Morphocompletion for #1991 ⟨a, b | aabbaabb=ba⟩

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

Step 1

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: arenaTotalLimit

#	Rule
1.	aabbba ⇒ baaabb
2.	aabbaabb ⇒ ba
3.	aabbbbaaabb ⇒ baaabbabbba
4.	baaabbabbaabb ⇒ aabbbba
5.	aabbbbabaaabb ⇒ baaabbabbbaba
6.	aabbaabaabbbba ⇒ baaaabbabbaabb
7.	baaabbabbbaaabb ⇒ aabbbbaba
8.	aabbbbababaaabb ⇒ baaabbabbbababa
9.	baaabbabbbabaaabb ⇒ aabbbbababa
10.	aabbbbabababaaabb ⇒ baaabbabbbabababa
11.	baaabbabbbababaaabb ⇒ aabbbbabababa
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	bb	48	`lf:39,ls:9,rf:28,rs:2`
[2/1]	aa	40	`lf:33,lp:7,rf:18,rp:4`
[2/2]	ba	36	`lf:30,lp:4,ls:2,rf:33,rp:7,rs:9,re:1,lsrp:2,lprs:4`
[2/3]	ab	35	`lf:35,rf:28`
[3/0]	abb	34	`lf:25,ls:9,rf:16,rs:2`
[3/1]	aab	29	`lf:22,lp:7,rf:11,rp:4`
[3/2]	baa	19	`lf:15,lp:4,rf:7,rp:6`
[3/3]	bba	18	`lf:16,ls:2,rf:14,rs:2`
[4/0]	aabb	37	`lf:21,lp:7,ls:9,rf:11,rp:4,rs:2,lsrp:4,lprs:2`
[4/1]	baaa	15	`lf:11,lp:4,rf:6,rp:6,a:1`
[4/2]	aaab	11	`lf:11,rf:6,a:1`
[4/3]	bbba	11	`lf:9,ls:2,rf:8,rs:2,a:1`
[5/0]	aaabb	18	`lf:11,ls:7,rf:6,rs:1,a:1`
[5/1]	baaab	15	`lf:11,lp:4,rf:5,rp:5,a:1`
[5/2]	aabbb	11	`lf:6,lp:5,rf:4,rp:4,a:1`
[5/3]	aabba	8	`lf:6,lp:2,rf:5`
[6/0]	baaabb	22	`lf:11,lp:4,ls:7,rf:5,rp:5,rs:1,re:1,lsrp:4,a:1`
[6/1]	aabbbb	9	`lf:5,lp:4,rf:4,rp:4,a:2`
[6/2]	abbbba	6	`lf:5,ls:1,rf:4,rs:1,a:2`
[6/3]	abaaab	5	`lf:5,a:7`

Considering [length 3 / frequency 0] abb=c.

Step 2

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = abb
Reduction order:
- Left-to-right shortlex with c < b < a

Rewriting system is not complete: roundsLimit

#	Rule
1.	abb ⇒ c
2.	acba ⇒ baac
3.	acac ⇒ ba
4.	baacbb ⇒ acbc
5.	abacbc ⇒ caacbb
6.	baaccac ⇒ acbba
7.	acbbaac ⇒ baaccba
8.	abacbba ⇒ caaccac
9.	caaccacbb ⇒ abacbbc
10.	babaaccba ⇒ acbcaac
11.	baaccbaac ⇒ acbbaba
12.	acbcaacbb ⇒ babaaccbc
13.	acbbabaac ⇒ baaccbaba
14.	caaccaccac ⇒ abacbbba
15.	acbcaaccac ⇒ babaaccbba
16.	acaabacbbc ⇒ baaaccacbb
17.	abacbbbaac ⇒ caaccaccba
18.	baaccbabaac ⇒ acbbababa
19.	acbbababaac ⇒ baaccbababa
20.	acaabacbbba ⇒ baaaccaccac
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	ac	54	`lf:35,lp:9,ls:10,rf:24,rp:5,rs:4,lsrp:3,lprs:2,a:2`
[2/1]	ba	34	`lf:25,lp:5,ls:4,rf:28,rp:9,rs:10,re:1,lsrp:2,lprs:3,a:2`
[2/2]	aa	17	`lf:17,rf:14,a:3`
[2/3]	bb	17	`lf:13,ls:4,rf:9,rs:2,a:1`
[2/4]	cb	17	`lf:17,rf:15,a:3`
[2/5]	ab	15	`lf:11,lp:4,rf:10,rp:2,a:1`
[2/6]	ca	14	`lf:12,lp:2,rf:9,rp:3,a:2`
[3/0]	aac	21	`lf:15,ls:6,rf:12,rs:2,a:3`
[3/1]	acb	20	`lf:14,lp:6,rf:9,rp:5,a:3`
[3/2]	baa	15	`lf:11,lp:4,rf:8,rp:6,a:3`
[3/3]	aba	13	`lf:10,lp:3,rf:10,rp:2,rs:4,a:7`
[3/4]	cbb	13	`lf:10,ls:3,rf:8,rs:2,a:4`
[3/5]	cac	10	`lf:6,ls:4,rf:5,rs:2,a:2`
[3/6]	acc	8	`lf:8,rf:11,a:5`
[4/0]	baac	21	`lf:11,lp:4,ls:6,rf:6,rp:4,rs:1,re:1,lsrp:3,a:3`
[4/1]	acbb	16	`lf:10,lp:3,ls:3,rf:7,rp:3,rs:2,a:4`
[4/2]	abac	8	`lf:5,lp:3,rf:2,rp:2,a:7`
[4/3]	ccac	8	`lf:5,ls:3,rf:5,rs:2,a:5`
[4/4]	aacc	7	`lf:7,rf:9,a:5`
[4/5]	acbc	6	`lf:3,lp:2,ls:1,rf:2,rp:2,rs:1,re:1,a:4`
[4/6]	baba	6	`lf:5,lp:1,rf:8,rp:2,rs:4,a:8`
[5/0]	abacb	8	`lf:5,lp:3,rf:2,rp:2,a:7`
[5/1]	acbba	8	`lf:4,lp:3,ls:1,rf:3,rp:3,rs:1,re:1,a:5`
[5/2]	accac	8	`lf:5,ls:3,rf:5,rs:2,a:5`
[5/3]	abaac	7	`lf:4,ls:3,rf:2,a:8`
[5/4]	baacc	7	`lf:4,lp:3,rf:5,rp:3,a:5`
[5/5]	babaa	5	`lf:4,lp:1,rf:2,rp:2,a:8`
[5/6]	caacc	5	`lf:3,lp:2,rf:2,rp:2,a:9`

Considering [length 2 / frequency 0] ac=d.

Step 3

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

Rewriting system is complete. See ⟨a, b | aabbaabb=ba⟩.