Morphocompletion for #1808 ⟨a, b | abbabaaab=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: rulesLimit

#	Rule
1.	aaaabbb ⇒ babaaab
2.	abbabb ⇒ bbabab
3.	abbabab ⇒ bbabaab
4.	abbabaab ⇒ bbabaaab
5.	abbabaaab ⇒ b
6.	aaaabbaabbb ⇒ babababaaab
7.	aaaabbaaabbb ⇒ babaababaaab
8.	bbabababaaab ⇒ abbb
9.	bbabaababaaab ⇒ aabbb
10.	bbabaaababaaab ⇒ aaabbb
11.	abbbbabab ⇒ bbabababb
12.	abbbbabaab ⇒ bbabababab
13.	abbbbabaaab ⇒ bbabababaab
14.	aaaabbaababbb ⇒ babaaaaababbb
15.	babaaababababaaab ⇒ aaaababbb
16.	bbabababababaaab ⇒ abbaabbb
17.	bbabababbbabaaab ⇒ abbbbabb
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	ab	76	`lf:57,lp:7,ls:12,rf:39,rp:3,rs:8,lsrp:3,lprs:5,lsrs:4`
[2/1]	ba	47	`lf:46,lp:1,rf:33,rp:4`
[2/2]	aa	43	`lf:39,lp:4,rf:22,rp:3`
[2/3]	bb	42	`lf:32,lp:5,ls:5,rf:24,rp:6,rs:8,lsrp:1,lprs:5,lsrs:1`
[3/0]	bab	33	`lf:30,lp:1,ls:2,rf:24,rp:4,rs:2`
[3/1]	aab	30	`lf:20,ls:10,rf:12,rp:1,rs:6,lsrp:1,lsrs:2`
[3/2]	aba	29	`lf:29,rf:21`
[3/3]	abb	24	`lf:16,lp:7,ls:1,rf:10,rp:3,rs:2,lprs:1`
[4/0]	baba	26	`lf:25,lp:1,rf:18,rp:4`
[4/1]	aaab	23	`lf:15,ls:8,rf:7,rp:1,rs:4,lsrp:1`
[4/2]	bbab	18	`lf:13,lp:5,rf:7,rp:6`
[4/3]	abab	18	`lf:16,ls:2,rf:13,rs:2,a:2`
[5/0]	baaab	19	`lf:11,ls:8,rf:4,rs:4`
[5/1]	bbaba	17	`lf:12,lp:5,rf:6,rp:6`
[5/2]	babab	14	`lf:12,ls:2,rf:10,rp:1,rs:2,a:2`
[5/3]	babaa	14	`lf:13,lp:1,rf:8,rp:3`
[6/0]	abaaab	18	`lf:10,ls:8,rf:4,rs:4`
[6/1]	babaaa	11	`lf:10,lp:1,rf:5,rp:2`
[6/2]	bbabab	10	`lf:5,lp:3,ls:2,rf:4,rp:4,rs:1,re:1,lsrp:1,a:2`
[6/3]	bababa	9	`lf:9,rf:7,rp:1,a:4`

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.	cbcaac ⇒ b
3.	acbcc ⇒ cbcac
4.	acbcac ⇒ b
5.	accbcc ⇒ cbcccaaccac
6.	accbcac ⇒ cbcccaaccaac
7.	bbcac ⇒ cbcc
8.	bbcaac ⇒ cbcac
9.	bbcccaaccac ⇒ ccbcc
10.	bbcccaaccaac ⇒ ccbcac
11.	cbb ⇒ bbcccaac
12.	cbcb ⇒ bbcc
13.	cbccbcaccaaccac ⇒ bcbcc
14.	cbccbcaccaaccaac ⇒ bcbcac
15.	bbb ⇒ cbccbcaccaac
16.	bbcb ⇒ cbccbcac
17.	bbccbcac ⇒ cbccbcc
18.	bbccbcccaaccac ⇒ cbcccbcc
19.	bbcccaaccb ⇒ ccbccbcac
20.	bbccbccbcac ⇒ cbccbccbcc
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	ac	40	`lf:24,lp:4,ls:12,rf:13,rs:10,lprs:3,lsrs:4,a:2`
[2/1]	cc	28	`lf:26,ls:2,rf:27,rp:3,rs:7,a:5`
[2/2]	cb	26	`lf:18,lp:5,ls:3,rf:22,rp:10,lsrp:1,a:2`
[2/3]	bb	24	`lf:12,lp:10,ls:2,rf:2,rp:2,lsrp:1,a:3`
[2/4]	bc	23	`lf:23,rf:26,rp:2,a:2`
[2/5]	ca	20	`lf:20,rf:13,a:2`
[2/6]	aa	10	`lf:10,rf:5,a:2`
[3/0]	bbc	18	`lf:9,lp:9,rf:2,rp:2,a:3`
[3/1]	cbc	18	`lf:14,lp:4,rf:22,rp:10,a:2`
[3/2]	cac	18	`lf:10,ls:8,rf:8,rs:7,a:3`
[3/3]	bcc	14	`lf:12,ls:2,rf:17,rs:7,a:5`
[3/4]	aac	14	`lf:10,ls:4,rf:5,rs:3,a:2`
[3/5]	acc	12	`lf:10,lp:2,rf:3,a:11`
[3/6]	cca	11	`lf:11,rf:6,a:9`
[4/0]	caac	14	`lf:10,ls:4,rf:5,rs:3,a:2`
[4/1]	bbcc	12	`lf:6,lp:6,rf:2,rp:2,rs:1,re:1,a:6`
[4/2]	bcac	12	`lf:7,ls:5,rf:7,rs:6,a:3`
[4/3]	cbcc	10	`lf:6,lp:2,ls:2,rf:15,rp:8,rs:6,re:1,lsrp:1,lprs:1,a:5`
[4/4]	ccbc	8	`lf:8,rf:10,rp:3,a:8`
[4/5]	cbca	8	`lf:7,lp:1,rf:7,rp:2,a:2`
[4/6]	ccaa	8	`lf:8,rf:5,a:9`
[5/0]	cbcac	10	`lf:6,ls:4,rf:7,rp:2,rs:6,re:2,a:3`
[5/1]	ccaac	10	`lf:8,ls:2,rf:5,rs:3,a:9`
[5/2]	bbccb	6	`lf:3,lp:3,a:10`
[5/3]	bccbc	6	`lf:6,rf:6,a:8`
[5/4]	bbccc	6	`lf:3,lp:3,rf:1,rp:1,a:9`
[5/5]	caacc	6	`lf:6,rf:2,a:12`
[5/6]	accac	6	`lf:3,ls:3,rf:1,rs:1,a:13`

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 | abbabaaab=b⟩.