Morphocompletion for #3761 ⟨a, b | ababaabaab=a⟩

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

Step 1

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: rulesLimit

#	Rule
1.	ababa ⇒ aaabb
2.	aaabbba ⇒ abaaabb
3.	aaabaabba ⇒ aabaabaab
4.	aaabbaba ⇒ aaabaabb
5.	aabaabaabb ⇒ a
6.	aaabaabbba ⇒ aaabbaaabb
7.	aaaaabbabba ⇒ aaabbaabaab
8.	aaababbaba ⇒ aaaaabbabb
9.	aaabbaabbba ⇒ abaaabbaabb
10.	aaabbaabaabba ⇒ aaab
11.	aaabbaabbaba ⇒ aaabbaabaabb
12.	aabaabaaaabbabba ⇒ aaabaab
	...

Collecting factors up to length 7 / frequency 3:

[2/0]	aa	45	`lf:34,lp:11,rf:34,rp:9,lprp:8,a:2`
[2/1]	ba	39	`lf:28,ls:11,rf:13,a:2`
[2/2]	ab	30	`lf:29,lp:1,rf:24,rp:2,rs:4,a:2`
[3/0]	aab	23	`lf:21,lp:2,rf:21,rp:1,rs:4,lprs:1,a:2`
[3/1]	bba	22	`lf:15,ls:7,rf:5,a:4`
[3/2]	aaa	22	`lf:13,lp:9,rf:13,rp:8,lprp:6,a:3`
[4/0]	aaab	18	`lf:10,lp:8,rf:11,rp:7,rs:1,re:1,lprp:4,lprs:1,a:3`
[4/1]	abba	16	`lf:12,ls:4,rf:5,a:4`
[4/2]	aabb	14	`lf:13,ls:1,rf:11,rs:6,a:2`
[5/0]	aaabb	12	`lf:7,lp:5,rf:8,rp:4,rs:3,re:1,lprp:1,lprs:1,a:3`
[5/1]	aabba	11	`lf:9,ls:2,rf:5,a:4`
[5/2]	aabaa	9	`lf:7,lp:2,rf:6,rp:1,a:2`
[6/0]	aaabba	10	`lf:6,lp:4,rf:5,rp:3,lprp:1,a:4`
[6/1]	aabaab	8	`lf:6,lp:2,rf:6,rp:1,rs:3,lprs:1,a:2`
[6/2]	abbaba	6	`lf:3,ls:3,a:4`

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

Step 2

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	ca ⇒ ac
2.	aa ⇒ c
3.	ccbba ⇒ cbabc
4.	acbba ⇒ ababc
5.	cbaba ⇒ ccbb
6.	ababa ⇒ acbb
7.	cbabcbc ⇒ acbcbcb
8.	ababcbc ⇒ cbcbcb
9.	ccbbba ⇒ cbacbb
10.	acbbba ⇒ abacbb
11.	ccbcbba ⇒ acbcbcb
12.	acbcbba ⇒ cbcbcb
13.	cbcbcba ⇒ acbcbbc
14.	cbabcba ⇒ ccbcbb
15.	ababcba ⇒ acbcbb
16.	cbcbcbb ⇒ a
17.	ccbbcbcbba ⇒ ccb
18.	acbbcbcbba ⇒ acb
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	ba	32	`lf:19,ls:13,rf:4,a:5`
[2/1]	cb	32	`lf:27,lp:5,rf:26,rp:4,rs:6,lprs:1,a:5`
[2/2]	bc	18	`lf:16,ls:2,rf:14,rs:3,a:5`
[2/3]	bb	14	`lf:13,ls:1,rf:7,rs:6,a:7`
[2/4]	ab	12	`lf:9,lp:3,rf:4,rp:2,a:5`
[3/0]	bba	16	`lf:8,ls:8,a:13`
[3/1]	bcb	14	`lf:14,rf:11,rs:4,a:5`
[3/2]	cbc	14	`lf:10,lp:2,ls:2,rf:11,rp:2,lsrp:1,a:5`
[3/3]	cbb	12	`lf:11,ls:1,rf:7,rs:6,a:7`
[3/4]	cba	12	`lf:6,lp:3,ls:3,rf:2,rp:2,a:6`
[4/0]	cbba	12	`lf:6,ls:6,a:13`
[4/1]	cbcb	10	`lf:8,lp:2,rf:11,rp:2,rs:4,a:5`
[4/2]	bcbc	8	`lf:6,ls:2,rf:4,a:5`
[4/3]	bcbb	6	`lf:5,ls:1,rf:3,rs:2,a:7`
[4/4]	bcba	6	`lf:3,ls:3,a:10`
[5/0]	bcbba	8	`lf:4,ls:4,a:31`
[5/1]	cbcbb	6	`lf:5,ls:1,rf:3,rs:2,a:7`
[5/2]	cbbba	4	`lf:2,ls:2,a:18`
[5/3]	babcb	4	`lf:4,a:5`
[5/4]	bcbcb	4	`lf:4,rf:4,rs:4,a:5`

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

Step 3

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	dddddadc ⇒ dcd
2.	ca ⇒ ac
3.	aa ⇒ c
4.	dddadad ⇒ da
5.	cddddadc ⇒ ccd
6.	dddddadac ⇒ dcda
7.	addddadc ⇒ acd
8.	cdadad ⇒ addadc
9.	cddadad ⇒ ac
10.	dadadad ⇒ dddadc
11.	addadad ⇒ c
12.	cddddadac ⇒ ccda
13.	addddadac ⇒ acda
14.	dddadab ⇒ d
15.	cdadab ⇒ addada
16.	cddadab ⇒ c
17.	dadadab ⇒ dddada
18.	addadab ⇒ a
19.	bc ⇒ da
20.	ba ⇒ d
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	ad	36	`lf:27,lp:4,ls:5,rf:6,rp:2,lsrp:1,a:3`
[2/1]	da	33	`lf:31,lp:2,rf:11,rp:2,rs:7,re:2,lprs:1,a:3`
[2/2]	dd	32	`lf:28,lp:4,rf:6,rp:2,a:3`
[2/3]	cd	12	`lf:6,lp:6,rf:6,rs:3,lprs:1,a:6`
[2/4]	ab	10	`lf:5,ls:5,a:3`
[3/0]	dad	30	`lf:23,lp:2,ls:5,rf:4,a:3`
[3/1]	ddd	20	`lf:16,lp:4,rf:2,rp:2,a:7`
[3/2]	ada	15	`lf:15,rf:2,rs:2,a:3`
[3/3]	dda	12	`lf:12,rf:4,a:3`
[3/4]	dab	10	`lf:5,ls:5,a:3`
[4/0]	dada	17	`lf:15,lp:2,rf:2,rs:2,lprs:1,a:3`
[4/1]	adad	12	`lf:7,ls:5,a:8`
[4/2]	ddad	12	`lf:12,rf:4,a:3`
[4/3]	adab	10	`lf:5,ls:5,a:3`
[4/4]	ddda	10	`lf:8,lp:2,rf:2,rp:2,a:7`
[5/0]	dadad	14	`lf:7,lp:2,ls:5,a:8`
[5/1]	dadab	10	`lf:5,ls:5,a:3`
[5/2]	dddad	10	`lf:8,lp:2,rf:2,rp:2,a:7`
[5/3]	ddada	9	`lf:9,rf:2,rs:2,a:3`
[5/4]	dadac	6	`lf:3,ls:3,a:21`

Considering [length 3 / frequency 0] dad=e.

Step 4

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

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