Morphocompletion for #1378 ⟨a, b | aaabbbaaab=1⟩

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

Step 1

Checking up to 20 rules for overlaps.

Reduction order:
- Right-to-left shortlex with b < a

Rewriting system is not complete: rulesLimit

#	Rule
1.	bbaaa ⇒ aaabb
2.	baaabbba ⇒ abaaabbb
3.	aaabbbbba ⇒ babaaabbb
4.	aaabaaabbb ⇒ 1
5.	baaabaaabb ⇒ 1
6.	aaabbabaaabbb ⇒ bba
7.	baaabaaaaaabb ⇒ aaa
8.	aaabaaaaaabbbb ⇒ baaa
9.	aaabbaabaaabbb ⇒ bbaa
10.	aaabbbbabaaabbb ⇒ bbbba
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	aa	48	`lf:41,lp:6,ls:1,rf:11,rp:2,rs:3,lsrp:1,lprs:2,a:4`
[2/1]	bb	33	`lf:25,lp:1,ls:7,rf:10,rp:3,rs:3,lsrp:3,lprs:1,a:4`
[2/2]	ba	21	`lf:16,lp:3,ls:2,rf:7,rp:2,rs:2,lsrp:1,a:4`
[2/3]	ab	19	`lf:19,rf:5,rp:1,a:4`
[3/0]	aaa	30	`lf:23,lp:6,ls:1,rf:5,rp:2,rs:2,re:1,lsrp:1,lprs:1,a:4`
[3/1]	aab	17	`lf:17,rf:3,a:4`
[3/2]	bbb	17	`lf:12,ls:5,rf:4,rp:1,rs:2,lsrp:1,a:27`
[3/3]	baa	15	`lf:12,lp:3,rf:4,rp:1,rs:1,a:4`
[4/0]	aaab	22	`lf:16,lp:6,rf:3,rp:1,a:4`
[4/1]	baaa	15	`lf:11,lp:3,ls:1,rf:3,rp:1,rs:1,re:1,a:4`
[4/2]	aabb	14	`lf:12,ls:2,rf:3,rs:1,a:4`
[4/3]	abbb	12	`lf:8,ls:4,rf:2,rs:2,a:27`
[5/0]	aaabb	18	`lf:12,lp:4,ls:2,rf:3,rp:1,rs:1,re:1,a:4`
[5/1]	aabbb	12	`lf:8,ls:4,rf:2,rs:2,a:27`
[5/2]	baaab	11	`lf:8,lp:3,rf:2,a:20`
[5/3]	abaaa	7	`lf:7,rf:2,rp:1,a:20`
[6/0]	aaabbb	14	`lf:8,lp:2,ls:4,rf:2,rs:2,lprs:1,a:27`
[6/1]	baaabb	8	`lf:6,lp:1,ls:1,rf:2,a:20`
[6/2]	aaabaa	6	`lf:4,lp:2,a:20`
[6/3]	aabaaa	5	`lf:5,a:20`

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

Step 2

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = aaa
Reduction order:
- Right-to-left shortlex with c < b < a

Rewriting system is not complete: roundsLimit

#	Rule
1.	ca ⇒ ac
2.	cbb ⇒ bbc
3.	aaa ⇒ c
4.	cbcb ⇒ bcbc
5.	cbccb ⇒ bccbc
6.	bcbcb ⇒ bbcbc
7.	bbbcbc ⇒ 1
8.	bcbccb ⇒ bbccbc
9.	bbbcba ⇒ abbbcb
10.	bbbcbac ⇒ a
11.	bcbcccb ⇒ bbcccbc
12.	bbccbcb ⇒ c
13.	bbbbccbc ⇒ cb
14.	bbbcbaac ⇒ aa
15.	bbbbcccbc ⇒ ccb
16.	bbbcbabbc ⇒ abb
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	cb	29	`lf:20,lp:3,ls:6,rf:8,rp:1,rs:3,re:1,a:6`
[2/1]	bb	28	`lf:19,lp:8,ls:1,rf:7,rp:4,rs:1,lsrp:10,lprs:1,a:6`
[2/2]	bc	28	`lf:21,lp:3,ls:4,rf:12,rp:2,rs:6,lprs:3,a:6`
[2/3]	cc	8	`lf:8,rf:5,rp:1,a:9`
[2/4]	aa	5	`lf:3,lp:1,ls:1,rf:1,rp:1,rs:1,re:1,a:1`
[2/5]	ba	5	`lf:4,ls:1,a:18`
[2/6]	ac	4	`lf:2,ls:2,rf:1,rp:1,rs:1,re:1,a:3`
[3/0]	bcb	17	`lf:11,lp:3,ls:3,rf:3,rp:1,rs:1,lsrp:10,a:6`
[3/1]	bbb	16	`lf:9,lp:7,rf:1,a:10`
[3/2]	cbc	14	`lf:9,lp:2,ls:3,rf:5,rs:5,lprs:11,a:6`
[3/3]	bbc	11	`lf:9,lp:1,ls:1,rf:5,rp:4,rs:1,re:1,a:6`
[3/4]	ccb	9	`lf:6,ls:3,rf:4,rp:1,rs:1,re:1,a:9`
[3/5]	bcc	6	`lf:6,rf:3,rp:1,a:9`
[3/6]	cba	5	`lf:4,ls:1,a:18`
[4/0]	bbbc	12	`lf:7,lp:5,rf:1,a:10`
[4/1]	bcbc	8	`lf:4,lp:3,ls:1,rf:2,rp:1,rs:2,re:1,lprs:10,a:6`
[4/2]	bccb	6	`lf:4,ls:2,rf:2,rp:1,lsrp:10,a:9`
[4/3]	bcba	5	`lf:4,ls:1,a:18`
[4/4]	bbcb	5	`lf:5,rf:2,rp:1,rs:1,a:6`
[4/5]	ccbc	5	`lf:3,ls:2,rf:3,rs:3,a:9`
[4/6]	bbbb	4	`lf:2,lp:2,a:10`
[5/0]	bbbcb	10	`lf:5,lp:5,rf:1,rs:1,lprs:10,a:16`
[5/1]	bbcba	5	`lf:4,ls:1,a:18`
[5/2]	bbbbc	4	`lf:2,lp:2,a:10`
[5/3]	bcbcc	4	`lf:2,lp:2,a:25`
[5/4]	bbccb	3	`lf:2,lp:1,rf:1,rp:1,a:9`
[5/5]	bcccb	3	`lf:2,ls:1,rf:1,a:17`
[5/6]	bccbc	3	`lf:2,ls:1,rf:2,rp:1,rs:2,re:1,a:9`

Considering [length 3 / frequency 0] bcb=d.

Step 3

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

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