Morphocompletion for #3817 ⟨a, b | abbabbaaab=a⟩

Solved by morph:2/0,3/1,4/1. (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.	aaaabbb ⇒ ababbaa
2.	abaaabbb ⇒ abbabbaa
3.	aabbaaab ⇒ ababbaaa
4.	ababbaaab ⇒ abbabbaaa
5.	abbabbaaab ⇒ a
6.	ababbaababbaaa ⇒ aaaab
7.	abbabbaababbaaa ⇒ abaaab
8.	ababbaabbabbaaa ⇒ aaaabb
9.	abbabbaabbabbaaa ⇒ abaaabb
10.	abbabbaaaaaab ⇒ aabbaababbaaa
11.	aaaababbbbabbaaa ⇒ aaaabab
12.	ababbaababbababbaa ⇒ aaaababbb
	...

Collecting factors up to length 7 / frequency 3:

[2/0]	ab	52	`lf:39,lp:9,ls:4,rf:21,rp:6,rs:3,lprp:4,lsrp:2,lprs:2`
[2/1]	aa	45	`lf:36,lp:3,ls:6,rf:26,rp:5,rs:5,lprp:1,lsrp:4,lprs:2`
[2/2]	ba	33	`lf:33,rf:15`
[3/0]	abb	29	`lf:25,lp:4,rf:11,rp:2,rs:2,lprs:1`
[3/1]	aaa	24	`lf:17,lp:2,ls:5,rf:13,rp:4,rs:3,lprp:1,lsrp:3`
[3/2]	bba	23	`lf:23,rf:8`
[4/0]	abba	26	`lf:22,lp:4,rf:8,rp:2`
[4/1]	bbaa	16	`lf:15,ls:1,rf:6,rs:2`
[4/2]	babb	16	`lf:16,rf:6`
[5/0]	abbaa	16	`lf:15,ls:1,rf:6,rs:2`
[5/1]	babba	15	`lf:15,rf:5`
[5/2]	bbaaa	14	`lf:9,ls:5,rf:3,rs:3`
[6/0]	babbaa	15	`lf:14,ls:1,rf:5,rs:2`
[6/1]	abbaaa	14	`lf:9,ls:5,rf:3,rs:3`
[6/2]	ababba	12	`lf:8,lp:4,rf:3,rp:2,a:1`

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

Step 2

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	ab ⇒ c
2.	cbcbaac ⇒ a
3.	ccbaacb ⇒ a
4.	caacbb ⇒ cbcbaa
5.	ccbaaccbb ⇒ cbcbccbaa
6.	caacbcbbb ⇒ cbcbacbcbccbac
7.	caacbcbbcb ⇒ cbcbacbcba
8.	cbcbaaa ⇒ ccbaac
9.	cbcbacbcbccbaa ⇒ caacbcbb
10.	acbaac ⇒ ccbaaa
11.	cbcbaccbaac ⇒ caacb
12.	cbcbccbaccbaac ⇒ ccbaaccb
13.	aaacb ⇒ ccbaccbaac
14.	ccbaccbaaa ⇒ aaac
15.	cbcbaccbaaa ⇒ caac
16.	ccbaaccbaac ⇒ acbaaa
17.	ccbaccbccbaccbaac ⇒ aaaccb
18.	ccbaacaacb ⇒ acbaccbaac
19.	acbaccbaaa ⇒ ccbaacaac
20.	ccbaccbaacaac ⇒ aaccbaaa
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	cb	55	`lf:45,lp:6,ls:4,rf:29,rp:4,rs:3,lsrp:1,lprs:2,a:2`
[2/1]	ac	37	`lf:28,lp:2,ls:7,rf:19,rp:2,rs:7,lsrp:1,lprs:1,a:2`
[2/2]	aa	33	`lf:27,lp:1,ls:5,rf:22,rp:3,rs:5,lsrp:1,a:2`
[2/3]	cc	27	`lf:20,lp:7,rf:12,rp:5,a:3`
[2/4]	ba	25	`lf:25,rf:16,rs:1,a:2`
[3/0]	ccb	27	`lf:20,lp:7,rf:12,rp:5,rs:2,lprs:1,a:3`
[3/1]	cba	25	`lf:25,rf:16,rs:1,a:2`
[3/2]	aac	24	`lf:17,ls:7,rf:12,rp:1,rs:6,lsrp:1,a:2`
[3/3]	cbc	18	`lf:12,lp:6,rf:9,rp:4,a:2`
[3/4]	baa	17	`lf:16,ls:1,rf:10,rs:2,a:2`
[4/0]	ccba	25	`lf:18,lp:7,rf:10,rp:5,a:3`
[4/1]	baac	17	`lf:11,ls:6,rf:5,rs:3,a:2`
[4/2]	cbaa	17	`lf:16,ls:1,rf:10,rs:2,a:2`
[4/3]	cbcb	15	`lf:9,lp:6,rf:7,rp:4,a:2`
[4/4]	accb	10	`lf:10,rf:5,rs:2,a:6`
[5/0]	ccbaa	18	`lf:13,lp:4,ls:1,rf:8,rp:4,rs:1,lprs:1,a:3`
[5/1]	cbaac	17	`lf:11,ls:6,rf:5,rs:3,a:2`
[5/2]	cbcba	10	`lf:5,lp:5,rf:4,rp:3,rs:1,a:2`
[5/3]	cbaaa	8	`lf:4,ls:4,rf:3,rs:3,a:3`
[5/4]	caacb	8	`lf:4,lp:3,ls:1,rf:2,rp:2,rs:1,re:1,a:14`

Considering [length 3 / frequency 1] cba=d.

Step 3

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	db ⇒ cbc
2.	cba ⇒ d
3.	cbdac ⇒ a
4.	ab ⇒ c
5.	cdacb ⇒ a
6.	ddacb ⇒ cbcdac
7.	cbdad ⇒ ca
8.	cbcdad ⇒ da
9.	cbdcdad ⇒ cdac
10.	cbcdcdad ⇒ ddac
11.	aa ⇒ cdad
12.	cbcdaca ⇒ ddad
13.	cbdcdaca ⇒ ccdadd
14.	adac ⇒ cdcdad
15.	adad ⇒ cdaca
16.	acdad ⇒ cdada
17.	adcdad ⇒ cdacdac
18.	acdaca ⇒ cdaddad
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	ad	20	`lf:10,lp:3,ls:7,rf:7,rs:4,lprs:1,a:5`
[2/1]	cb	20	`lf:10,lp:8,ls:2,rf:2,rp:2,lsrp:1,a:2`
[2/2]	da	14	`lf:14,rf:15,rp:1,rs:2,re:1,a:3`
[2/3]	ac	13	`lf:9,lp:2,ls:2,rf:6,rs:4,a:3`
[2/4]	cd	11	`lf:10,lp:1,rf:11,rp:7,a:6`
[3/0]	dad	14	`lf:7,ls:7,rf:7,rs:4,a:5`
[3/1]	cda	10	`lf:9,lp:1,rf:10,rp:6,a:6`
[3/2]	dac	9	`lf:7,ls:2,rf:6,rs:4,a:3`
[3/3]	cbd	8	`lf:4,lp:4,a:3`
[3/4]	aca	6	`lf:3,ls:3,rf:1,rs:1,a:15`
[4/0]	cdad	10	`lf:5,ls:5,rf:5,rp:3,rs:2,re:1,lsrp:10,a:6`
[4/1]	daca	6	`lf:3,ls:3,rf:1,rs:1,a:15`
[4/2]	cbcd	6	`lf:3,lp:3,rf:1,rp:1,a:8`
[4/3]	cdac	5	`lf:4,lp:1,rf:5,rp:3,rs:3,re:1,a:6`
[4/4]	acda	4	`lf:2,lp:2,rf:1,a:10`
[5/0]	cdaca	6	`lf:3,ls:3,rf:1,rp:1,rs:1,re:1,a:15`
[5/1]	dcdad	6	`lf:3,ls:3,rf:1,rs:1,a:6`
[5/2]	cbcda	4	`lf:2,lp:2,rf:1,rp:1,a:8`
[5/3]	cbdcd	4	`lf:2,lp:2,a:6`
[5/4]	acdac	2	`lf:1,lp:1,rf:1,rs:1,a:17`

Considering [length 4 / frequency 1] daca=e.

Step 4

Auxiliary generators:
1. c = ab
2. d = cba
3. e = daca
Reduction order:
- Right-to-left recursive path with deg(c) = deg(b) = 0, c < b; deg(d) = 1; deg(e) = deg(a) = 2, e < a

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