Morphocompletion for #2333 ⟨a, b | abababa=bab⟩

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

Step 1

Checking up to 20 rules for overlaps.

Reduction order:
- Left-to-right shortlex with b < a

Rewriting system is not complete: rulesLimit

#	Rule
1.	abbab ⇒ babba
2.	abababa ⇒ bab
3.	abbbabba ⇒ bbabbaab
4.	abbbbabba ⇒ bbabbaabb
5.	babbaababa ⇒ abbbab
6.	abbbbbabba ⇒ bbabbaabbb
7.	abbbbbbabba ⇒ bbabbaabbbb
8.	ababaabbbab ⇒ babbbaababa
9.	bbabbaaababa ⇒ ababbbab
10.	abbbbbbbabba ⇒ bbabbaabbbbb
11.	bbabbaaaababa ⇒ aababbbab
12.	bbbabbaabbaaba ⇒ abbbabbbab
13.	bbabbaabaababa ⇒ abababbbab
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	ba	50	`lf:38,lp:1,ls:11,rf:27,rp:3,rs:2,lsrp:1`
[2/1]	ab	45	`lf:35,lp:8,ls:2,rf:30,rp:4,rs:7,lprs:2`
[2/2]	bb	43	`lf:39,lp:4,rf:35,rp:5,rs:4,a:1`
[2/3]	aa	11	`lf:11,rf:7,rp:1,a:3`
[3/0]	bba	30	`lf:22,lp:3,ls:5,rf:18,rp:5,rs:1,lsrp:5,a:1`
[3/1]	abb	24	`lf:18,lp:6,rf:17,rp:2,rs:1,lprs:1,a:1`
[3/2]	aba	23	`lf:15,lp:2,ls:6,rf:6,rp:2,rs:1,lsrp:2,lprs:1`
[3/3]	bab	22	`lf:19,lp:1,ls:2,rf:19,rp:3,rs:6,re:1,lsrp:2,lprs:1`
[4/0]	abba	18	`lf:12,lp:1,ls:5,rf:6,rs:1,lprs:10,a:1`
[4/1]	bbab	16	`lf:11,lp:3,ls:2,rf:11,rp:5,rs:5,lprs:3,a:1`
[4/2]	baba	12	`lf:7,ls:5,rf:2,rs:1`
[4/3]	abbb	11	`lf:6,lp:5,rf:10,rp:2,rs:1,lprs:1,a:3`
[5/0]	babba	16	`lf:10,lp:1,ls:5,rf:6,rp:1,rs:1,re:1,a:1`
[5/1]	ababa	14	`lf:7,lp:2,ls:5,rf:2,rp:1,rs:1,lsrp:1,lprs:1`
[5/2]	bbabb	12	`lf:9,lp:3,rf:6,rp:5,a:4`
[5/3]	bbbab	9	`lf:7,lp:1,ls:1,rf:6,rs:5,lprs:1,a:3`
[6/0]	bbabba	17	`lf:9,lp:3,ls:5,rf:5,rp:5,lsrp:5,a:4`
[6/1]	aababa	8	`lf:4,ls:4,rf:1,rs:1,a:3`
[6/2]	bbbabb	7	`lf:6,lp:1,rf:1,a:4`
[6/3]	abbbbb	6	`lf:3,lp:3,rf:1,rs:1,lprs:1,a:14`

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

Step 2

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	cccccb ⇒ bccccc
2.	accc ⇒ cb
3.	cccca ⇒ bcc
4.	bcb ⇒ cccc
5.	ba ⇒ c
6.	abcc ⇒ cbca
7.	acbcc ⇒ cbcca
8.	accbcc ⇒ cbccca
9.	abbcc ⇒ cbcacca
10.	acbbcc ⇒ cbccacca
11.	accbbcc ⇒ cbcccacca
12.	abbbcc ⇒ cbcaccacca
13.	acbbbcc ⇒ cbccaccacca
14.	accbbbcc ⇒ cbcccaccacca
15.	abbbbcc ⇒ cbcaccaccacca
16.	acbbbbcc ⇒ cbccaccaccacca
17.	accbbbbcc ⇒ cbcccaccaccacca
18.	abbbbbcc ⇒ cbcaccaccaccacca
19.	acbbbbbcc ⇒ cbccaccaccaccacca
20.	accbbbbbcc ⇒ cbcccaccaccaccacca
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	cc	47	`lf:29,lp:2,ls:16,rf:53,rp:1,rs:3,lprs:2,a:2`
[2/1]	bb	30	`lf:30,a:9`
[2/2]	ac	22	`lf:11,lp:11,rf:30,a:2`
[2/3]	bc	17	`lf:16,lp:1,rf:17,rp:2,a:3`
[2/4]	cb	14	`lf:12,ls:2,rf:16,rp:16,rs:1,re:1,a:2`
[2/5]	ab	10	`lf:5,lp:5,a:6`
[2/6]	ca	2	`lf:1,ls:1,rf:45,rs:15,a:4`
[3/0]	bcc	30	`lf:15,ls:15,rf:12,rp:2,rs:1,re:1,a:4`
[3/1]	bbb	18	`lf:18,a:12`
[3/2]	bbc	12	`lf:12,a:9`
[3/3]	acc	12	`lf:6,lp:6,rf:30,a:2`
[3/4]	acb	10	`lf:5,lp:5,a:7`
[3/5]	ccc	9	`lf:6,lp:2,ls:1,rf:10,rp:1,rs:2,lprs:1,a:2`
[3/6]	abb	8	`lf:4,lp:4,a:9`
[4/0]	bbcc	24	`lf:12,ls:12,a:9`
[4/1]	accb	10	`lf:5,lp:5,a:8`
[4/2]	bbbb	9	`lf:9,a:15`
[4/3]	bbbc	9	`lf:9,a:12`
[4/4]	acbb	8	`lf:4,lp:4,a:10`
[4/5]	abbb	6	`lf:3,lp:3,a:12`
[4/6]	cbbb	6	`lf:6,a:13`
[5/0]	bbbcc	18	`lf:9,ls:9,a:12`
[5/1]	accbb	8	`lf:4,lp:4,a:11`
[5/2]	acbbb	6	`lf:3,lp:3,a:13`
[5/3]	bbbbc	6	`lf:6,a:15`
[5/4]	abbbb	4	`lf:2,lp:2,a:15`
[5/5]	cbbbb	4	`lf:4,a:16`
[5/6]	cbbcc	4	`lf:2,ls:2,a:10`

Considering [length 3 / frequency 0] bcc=d.

Step 3

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

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