Morphocompletion for #4681 ⟨a, b | aabbaaab=aba⟩

Solved by morph:2/0,4/4,5/4. (See Morphocompletion.)

Step 1

Checking up to 20 rules for overlaps.

Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1

Rewriting system is not complete: arenaTotalLimit

#	Rule
1.	aabbaaab ⇒ aba
2.	ababaaab ⇒ aabbaaba
3.	aabbaaaabbaaba ⇒ abaabaaab
4.	ababaaaabbaaba ⇒ aabbaabaabaaab
5.	abaabaaababbaaab ⇒ abaabaaabba
6.	abaabaaabbabaaab ⇒ abaabaaababbaaba
7.	abaaabaaababbaaab ⇒ abaaabaaabba
8.	aabbaabaaaababbaaab ⇒ aabbaabaaaabba
9.	abaaaabaaababbaaab ⇒ abaaaabaaabba
10.	ababaabaaaababbaaab ⇒ ababaabaaaabba
	...

Collecting factors up to length 7 / frequency 3:

[2/0]	ab	58	`lf:43,lp:7,ls:8,rf:31,rp:7,rs:2,lprp:5,lsrp:6,lprs:1`
[2/1]	aa	53	`lf:50,lp:3,rf:35,rp:3,lprp:1`
[2/2]	ba	37	`lf:35,ls:2,rf:29,rs:8`
[3/0]	aab	38	`lf:27,lp:3,ls:8,rf:22,rp:3,rs:2,lprp:1,lsrp:2,lprs:1`
[3/1]	aba	33	`lf:24,lp:7,ls:2,rf:20,rp:7,rs:3,re:1,lprp:5,lsrp:1,lprs:2`
[3/2]	baa	24	`lf:24,rf:19`
[4/0]	aaab	26	`lf:18,ls:8,rf:10,rs:2`
[4/1]	baaa	18	`lf:18,rf:10`
[4/2]	abaa	18	`lf:14,lp:4,rf:15,rp:5,lprp:4,a:1`
[5/0]	baaab	21	`lf:13,ls:8,rf:7,rs:2`
[5/1]	abaaa	13	`lf:11,lp:2,rf:10,rp:2,lprp:2,a:1`
[5/2]	abbaa	10	`lf:10,rf:4`
[6/0]	bbaaab	12	`lf:6,ls:6`
[6/1]	abaaab	10	`lf:7,lp:1,ls:2,rf:7,rp:1,rs:2,lprp:1,a:1`
[6/2]	aabbaa	8	`lf:5,lp:3,rf:3,rp:3,lprp:1`

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(b) = 0; deg(c) = 1; deg(a) = 2

Rewriting system is not complete: pendingRulesLimit

#	Rule
1.	ab ⇒ c
2.	ccaacb ⇒ acbacc
3.	acbaac ⇒ ca
4.	acbaca ⇒ ccaac
5.	acbaccaac ⇒ ccaca
6.	acbaccaca ⇒ ccaccaac
7.	ccaaccbaac ⇒ acbacca
8.	ccaaccbaca ⇒ acbacccaac
9.	acbaaacbacc ⇒ cacaacb
10.	acbaccaccaac ⇒ ccaccaca
11.	acbaccaccaca ⇒ ccaccaccaac
12.	cacaaccbaac ⇒ cacaacba
13.	cacaacbcaac ⇒ cacaaccbaca
14.	ccaaccbaccaac ⇒ acbacccaca
15.	caacaaccbaac ⇒ caacaacba
16.	ccacaaaccbaac ⇒ ccacaaacba
17.	caaacaaccbaac ⇒ caaacaacba
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	ac	61	`lf:44,lp:7,ls:10,rf:32,rp:4,rs:4,lsrp:2,lprs:3,a:2`
[2/1]	ca	34	`lf:26,lp:4,ls:4,rf:29,rp:6,rs:6,re:1,lprp:4,lprs:1,a:2`
[2/2]	cc	26	`lf:20,lp:5,ls:1,rf:17,rp:6,rs:1,lprp:1,lprs:1,a:3`
[2/3]	aa	25	`lf:25,rf:14,a:2`
[2/4]	cb	18	`lf:17,ls:1,rf:10,rs:1,a:2`
[3/0]	aac	32	`lf:22,ls:10,rf:12,rs:4,a:2`
[3/1]	acb	18	`lf:10,lp:7,ls:1,rf:9,rp:4,rs:1,lsrp:1,lprs:1,a:2`
[3/2]	caa	17	`lf:15,lp:2,rf:12,rp:2,lprp:2,a:3`
[3/3]	cca	17	`lf:12,lp:5,rf:13,rp:6,rs:1,lprp:1,lprs:1,a:3`
[3/4]	acc	16	`lf:15,ls:1,rf:9,rs:1,a:4`
[4/0]	caac	18	`lf:13,lp:1,ls:4,rf:10,rp:1,rs:4,lprp:1,a:3`
[4/1]	acba	15	`lf:8,lp:7,rf:8,rp:4,rs:4,a:2`
[4/2]	baac	12	`lf:6,ls:6,a:2`
[4/3]	ccaa	11	`lf:7,lp:4,rf:4,rp:1,a:3`
[4/4]	caca	9	`lf:5,lp:2,ls:2,rf:7,rp:3,rs:3,lprp:2,a:4`
[5/0]	ccaac	14	`lf:7,lp:4,ls:3,rf:4,rp:1,rs:4,re:1,lprs:1,a:3`
[5/1]	cbaac	12	`lf:6,ls:6,a:2`
[5/2]	acbac	11	`lf:6,lp:5,rf:4,rp:4,a:3`
[5/3]	accba	7	`lf:7,rf:1,a:6`
[5/4]	aaccb	7	`lf:7,rf:1,a:6`

Considering [length 4 / frequency 4] caca=d.

Step 3

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	ab ⇒ c
2.	cadb ⇒ dcc
3.	cacc ⇒ db
4.	caddb ⇒ ddcc
5.	cadcc ⇒ ddb
6.	cadddb ⇒ dddcc
7.	caddcc ⇒ dddb
8.	cadddcc ⇒ ddddb
9.	dbadb ⇒ cacdcc
10.	dbacc ⇒ cacdb
11.	dbadcc ⇒ cacddb
12.	dca ⇒ cad
13.	caca ⇒ d
14.	dbaca ⇒ cacd
15.	ccaacb ⇒ acbacc
16.	dcbaac ⇒ dba
17.	acbaac ⇒ ca
18.	acbaca ⇒ ccaac
19.	caaca ⇒ acbaad
20.	acbaccaac ⇒ cd
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	ca	30	`lf:16,lp:9,ls:5,rf:7,rp:6,rs:1,re:1,lsrp:11,a:2`
[2/1]	ac	20	`lf:14,lp:3,ls:3,rf:8,rp:2,rs:1,lprs:1,a:2`
[2/2]	db	16	`lf:8,lp:4,ls:4,rf:7,rp:2,rs:6,re:1,lprs:2,a:4`
[2/3]	cc	15	`lf:8,lp:1,ls:6,rf:6,rp:1,rs:5,lprs:1,a:4`
[2/4]	ba	8	`lf:8,rf:3,rs:1,a:3`
[3/0]	cad	12	`lf:6,lp:6,rf:1,rp:1,rs:1,re:1,a:5`
[3/1]	aca	8	`lf:4,ls:4,a:2`
[3/2]	aac	8	`lf:5,ls:3,rf:1,rs:1,a:3`
[3/3]	dba	8	`lf:4,lp:4,rf:1,rp:1,rs:1,re:1,a:7`
[3/4]	acb	8	`lf:4,lp:3,ls:1,rf:2,rp:2,lsrp:1,a:3`
[4/0]	cadd	8	`lf:4,lp:4,a:11`
[4/1]	acba	6	`lf:3,lp:3,rf:2,rp:2,a:3`
[4/2]	caac	5	`lf:3,lp:1,ls:1,rf:1,rs:1,a:15`
[4/3]	baca	4	`lf:2,ls:2,a:7`
[4/4]	baac	4	`lf:2,ls:2,a:3`
[5/0]	ccaac	4	`lf:2,lp:1,ls:1,rf:1,rp:1,rs:1,re:1,a:16`
[5/1]	cbaac	4	`lf:2,ls:2,a:3`
[5/2]	acbac	4	`lf:2,lp:2,rf:1,rp:1,a:16`
[5/3]	caddd	4	`lf:2,lp:2,a:22`
[5/4]	acbaa	2	`lf:1,lp:1,rf:1,rp:1,a:3`

Considering [length 5 / frequency 4] acbaa=e.

Step 4

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

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