Morphocompletion for #631 ⟨a, b | aaabaabba=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.	aabbaa ⇒ baaaab
2.	aabaab ⇒ bbaaaa
3.	bbaaaabaa ⇒ 1
4.	baabbaa ⇒ bbaaaab
5.	abbaaaab ⇒ bbaaaaba
6.	abaabb ⇒ baabba
7.	aabbbaaaa ⇒ bbaaaaaab
8.	bbaaaaaabbaa ⇒ aab
9.	baaaabbbaa ⇒ bbaaaaaabb
10.	bbaaaababbaaaa ⇒ abaab
11.	bbaaaababaaaab ⇒ abbaa
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	aa	50	`lf:40,lp:3,ls:7,rf:26,rp:1,rs:2,lsrp:1,lprs:1,a:7`
[2/1]	ab	22	`lf:17,lp:2,ls:3,rf:10,rp:2,rs:5,lsrp:1,a:7`
[2/2]	ba	21	`lf:19,lp:2,rf:11,rp:2,rs:2,a:7`
[2/3]	bb	19	`lf:14,lp:4,ls:1,rf:8,rp:5,rs:1,a:7`
[3/0]	baa	24	`lf:17,lp:2,ls:5,rf:9,rp:2,rs:1,lsrp:1,a:7`
[3/1]	aaa	22	`lf:20,ls:2,rf:16,rs:1,a:10`
[3/2]	aab	19	`lf:13,lp:3,ls:3,rf:8,rp:1,rs:5,re:1,lprs:2,a:7`
[3/3]	bba	15	`lf:11,lp:4,rf:7,rp:5,rs:1,a:7`
[4/0]	bbaa	19	`lf:11,lp:4,ls:4,rf:6,rp:5,rs:1,lsrp:2,lprs:1,a:10`
[4/1]	aaaa	13	`lf:11,ls:2,rf:10,rs:1,a:10`
[4/2]	baaa	10	`lf:9,lp:1,rf:6,rp:1,a:10`
[4/3]	aabb	9	`lf:6,lp:2,ls:1,rf:2,rs:1,a:7`
[5/0]	baaaa	12	`lf:9,lp:1,ls:2,rf:6,rp:1,rs:1,a:10`
[5/1]	bbaaa	11	`lf:7,lp:4,rf:5,rp:5,a:10`
[5/2]	abbaa	9	`lf:5,lp:1,ls:3,rf:1,rp:1,rs:1,re:1,a:14`
[5/3]	aaaab	9	`lf:7,ls:2,rf:5,rs:3,a:14`
[6/0]	bbaaaa	13	`lf:7,lp:4,ls:2,rf:5,rp:5,rs:1,re:1,lsrp:1,a:10`
[6/1]	baaaab	9	`lf:6,lp:1,ls:2,rf:3,rp:1,rs:2,re:1,a:14`
[6/2]	aabbaa	4	`lf:2,ls:2,a:14`
[6/3]	aabbba	3	`lf:2,lp:1,a:15`

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

Step 2

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	caaccc ⇒ aac
2.	baa ⇒ c
3.	bcaac ⇒ 1
4.	cbcaa ⇒ 1
5.	ccbc ⇒ b
6.	acbc ⇒ cbca
7.	aacb ⇒ bcaa
8.	caab ⇒ aabc
9.	caaccb ⇒ aab
10.	bbcaa ⇒ ccb
11.	bcaab ⇒ cbc
12.	cbccaab ⇒ bc
13.	ccbb ⇒ bcbc
14.	acbb ⇒ cbba
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	aa	14	`lf:10,lp:1,ls:3,rf:4,rp:3,rs:1,lprs:1,a:1`
[2/1]	cb	12	`lf:8,lp:2,ls:2,rf:5,rp:3,rs:1,a:9`
[2/2]	bc	11	`lf:7,lp:2,ls:2,rf:7,rp:3,rs:4,re:1,lprs:1,a:9`
[2/3]	ca	11	`lf:8,lp:3,rf:2,rs:1,a:16`
[2/4]	ac	9	`lf:6,lp:2,ls:1,rf:1,rs:1,a:16`
[2/5]	cc	9	`lf:6,lp:2,ls:1,rf:1,rp:1,a:9`
[2/6]	bb	6	`lf:3,lp:1,ls:2,rf:1,a:13`
[3/0]	caa	13	`lf:8,lp:3,ls:2,rf:1,rs:1,a:22`
[3/1]	cbc	8	`lf:4,lp:2,ls:2,rf:3,rp:2,rs:2,re:1,lsrp:10,a:9`
[3/2]	aab	6	`lf:3,ls:3,rf:2,rp:2,rs:1,re:1,lsrp:10,a:30`
[3/3]	acb	6	`lf:3,lp:2,ls:1,a:16`
[3/4]	ccb	6	`lf:3,lp:2,ls:1,rf:1,rp:1,rs:1,re:1,a:9`
[3/5]	bca	6	`lf:4,lp:2,rf:2,rp:1,rs:1,a:16`
[3/6]	aac	6	`lf:4,lp:1,ls:1,rf:1,rp:1,rs:1,re:1,a:22`
[4/0]	bcaa	8	`lf:4,lp:2,ls:2,rf:1,rp:1,rs:1,re:1,a:22`
[4/1]	caac	6	`lf:3,lp:2,ls:1,a:27`
[4/2]	caab	4	`lf:2,ls:2,a:30`
[4/3]	bbca	2	`lf:1,lp:1,a:23`
[4/4]	accb	2	`lf:1,ls:1,a:45`
[4/5]	cbca	2	`lf:1,lp:1,rf:1,rp:1,rs:1,re:1,a:16`
[4/6]	cbcc	2	`lf:1,lp:1,a:37`
[5/0]	caacc	4	`lf:2,lp:2,a:45`
[5/1]	ccaab	2	`lf:1,ls:1,a:37`
[5/2]	aaccb	2	`lf:1,ls:1,a:45`
[5/3]	cbcca	2	`lf:1,lp:1,a:37`
[5/4]	aaccc	2	`lf:1,ls:1,a:47`
[5/5]	bccaa	1	`lf:1,a:37`

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

Step 3

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

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