Morphocompletion for #3767 ⟨a, b | abababaaab=a⟩

Solved by morph:3/0,2/1,4/0. (See Morphocompletion.)

Step 1

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: rulesLimit

#	Rule
1.	aabaaab ⇒ aaaabba
2.	aaaabbab ⇒ abababaa
3.	aababaaab ⇒ abababaaa
4.	abababaaab ⇒ a
5.	aaaabbaaab ⇒ aaaabaabba
6.	aaaabbaaaab ⇒ aabaaaaabba
7.	aaaabbbababaaa ⇒ aaaab
8.	abababaabababaa ⇒ aaaabb
	...

Collecting factors up to length 7 / frequency 3:

[2/0]	aa	37	`lf:29,lp:6,ls:2,rf:21,rp:5,rs:2,lprp:4,lsrp:2,lprs:2`
[2/1]	ab	32	`lf:24,lp:2,ls:6,rf:13,rp:2,rs:1,lsrp:2`
[2/2]	ba	18	`lf:18,rf:11,rs:3`
[3/0]	aaa	20	`lf:15,lp:4,ls:1,rf:12,rp:4,rs:1,lprp:2,lsrp:1`
[3/1]	aab	19	`lf:12,lp:2,ls:5,rf:7,rp:1,rs:1,lsrp:1`
[3/2]	aba	16	`lf:14,lp:2,rf:8,rp:2`
[4/0]	aaab	14	`lf:9,ls:5,rf:5,rs:1`
[4/1]	abab	10	`lf:8,lp:2,rf:4,rp:2`
[4/2]	baba	9	`lf:9,rf:4`
[5/0]	aaaab	10	`lf:5,lp:4,ls:1,rf:5,rp:4,rs:1,re:1,lprp:2,lprs:1,a:6`
[5/1]	ababa	10	`lf:8,lp:2,rf:4,rp:2`
[5/2]	baaab	8	`lf:4,ls:4`
[6/0]	aaaabb	8	`lf:4,lp:4,rf:3,rp:2,rs:1,re:1,a:6`
[6/1]	abaaab	6	`lf:3,ls:3`
[6/2]	ababaa	6	`lf:5,ls:1,rf:2,rs:1`

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 < a < b

Rewriting system is not complete: roundsLimit

#	Rule
1.	ca ⇒ ac
2.	aaa ⇒ c
3.	acbcb ⇒ ccbba
4.	aabcb ⇒ acbba
5.	cbcbaa ⇒ aacbbc
6.	aacbba ⇒ cbcb
7.	cbabcb ⇒ cbcbba
8.	acbcbba ⇒ cbababc
9.	aabcbba ⇒ abababc
10.	ccbabcb ⇒ ccbcbba
11.	acbabcb ⇒ cbababc
12.	aababcb ⇒ abababc
13.	cbcbbab ⇒ aa
14.	cbabcbb ⇒ aa
15.	aabababc ⇒ cbabcb
16.	cbababaa ⇒ acbcbb
17.	abababaa ⇒ aabcbb
18.	cbababcb ⇒ c
19.	abababcb ⇒ a
20.	ccbcbbab ⇒ aac
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	cb	40	`lf:26,lp:6,ls:8,rf:16,rp:5,rs:2,lprp:1,lsrp:2,a:2`
[2/1]	ab	27	`lf:23,lp:2,ls:2,rf:12,rp:2,a:2`
[2/2]	ba	26	`lf:23,ls:3,rf:13,rs:4,a:2`
[2/3]	aa	20	`lf:10,lp:6,ls:4,rf:5,rp:5,rs:2,re:2,lsrp:2,a:1`
[2/4]	bc	16	`lf:15,ls:1,rf:11,rs:5,a:2`
[3/0]	bcb	22	`lf:14,ls:8,rf:6,rs:2,a:2`
[3/1]	bab	19	`lf:17,ls:2,rf:9,a:2`
[3/2]	aba	13	`lf:11,lp:2,rf:6,rp:2,a:2`
[3/3]	cba	11	`lf:7,lp:4,rf:3,rp:3,a:4`
[3/4]	abc	11	`lf:10,ls:1,rf:6,rs:4,a:2`
[4/0]	abcb	16	`lf:9,ls:7,rf:2,rs:1,a:2`
[4/1]	abab	11	`lf:9,lp:2,rf:6,rp:2,a:2`
[4/2]	cbab	10	`lf:6,lp:4,rf:3,rp:3,a:4`
[4/3]	babc	9	`lf:8,ls:1,rf:5,rs:4,a:2`
[4/4]	cbcb	8	`lf:5,lp:2,ls:1,rf:4,rp:2,rs:1,re:1,a:13`
[5/0]	babcb	13	`lf:7,ls:6,rf:1,rs:1,a:2`
[5/1]	ababa	7	`lf:5,lp:2,rf:2,rp:2,a:2`
[5/2]	bcbba	6	`lf:4,ls:2,rf:2,rs:2,a:18`
[5/3]	cbabc	6	`lf:4,lp:2,rf:1,rp:1,a:6`
[5/4]	babab	5	`lf:5,rf:4,a:2`

Considering [length 2 / frequency 1] ab=d.

Step 3

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	ca ⇒ ac
2.	dddaad ⇒ a
3.	cb ⇒ aad
4.	cdbd ⇒ dddaa
5.	ab ⇒ d
6.	dddadddadddc ⇒ cd
7.	dddcdaad ⇒ addadddc
8.	cddaad ⇒ aadddc
9.	aaa ⇒ c
10.	dddadddaa ⇒ cdb
11.	adaad ⇒ dddadddc
12.	addaad ⇒ dddc
13.	cdba ⇒ dddadddc
14.	cdbb ⇒ dddadddad
15.	dddadddadddac ⇒ cda
16.	aadddadddc ⇒ cdaad
17.	dddacdbc ⇒ cdaa
18.	acdaad ⇒ cdddadddc
19.	cdbcdb ⇒ adadddaa
20.	cdaadb ⇒ aadddaa
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	dd	34	`lf:28,lp:6,rf:29,rp:5,a:3`
[2/1]	ad	24	`lf:16,lp:2,ls:6,rf:13,rp:2,rs:3,lsrp:1,a:3`
[2/2]	da	16	`lf:16,rf:13,rs:1,a:3`
[2/3]	cd	16	`lf:10,lp:6,rf:6,rp:6,rs:1,re:1,a:7`
[2/4]	aa	15	`lf:11,lp:2,ls:2,rf:8,rp:3,rs:4,a:1`
[3/0]	ddd	19	`lf:13,lp:6,rf:14,rp:5,a:3`
[3/1]	aad	15	`lf:8,lp:1,ls:6,rf:4,rp:3,rs:2,re:1,lsrp:1,lprs:1,a:3`
[3/2]	dda	12	`lf:12,rf:9,a:3`
[3/3]	cdb	11	`lf:6,lp:4,ls:1,rf:1,rp:1,rs:1,re:1,a:20`
[3/4]	daa	9	`lf:8,ls:1,rf:5,rs:4,a:3`
[4/0]	ddda	15	`lf:10,lp:5,rf:8,rp:4,a:3`
[4/1]	daad	13	`lf:7,ls:6,rf:1,rs:1,a:3`
[4/2]	addd	7	`lf:7,rf:8,a:7`
[4/3]	dadd	6	`lf:6,rf:6,a:8`
[4/4]	ddad	6	`lf:6,rf:6,rs:1,a:8`
[5/0]	dddad	9	`lf:6,lp:3,rf:5,rp:3,rs:1,a:8`
[5/1]	cdaad	6	`lf:3,lp:1,ls:2,rf:1,rp:1,rs:1,re:1,a:9`
[5/2]	ddaad	6	`lf:3,ls:3,a:3`
[5/3]	daddd	6	`lf:6,rf:6,a:8`
[5/4]	ddadd	6	`lf:6,rf:5,a:8`

Considering [length 4 / frequency 0] ddda=e.

Step 4

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

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