Morphocompletion for #3813 ⟨a, b | abbabaaaab=b⟩

Solved by morph:2/0,3/0. (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: roundsLimit

#	Rule
1.	aaaaabbb ⇒ babaaaab
2.	abbabb ⇒ bbabab
3.	abbabab ⇒ bbabaab
4.	abbabaab ⇒ bbabaaab
5.	abbabaaab ⇒ bbabaaaab
6.	abbabaaaab ⇒ b
7.	bbabababaaaab ⇒ abbb
8.	bbabaababaaaab ⇒ aabbb
9.	bbabaaababaaaab ⇒ aaabbb
10.	bbabaaaababaaaab ⇒ aaaabbb
11.	abbbbabab ⇒ bbabababb
12.	abbbbabaab ⇒ bbabababab
13.	abbbbabaaab ⇒ bbabababaab
14.	abbbbabaaaab ⇒ bbabababaaab
15.	bbabababababaaaab ⇒ abbaabbb
16.	bbabababaababaaaab ⇒ abbaaabbb
17.	bbabaababababaaaab ⇒ aabbaabbb
18.	bbabababbbabaaaab ⇒ abbbbabb
19.	bbabaababbbabaaaab ⇒ aabbbbabb
20.	abbbbabbbabab ⇒ bbabababbbabb
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	ab	103	`lf:75,lp:10,ls:18,rf:43,rp:4,rs:8,lsrp:4,lprs:7,lsrs:6`
[2/1]	ba	64	`lf:64,rf:34,rp:1`
[2/2]	aa	53	`lf:52,lp:1,rf:24,rp:5`
[2/3]	bb	49	`lf:38,lp:9,ls:2,rf:38,rp:9,rs:11,lsrp:1,lprs:9`
[3/0]	bab	46	`lf:43,ls:3,rf:25,rp:1,rs:2`
[3/1]	aba	42	`lf:42,rf:18`
[3/2]	aab	37	`lf:22,ls:15,rf:14,rp:3,rs:6,lsrp:3,lsrs:4`
[3/3]	bba	31	`lf:22,lp:9,rf:15,rp:9`
[4/0]	baba	36	`lf:36,rf:18,rp:1`
[4/1]	bbab	31	`lf:22,lp:9,rf:12,rp:9`
[4/2]	aaab	29	`lf:16,ls:13,rf:7,rp:1,rs:4,lsrp:1,lsrs:2`
[4/3]	abab	24	`lf:21,ls:3,rf:12,rs:2,a:3`
[5/0]	bbaba	29	`lf:20,lp:9,rf:9,rp:9`
[5/1]	aaaab	24	`lf:13,ls:11,rf:3,rp:1,rs:2,lsrp:1`
[5/2]	babaa	21	`lf:21,rf:6,rp:1`
[5/3]	babab	18	`lf:15,ls:3,rf:12,rs:2,a:3`
[6/0]	baaaab	23	`lf:12,ls:11,rf:2,rs:2`
[6/1]	bbabaa	18	`lf:13,lp:5,rf:3,rp:3`
[6/2]	babaaa	15	`lf:15,rf:4,rp:1`
[6/3]	bbabab	14	`lf:7,lp:4,ls:3,rf:6,rp:6,rs:1,re:1,lsrp:2,a:3`

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

Step 2

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	ab ⇒ c
2.	cbcaaac ⇒ b
3.	acbcc ⇒ cbcac
4.	acbcac ⇒ cbcaac
5.	acbcaac ⇒ b
6.	accbcc ⇒ cbcccaaaccac
7.	accbcac ⇒ cbcccaaaccaac
8.	bbcac ⇒ cbcc
9.	bbcaac ⇒ cbcac
10.	bbcaaac ⇒ cbcaac
11.	bbcccaaaccac ⇒ ccbcc
12.	bbcccaaaccaac ⇒ ccbcac
13.	bbcccaaaccaaac ⇒ ccbcaac
14.	cbb ⇒ bbcccaaac
15.	cbcb ⇒ bbcc
16.	bbb ⇒ cbccbcaaccaaac
17.	bbcb ⇒ cbccbcaac
18.	bbccbcac ⇒ cbccbcc
19.	bbccbcaac ⇒ cbccbcac
20.	bbcccaaaccb ⇒ ccbccbcaac
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	ac	38	`lf:21,lp:5,ls:12,rf:16,rs:13,lprs:4,lsrs:7,a:2`
[2/1]	bb	26	`lf:13,lp:11,ls:2,rf:2,rp:2,lsrp:1,a:3`
[2/2]	cc	20	`lf:18,ls:2,rf:22,rp:4,rs:4,a:6`
[2/3]	cb	19	`lf:13,lp:3,ls:3,rf:20,rp:11,lsrp:1,a:2`
[2/4]	bc	19	`lf:19,rf:22,a:2`
[2/5]	aa	18	`lf:18,rf:15,a:2`
[2/6]	ca	16	`lf:16,rf:16,a:2`
[3/0]	bbc	20	`lf:10,lp:10,rf:2,rp:2,a:3`
[3/1]	aac	18	`lf:11,ls:7,rf:11,rs:8,lsrs:2,a:2`
[3/2]	cbc	11	`lf:9,lp:2,rf:20,rp:11,a:2`
[3/3]	caa	11	`lf:11,rf:11,a:2`
[3/4]	bcc	10	`lf:8,ls:2,rf:12,rs:4,a:6`
[3/5]	cac	10	`lf:5,ls:5,rf:5,rs:5,a:5`
[3/6]	bca	9	`lf:9,rf:10,a:2`
[4/0]	bbcc	12	`lf:6,lp:6,rf:2,rp:2,rs:1,re:1,a:9`
[4/1]	aaac	10	`lf:7,ls:3,rf:4,rs:2,a:2`
[4/2]	bcac	8	`lf:4,ls:4,rf:4,rs:4,a:5`
[4/3]	caac	8	`lf:4,ls:4,rf:7,rs:6,a:3`
[4/4]	cbca	7	`lf:6,lp:1,rf:10,rp:4,a:2`
[4/5]	caaa	7	`lf:7,rf:4,a:2`
[4/6]	bbca	6	`lf:3,lp:3,a:3`
[5/0]	caaac	10	`lf:7,ls:3,rf:4,rs:2,a:2`
[5/1]	bbccc	8	`lf:4,lp:4,rf:1,rp:1,a:11`
[5/2]	cbcac	6	`lf:3,ls:3,rf:4,rp:2,rs:4,re:2,a:5`
[5/3]	bcaac	6	`lf:3,ls:3,rf:6,rs:5,a:3`
[5/4]	ccaaa	5	`lf:5,rf:4,a:11`
[5/5]	bbccb	4	`lf:2,lp:2,a:12`
[5/6]	bbcaa	4	`lf:2,lp:2,a:3`

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

Step 3

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

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