Morphocompletion for #315 ⟨a, b | aabbabba=1⟩

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 a < b

Rewriting system is not complete: rulesLimit

#	Rule
1.	bbaa ⇒ aabb
2.	bbabba ⇒ abbabb
3.	baaabba ⇒ aaabbab
4.	aaabbabb ⇒ 1
5.	baaaaabb ⇒ aaabbaba
6.	bbabbbba ⇒ abbbbabb
7.	abbabbbba ⇒ aabbbbabb
8.	bbaabbabb ⇒ abbabbbba
9.	abbabbbbaa ⇒ bb
10.	aaaabbbbabb ⇒ bba
11.	aaabbabaabb ⇒ baa
12.	aaaabbbbbbabb ⇒ bbbba
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	bb	44	`lf:34,lp:4,ls:6,rf:22,rp:3,rs:5,re:1,lsrp:2,lprs:3,a:3`
[2/1]	aa	26	`lf:20,lp:4,ls:2,rf:7,rp:4,rs:1,lsrp:1,lprs:1,a:5`
[2/2]	ba	25	`lf:19,lp:2,ls:4,rf:11,rp:1,rs:4,lprs:1,a:3`
[2/3]	ab	21	`lf:19,lp:2,rf:13,rp:3,rs:1,a:3`
[3/0]	abb	26	`lf:18,lp:2,ls:6,rf:11,rp:3,rs:4,lsrp:1,lprs:1,a:3`
[3/1]	bba	24	`lf:16,lp:4,ls:4,rf:9,rp:1,rs:3,re:1,lprs:1,a:3`
[3/2]	aaa	14	`lf:10,lp:4,rf:2,rp:2,a:20`
[3/3]	bbb	12	`lf:12,rf:8,rp:1,a:5`
[4/0]	babb	12	`lf:8,ls:4,rf:4,rs:3,a:3`
[4/1]	bbab	11	`lf:9,lp:2,rf:6,rs:1,a:3`
[4/2]	abba	11	`lf:7,lp:2,ls:2,rf:4,rp:2,lsrp:1,a:3`
[4/3]	aabb	10	`lf:8,ls:2,rf:4,rp:2,rs:1,re:1,a:5`
[5/0]	bbabb	14	`lf:8,lp:2,ls:4,rf:4,rs:3,lprs:11,a:3`
[5/1]	aaabb	9	`lf:6,lp:2,ls:1,rf:2,rp:2,lsrp:1,a:20`
[5/2]	bbbba	7	`lf:5,ls:2,rf:4,rp:1,rs:2,re:1,a:5`
[5/3]	abbab	7	`lf:5,lp:2,rf:4,rp:2,rs:1,a:3`
[6/0]	abbabb	8	`lf:4,lp:2,ls:2,rf:2,rp:2,rs:1,re:1,lsrp:1,a:3`
[6/1]	abbbba	6	`lf:4,ls:2,rf:3,rp:1,rs:1,lsrp:1,a:5`
[6/2]	aaabba	6	`lf:3,lp:2,ls:1,rf:2,rp:2,lsrp:10,a:20`
[6/3]	aaaabb	6	`lf:3,lp:2,ls:1,a:28`

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 recursive path with deg(c) = 0; deg(a) = deg(b) = 1, a < b

Rewriting system is not complete: roundsLimit

#	Rule
1.	cca ⇒ acc
2.	aacc ⇒ 1
3.	caa ⇒ aac
4.	baccc ⇒ acccb
5.	cbca ⇒ abcc
6.	bb ⇒ accc
7.	aacacc ⇒ ca
8.	bacacc ⇒ acccba
9.	cbaa ⇒ abac
10.	aacacacc ⇒ caca
11.	aacabcc ⇒ bca
12.	baaca ⇒ aacab
13.	aacacabcc ⇒ cabca
14.	aacabac ⇒ baa
15.	baaaac ⇒ aacaba
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	aa	20	`lf:12,lp:6,ls:2,rf:4,rp:3,rs:1,lsrp:10,lprs:1,a:17`
[2/1]	ac	18	`lf:16,ls:2,rf:9,rp:4,rs:2,a:3`
[2/2]	cc	17	`lf:9,lp:1,ls:7,rf:8,rs:3,lprs:10,a:3`
[2/3]	ca	16	`lf:12,lp:1,ls:3,rf:8,rp:3,rs:4,re:1,a:3`
[2/4]	ba	10	`lf:6,lp:4,rf:4,rp:1,rs:2,lprs:2,a:6`
[2/5]	cb	4	`lf:2,lp:2,rf:2,rs:1,a:6`
[2/6]	ab	3	`lf:3,rf:5,rp:2,rs:1,a:11`
[3/0]	aac	15	`lf:8,lp:6,ls:1,rf:3,rp:3,rs:1,re:1,lsrp:1,a:19`
[3/1]	aca	10	`lf:9,ls:1,rf:3,rs:1,a:8`
[3/2]	acc	9	`lf:5,ls:4,rf:4,rp:4,rs:1,re:1,lsrp:1,a:3`
[3/3]	baa	6	`lf:3,lp:2,ls:1,rf:1,rp:1,rs:1,re:1,a:17`
[3/4]	bac	6	`lf:3,lp:2,ls:1,rf:1,rs:1,a:6`
[3/5]	cac	5	`lf:5,rf:1,rp:1,a:8`
[3/6]	bcc	4	`lf:2,ls:2,rf:1,rs:1,a:11`
[4/0]	aaca	12	`lf:6,lp:5,ls:1,rf:2,rp:2,lsrp:10,a:20`
[4/1]	cacc	6	`lf:3,ls:3,a:8`
[4/2]	acac	5	`lf:5,a:8`
[4/3]	abcc	4	`lf:2,ls:2,rf:1,rp:1,rs:1,re:1,a:11`
[4/4]	acab	3	`lf:3,rf:2,rs:1,a:21`
[4/5]	baaa	2	`lf:1,lp:1,a:35`
[4/6]	baca	2	`lf:1,lp:1,a:8`
[5/0]	aacac	6	`lf:3,lp:3,a:20`
[5/1]	acacc	6	`lf:3,ls:3,a:8`
[5/2]	aacab	4	`lf:2,lp:2,rf:2,rp:2,rs:1,re:1,a:21`
[5/3]	cabcc	4	`lf:2,ls:2,a:21`
[5/4]	baaaa	2	`lf:1,lp:1,a:35`
[5/5]	aaaac	2	`lf:1,ls:1,a:35`
[5/6]	bacac	2	`lf:1,lp:1,a:8`

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

Step 3

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

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