=	f(α)f(β)f(γ))=	PROPN
cana-1315	196	6	q	q	VERB
cana-1315	196	7	(	(	PUNCT
cana-1315	196	8	f(γβα	f(γβα	ADJ
cana-1315	196	9	)	)	PUNCT
cana-1315	196	10	)	)	PUNCT
cana-1315	196	11	)	)	PUNCT
cana-1315	197	1	≤	≤	NUM
cana-1315	197	2	p	p	NOUN
cana-1315	197	3	(	(	PUNCT
cana-1315	197	4	γβα	γβα	NOUN
cana-1315	197	5	)	)	PUNCT
cana-1315	197	6	≤	≤	NUM
cana-1315	197	7	max	max	PROPN
cana-1315	197	8	{	{	PUNCT
cana-1315	197	9	p	p	X
cana-1315	197	10	(	(	PUNCT
cana-1315	197	11	γ	γ	NOUN
cana-1315	197	12	)	)	PUNCT
cana-1315	197	13	,	,	PUNCT
cana-1315	197	14	p	p	X
cana-1315	197	15	(	(	PUNCT
cana-1315	197	16	β	β	NOUN
cana-1315	197	17	)	)	PUNCT
cana-1315	197	18	,	,	PUNCT
cana-1315	197	19	p	p	X
cana-1315	197	20	(	(	PUNCT
cana-1315	197	21	α)}=	α)}=	NUM
cana-1315	197	22	max	max	PROPN
cana-1315	197	23	{	{	PUNCT
cana-1315	197	24	p	p	X
cana-1315	197	25	(	(	PUNCT
cana-1315	197	26	α	α	NOUN
cana-1315	197	27	)	)	PUNCT
cana-1315	197	28	,	,	PUNCT
cana-1315	197	29	p	p	X
cana-1315	197	30	(	(	PUNCT
cana-1315	197	31	β	β	NOUN
cana-1315	197	32	)	)	PUNCT
cana-1315	197	33	,	,	PUNCT
cana-1315	197	34	p	p	X
cana-1315	197	35	(	(	PUNCT
cana-1315	197	36	γ	γ	NOUN
cana-1315	197	37	)	)	PUNCT
cana-1315	197	38	}	}	PUNCT
cana-1315	197	39	,	,	PUNCT
cana-1315	197	40			NOUN
cana-1315	197	41	q	q	X
cana-1315	197	42	(	(	PUNCT
cana-1315	197	43	f(α)f(β)f(γ	f(α)f(β)f(γ	NUM
cana-1315	197	44	)	)	PUNCT
cana-1315	197	45	)	)	PUNCT
cana-1315	198	1	≤	≤	NUM
cana-1315	198	2	max	max	PROPN
cana-1315	198	3	{	{	PUNCT
cana-1315	198	4	q	q	PROPN
cana-1315	198	5	(	(	PUNCT
cana-1315	198	6	f(α	f(α	NOUN
cana-1315	198	7	)	)	PUNCT
cana-1315	198	8	)	)	PUNCT
cana-1315	198	9	,	,	PUNCT
cana-1315	198	10	q	q	VERB
cana-1315	198	11	(	(	PUNCT
cana-1315	198	12	f(β	f(β	PROPN
cana-1315	198	13	)	)	PUNCT
cana-1315	198	14	)	)	PUNCT
cana-1315	198	15	,	,	PUNCT
cana-1315	198	16	q	q	X
cana-1315	198	17	(	(	PUNCT
cana-1315	198	18	f(γ	f(γ	NOUN
cana-1315	198	19	)	)	PUNCT
cana-1315	198	20	)	)	PUNCT
cana-1315	198	21	}	}	PUNCT
cana-1315	198	22	.	.	PUNCT
cana-1315	199	1	hence	hence	ADV
cana-1315	199	2	q	q	X
cana-1315	199	3	is	be	AUX
cana-1315	199	4	an	an	DET
cana-1315	199	5	aftssr	aftssr	NOUN
cana-1315	199	6	of	of	ADP
cana-1315	199	7	t1	t1	PROPN
cana-1315	199	8	.	.	PUNCT
cana-1315	200	1	th.3.14	th.3.14	ADV
cana-1315	200	2	:	:	PUNCT
cana-1315	200	3	let	let	VERB
cana-1315	200	4	(	(	PUNCT
cana-1315	200	5	t	t	PROPN
cana-1315	200	6	,	,	PUNCT
cana-1315	200	7	+	+	PROPN
cana-1315	200	8	,	,	PUNCT
cana-1315	200	9	.	.	PUNCT
cana-1315	200	10	)	)	PUNCT
cana-1315	201	1	and	and	CCONJ
cana-1315	201	2	(	(	PUNCT
cana-1315	201	3	t1	t1	NOUN
cana-1315	201	4	,	,	PUNCT
cana-1315	201	5	+	+	ADJ
cana-1315	201	6	,	,	PUNCT
cana-1315	201	7	.	.	PUNCT
cana-1315	201	8	)	)	PUNCT
cana-1315	201	9	be	be	AUX
cana-1315	201	10	any	any	DET
cana-1315	201	11	two	two	NUM
cana-1315	201	12	tsrs	tsr	NOUN
cana-1315	201	13	.	.	PUNCT
cana-1315	202	1	the	the	DET
cana-1315	202	2	anti	anti	ADJ
cana-1315	202	3	-	-	ADJ
cana-1315	202	4	homo	homo	ADJ
cana-1315	202	5	-	-	PUNCT
cana-1315	202	6	morphic	morphic	ADJ
cana-1315	202	7	pre	pre	NOUN
cana-1315	202	8	-	-	NOUN
cana-1315	202	9	image	image	NOUN
cana-1315	202	10	of	of	ADP
cana-1315	202	11	an	an	DET
cana-1315	202	12	aftssr	aftssr	NOUN
cana-1315	202	13	of	of	ADP
cana-1315	202	14	t1	t1	PROPN
cana-1315	202	15	is	be	AUX
cana-1315	202	16	an	an	DET
cana-1315	202	17	aftssr	aftssr	NOUN
cana-1315	202	18	of	of	ADP
cana-1315	202	19	t.	t.	PROPN
cana-1315	202	20	pf	pf	PROPN
cana-1315	202	21	.	.	PROPN
cana-1315	202	22	:	:	PUNCT
cana-1315	203	1	given	give	VERB
cana-1315	203	2	(	(	PUNCT
cana-1315	203	3	t	t	PROPN
cana-1315	203	4	,	,	PUNCT
cana-1315	203	5	+	+	NOUN
cana-1315	203	6	,	,	PUNCT
cana-1315	203	7	.	.	PUNCT
cana-1315	203	8	)	)	PUNCT
cana-1315	204	1	and	and	CCONJ
cana-1315	204	2	(	(	PUNCT
cana-1315	204	3	t1	t1	NOUN
cana-1315	204	4	,	,	PUNCT
cana-1315	204	5	+	+	ADJ
cana-1315	204	6	,	,	PUNCT
cana-1315	204	7	.	.	PUNCT
cana-1315	204	8	)	)	PUNCT
cana-1315	204	9	are	be	AUX
cana-1315	204	10	two	two	NUM
cana-1315	204	11	tsrs	tsr	NOUN
cana-1315	204	12	.	.	PUNCT
cana-1315	205	1	let	let	VERB
cana-1315	205	2	f	f	NOUN
cana-1315	205	3	:	:	PUNCT
cana-1315	205	4	tt1	tt1	ADV
cana-1315	205	5	be	be	AUX
cana-1315	205	6	a	a	DET
cana-1315	205	7	homomorphism	homomorphism	NOUN
cana-1315	205	8	.	.	PUNCT
cana-1315	206	1	then	then	ADV
cana-1315	206	2	,	,	PUNCT
cana-1315	206	3	f(α	f(α	PROPN
cana-1315	206	4	+	+	NOUN
cana-1315	206	5	β	β	X
cana-1315	206	6	)	)	PUNCT
cana-1315	206	7	=	=	SYM
cana-1315	206	8	f(β	f(β	NOUN
cana-1315	206	9	)	)	PUNCT
cana-1315	207	1	+	+	NUM
cana-1315	207	2	f(α	f(α	NOUN
cana-1315	207	3	)	)	PUNCT
cana-1315	207	4	and	and	CCONJ
cana-1315	207	5	f(αβγ	f(αβγ	NOUN
cana-1315	207	6	)	)	PUNCT
cana-1315	207	7	=	=	SYM
cana-1315	207	8	f(γ)f(β)f(α	f(γ)f(β)f(α	PROPN
cana-1315	207	9	)	)	PUNCT
cana-1315	207	10	,	,	PUNCT
cana-1315	207	11	.	.	PUNCT
cana-1315	208	1	let	let	VERB
cana-1315	208	2	q	q	NOUN
cana-1315	208	3	=	=	SYM
cana-1315	208	4	f(p	f(p	NOUN
cana-1315	208	5	)	)	PUNCT
cana-1315	208	6	,	,	PUNCT
cana-1315	208	7	where	where	SCONJ
cana-1315	208	8	p	p	NOUN
cana-1315	208	9	is	be	AUX
cana-1315	208	10	an	an	DET
cana-1315	208	11	aftssr	aftssr	NOUN
cana-1315	208	12	of	of	ADP
cana-1315	208	13	t.	t.	PROPN
cana-1315	208	14	we	we	PRON
cana-1315	208	15	have	have	VERB
cana-1315	208	16	to	to	PART
cana-1315	208	17	prove	prove	VERB
cana-1315	208	18	that	that	SCONJ
cana-1315	208	19	p	p	NOUN
cana-1315	208	20	is	be	AUX
cana-1315	208	21	an	an	DET
cana-1315	208	22	aftssr	aftssr	NOUN
cana-1315	208	23	of	of	ADP
cana-1315	208	24	t.	t.	PROPN
cana-1315	208	25	let	let	VERB
cana-1315	208	26	α	α	PRON
cana-1315	208	27	,	,	PUNCT
cana-1315	208	28	β	β	X
cana-1315	208	29	and	and	CCONJ
cana-1315	208	30	γ	γ	PROPN
cana-1315	208	31	in	in	ADP
cana-1315	208	32	t.	t.	PROPN
cana-1315	208	33	then	then	ADV
cana-1315	208	34	p	p	PROPN
cana-1315	208	35	(	(	PUNCT
cana-1315	208	36	α	α	NOUN
cana-1315	208	37	+	+	X
cana-1315	208	38	β	β	X
cana-1315	208	39	)	)	PUNCT
cana-1315	209	1	=	=	PRON
cana-1315	209	2	q	q	VERB
cana-1315	209	3	(	(	PUNCT
cana-1315	209	4	f(α	f(α	NOUN
cana-1315	209	5	+	+	CCONJ
cana-1315	209	6	β	β	NOUN
cana-1315	209	7	)	)	PUNCT
cana-1315	209	8	)	)	PUNCT
cana-1315	210	1	=	=	PRON
cana-1315	210	2	q	q	VERB
cana-1315	210	3	(	(	PUNCT
cana-1315	210	4	f(α	f(α	NOUN
cana-1315	210	5	)	)	PUNCT
cana-1315	210	6	+	+	X
cana-1315	210	7	f(β	f(β	NOUN
cana-1315	210	8	)	)	PUNCT
cana-1315	210	9	)	)	PUNCT
cana-1315	211	1	≤	≤	NUM
cana-1315	211	2	max	max	PROPN
cana-1315	211	3	{	{	PUNCT
cana-1315	211	4	q	q	NOUN
cana-1315	211	5	(	(	PUNCT
cana-1315	211	6	f(γ	f(γ	NOUN
cana-1315	211	7	)	)	PUNCT
cana-1315	211	8	)	)	PUNCT
cana-1315	211	9	,	,	PUNCT
cana-1315	211	10	q	q	VERB
cana-1315	211	11	(	(	PUNCT
cana-1315	211	12	f(β	f(β	PROPN
cana-1315	211	13	)	)	PUNCT
cana-1315	211	14	)	)	PUNCT
cana-1315	211	15	,	,	PUNCT
cana-1315	211	16	q	q	VERB
cana-1315	211	17	(	(	PUNCT
cana-1315	211	18	f(α))}=	f(α))}=	PROPN
cana-1315	211	19	max	max	PROPN
cana-1315	211	20	{	{	PUNCT
cana-1315	211	21	q	q	PROPN
cana-1315	211	22	(	(	PUNCT
cana-1315	211	23	f(α	f(α	NOUN
cana-1315	211	24	)	)	PUNCT
cana-1315	211	25	)	)	PUNCT
cana-1315	211	26	,	,	PUNCT
cana-1315	211	27	q	q	VERB
cana-1315	211	28	(	(	PUNCT
cana-1315	211	29	f(β	f(β	PROPN
cana-1315	211	30	)	)	PUNCT
cana-1315	211	31	)	)	PUNCT
cana-1315	211	32	,	,	PUNCT
cana-1315	211	33	q	q	VERB
cana-1315	211	34	(	(	PUNCT
cana-1315	211	35	f(γ))}=	f(γ))}=	PROPN
cana-1315	211	36	max	max	PROPN
cana-1315	211	37	{	{	PUNCT
cana-1315	211	38	p	p	X
cana-1315	211	39	(	(	PUNCT
cana-1315	211	40	α	α	NOUN
cana-1315	211	41	)	)	PUNCT
cana-1315	211	42	,	,	PUNCT
cana-1315	211	43	p	p	X
cana-1315	211	44	(	(	PUNCT
cana-1315	211	45	β	β	NOUN
cana-1315	211	46	)	)	PUNCT
cana-1315	211	47	,	,	PUNCT
cana-1315	211	48	p	p	X
cana-1315	211	49	(	(	PUNCT
cana-1315	211	50	γ	γ	NOUN
cana-1315	211	51	)	)	PUNCT
cana-1315	211	52	}	}	PUNCT
cana-1315	211	53	,	,	PUNCT
cana-1315	211	54			NOUN
cana-1315	211	55	p	p	NOUN
cana-1315	211	56	(	(	PUNCT
cana-1315	211	57	α	α	NOUN
cana-1315	211	58	+	+	CCONJ
cana-1315	211	59	β)≤	β)≤	ADJ
cana-1315	211	60	max	max	PROPN
cana-1315	211	61	{	{	PUNCT
cana-1315	211	62	p	p	X
cana-1315	211	63	(	(	PUNCT
cana-1315	211	64	α	α	NOUN
cana-1315	211	65	)	)	PUNCT
cana-1315	211	66	,	,	PUNCT
cana-1315	211	67	p	p	X
cana-1315	211	68	(	(	PUNCT
cana-1315	211	69	β	β	NOUN
cana-1315	211	70	)	)	PUNCT
cana-1315	211	71	,	,	PUNCT
cana-1315	211	72	p	p	X
cana-1315	211	73	(	(	PUNCT
cana-1315	211	74	γ	γ	NOUN
cana-1315	211	75	)	)	PUNCT
cana-1315	211	76	}	}	PUNCT
cana-1315	211	77	.	.	PUNCT
cana-1315	212	1	again	again	ADV
cana-1315	212	2	,	,	PUNCT
cana-1315	212	3	p	p	X
cana-1315	212	4	(	(	PUNCT
cana-1315	212	5	(	(	PUNCT
cana-1315	212	6	αβγ))=	αβγ))=	PROPN
cana-1315	212	7	q	q	VERB
cana-1315	212	8	(	(	PUNCT
cana-1315	212	9	f(αβγ))=	f(αβγ))=	INTJ
cana-1315	212	10	q	q	INTJ
cana-1315	212	11	(	(	PUNCT
cana-1315	212	12	f(γ)f(β)f(α))≤max	f(γ)f(β)f(α))≤max	VERB
cana-1315	212	13	{	{	PUNCT
cana-1315	212	14	{	{	PUNCT
cana-1315	212	15	q	q	VERB
cana-1315	212	16	(	(	PUNCT
cana-1315	212	17	f(γ	f(γ	NOUN
cana-1315	212	18	)	)	PUNCT
cana-1315	212	19	)	)	PUNCT
cana-1315	212	20	,	,	PUNCT
cana-1315	212	21	q	q	VERB
cana-1315	212	22	(	(	PUNCT
cana-1315	212	23	f(β	f(β	PROPN
cana-1315	212	24	)	)	PUNCT
cana-1315	212	25	)	)	PUNCT
cana-1315	212	26	,	,	PUNCT
cana-1315	212	27	q	q	VERB
cana-1315	212	28	(	(	PUNCT
cana-1315	212	29	f(α))}=	f(α))}=	PROPN
cana-1315	212	30	max	max	PROPN
cana-1315	212	31	{	{	PUNCT
cana-1315	212	32	q	q	PROPN
cana-1315	212	33	(	(	PUNCT
cana-1315	212	34	f(α	f(α	NOUN
cana-1315	212	35	)	)	PUNCT
cana-1315	212	36	)	)	PUNCT
cana-1315	212	37	,	,	PUNCT
cana-1315	212	38	q	q	VERB
cana-1315	212	39	(	(	PUNCT
cana-1315	212	40	f(β	f(β	PROPN
cana-1315	212	41	)	)	PUNCT
cana-1315	212	42	)	)	PUNCT
cana-1315	212	43	,	,	PUNCT
cana-1315	212	44	q	q	VERB
cana-1315	212	45	(	(	PUNCT
cana-1315	212	46	f(γ))}=	f(γ))}=	PROPN
cana-1315	212	47	max	max	PROPN
cana-1315	212	48	{	{	PUNCT
cana-1315	212	49	p	p	X
cana-1315	212	50	(	(	PUNCT
cana-1315	212	51	α	α	NOUN
cana-1315	212	52	)	)	PUNCT
cana-1315	212	53	,	,	PUNCT
cana-1315	212	54	p	p	X
cana-1315	212	55	(	(	PUNCT
cana-1315	212	56	β	β	NOUN
cana-1315	212	57	)	)	PUNCT
cana-1315	212	58	,	,	PUNCT
cana-1315	212	59	p	p	X
cana-1315	212	60	(	(	PUNCT
cana-1315	212	61	γ	γ	NOUN
cana-1315	212	62	)	)	PUNCT
cana-1315	212	63	)	)	PUNCT
cana-1315	212	64	}	}	PUNCT
cana-1315	212	65			NOUN
cana-1315	212	66	p	p	NOUN
cana-1315	212	67	(	(	PUNCT
cana-1315	212	68	(	(	PUNCT
cana-1315	212	69	αβγ))≤	αβγ))≤	X
cana-1315	212	70	max	max	PROPN
cana-1315	212	71	{	{	PUNCT
cana-1315	212	72	p	p	X
cana-1315	212	73	(	(	PUNCT
cana-1315	212	74	α	α	NOUN
cana-1315	212	75	)	)	PUNCT
cana-1315	212	76	,	,	PUNCT
cana-1315	212	77	p	p	X
cana-1315	212	78	(	(	PUNCT
cana-1315	212	79	β	β	NOUN
cana-1315	212	80	)	)	PUNCT
cana-1315	212	81	,	,	PUNCT
cana-1315	212	82	p	p	X
cana-1315	212	83	(	(	PUNCT
cana-1315	212	84	γ	γ	NOUN
cana-1315	212	85	)	)	PUNCT
cana-1315	212	86	)	)	PUNCT
cana-1315	212	87	}	}	PUNCT
cana-1315	212	88	.	.	PUNCT
cana-1315	213	1	hence	hence	ADV
cana-1315	213	2	p	p	PROPN
cana-1315	213	3	is	be	AUX
cana-1315	213	4	an	an	DET
cana-1315	213	5	aftssr	aftssr	NOUN
cana-1315	213	6	of	of	ADP
cana-1315	213	7	t.	t.	PROPN
cana-1315	213	8	references	reference	NOUN
cana-1315	213	9	[	[	X
cana-1315	213	10	1	1	X
cana-1315	213	11	]	]	PUNCT
cana-1315	213	12	a	a	DET
cana-1315	213	13	zaid	zaid	PROPN
cana-1315	213	14	.	.	PUNCT
cana-1315	214	1	s	s	X
cana-1315	214	2	,	,	PUNCT
cana-1315	214	3	on	on	ADP
cana-1315	214	4	fuzzy	fuzzy	ADJ
cana-1315	214	5	sub	sub	ADJ
cana-1315	214	6	-	-	ADJ
cana-1315	214	7	near	near	ADJ
cana-1315	214	8	rings	ring	NOUN
cana-1315	214	9	and	and	CCONJ
cana-1315	214	10	ideals	ideal	NOUN
cana-1315	214	11	,	,	PUNCT
cana-1315	214	12	fuzzy	fuzzy	ADJ
cana-1315	214	13	sets	set	NOUN
cana-1315	214	14	and	and	CCONJ
cana-1315	214	15	systems	system	NOUN
cana-1315	214	16	,	,	PUNCT
cana-1315	214	17	44(1991	44(1991	NUM
cana-1315	214	18	)	)	PUNCT
cana-1315	214	19	,	,	PUNCT
cana-1315	214	20	139	139	NUM
cana-1315	214	21	-	-	SYM
cana-1315	214	22	146	146	NUM
cana-1315	214	23	.	.	PUNCT
cana-1315	215	1	[	[	X
cana-1315	215	2	2	2	X
cana-1315	215	3	]	]	PUNCT
cana-1315	215	4	akram.m	akram.m	PROPN
cana-1315	215	5	and	and	CCONJ
cana-1315	215	6	dar.k.h	dar.k.h	NOUN
cana-1315	215	7	,	,	PUNCT
cana-1315	215	8	on	on	ADP
cana-1315	215	9	fuzzy	fuzzy	ADJ
cana-1315	215	10	d	d	NOUN
cana-1315	215	11	-	-	PUNCT
cana-1315	215	12	algebras	algebras	PROPN
cana-1315	215	13	,	,	PUNCT
cana-1315	215	14	punjab	punjab	PROPN
cana-1315	215	15	university	university	NOUN
cana-1315	215	16	journal	journal	NOUN
cana-1315	215	17	of	of	ADP
cana-1315	215	18	mathematics	mathematic	NOUN
cana-1315	215	19	,	,	PUNCT
cana-1315	215	20	37(2005	37(2005	NUM
cana-1315	215	21	)	)	PUNCT
cana-1315	215	22	,	,	PUNCT
cana-1315	215	23	61	61	NUM
cana-1315	215	24	-	-	SYM
cana-1315	215	25	76	76	NUM
cana-1315	215	26	.	.	PUNCT
cana-1315	216	1	[	[	X
cana-1315	216	2	3	3	X
cana-1315	216	3	]	]	SYM
cana-1315	216	4	akram.m	akram.m	PROPN
cana-1315	216	5	and	and	CCONJ
cana-1315	216	6	dar.k.h	dar.k.h	NOUN
cana-1315	216	7	,	,	PUNCT
cana-1315	216	8	fuzzy	fuzzy	ADJ
cana-1315	216	9	left	leave	VERB
cana-1315	216	10	h	h	NOUN
cana-1315	216	11	-	-	PUNCT
cana-1315	216	12	ideals	ideal	NOUN
cana-1315	216	13	in	in	ADP
cana-1315	216	14	hemi	hemi	NOUN
cana-1315	216	15	-	-	PUNCT
cana-1315	216	16	rings	ring	NOUN
cana-1315	216	17	with	with	ADP
cana-1315	216	18	respect	respect	NOUN
cana-1315	216	19	to	to	ADP
cana-1315	216	20	a	a	DET
cana-1315	216	21	s	s	NOUN
cana-1315	216	22	-	-	NOUN
cana-1315	216	23	norm	norm	NOUN
cana-1315	216	24	,	,	PUNCT
cana-1315	216	25	international	international	ADJ
cana-1315	216	26	journal	journal	NOUN
cana-1315	216	27	of	of	ADP
cana-1315	216	28	computational	computational	ADJ
cana-1315	216	29	and	and	CCONJ
cana-1315	216	30	applied	applied	ADJ
cana-1315	216	31	mathematics	mathematic	NOUN
cana-1315	216	32	,	,	PUNCT
cana-1315	216	33	volume	volume	NOUN
cana-1315	216	34	2	2	NUM
cana-1315	216	35	number	number	NOUN
cana-1315	216	36	1	1	NUM
cana-1315	216	37	(	(	PUNCT
cana-1315	216	38	2007	2007	NUM
cana-1315	216	39	)	)	PUNCT
cana-1315	216	40	,	,	PUNCT
cana-1315	216	41	pp	pp	ADP
cana-1315	216	42	.	.	PUNCT
cana-1315	217	1	7–14	7–14	NOUN
cana-1315	218	1	[	[	X
cana-1315	218	2	4	4	NUM
cana-1315	218	3	]	]	PUNCT
cana-1315	218	4	asok	asok	PROPN
cana-1315	218	5	kumer	kumer	PROPN
cana-1315	218	6	ray	ray	PROPN
cana-1315	218	7	,	,	PUNCT
cana-1315	218	8	on	on	ADP
cana-1315	218	9	product	product	NOUN
cana-1315	218	10	of	of	ADP
cana-1315	218	11	fuzzy	fuzzy	ADJ
cana-1315	218	12	subgroups	subgroup	NOUN
cana-1315	218	13	,	,	PUNCT
cana-1315	218	14	fuzzy	fuzzy	ADJ
cana-1315	218	15	sets	set	NOUN
cana-1315	218	16	and	and	CCONJ
cana-1315	218	17	systems,105,181	systems,105,181	NUM
cana-1315	218	18	-	-	PUNCT
cana-1315	218	19	183(1999	183(1999	NUM
cana-1315	218	20	)	)	PUNCT
cana-1315	218	21	.	.	PUNCT
cana-1315	219	1	[	[	X
cana-1315	219	2	5	5	NUM
cana-1315	219	3	]	]	SYM
cana-1315	219	4	davvaz.b	davvaz.b	NOUN
cana-1315	219	5	and	and	CCONJ
cana-1315	219	6	wieslaw	wieslaw	NOUN
cana-1315	219	7	.	.	PUNCT
cana-1315	219	8	a.	a.	PROPN
cana-1315	219	9	dudek	dudek	PROPN
cana-1315	219	10	,	,	PUNCT
cana-1315	219	11	fuzzy	fuzzy	ADJ
cana-1315	219	12	n	n	CCONJ
cana-1315	219	13	-	-	PUNCT
cana-1315	219	14	ary	ary	NOUN
cana-1315	219	15	groups	group	NOUN
cana-1315	219	16	as	as	ADP
cana-1315	219	17	a	a	DET
cana-1315	219	18	generalization	generalization	NOUN
cana-1315	219	19	of	of	ADP
cana-1315	219	20	rosenfeld	rosenfeld	PROPN
cana-1315	219	21	fuzzy	fuzzy	ADJ
cana-1315	219	22	groups	group	NOUN
cana-1315	219	23	,	,	PUNCT
cana-1315	219	24	arxiv0710.3884vi	arxiv0710.3884vi	PROPN
cana-1315	219	25	(	(	PUNCT
cana-1315	219	26	math.ra	math.ra	PROPN
cana-1315	219	27	)	)	PUNCT
cana-1315	219	28	20	20	NUM
cana-1315	219	29	oct	oct	NOUN
cana-1315	219	30	2007	2007	NUM
cana-1315	219	31	,	,	PUNCT
cana-1315	219	32	1	1	NUM
cana-1315	219	33	-	-	SYM
cana-1315	219	34	16	16	NUM
cana-1315	219	35	.	.	PUNCT
cana-1315	220	1	[	[	X
cana-1315	220	2	6	6	NUM
cana-1315	220	3	]	]	PUNCT
cana-1315	220	4	dixit.v.n	dixit.v.n	PROPN
cana-1315	220	5	.	.	PUNCT
cana-1315	221	1	,	,	PUNCT
cana-1315	221	2	rajesh	rajesh	PROPN
cana-1315	221	3	kumar	kumar	PROPN
cana-1315	221	4	,	,	PUNCT
cana-1315	221	5	naseem	naseem	PROPN
cana-1315	221	6	ajmal	ajmal	PROPN
cana-1315	221	7	.	.	PUNCT
cana-1315	221	8	,	,	PUNCT
cana-1315	221	9	level	level	NOUN
cana-1315	221	10	subgroups	subgroup	NOUN
cana-1315	221	11	and	and	CCONJ
cana-1315	221	12	union	union	NOUN
cana-1315	221	13	of	of	ADP
cana-1315	221	14	fuzzy	fuzzy	ADJ
cana-1315	221	15	subgroups	subgroup	NOUN
cana-1315	221	16	,	,	PUNCT
cana-1315	221	17	fuzzy	fuzzy	ADJ
cana-1315	221	18	sets	set	NOUN
cana-1315	221	19	and	and	CCONJ
cana-1315	221	20	systems	system	NOUN
cana-1315	221	21	,	,	PUNCT
cana-1315	221	22	37	37	NUM
cana-1315	221	23	,	,	PUNCT
cana-1315	221	24	359	359	NUM
cana-1315	221	25	-	-	SYM
cana-1315	221	26	371	371	NUM
cana-1315	221	27	(	(	PUNCT
cana-1315	221	28	1990	1990	NUM
cana-1315	221	29	)	)	PUNCT
cana-1315	221	30	.	.	PUNCT
cana-1315	222	1	[	[	X
cana-1315	222	2	7	7	X
cana-1315	222	3	]	]	X
cana-1315	222	4	rajesh	rajesh	PROPN
cana-1315	222	5	kumar	kumar	PROPN
cana-1315	222	6	,	,	PUNCT
cana-1315	222	7	fuzzy	fuzzy	ADJ
cana-1315	222	8	algebra	algebra	NOUN
cana-1315	222	9	,	,	PUNCT
cana-1315	222	10	volume	volume	NOUN
cana-1315	222	11	1	1	NUM
cana-1315	222	12	,	,	PUNCT
cana-1315	222	13	university	university	NOUN
cana-1315	222	14	of	of	ADP
cana-1315	222	15	delhi	delhi	PROPN
cana-1315	222	16	publication	publication	NOUN
cana-1315	222	17	division	division	NOUN
cana-1315	222	18	,	,	PUNCT
cana-1315	222	19	july	july	PROPN
cana-1315	222	20	–	–	PUNCT
cana-1315	222	21	1993	1993	NUM
cana-1315	222	22	.	.	PUNCT
cana-1315	223	1	[	[	X
cana-1315	223	2	8	8	NUM
cana-1315	223	3	]	]	X
cana-1315	223	4	siva	siva	NOUN
cana-1315	223	5	ramakrishna	ramakrishna	PROPN
cana-1315	223	6	das.p	das.p	PROPN
cana-1315	223	7	,	,	PUNCT
cana-1315	223	8	fuzzy	fuzzy	ADJ
cana-1315	223	9	groups	group	NOUN
cana-1315	223	10	and	and	CCONJ
cana-1315	223	11	level	level	NOUN
cana-1315	223	12	subgroups	subgroup	NOUN
cana-1315	223	13	,	,	PUNCT
cana-1315	223	14	journal	journal	NOUN
cana-1315	223	15	of	of	ADP
cana-1315	223	16	mathematical	mathematical	ADJ
cana-1315	223	17	analysis	analysis	NOUN
cana-1315	223	18	and	and	CCONJ
cana-1315	223	19	applications	application	NOUN
cana-1315	223	20	,	,	PUNCT
cana-1315	223	21	84	84	NUM
cana-1315	223	22	,	,	PUNCT
cana-1315	223	23	264	264	NUM
cana-1315	223	24	-	-	SYM
cana-1315	223	25	269	269	NUM
cana-1315	223	26	(	(	PUNCT
cana-1315	223	27	1981	1981	NUM
cana-1315	223	28	)	)	PUNCT
cana-1315	223	29	.	.	PUNCT
cana-1315	224	1	[	[	X
cana-1315	224	2	9	9	NUM
cana-1315	224	3	]	]	PUNCT
cana-1315	224	4	zadeh.l.a	zadeh.l.a	NOUN
cana-1315	224	5	.	.	PUNCT
cana-1315	224	6	,	,	PUNCT
cana-1315	224	7	fuzzy	fuzzy	ADJ
cana-1315	224	8	sets	set	NOUN
cana-1315	224	9	,	,	PUNCT
cana-1315	224	10	information	information	NOUN
cana-1315	224	11	and	and	CCONJ
cana-1315	224	12	control	control	NOUN
cana-1315	224	13	,	,	PUNCT
cana-1315	224	14	vol.8	vol.8	PROPN
cana-1315	224	15	,	,	PUNCT
cana-1315	224	16	338	338	NUM
cana-1315	224	17	-	-	SYM
cana-1315	224	18	353	353	NUM
cana-1315	224	19	(	(	PUNCT
cana-1315	224	20	1965	1965	NUM
cana-1315	224	21	)	)	PUNCT
cana-1315	224	22	.	.	PUNCT
cana-1315	225	1	[	[	X
cana-1315	225	2	10	10	NUM
cana-1315	225	3	]	]	PUNCT
cana-1315	225	4	g.	g.	PROPN
cana-1315	225	5	srinivasa	srinivasa	PROPN
cana-1315	225	6	rao	rao	PROPN
cana-1315	225	7	&	&	CCONJ
cana-1315	225	8	d.	d.	PROPN
cana-1315	225	9	madhusudhana	madhusudhana	PROPN
cana-1315	225	10	rao	rao	PROPN
cana-1315	225	11	,	,	PUNCT
cana-1315	225	12	structure	structure	NOUN
cana-1315	225	13	of	of	ADP
cana-1315	225	14	certain	certain	ADJ
cana-1315	225	15	ideals	ideal	NOUN
cana-1315	225	16	in	in	ADP
cana-1315	225	17	ternary	ternary	ADJ
cana-1315	225	18	semi	semi	NOUN
cana-1315	225	19	-	-	NOUN
cana-1315	225	20	rings	ring	NOUN
cana-1315	225	21	,	,	PUNCT
cana-1315	225	22	international	international	ADJ
cana-1315	225	23	journal	journal	NOUN
cana-1315	225	24	of	of	ADP
cana-1315	225	25	innovative	innovative	ADJ
cana-1315	225	26	science	science	NOUN
cana-1315	225	27	and	and	CCONJ
cana-1315	225	28	modern	modern	ADJ
cana-1315	225	29	engineering	engineering	NOUN
cana-1315	225	30	,	,	PUNCT
cana-1315	225	31	vol.3	vol.3	PROPN
cana-1315	225	32	,	,	PUNCT
cana-1315	225	33	issue	issue	VERB
cana-1315	225	34	3	3	NUM
cana-1315	225	35	2015	2015	NUM
cana-1315	225	36	,	,	PUNCT
cana-1315	225	37	pp:49	pp:49	PROPN
cana-1315	225	38	-	-	SYM
cana-1315	225	39	56	56	NUM
cana-1315	225	40	.	.	PUNCT
cana-1315	226	1	[	[	X
cana-1315	226	2	11	11	NUM
cana-1315	226	3	]	]	PUNCT
cana-1315	226	4	g.	g.	PROPN
cana-1315	226	5	srinivasa	srinivasa	PROPN
cana-1315	226	6	rao	rao	PROPN
cana-1315	226	7	&	&	CCONJ
cana-1315	226	8	d.	d.	PROPN
cana-1315	226	9	madhusudhana	madhusudhana	PROPN
cana-1315	226	10	rao	rao	PROPN
cana-1315	226	11	,	,	PUNCT
cana-1315	226	12	a	a	DET
cana-1315	226	13	study	study	NOUN
cana-1315	226	14	on	on	ADP
cana-1315	226	15	ternary	ternary	ADJ
cana-1315	226	16	semi	semi	NOUN
cana-1315	226	17	-	-	NOUN
cana-1315	226	18	rings	ring	NOUN
cana-1315	226	19	,	,	PUNCT
cana-1315	226	20	international	international	ADJ
cana-1315	226	21	journal	journal	NOUN
cana-1315	226	22	of	of	ADP
cana-1315	226	23	mathematical	mathematical	ADJ
cana-1315	226	24	archive	archive	NOUN
cana-1315	226	25	,	,	PUNCT
cana-1315	226	26	2014	2014	NUM
cana-1315	226	27	.	.	PUNCT
cana-1315	227	1	[	[	X
cana-1315	227	2	12	12	NUM
cana-1315	227	3	]	]	X
cana-1315	227	4	g.	g.	PROPN
cana-1315	227	5	srinivasa	srinivasa	PROPN
cana-1315	227	6	rao	rao	PROPN
cana-1315	227	7	,	,	PUNCT
cana-1315	227	8	d.	d.	PROPN
cana-1315	227	9	madhusudhana	madhusudhana	PROPN
cana-1315	227	10	rao	rao	PROPN
cana-1315	227	11	,	,	PUNCT
cana-1315	227	12	characteristics	characteristic	NOUN
cana-1315	227	13	of	of	ADP
cana-1315	227	14	ternary	ternary	ADJ
cana-1315	227	15	semi	semi	ADJ
cana-1315	227	16	rings	ring	NOUN
cana-1315	227	17	,	,	PUNCT
cana-1315	227	18	international	international	ADJ
cana-1315	227	19	journal	journal	NOUN
cana-1315	227	20	of	of	ADP
cana-1315	227	21	engineering	engineering	NOUN
cana-1315	227	22	research	research	NOUN
cana-1315	227	23	and	and	CCONJ
cana-1315	227	24	management	management	NOUN
cana-1315	227	25	,	,	PUNCT
cana-1315	227	26	vol.2	vol.2	PROPN
cana-1315	227	27	,	,	PUNCT
cana-1315	227	28	issue	issue	NOUN
cana-1315	227	29	1	1	NUM
cana-1315	227	30	,	,	PUNCT
cana-1315	227	31	pp:3	pp:3	NOUN
cana-1315	227	32	-	-	PUNCT
cana-1315	227	33	6	6	NUM
cana-1315	227	34	.	.	PUNCT
cana-1315	228	1	[	[	X
cana-1315	228	2	13	13	NUM
cana-1315	228	3	]	]	PUNCT
cana-1315	228	4	g.	g.	PROPN
cana-1315	228	5	srinivasa	srinivasa	PROPN
cana-1315	228	6	rao	rao	PROPN
cana-1315	228	7	,	,	PUNCT
cana-1315	228	8	d.	d.	PROPN
cana-1315	228	9	madhusudhana	madhusudhana	PROPN
cana-1315	228	10	rao	rao	PROPN
cana-1315	228	11	&	&	CCONJ
cana-1315	228	12	p.	p.	PROPN
cana-1315	228	13	siva	siva	PROPN
cana-1315	228	14	prasad	prasad	PROPN
cana-1315	228	15	,	,	PUNCT
cana-1315	228	16	simple	simple	ADJ
cana-1315	228	17	ternary	ternary	ADJ
cana-1315	228	18	semi	semi	NOUN
cana-1315	228	19	-	-	NOUN
cana-1315	228	20	rings	ring	NOUN
cana-1315	228	21	,	,	PUNCT
cana-1315	228	22	the	the	DET
cana-1315	228	23	global	global	ADJ
cana-1315	228	24	journal	journal	NOUN
cana-1315	228	25	of	of	ADP
cana-1315	228	26	mathematics	mathematics	PROPN
cana-1315	228	27	&	&	CCONJ
cana-1315	228	28	mathematical	mathematical	PROPN
cana-1315	228	29	sciences	sciences	PROPN
cana-1315	228	30	,	,	PUNCT
cana-1315	228	31	vol.9	vol.9	PROPN
cana-1315	228	32	,	,	PUNCT
cana-1315	228	33	no.2	no.2	PROPN
cana-1315	228	34	,	,	PUNCT
cana-1315	228	35	2016	2016	NUM
cana-1315	228	36	,	,	PUNCT
cana-1315	228	37	pp:185196	pp:185196	ADJ
cana-1315	228	38	.	.	PUNCT
cana-1315	229	1	[	[	X
cana-1315	229	2	14	14	NUM
cana-1315	229	3	]	]	X
cana-1315	229	4	d.	d.	PROPN
cana-1315	229	5	madhusudhana	madhusudhana	PROPN
cana-1315	229	6	rao	rao	PROPN
cana-1315	229	7	,	,	PUNCT
cana-1315	229	8	g.	g.	PROPN
cana-1315	229	9	srinivasa	srinivasa	PROPN
cana-1315	229	10	rao	rao	PROPN
cana-1315	229	11	,	,	PUNCT
cana-1315	229	12	special	special	ADJ
cana-1315	229	13	elements	element	NOUN
cana-1315	229	14	in	in	ADP
cana-1315	229	15	ternary	ternary	ADJ
cana-1315	229	16	semi	semi	ADJ
cana-1315	229	17	rings	ring	NOUN
cana-1315	229	18	,	,	PUNCT
cana-1315	229	19	international	international	ADJ
cana-1315	229	20	journal	journal	NOUN
cana-1315	229	21	of	of	ADP
cana-1315	229	22	engineering	engineering	NOUN
cana-1315	229	23	research	research	NOUN
cana-1315	229	24	and	and	CCONJ
cana-1315	229	25	applications	application	NOUN
cana-1315	229	26	,	,	PUNCT
cana-1315	229	27	vol.4	vol.4	PROPN
cana-1315	229	28	,	,	PUNCT
cana-1315	229	29	issue	issue	NOUN
cana-1315	229	30	11	11	NUM
cana-1315	229	31	,	,	PUNCT
cana-1315	229	32	november	november	PROPN
cana-1315	229	33	2014	2014	NUM
cana-1315	229	34	,	,	PUNCT
cana-1315	229	35	pp:123	pp:123	NOUN
cana-1315	229	36	-	-	SYM
cana-1315	229	37	130	130	NUM
cana-1315	229	38	.	.	PUNCT