Morphocompletion for #1513 ⟨a, b | ababababba=1⟩

Solved by morph:2/0,5/0. (See Morphocompletion.)

Step 1

Checking up to 20 rules for overlaps.

Reduction order:
- Left-to-right shortlex with a < b

Rewriting system is not complete: rulesLimit

#	Rule
1.	baab ⇒ abba
2.	baaabb ⇒ aabbba
3.	bbaaab ⇒ abbbaa
4.	baaabba ⇒ abbaaab
5.	bababbaa ⇒ abababab
6.	baaababba ⇒ abbaaabab
7.	babababba ⇒ ababababb
8.	aababababb ⇒ 1
9.	baaabababab ⇒ abababbabaa
10.	aabababababbbaa ⇒ baaab
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	ba	37	`lf:27,lp:7,ls:3,rf:17,rp:1,rs:2,lprs:2,a:1`
[2/1]	ab	27	`lf:24,ls:3,rf:21,rp:7,rs:4,lsrp:3,a:1`
[2/2]	aa	19	`lf:15,lp:2,ls:2,rf:9,rp:1,rs:2,a:9`
[2/3]	bb	12	`lf:9,lp:1,ls:2,rf:9,rs:1,a:1`
[3/0]	bab	19	`lf:16,lp:2,ls:1,rf:10,rs:2,lprs:1,a:1`
[3/1]	baa	15	`lf:8,lp:5,ls:2,rf:5,rp:1,rs:2,lsrp:1,lprs:1,a:9`
[3/2]	aba	14	`lf:14,rf:10,rp:3,a:1`
[3/3]	aab	12	`lf:8,lp:2,ls:2,rf:4,rp:1,rs:2,lprs:1,a:16`
[4/0]	abab	15	`lf:14,ls:1,rf:9,rp:3,rs:2,lsrp:1,a:1`
[4/1]	baba	12	`lf:10,lp:2,rf:6,a:1`
[4/2]	baaa	9	`lf:5,lp:4,rf:3,rp:1,a:19`
[4/3]	abba	7	`lf:4,ls:3,rf:4,rp:3,rs:1,re:1,lsrp:2,a:1`
[5/0]	babab	13	`lf:10,lp:2,ls:1,rf:5,rs:1,lprs:1,a:1`
[5/1]	baaab	10	`lf:5,lp:4,ls:1,rf:3,rp:1,rs:2,re:1,lprs:1,a:19`
[5/2]	ababa	8	`lf:8,rf:5,rp:3,a:1`
[5/3]	ababb	6	`lf:5,ls:1,rf:2,rs:1,a:1`
[6/0]	ababab	9	`lf:8,ls:1,rf:5,rp:3,rs:1,lsrp:1,a:1`
[6/1]	bababb	6	`lf:4,lp:1,ls:1,rf:2,rs:1,a:1`
[6/2]	bababa	6	`lf:5,lp:1,rf:2,a:1`
[6/3]	ababba	5	`lf:3,ls:2,rf:1,a:1`

Considering [length 2 / frequency 0] ba=c.

Step 2

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = ba
Reduction order:
- Left-to-right recursive path with deg(c) = 0; deg(a) = deg(b) = 1, a < b

Rewriting system is not complete: roundsLimit

#	Rule
1.	cacccc ⇒ a
2.	ccccbc ⇒ b
3.	caccca ⇒ aacccc
4.	acccbc ⇒ 1
5.	cab ⇒ abc
6.	cacb ⇒ acbc
7.	caccb ⇒ accbc
8.	cacccb ⇒ 1
9.	ba ⇒ c
10.	cbcca ⇒ bccac
11.	cbccca ⇒ bcccac
12.	ccccbb ⇒ bcccbc
13.	aacccb ⇒ caccc
14.	abca ⇒ cac
15.	abcca ⇒ ccac
16.	abccca ⇒ cccac
17.	acccbb ⇒ cccbc
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	cc	29	`lf:26,lp:2,ls:1,rf:16,rp:3,rs:2,a:2`
[2/1]	ca	24	`lf:12,lp:6,ls:6,rf:6,rp:2,lsrp:1,a:11`
[2/2]	cb	16	`lf:10,lp:2,ls:4,rf:4,a:2`
[2/3]	ac	10	`lf:8,lp:2,rf:9,rp:2,rs:5,a:2`
[2/4]	bc	9	`lf:7,ls:2,rf:8,rp:3,rs:5,a:2`
[2/5]	ab	8	`lf:4,lp:3,ls:1,rf:1,rp:1,lsrp:10,a:14`
[2/6]	bb	4	`lf:2,ls:2,a:4`
[3/0]	ccc	16	`lf:13,lp:2,ls:1,rf:7,rp:2,rs:2,a:2`
[3/1]	ccb	10	`lf:7,ls:3,rf:3,a:2`
[3/2]	cca	10	`lf:5,ls:5,rf:4,rp:1,lsrp:1,a:18`
[3/3]	cac	10	`lf:5,lp:5,rf:6,rp:2,rs:5,re:1,a:11`
[3/4]	acc	9	`lf:7,lp:2,rf:3,rp:1,a:2`
[3/5]	cbc	8	`lf:4,lp:2,ls:2,rf:4,rs:4,a:2`
[3/6]	abc	6	`lf:3,lp:3,rf:1,rp:1,rs:1,re:1,a:14`
[4/0]	cccb	8	`lf:6,ls:2,rf:2,rp:1,a:2`
[4/1]	cacc	8	`lf:4,lp:4,rf:1,rp:1,a:11`
[4/2]	accc	8	`lf:6,lp:2,rf:2,rs:1,a:2`
[4/3]	ccca	6	`lf:3,ls:3,rf:2,rp:1,lsrp:1,a:18`
[4/4]	cccc	6	`lf:3,lp:2,ls:1,rf:1,rs:1,a:3`
[4/5]	ccbb	4	`lf:2,ls:2,a:4`
[4/6]	bcca	4	`lf:2,ls:2,rf:1,rp:1,lsrp:10,a:21`
[5/0]	acccb	8	`lf:4,lp:2,ls:2,a:2`
[5/1]	caccc	6	`lf:3,lp:3,rf:1,rp:1,rs:1,re:1,a:11`
[5/2]	cccbb	4	`lf:2,ls:2,a:4`
[5/3]	bccca	4	`lf:2,ls:2,rf:1,rp:1,lsrp:10,a:24`
[5/4]	ccccb	4	`lf:2,lp:2,a:3`
[5/5]	cccbc	4	`lf:2,ls:2,rf:2,rp:1,rs:2,re:1,a:2`
[5/6]	abccc	2	`lf:1,lp:1,a:24`

Considering [length 5 / frequency 0] acccb=d.

Step 3

Auxiliary generators:
1. c = ba
2. d = acccb
Reduction order:
- Left-to-right recursive path with deg(c) = deg(d) = 0, c < d; deg(a) = deg(b) = 1, a < b

Rewriting system is complete. See ⟨a, b | ababababba=1⟩.