Morphocompletion for #4227 ⟨a, b | abaaaaaab=ba⟩

Solved by morph:7/2. (See Morphocompletion.)

Step 1

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: rulesLimit

#	Rule
1.	abaaaaaab ⇒ ba
2.	baaaaaaab ⇒ abaaaaaba
3.	baaaaaaaab ⇒ aabaaaabaa
4.	baaaaaaaaab ⇒ aaabaaabaaa
5.	baaaaaaaaaab ⇒ aaaabaabaaaa
6.	baaaaaaaaaaab ⇒ aaaaababaaaaa
7.	baaaaaaaaaaaab ⇒ aaaaaabbaaaaaa
8.	baaaaaaaaaaaaabb ⇒ aaaaaaabbaaaaaba
9.	aaaaaaabbaaaaaabaaaaaa ⇒ baaaaaaaaaaaaab
	...

Collecting factors up to length 8 / frequency 7:

[2/0]	aa	86	`lf:84,lp:1,ls:1,rf:62,rp:6,rs:5`
[2/1]	ab	19	`lf:11,lp:1,ls:7,rf:14,rp:1,rs:1,lsrp:1`
[2/2]	ba	17	`lf:10,lp:7,rf:15,rp:2,rs:3,re:1,lprs:2`
[2/3]	bb	3	`lf:2,ls:1,rf:2,a:15`
[3/0]	aaa	75	`lf:73,lp:1,ls:1,rf:45,rp:5,rs:4`
[3/1]	baa	17	`lf:10,lp:7,rf:11,rp:1,rs:1,lprs:1`
[3/2]	aab	17	`lf:10,ls:7,rf:12,rp:1,rs:1,lsrp:1`
[3/3]	aba	3	`lf:2,lp:1,rf:11,rp:1,rs:2`
[3/4]	abb	3	`lf:2,ls:1,rf:2,a:15`
[3/5]	bba	1	`lf:1,rf:2,a:15`
[3/6]	bab	0	`rf:1,a:9`
[4/0]	aaaa	64	`lf:62,lp:1,ls:1,rf:31,rp:4,rs:3`
[4/1]	baaa	17	`lf:10,lp:7,rf:9,rp:1,rs:1,lprs:1`
[4/2]	aaab	17	`lf:10,ls:7,rf:10,rp:1,rs:1,lsrp:1`
[4/3]	abaa	3	`lf:2,lp:1,rf:8,rp:1,rs:1`
[4/4]	aabb	3	`lf:2,ls:1,rf:2,a:15`
[4/5]	aaba	1	`lf:1,rf:9,rp:1,rs:2,a:1`
[4/6]	bbaa	1	`lf:1,rf:2,a:15`
[5/0]	aaaaa	53	`lf:51,lp:1,ls:1,rf:20,rp:3,rs:2`
[5/1]	baaaa	17	`lf:10,lp:7,rf:7,rp:1,rs:1,lprs:1`
[5/2]	aaaab	17	`lf:10,ls:7,rf:8,rp:1,rs:1,lsrp:1`
[5/3]	abaaa	3	`lf:2,lp:1,rf:6,rp:1,rs:1`
[5/4]	aaabb	3	`lf:2,ls:1,rf:2,a:15`
[5/5]	aabaa	1	`lf:1,rf:6,rp:1,rs:1,a:2`
[5/6]	aaaba	1	`lf:1,rf:7,rp:1,rs:2,a:1`
[6/0]	aaaaaa	42	`lf:40,lp:1,ls:1,rf:12,rp:2,rs:1`
[6/1]	baaaaa	17	`lf:10,lp:7,rf:5,rp:1,rs:1,lprs:1`
[6/2]	aaaaab	17	`lf:10,ls:7,rf:6,rp:1,rs:1,lsrp:1`
[6/3]	abaaaa	3	`lf:2,lp:1,rf:4,rp:1,rs:1`
[6/4]	aaaabb	3	`lf:2,ls:1,rf:2,a:15`
[6/5]	aabaaa	1	`lf:1,rf:4,rp:1,rs:1,a:2`
[6/6]	aaabaa	1	`lf:1,rf:4,rp:1,rs:1,a:2`
[7/0]	aaaaaaa	30	`lf:29,lp:1,rf:8,rp:1,a:1`
[7/1]	baaaaaa	18	`lf:10,lp:7,ls:1,rf:2,rp:1,rs:1,lsrp:1,lprs:1`
[7/2]	aaaaaab	17	`lf:10,ls:7,rf:3,rp:1,rs:1,lsrp:1`
[7/3]	abaaaaa	3	`lf:2,lp:1,rf:2,rp:1,rs:1`
[7/4]	aaaaabb	3	`lf:2,ls:1,rf:2,a:15`
[7/5]	aabaaaa	1	`lf:1,rf:2,rp:1,rs:1,a:2`
[7/6]	aaabaaa	1	`lf:1,rf:2,rp:1,rs:1,a:3`

Considering [length 7 / frequency 2] aaaaaab=c.

Step 2

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

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