Morphocompletion for #5874 ⟨a, b | ababab=baaba⟩

Solved by morph:2/0,5/1,3/0. (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.	abbaaba ⇒ baabaab
2.	ababab ⇒ baaba
3.	baabaabbab ⇒ abbabaaba
4.	baabaababbab ⇒ ababbabaaba
5.	abbabaabaabab ⇒ baabaabbbaaba
6.	ababaabbabaaba ⇒ baabaaabaabbab
7.	baabaabbbaabaab ⇒ abbabaababaaba
8.	baabaababaabbab ⇒ abbaaabbabaaba
9.	ababbaaabbabaaba ⇒ baababaabaaabbab
	...

Collecting factors up to length 7 / frequency 3:

[2/0]	ab	47	`lf:36,lp:5,ls:6,rf:31,rp:4,rs:3,lsrp:4,lprs:3`
[2/1]	ba	41	`lf:34,lp:4,ls:3,rf:33,rp:5,rs:6,lsrp:3,lprs:4`
[2/2]	aa	19	`lf:19,rf:21`
[3/0]	aba	27	`lf:21,lp:3,ls:3,rf:20,rp:1,rs:6,lprs:1`
[3/1]	baa	22	`lf:18,lp:4,rf:18,rp:5`
[3/2]	aab	19	`lf:18,ls:1,rf:18,rs:1`
[4/0]	baab	22	`lf:17,lp:4,ls:1,rf:15,rp:5,rs:1`
[4/1]	aaba	15	`lf:12,ls:3,rf:13,rs:6`
[4/2]	abab	12	`lf:7,lp:3,ls:2,rf:3,rp:1`
[5/0]	baaba	19	`lf:12,lp:4,ls:3,rf:12,rp:5,rs:6,re:1,lsrp:3,lprs:4`
[5/1]	abaab	12	`lf:11,ls:1,rf:9,rs:1,a:1`
[5/2]	abbab	10	`lf:6,lp:1,ls:3,rf:6,rp:2,rs:2,lsrp:1,a:2`
[6/0]	baabaa	10	`lf:6,lp:4,rf:4,rp:3,a:1`
[6/1]	abaaba	8	`lf:6,ls:2,rf:6,rs:4,a:2`
[6/2]	aabaab	7	`lf:6,ls:1,rf:3,rs:1,a: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(c) = 0; deg(a) = 1; deg(b) = 2

Rewriting system is not complete: roundsLimit

#	Rule
1.	caaccc ⇒ acccca
2.	caca ⇒ accc
3.	accccaaca ⇒ caaccaccc
4.	caaccacccca ⇒ accccaaaccc
5.	baaccc ⇒ cccca
6.	baca ⇒ ccc
7.	baaccaccc ⇒ ccccaaca
8.	baaccaccaccc ⇒ ccccaacaaca
9.	baccaaccaccc ⇒ cccccccaaca
10.	cccb ⇒ bacc
11.	ab ⇒ c
12.	caacbacc ⇒ accccacb
13.	caaccbacc ⇒ accccaccb
14.	baacbacc ⇒ ccccacb
15.	baaccbacc ⇒ ccccaccb
16.	baaccacbacc ⇒ ccccaacacb
17.	ccccacbcb ⇒ baacbcacc
18.	ccccaccbcb ⇒ baaccbcacc
19.	caacbacbacc ⇒ accccacbccb
20.	baacbacbacc ⇒ ccccacbccb
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	cc	56	`lf:41,lp:3,ls:12,rf:59,rp:9,rs:7,lsrp:8,lprs:3,a:2`
[2/1]	ac	36	`lf:35,lp:1,rf:26,rp:6,a:2`
[2/2]	ca	30	`lf:20,lp:6,ls:4,rf:22,rp:1,rs:5,lsrp:1,lprs:1,a:2`
[2/3]	ba	27	`lf:18,lp:9,rf:3,rp:3,a:2`
[2/4]	cb	17	`lf:14,ls:3,rf:11,rs:7,a:4`
[3/0]	acc	32	`lf:24,lp:1,ls:7,rf:15,rp:6,rs:3,lsrp:3,a:3`
[3/1]	ccc	22	`lf:14,lp:3,ls:5,rf:33,rp:9,rs:4,re:1,lsrp:4,a:2`
[3/2]	baa	14	`lf:7,lp:7,rf:2,rp:2,a:5`
[3/3]	aac	14	`lf:14,rf:9,a:5`
[3/4]	bac	13	`lf:11,lp:2,rf:1,rp:1,a:2`
[4/0]	bacc	16	`lf:8,lp:1,ls:7,rf:1,rp:1,rs:1,re:1,a:4`
[4/1]	baac	14	`lf:7,lp:7,rf:2,rp:2,a:5`
[4/2]	accc	13	`lf:7,lp:1,ls:5,rf:8,rp:6,rs:3,re:1,lsrp:1,lprs:1,a:3`
[4/3]	caac	12	`lf:7,lp:5,rf:6,rp:1,a:6`
[4/4]	cbac	9	`lf:9,a:8`
[5/0]	cbacc	14	`lf:7,ls:7,a:8`
[5/1]	baacc	10	`lf:5,lp:5,rf:1,rp:1,a:5`
[5/2]	acbac	7	`lf:7,a:8`
[5/3]	caacc	7	`lf:4,lp:3,rf:1,rp:1,a:6`
[5/4]	cccca	7	`lf:4,lp:2,ls:1,rf:13,rp:7,rs:2,re:1,a:5`

Considering [length 5 / frequency 1] baacc=d.

Step 3

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	cccad ⇒ dcacc
2.	cdcad ⇒ ddccc
3.	cdcacc ⇒ dcd
4.	dcca ⇒ cccaccc
5.	cccca ⇒ dc
6.	caad ⇒ acccacc
7.	caacc ⇒ ad
8.	caacdc ⇒ adccca
9.	caca ⇒ accc
10.	caacad ⇒ adaacc
11.	baad ⇒ cccacc
12.	baacc ⇒ d
13.	baacdc ⇒ dccca
14.	baca ⇒ ccc
15.	baacad ⇒ daacc
16.	baacaccc ⇒ daca
17.	dcb ⇒ ccccc
18.	cccb ⇒ bacc
19.	ab ⇒ c
20.	baacbacc ⇒ dccb
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	ca	24	`lf:15,lp:5,ls:4,rf:7,rs:3,lprs:1,a:3`
[2/1]	cc	22	`lf:14,lp:3,ls:5,rf:29,rp:4,rs:11,lprs:2,a:2`
[2/2]	ba	15	`lf:8,lp:7,rf:1,rp:1,a:2`
[2/3]	ac	13	`lf:13,rf:10,rp:2,a:2`
[2/4]	ad	12	`lf:6,ls:6,rf:3,rp:3,rs:1,re:1,lsrp:1,a:4`
[3/0]	baa	12	`lf:6,lp:6,a:2`
[3/1]	acc	9	`lf:5,ls:4,rf:9,rp:2,rs:6,a:2`
[3/2]	ccc	9	`lf:5,lp:3,ls:1,rf:12,rp:4,rs:5,re:1,a:3`
[3/3]	caa	8	`lf:4,lp:4,a:4`
[3/4]	aac	8	`lf:8,rf:2,a:2`
[4/0]	baac	10	`lf:5,lp:5,a:2`
[4/1]	caac	6	`lf:3,lp:3,a:4`
[4/2]	acad	4	`lf:2,ls:2,a:5`
[4/3]	aacc	4	`lf:2,ls:2,rf:2,rs:2,a:2`
[4/4]	cdca	4	`lf:2,lp:2,a:19`
[5/0]	baaca	4	`lf:2,lp:2,a:5`
[5/1]	aacad	4	`lf:2,ls:2,a:5`
[5/2]	aacdc	4	`lf:2,ls:2,a:15`
[5/3]	baacb	2	`lf:1,lp:1,a:20`
[5/4]	cbacc	2	`lf:1,ls:1,a:20`

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

Step 4

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

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