Morphocompletion for #1807 ⟨a, b | abbabaaab=a⟩

Solved by morph:2/1,2/0,5/1. (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 ⇒ abbabaa
2.	aabaaab ⇒ ababaaa
3.	ababaaab ⇒ abbabaaa
4.	abbabaaab ⇒ a
5.	aaaababbbab ⇒ abbabaababa
6.	aaaabbaaabbb ⇒ abbabaababaa
7.	abbabaababaaa ⇒ aaaab
8.	abbabaabbabaaa ⇒ aaaabb
9.	ababaaaaaab ⇒ aabaababaaa
10.	abbabaaaaaab ⇒ ababaababaaa
11.	aaaababbbbabaaa ⇒ aaaabab
12.	abbabaabababbabaa ⇒ aaaababbb
	...

Collecting factors up to length 7 / frequency 3:

[2/0]	aa	50	`lf:41,lp:5,ls:4,rf:27,rp:5,rs:6,lprp:1,lsrp:4,lprs:3`
[2/1]	ab	50	`lf:37,lp:7,ls:6,rf:27,rp:6,rs:2,lprp:2,lsrp:4,lprs:1`
[2/2]	ba	29	`lf:29,rf:23,rs:1`
[3/0]	aaa	30	`lf:23,lp:4,ls:3,rf:12,rp:4,rs:4,lprp:1,lsrp:3`
[3/1]	aba	21	`lf:19,lp:2,rf:19,rp:2,rs:1`
[3/2]	aab	20	`lf:14,lp:1,ls:5,rf:9,rp:1,rs:1,lsrp:1`
[4/0]	aaab	15	`lf:10,ls:5,rf:4,rs:1`
[4/1]	aaaa	14	`lf:10,lp:4,rf:4,rp:4,lprp:1,a:3`
[4/2]	abaa	13	`lf:12,ls:1,rf:10,rs:2`
[5/0]	aaaab	12	`lf:6,lp:4,ls:2,rf:4,rp:4,rs:1,re:1,lprp:1,a:3`
[5/1]	babaa	12	`lf:11,ls:1,rf:9,rs:2`
[5/2]	abbab	12	`lf:7,lp:5,rf:4,rp:4`
[6/0]	abbaba	12	`lf:7,lp:5,rf:4,rp:4`
[6/1]	babaaa	10	`lf:7,ls:3,rf:4,rs:4`
[6/2]	bbabaa	9	`lf:8,ls:1,rf:4,rs:1`

Considering [length 2 / frequency 1] 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(b) = 0; deg(c) = 1; deg(a) = 2

Rewriting system is not complete: roundsLimit

#	Rule
1.	ab ⇒ c
2.	cbcaac ⇒ a
3.	ccaacb ⇒ a
4.	ccaaccbb ⇒ cbccbcaa
5.	ccaacccbbc ⇒ cbccbcacca
6.	cbcaaa ⇒ ccaac
7.	cbccbcacccbcaa ⇒ ccaacccbb
8.	acaac ⇒ ccaaa
9.	cbccbcaccaac ⇒ ccaaccb
10.	aaacb ⇒ cbcaccaac
11.	ccaacacbb ⇒ cbcacbcaa
12.	aaaccbb ⇒ cbcacccbcaa
13.	cbcaccaaa ⇒ aaac
14.	ccaaccaac ⇒ acaaa
15.	cbcacbcaccaac ⇒ ccaacacb
16.	cbcacccbcaccaac ⇒ aaaccb
17.	ccaaaaac ⇒ acaccaaa
18.	cbcaccacbcaccaac ⇒ aaacacb
19.	cbcaccaaccaaa ⇒ aaaccaac
20.	acaaaaac ⇒ ccaaccaccaaa
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	ac	42	`lf:31,lp:2,ls:9,rf:21,rp:2,rs:4,lsrp:2,a:2`
[2/1]	aa	38	`lf:32,lp:2,ls:4,rf:26,rp:4,rs:7,lsrp:2,lprs:1,a:2`
[2/2]	cb	32	`lf:21,lp:9,ls:2,rf:14,rp:5,rs:4,lsrp:1,lprs:4,a:2`
[2/3]	ca	31	`lf:31,rf:23,rs:1,a:2`
[2/4]	cc	31	`lf:25,lp:6,rf:20,rp:6,a:3`
[3/0]	aac	26	`lf:17,ls:9,rf:11,rs:4,a:2`
[3/1]	cbc	24	`lf:15,lp:9,rf:9,rp:5,a:2`
[3/2]	cca	21	`lf:15,lp:6,rf:12,rp:6,rs:1,lprs:1,a:3`
[3/3]	caa	20	`lf:19,ls:1,rf:14,rs:3,a:2`
[3/4]	aaa	16	`lf:11,lp:2,ls:3,rf:8,rp:4,rs:4,lsrp:2,a:3`
[4/0]	caac	20	`lf:13,ls:7,rf:7,rs:3,a:2`
[4/1]	ccaa	20	`lf:14,lp:6,rf:10,rp:6,a:3`
[4/2]	cbca	20	`lf:13,lp:7,rf:7,rp:3,a:2`
[4/3]	bcac	10	`lf:10,rf:4,a:7`
[4/4]	acca	9	`lf:9,rf:6,rs:1,a:6`
[5/0]	ccaac	21	`lf:11,lp:5,ls:5,rf:7,rp:5,rs:3,re:1,lsrp:2,a:3`
[5/1]	cbcac	15	`lf:10,lp:5,rf:4,rp:3,a:7`
[5/2]	bcacc	9	`lf:9,rf:3,a:7`
[5/3]	accaa	8	`lf:8,rf:4,a:6`
[5/4]	cacca	7	`lf:7,rf:4,rs:1,a:7`

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

Step 3

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	ab ⇒ c
2.	cbcad ⇒ a
3.	dadb ⇒ ccad
4.	dcadb ⇒ dbcad
5.	dbcadb ⇒ d
6.	ccadb ⇒ a
7.	daddb ⇒ ccdbcdcad
8.	dbcaddb ⇒ cbcdcad
9.	ac ⇒ d
10.	dadc ⇒ ccdbcadd
11.	dcadc ⇒ dbcdbcadd
12.	dbcadc ⇒ ad
13.	ccadc ⇒ cbcdbcadd
14.	aa ⇒ dbcad
15.	dbcdbcada ⇒ dcad
16.	ccdbcada ⇒ dad
17.	cbcdbcada ⇒ ccad
18.	cbcdcdbcada ⇒ dbcadd
19.	adad ⇒ dcdbcada
20.	adbcad ⇒ dbcada
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	db	25	`lf:15,lp:4,ls:6,rf:10,rp:5,lsrp:1,a:4`
[2/1]	ad	24	`lf:19,lp:2,ls:3,rf:15,rp:1,rs:9,re:1,a:3`
[2/2]	da	15	`lf:8,lp:3,ls:4,rf:3,rp:1,rs:2,lsrp:1,a:7`
[2/3]	ca	13	`lf:13,rf:13,a:3`
[2/4]	dc	13	`lf:7,lp:2,ls:4,rf:4,rp:2,a:6`
[3/0]	cad	15	`lf:13,ls:2,rf:13,rs:7,a:3`
[3/1]	dbc	13	`lf:9,lp:4,rf:10,rp:5,a:4`
[3/2]	ada	10	`lf:5,lp:1,ls:4,rf:2,rs:2,lprs:1,a:7`
[3/3]	adb	10	`lf:5,lp:1,ls:4,a:5`
[3/4]	bca	9	`lf:9,rf:8,a:3`
[4/0]	bcad	11	`lf:9,ls:2,rf:8,rs:2,a:3`
[4/1]	dbca	11	`lf:8,lp:3,rf:8,rp:4,a:4`
[4/2]	cada	8	`lf:4,ls:4,rf:2,rs:2,a:7`
[4/3]	cadc	6	`lf:3,ls:3,a:6`
[4/4]	cadb	6	`lf:3,ls:3,a:5`
[5/0]	dbcad	12	`lf:8,lp:3,ls:1,rf:8,rp:4,rs:2,re:2,lsrp:10,a:4`
[5/1]	bcada	8	`lf:4,ls:4,rf:2,rs:2,a:7`
[5/2]	cdbca	4	`lf:4,rf:4,a:12`
[5/3]	adbca	2	`lf:1,lp:1,a:7`
[5/4]	bcadc	2	`lf:1,ls:1,a:6`

Considering [length 5 / frequency 1] bcada=e.

Step 4

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

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