Morphocompletion for #2875 ⟨a, b | aaaabbaabba=1⟩

Solved by morph:3/0,4/0. (See Morphocompletion.)

Step 1

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: rulesLimit

#	Rule
1.	aaabb ⇒ bbaaa
2.	abaabbaaaaa ⇒ bbaaaaaaaab
3.	aabbaaaaab ⇒ baabbaaaaa
4.	bbaabbaaaaa ⇒ 1
5.	abbaabb ⇒ bbaabba
6.	bbaaabaabbaaaaa ⇒ aaab
7.	bbaabbbbaaaaaa ⇒ abb
8.	bbaabbabbaaaaaa ⇒ aabb
9.	abbbbaabb ⇒ bbaabbbba
10.	bbaabbbbbbaaaaaa ⇒ abbbb
11.	bbaabbbbabbaaaaaa ⇒ abbabb
12.	bbaabbabbbbaaaaaa ⇒ aabbbb
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	aa	66	`lf:56,lp:2,ls:8,rf:20,rp:3,rs:2,lsrp:3,lprs:2,a:5`
[2/1]	bb	46	`lf:36,lp:7,ls:3,rf:19,rp:4,rs:5,lsrp:3,lprs:5,a:5`
[2/2]	ab	24	`lf:20,lp:3,ls:1,rf:11,rp:3,rs:2,lprs:1,a:5`
[2/3]	ba	23	`lf:23,rf:9,rp:1,rs:2,a:5`
[3/0]	aaa	43	`lf:34,lp:1,ls:8,rf:11,rp:1,rs:2,lsrp:1,lprs:1,a:6`
[3/1]	bba	28	`lf:21,lp:7,rf:8,rp:4,rs:2,a:5`
[3/2]	abb	22	`lf:17,lp:2,ls:3,rf:9,rp:3,rs:3,re:1,a:5`
[3/3]	baa	20	`lf:20,rf:6,rp:1,a:5`
[4/0]	aaaa	31	`lf:23,ls:8,rf:7,rs:1,a:6`
[4/1]	bbaa	25	`lf:18,lp:7,rf:5,rp:4,a:5`
[4/2]	aabb	16	`lf:12,lp:1,ls:3,rf:5,rp:2,rs:1,re:1,a:5`
[4/3]	abba	10	`lf:9,lp:1,rf:3,rp:1,rs:1,lprs:1,a:5`
[5/0]	aaaaa	22	`lf:14,ls:8,rf:5,rs:1,a:6`
[5/1]	bbaab	14	`lf:8,lp:6,rf:2,rp:2,a:5`
[5/2]	baabb	12	`lf:10,ls:2,rf:3,rp:1,a:5`
[5/3]	bbaaa	11	`lf:10,lp:1,rf:3,rp:2,rs:1,re:1,a:6`
[6/0]	bbaabb	16	`lf:8,lp:6,ls:2,rf:2,rp:2,lsrp:11,a:5`
[6/1]	baaaaa	12	`lf:9,ls:3,rf:2,rs:1,a:6`
[6/2]	aaaaaa	10	`lf:5,ls:5,rf:3,a:7`
[6/3]	bbaaaa	9	`lf:9,rf:2,rp:1,a:6`

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

Step 2

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	ac ⇒ ca
2.	aaa ⇒ c
3.	cbb ⇒ bbc
4.	cabb ⇒ abbc
5.	caabb ⇒ aabbc
6.	bbaabbcc ⇒ a
7.	bbaabbcaa ⇒ 1
8.	cbbaabb ⇒ bbaabbc
9.	abbaabb ⇒ bbaabba
10.	abbaabbc ⇒ bbaabbca
11.	bbcbaabbcc ⇒ cba
12.	bbcbaabbcaa ⇒ cb
13.	bbccbaabbcc ⇒ ccba
14.	bbaabbbbcc ⇒ abb
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	bb	34	`lf:23,lp:6,ls:5,rf:10,rp:4,rs:1,lsrp:12,lprs:1,a:15`
[2/1]	aa	18	`lf:14,lp:1,ls:3,rf:4,rp:1,a:1`
[2/2]	ab	15	`lf:13,lp:2,rf:6,rp:2,a:15`
[2/3]	bc	11	`lf:10,ls:1,rf:5,rs:4,a:15`
[2/4]	ba	9	`lf:9,rf:6,rs:3,a:15`
[2/5]	cc	9	`lf:5,ls:4,rf:1,rp:1,lsrp:1,a:20`
[2/6]	cb	7	`lf:5,lp:2,rf:3,rp:2,rs:1,re:1,a:17`
[3/0]	abb	19	`lf:13,lp:2,ls:4,rf:6,rp:2,rs:1,re:1,lsrp:10,a:15`
[3/1]	bbc	14	`lf:10,lp:3,ls:1,rf:5,rp:1,rs:4,re:1,a:15`
[3/2]	aab	10	`lf:10,rf:4,rp:1,a:15`
[3/3]	bba	9	`lf:6,lp:3,rf:4,rp:3,rs:1,a:15`
[3/4]	baa	9	`lf:9,rf:3,a:15`
[3/5]	bcc	9	`lf:5,ls:4,a:20`
[3/6]	caa	6	`lf:3,lp:1,ls:2,a:23`
[4/0]	aabb	13	`lf:10,ls:3,rf:4,rp:1,lsrp:10,a:15`
[4/1]	bbcc	10	`lf:5,lp:1,ls:4,a:20`
[4/2]	baab	9	`lf:9,rf:3,a:15`
[4/3]	bbaa	9	`lf:6,lp:3,rf:3,rp:3,a:15`
[4/4]	abbc	7	`lf:6,ls:1,rf:4,rp:1,rs:3,re:1,a:15`
[4/5]	bbcb	4	`lf:2,lp:2,a:34`
[4/6]	abba	4	`lf:2,lp:2,rf:1,rs:1,lprs:1,a:15`
[5/0]	baabb	11	`lf:9,ls:2,rf:3,a:15`
[5/1]	bbaab	9	`lf:6,lp:3,rf:3,rp:3,a:15`
[5/2]	aabbc	7	`lf:6,ls:1,rf:3,rp:1,rs:2,re:1,a:15`
[5/3]	abbcc	6	`lf:3,ls:3,a:20`
[5/4]	bbcba	4	`lf:2,lp:2,a:34`
[5/5]	abbaa	4	`lf:2,lp:2,a:15`
[5/6]	bbcaa	4	`lf:2,ls:2,a:23`

Considering [length 4 / frequency 0] aabb=d.

Step 3

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

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