Morphocompletion for #331 ⟨a, b | abababba=1⟩

Solved by morph:2/0,3/0. (See Morphocompletion.)

Step 1

Checking up to 20 rules for overlaps.

Reduction order:
- Right-to-left shortlex with a < b

Rewriting system is not complete: rulesLimit

#	Rule
1.	baab ⇒ abba
2.	bbaab ⇒ babba
3.	bbaaab ⇒ abbbaa
4.	ababab ⇒ babbaa
5.	baaabba ⇒ aabbbaa
6.	bababbaa ⇒ 1
7.	baabbabbaa ⇒ ab
8.	baabbababba ⇒ abb
9.	baaabbbabbaa ⇒ aabb
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	ba	28	`lf:20,lp:6,ls:2,rf:7,rp:2,rs:2,lprs:1,a:2`
[2/1]	ab	21	`lf:16,lp:1,ls:4,rf:8,rp:4,rs:1,re:1,lsrp:2,a:2`
[2/2]	aa	16	`lf:13,ls:3,rf:5,rp:2,rs:3,lsrp:1,a:2`
[2/3]	bb	13	`lf:11,lp:2,rf:9,rs:2,a:2`
[3/0]	baa	18	`lf:10,lp:5,ls:3,rf:3,rs:3,lprs:1,a:2`
[3/1]	bba	14	`lf:10,lp:2,ls:2,rf:5,rs:2,lprs:1,a:2`
[3/2]	bab	10	`lf:8,lp:1,ls:1,rf:2,rp:2,lsrp:1,a:2`
[3/3]	aab	10	`lf:7,ls:3,rf:2,rp:2,a:9`
[4/0]	bbaa	10	`lf:5,lp:2,ls:3,rf:3,rs:3,lprs:1,a:2`
[4/1]	abba	9	`lf:7,ls:2,rf:3,rp:1,rs:2,re:1,a:2`
[4/2]	abab	6	`lf:4,lp:1,ls:1,a:2`
[4/3]	baab	6	`lf:3,lp:2,ls:1,a:9`
[5/0]	baaab	6	`lf:3,lp:2,ls:1,a:13`
[5/1]	abbaa	6	`lf:3,ls:3,rf:1,rs:1,a:2`
[5/2]	babab	5	`lf:3,lp:1,ls:1,a:2`
[5/3]	babba	5	`lf:4,ls:1,rf:2,rp:2,rs:1,re:1,a:2`
[6/0]	babbaa	6	`lf:3,ls:3,rf:1,rp:1,rs:1,re:1,a:2`
[6/1]	baaabb	4	`lf:2,lp:2,a:38`
[6/2]	baabba	4	`lf:2,lp:2,a:14`
[6/3]	bababb	3	`lf:2,lp:1,a:2`

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

Step 2

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	caccc ⇒ a
2.	cccbc ⇒ b
3.	aaccc ⇒ cacca
4.	ba ⇒ c
5.	ccbca ⇒ 1
6.	bcac ⇒ cbca
7.	bccac ⇒ cbcca
8.	accb ⇒ cbca
9.	acccccb ⇒ bca
10.	abc ⇒ cab
11.	acbc ⇒ cacb
12.	bccbc ⇒ cccbb
13.	bcaa ⇒ acccccc
14.	bcbca ⇒ cccb
15.	bcab ⇒ cbc
16.	bccab ⇒ cbcc
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	bc	24	`lf:13,lp:7,ls:4,rf:6,rp:1,rs:1,lprs:1,a:3`
[2/1]	cc	19	`lf:15,lp:2,ls:2,rf:12,rp:2,rs:2,a:3`
[2/2]	ac	12	`lf:7,lp:3,ls:2,rf:3,rp:1,a:7`
[2/3]	ca	11	`lf:8,lp:1,ls:2,rf:8,rp:3,rs:5,a:6`
[2/4]	cb	9	`lf:7,ls:2,rf:8,rp:5,rs:2,lsrp:1,a:3`
[2/5]	ab	6	`lf:3,lp:1,ls:2,rf:1,rs:1,lprs:10,a:14`
[2/6]	aa	4	`lf:2,lp:1,ls:1,a:19`
[3/0]	bca	10	`lf:5,lp:3,ls:2,rf:3,rp:1,rs:3,re:1,lprs:10,a:6`
[3/1]	ccc	9	`lf:6,lp:1,ls:2,rf:6,rp:2,rs:1,a:3`
[3/2]	cbc	8	`lf:5,ls:3,rf:5,rp:5,rs:1,re:1,a:3`
[3/3]	ccb	8	`lf:5,lp:1,ls:2,rf:2,rs:1,a:3`
[3/4]	bcc	6	`lf:3,lp:3,rf:2,rs:1,lprs:1,a:5`
[3/5]	acc	6	`lf:4,lp:2,rf:2,rp:1,a:7`
[3/6]	cac	6	`lf:3,lp:1,ls:2,rf:2,rp:2,a:12`
[4/0]	ccbc	6	`lf:3,lp:1,ls:2,a:3`
[4/1]	accc	6	`lf:3,lp:1,ls:2,rf:1,rp:1,a:19`
[4/2]	bcca	4	`lf:2,lp:2,rf:1,rs:1,lprs:10,a:27`
[4/3]	cbca	4	`lf:2,ls:2,rf:2,rp:2,rs:2,re:2,a:6`
[4/4]	cccb	4	`lf:2,lp:1,ls:1,rf:2,rp:2,rs:1,re:1,a:3`
[4/5]	bcbc	2	`lf:1,lp:1,a:8`
[4/6]	bccb	2	`lf:1,lp:1,a:5`
[5/0]	ccccb	2	`lf:1,ls:1,a:22`
[5/1]	acccc	2	`lf:1,lp:1,rf:1,rp:1,a:19`
[5/2]	ccccc	1	`lf:1,rf:2,rs:1,a:19`
[5/3]	cccbb	0	`rf:1,rp:1,rs:1,re:1,a:5`
[5/4]	cbcca	0	`rf:1,rp:1,rs:1,re:1,a:34`
[5/5]	cacca	0	`rf:1,rp:1,rs:1,re:1,a:26`

Considering [length 3 / frequency 0] bca=d.

Step 3

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

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