Morphocompletion for #1115 ⟨a, b | abaaba=bab⟩

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

Step 1

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: rulesLimit

#	Rule
1.	abaaba ⇒ bab
2.	bababa ⇒ ababab
3.	baababab ⇒ abababba
4.	babbaaba ⇒ abaabbab
5.	babbabba ⇒ abbabbab
6.	aabababba ⇒ babbab
7.	baaababab ⇒ abababbaa
8.	abababbaba ⇒ bbabbab
9.	baaaababab ⇒ abababbaaa
10.	abababbbaba ⇒ bbbabbab
11.	aabaabbabbab ⇒ babbabbba
12.	abaaabaabbab ⇒ babbbaaba
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	ba	50	`lf:37,lp:6,ls:7,rf:28,rp:4,rs:3,lsrp:2,lprs:1`
[2/1]	ab	45	`lf:36,lp:4,ls:5,rf:29,rp:6,rs:7,lsrp:3,lprs:3`
[2/2]	aa	16	`lf:14,lp:2,rf:5,rs:2`
[2/3]	bb	10	`lf:10,rf:17,rp:2,a:2`
[3/0]	aba	31	`lf:22,lp:4,ls:5,rf:10,rp:5,rs:1,lsrp:2,lprs:1`
[3/1]	bab	30	`lf:22,lp:3,ls:5,rf:21,rp:4,rs:7,re:1,lsrp:2,lprs:3`
[3/2]	aab	12	`lf:10,lp:2,rf:2`
[3/3]	bba	11	`lf:9,ls:2,rf:14,rp:1,rs:2,a:2`
[4/0]	abab	18	`lf:13,lp:2,ls:3,rf:8,rp:4,rs:1,lsrp:3,a:1`
[4/1]	baba	14	`lf:10,lp:1,ls:3,rf:4,a:1`
[4/2]	aaba	12	`lf:8,lp:2,ls:2,rf:1,rs:1`
[4/3]	abba	10	`lf:8,ls:2,rf:10,rp:1,rs:1,lsrp:1,a:2`
[5/0]	babab	11	`lf:7,lp:1,ls:3,rf:4,rs:1,lprs:10,a:1`
[5/1]	babba	10	`lf:6,lp:2,ls:2,rf:8,rp:2,rs:1,lsrp:1,a:2`
[5/2]	ababa	10	`lf:7,lp:2,ls:1,rf:4,rp:4,lsrp:10,a:1`
[5/3]	abbab	7	`lf:5,ls:2,rf:7,rp:1,rs:5,a:2`
[6/0]	ababab	11	`lf:6,lp:2,ls:3,rf:4,rp:4,rs:1,re:1,lsrp:3,a:1`
[6/1]	babbab	5	`lf:3,lp:1,ls:1,rf:5,rp:2,rs:4,re:1,lsrp:1,lprs:1,a:4`
[6/2]	aababa	5	`lf:4,lp:1,a:4`
[6/3]	bbabba	3	`lf:2,ls:1,rf:3,rp:1,a:6`

Considering [length 3 / frequency 0] aba=c.

Step 2

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	ccca ⇒ accc
2.	bc ⇒ cca
3.	cb ⇒ acc
4.	bacc ⇒ ccab
5.	accacca ⇒ cccc
6.	accab ⇒ ccc
7.	aba ⇒ c
8.	baaccc ⇒ ccaccaa
9.	bacacc ⇒ ccabb
10.	bab ⇒ cc
11.	baaaccc ⇒ ccaccaaa
12.	baacaccc ⇒ ccaccaaca
13.	baaccacc ⇒ ccaccaab
14.	bacaaccc ⇒ ccaccacaa
15.	bacacacc ⇒ ccabbb
16.	baaaaccc ⇒ ccaccaaaa
17.	baaacaccc ⇒ ccaccaaaca
18.	baaaccacc ⇒ ccaccaaab
19.	baacaaccc ⇒ ccaccaacaa
20.	bacacacacc ⇒ ccabbbb
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	cc	41	`lf:27,lp:1,ls:13,rf:32,rp:17,rs:5,re:1,lsrp:13,lprs:1,a:2`
[2/1]	ba	30	`lf:15,lp:14,ls:1,a:1`
[2/2]	ac	30	`lf:28,lp:2,rf:15,rp:2,a:4`
[2/3]	ca	18	`lf:16,ls:2,rf:27,rs:3,a:5`
[2/4]	aa	15	`lf:15,rf:15,rs:5,a:12`
[2/5]	ab	6	`lf:3,lp:1,ls:2,rf:6,rs:3,a:1`
[2/6]	bb	0	`rf:6,rs:3,a:11`
[3/0]	acc	26	`lf:18,lp:2,ls:6,rf:11,rp:2,rs:1,re:1,a:4`
[3/1]	baa	16	`lf:8,lp:8,a:12`
[3/2]	ccc	16	`lf:8,lp:1,ls:7,rf:4,rp:2,rs:3,re:1,lprs:10,a:7`
[3/3]	cac	11	`lf:11,rf:10,a:10`
[3/4]	bac	10	`lf:5,lp:5,a:9`
[3/5]	aca	10	`lf:10,rf:4,rs:2,a:11`
[3/6]	aac	10	`lf:10,rf:3,a:12`
[4/0]	accc	14	`lf:7,ls:7,rf:1,rp:1,rs:1,re:1,a:8`
[4/1]	cacc	13	`lf:8,ls:5,rf:9,a:10`
[4/2]	baaa	8	`lf:4,lp:4,a:16`
[4/3]	baca	8	`lf:4,lp:4,a:11`
[4/4]	baac	8	`lf:4,lp:4,a:12`
[4/5]	acca	8	`lf:5,lp:2,ls:1,rf:9,a:7`
[4/6]	acac	8	`lf:8,a:11`
[5/0]	aaccc	10	`lf:5,ls:5,a:12`
[5/1]	acacc	8	`lf:5,ls:3,a:11`
[5/2]	baaac	6	`lf:3,lp:3,a:16`
[5/3]	bacac	6	`lf:3,lp:3,a:11`
[5/4]	ccacc	5	`lf:3,ls:2,rf:9,rp:9,lsrp:2,a:10`
[5/5]	baaca	4	`lf:2,lp:2,a:17`
[5/6]	baacc	4	`lf:2,lp:2,a:12`

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

Step 3

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

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