Morphocompletion for #71 ⟨a, b | ababba=1⟩

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

Step 1

Checking up to 20 rules for overlaps.

Reduction order:
- Right-to-left recursive path with deg(b) = 0; deg(a) = 1

Rewriting system is not complete: rulesLimit

#	Rule
1.	baab ⇒ abba
2.	abab ⇒ bbaa
3.	babbaa ⇒ 1
4.	bbaaab ⇒ abbbaa
5.	baaabb ⇒ aabbba
6.	baaabba ⇒ aabbbaa
7.	bbaaaab ⇒ aabbaba
8.	bbabaaab ⇒ abbbabaa
9.	baaaabbb ⇒ aaabbbba
10.	baaabbbbaa ⇒ aabb
11.	baaabbbabba ⇒ aabbb
12.	aabbabbabaa ⇒ baaab
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	ba	29	`lf:20,lp:7,ls:2,rf:11,rp:1,rs:4,lprs:3,a:2`
[2/1]	aa	27	`lf:23,lp:1,ls:3,rf:13,rp:6,rs:4,lsrp:1,a:2`
[2/2]	ab	23	`lf:17,lp:1,ls:5,rf:12,rp:3,rs:1,lsrp:3,a:2`
[2/3]	bb	21	`lf:16,lp:3,ls:2,rf:17,rp:1,rs:2,a:2`
[3/0]	baa	21	`lf:12,lp:6,ls:3,rf:5,rp:1,rs:4,lsrp:1,lprs:1,a:2`
[3/1]	aab	15	`lf:10,lp:1,ls:4,rf:7,rp:5,rs:1,lsrp:1,lprs:1,a:8`
[3/2]	bba	15	`lf:10,lp:3,ls:2,rf:8,rp:1,rs:3,a:2`
[3/3]	aaa	10	`lf:10,rf:2,rp:1,a:8`
[4/0]	baaa	13	`lf:8,lp:5,rf:1,rp:1,a:8`
[4/1]	aaab	11	`lf:8,ls:3,rf:2,rp:1,rs:1,a:8`
[4/2]	aabb	8	`lf:6,lp:1,ls:1,rf:6,rp:5,rs:1,re:1,lsrp:1,a:17`
[4/3]	bbaa	8	`lf:4,lp:2,ls:2,rf:3,rp:1,rs:3,re:1,lprs:1,a:2`
[5/0]	baaab	12	`lf:6,lp:4,ls:2,rf:1,rp:1,rs:1,re:1,a:8`
[5/1]	aaabb	6	`lf:5,ls:1,rf:1,rp:1,a:19`
[5/2]	babba	5	`lf:3,lp:1,ls:1,a:2`
[5/3]	aabba	4	`lf:2,lp:1,ls:1,rf:1,rp:1,a:17`
[6/0]	baaabb	6	`lf:3,lp:3,a:19`
[6/1]	baaaab	4	`lf:2,lp:1,ls:1,a:17`
[6/2]	aaabbb	4	`lf:3,ls:1,rf:1,rp:1,lsrp:1,a:23`
[6/3]	bbabaa	4	`lf:2,lp:1,ls:1,rf:1,rs:1,lprs:1,a:22`

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(b) = 1; deg(a) = 2

Rewriting system is not complete: roundsLimit

#	Rule
1.	ccbc ⇒ b
2.	bbc ⇒ ccccbb
3.	bcbc ⇒ ccbb
4.	ba ⇒ c
5.	cbca ⇒ 1
6.	bbca ⇒ ccb
7.	bcac ⇒ 1
8.	bccac ⇒ cbcca
9.	cbccac ⇒ bca
10.	cacc ⇒ a
11.	bcab ⇒ cbc
12.	bccab ⇒ cbcc
13.	bcccab ⇒ cbccc
14.	acb ⇒ bca
15.	acccb ⇒ cbcca
16.	abc ⇒ cab
17.	bcaa ⇒ acc
18.	aacc ⇒ caca
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	bc	25	`lf:14,lp:7,ls:4,rf:7,rp:2,rs:1,lprs:1,a:3`
[2/1]	ca	13	`lf:10,lp:1,ls:2,rf:7,rp:2,rs:5,a:6`
[2/2]	cc	13	`lf:10,lp:1,ls:2,rf:11,rp:3,rs:3,a:3`
[2/3]	ac	12	`lf:7,lp:2,ls:3,rf:2,rp:1,a:7`
[2/4]	cb	10	`lf:6,lp:2,ls:2,rf:8,rp:5,rs:1,lsrp:1,a:3`
[2/5]	ab	8	`lf:4,lp:1,ls:3,rf:1,rs:1,lprs:10,a:10`
[2/6]	aa	4	`lf:2,lp:1,ls:1,a:11`
[3/0]	bca	10	`lf:5,lp:3,ls:2,rf:2,rp:2,rs:2,re:2,a:6`
[3/1]	cac	8	`lf:4,lp:1,ls:3,rf:1,rp:1,a:9`
[3/2]	cbc	8	`lf:4,lp:2,ls:2,rf:5,rp:5,rs:1,re:1,a:3`
[3/3]	bcc	7	`lf:4,lp:3,rf:4,rs:1,lprs:1,a:12`
[3/4]	cab	6	`lf:3,ls:3,rf:1,rp:1,rs:1,re:1,a:10`
[3/5]	acc	6	`lf:3,lp:1,ls:2,rf:1,rp:1,rs:1,re:1,a:11`
[3/6]	cca	4	`lf:4,rf:2,rs:2,a:12`
[4/0]	bcca	5	`lf:3,lp:2,rf:2,rs:2,lprs:10,a:12`
[4/1]	ccab	4	`lf:2,ls:2,a:22`
[4/2]	ccac	4	`lf:2,ls:2,a:12`
[4/3]	accc	2	`lf:1,lp:1,a:13`
[4/4]	bccc	2	`lf:1,lp:1,rf:1,rs:1,lprs:1,a:28`
[4/5]	cbcc	2	`lf:1,lp:1,rf:4,rp:4,rs:1,re:1,a:12`
[4/6]	cccb	2	`lf:1,ls:1,rf:1,a:13`
[5/0]	cccab	2	`lf:1,ls:1,a:28`
[5/1]	bccac	2	`lf:1,ls:1,a:12`
[5/2]	bccca	2	`lf:1,lp:1,a:28`
[5/3]	cbcca	2	`lf:1,lp:1,rf:2,rp:2,rs:2,re:2,a:12`
[5/4]	cccbb	0	`rf:1,rs:1,a:24`
[5/5]	cbccc	0	`rf:1,rp:1,rs:1,re:1,a:28`
[5/6]	ccccb	0	`rf:1,rp:1,a:24`

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(d) = deg(c) = 0, d < c; deg(b) = 1; deg(a) = 2

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