Morphocompletion for #4762 ⟨a, b | abaaaaba=aab⟩

Solved by morph:2/1,4/0. (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.	abaaaaba ⇒ aab
2.	aabaaaba ⇒ abaaaaab
3.	aaabaabaa ⇒ abaaaaaab
4.	abaaabaaaaab ⇒ aabaaba
5.	abaaaaabaaaab ⇒ aaabaaba
6.	aabbaaaaba ⇒ aabab
7.	aababaaaba ⇒ aabbaaaaab
8.	aabbbaaaaba ⇒ aabbab
9.	aababbaaaaba ⇒ aababab
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	aa	45	`lf:38,lp:6,ls:1,rf:23,rp:7,lprp:4`
[2/1]	ab	27	`lf:22,lp:3,ls:2,rf:18,rp:2,rs:7,lprs:1`
[2/2]	ba	26	`lf:20,ls:6,rf:11,rs:2`
[2/3]	bb	4	`lf:4,rf:2,a:2`
[3/0]	aba	26	`lf:17,lp:3,ls:6,rf:9,rp:2,rs:2,lsrp:1,lprs:2`
[3/1]	aab	24	`lf:17,lp:5,ls:2,rf:12,rp:6,rs:4,re:1,lprp:4,lsrp:1,lprs:2`
[3/2]	aaa	21	`lf:20,lp:1,rf:11,rp:1`
[3/3]	baa	13	`lf:12,ls:1,rf:5`
[4/0]	aaba	22	`lf:13,lp:3,ls:6,rf:6,rp:3,rs:2,lprp:1,lsrp:2`
[4/1]	aaab	14	`lf:11,lp:1,ls:2,rf:4,rp:1,rs:3,lsrp:1,lprs:1`
[4/2]	abaa	13	`lf:9,lp:3,ls:1,rf:4,rp:2,lsrp:1`
[4/3]	baaa	10	`lf:10,rf:3`
[5/0]	aaaba	16	`lf:9,lp:1,ls:6,rf:1,rp:1`
[5/1]	abaaa	10	`lf:7,lp:3,rf:2,rp:2`
[5/2]	aaaab	9	`lf:7,ls:2,rf:3,rs:3`
[5/3]	aabaa	7	`lf:5,lp:1,ls:1,rf:2,rp:1,a:1`
[6/0]	aaaaba	9	`lf:5,ls:4`
[6/1]	baaaab	6	`lf:5,ls:1`
[6/2]	abaaaa	6	`lf:4,lp:2,rf:2,rp:2`
[6/3]	baaaba	5	`lf:3,ls:2,a:1`

Considering [length 2 / frequency 1] 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) = deg(a) = 0, c < a; deg(b) = 1

Rewriting system is not complete: roundsLimit

#	Rule
1.	caaaca ⇒ ac
2.	acaaca ⇒ caaaac
3.	aacacaa ⇒ caaaaac
4.	aaaccaaa ⇒ caaaaaac
5.	cacaaaaac ⇒ accaa
6.	caacaaaac ⇒ acaca
7.	accaaaaac ⇒ caaaaccaa
8.	acacaaaac ⇒ caaaacaca
9.	aaccaaaac ⇒ caaaaacca
10.	caaaacaaac ⇒ aacaca
11.	caaaaacaca ⇒ aacaac
12.	caaaaaacca ⇒ aaacac
13.	acaaaacaca ⇒ caaaaacaac
14.	acaaaaacca ⇒ caaaaaacac
15.	ccaaaaaacac ⇒ accaaca
16.	caaaaacaaac ⇒ aaaccaa
17.	caacaaaaacaac ⇒ aacca
18.	ab ⇒ c
19.	acb ⇒ caaacc
20.	accb ⇒ caaaccaaacc
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	aa	71	`lf:66,lp:3,ls:2,rf:50,rp:5,rs:3,a:2`
[2/1]	ac	52	`lf:36,lp:7,ls:9,rf:28,rp:4,rs:8,re:1,lsrp:3,lprs:3,a:2`
[2/2]	ca	48	`lf:34,lp:8,ls:6,rf:28,rp:10,rs:6,lsrp:3,lprs:3,a:2`
[2/3]	cc	8	`lf:7,lp:1,rf:9,rs:2,a:3`
[2/4]	cb	4	`lf:2,ls:2,a:3`
[3/0]	aaa	43	`lf:41,lp:1,ls:1,rf:28,rp:2,a:2`
[3/1]	aac	33	`lf:23,lp:2,ls:8,rf:19,rp:3,rs:5,lsrp:2,lprs:1,a:2`
[3/2]	caa	30	`lf:22,lp:7,ls:1,rf:17,rp:10,rs:3,lsrp:1,lprs:1,a:2`
[3/3]	aca	28	`lf:20,lp:4,ls:4,rf:11,rp:1,rs:4,lprs:1,a:2`
[3/4]	cca	9	`lf:6,lp:1,ls:2,rf:7,rs:2,a:5`
[3/5]	acc	8	`lf:6,lp:2,rf:9,rp:2,rs:2,lprs:1,a:3`
[3/6]	cac	8	`lf:6,lp:1,ls:1,rf:5,rs:2,a:6`
[4/0]	aaac	25	`lf:17,lp:1,ls:7,rf:13,rp:2,rs:3,lsrp:1,lprs:1,a:2`
[4/1]	aaaa	23	`lf:23,rf:15,a:4`
[4/2]	caaa	23	`lf:17,lp:5,ls:1,rf:11,rp:10,lsrp:1,a:2`
[4/3]	acaa	15	`lf:11,lp:3,ls:1,rf:2,a:4`
[4/4]	aaca	14	`lf:11,lp:1,ls:2,rf:7,rp:2,rs:1,a:2`
[4/5]	acca	8	`lf:5,lp:1,ls:2,rf:7,rp:2,rs:2,a:5`
[4/6]	caca	8	`lf:5,lp:1,ls:2,rf:3,rs:3,a:6`
[5/0]	aaaac	18	`lf:13,ls:5,rf:8,rs:3,a:4`
[5/1]	caaaa	17	`lf:13,lp:4,rf:8,rp:8,a:4`
[5/2]	aaaaa	10	`lf:10,rf:7,a:13`
[5/3]	acaaa	10	`lf:8,lp:2,a:6`
[5/4]	aaaca	8	`lf:7,ls:1,rf:4,rp:1,a:2`
[5/5]	aacca	7	`lf:4,lp:1,ls:2,rf:5,rp:1,rs:2,re:1,lprs:1,a:5`
[5/6]	acaca	7	`lf:4,lp:1,ls:2,rf:3,rp:1,rs:3,re:1,lprs:1,a:6`

Considering [length 4 / frequency 0] aaac=d.

Step 3

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

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