Morphocompletion for #1763 ⟨a, b | abaabaaab=a⟩

Solved by morph:5/0,3/0,3/0. (See Morphocompletion.)

Step 1

Checking up to 20 rules for overlaps.

Reduction order:
- Right-to-left shortlex with a < b

Rewriting system is not complete: rulesLimit

#	Rule
1.	aaaabb ⇒ abaaba
2.	aaabaaab ⇒ abaabaaa
3.	abaabaaab ⇒ a
4.	abaabaaaab ⇒ aaaababbaa
5.	aaaababaaab ⇒ aaaabaabbaa
6.	aaaababbaab ⇒ abaababaaba
7.	abaabaaaaaab ⇒ aaababaabaaa
8.	abaababaabaaa ⇒ aaaab
9.	aaaababbbaabaaa ⇒ aaaabab
10.	abaababaababaaba ⇒ aaaababb
	...

Collecting factors up to length 7 / frequency 3:

[2/0]	aa	49	`lf:42,lp:5,ls:2,rf:29,rp:6,rs:4,lprp:2,lsrp:2,lprs:2`
[2/1]	ab	42	`lf:31,lp:5,ls:6,rf:20,rp:3,rs:2,lsrp:2,lprs:1`
[2/2]	ba	25	`lf:24,ls:1,rf:17,rs:2`
[3/0]	aba	28	`lf:22,lp:5,ls:1,rf:15,rp:3,rs:2`
[3/1]	aaa	27	`lf:20,lp:5,ls:2,rf:13,rp:6,rs:2,lprp:2,lsrp:2,lprs:1`
[3/2]	aab	26	`lf:20,ls:6,rf:12,rs:1`
[4/0]	abaa	20	`lf:15,lp:5,rf:8,rp:3`
[4/1]	aaab	16	`lf:10,lp:1,ls:5,rf:6,rp:1,rs:1,lsrp:1`
[4/2]	aaba	14	`lf:13,ls:1,rf:10,rs:2`
[5/0]	abaab	13	`lf:8,lp:5,rf:6,rp:3`
[5/1]	aaaab	12	`lf:6,lp:4,ls:2,rf:5,rp:5,rs:1,re:1,lprp:2,lsrp:1,a:2`
[5/2]	baaba	10	`lf:9,ls:1,rf:5,rs:2`
[6/0]	abaaba	14	`lf:8,lp:5,ls:1,rf:5,rp:3,rs:2,re:1`
[6/1]	aabaaa	8	`lf:6,ls:2,rf:2,rs:2`
[6/2]	abaaab	6	`lf:3,ls:3`

Considering [length 5 / frequency 0] abaab=c.

Step 2

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = abaab
Reduction order:
- Right-to-left recursive path with deg(c) = 0; deg(a) = deg(b) = 1, a < b

Rewriting system is not complete: roundsLimit

#	Rule
1.	ccaac ⇒ a
2.	acaac ⇒ ccaaa
3.	caab ⇒ abac
4.	ccaccaaa ⇒ aaac
5.	aaab ⇒ caac
6.	aaacb ⇒ ccaca
7.	aaaccb ⇒ ccaccccaca
8.	aaacccb ⇒ ccaccccaccccaca
9.	ccaaaaac ⇒ acaccaaa
10.	aaacab ⇒ ccaccccaaa
11.	aaacacb ⇒ ccaccaccaca
12.	abaab ⇒ c
13.	ccaaacaccaaa ⇒ acaaaaac
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	aa	34	`lf:26,lp:6,ls:2,rf:13,rp:1,rs:3,lsrp:1,lprs:1,a:1`
[2/1]	ac	17	`lf:13,lp:1,ls:3,rf:17,rp:2,rs:4,lsrp:1,a:3`
[2/2]	cc	13	`lf:9,lp:4,rf:21,rp:6,a:5`
[2/3]	ca	12	`lf:11,lp:1,rf:20,rp:1,rs:4,a:3`
[2/4]	ab	10	`lf:5,lp:1,ls:4,rf:1,rp:1,lsrp:1,a:1`
[3/0]	aaa	20	`lf:12,lp:6,ls:2,rf:7,rp:1,rs:3,lsrp:1,lprs:1,a:4`
[3/1]	aac	12	`lf:9,ls:3,rf:3,rs:3,a:4`
[3/2]	cca	10	`lf:6,lp:4,rf:13,rp:6,a:5`
[3/3]	caa	8	`lf:7,lp:1,rf:5,rp:1,a:3`
[3/4]	aab	6	`lf:3,ls:3,a:1`
[4/0]	aaac	13	`lf:7,lp:5,ls:1,rf:2,rp:1,rs:2,re:1,a:7`
[4/1]	ccaa	8	`lf:5,lp:3,rf:3,rp:1,a:5`
[4/2]	caaa	6	`lf:4,ls:2,rf:4,rs:3,a:6`
[4/3]	caac	4	`lf:2,ls:2,rf:1,rp:1,rs:1,re:1,a:4`
[4/4]	aaca	3	`lf:3,a:9`
[5/0]	ccaaa	8	`lf:4,lp:2,ls:2,rf:3,rp:1,rs:3,re:1,lprs:1,a:6`
[5/1]	aaaca	5	`lf:3,lp:2,a:9`
[5/2]	aaacc	4	`lf:2,lp:2,a:12`
[5/3]	aacab	2	`lf:1,ls:1,a:11`
[5/4]	aaaac	2	`lf:1,ls:1,rf:1,rs:1,a:8`

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

Step 3

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = abaab
2. d = aaa
Reduction order:
- Right-to-left recursive path with deg(c) = 0; deg(d) = deg(a) = deg(b) = 1, d < a < b

Rewriting system is not complete: roundsLimit

#	Rule
1.	ccaccd ⇒ dc
2.	da ⇒ ad
3.	ccaac ⇒ a
4.	db ⇒ caac
5.	dcb ⇒ ccaca
6.	ccaccad ⇒ dca
7.	ccaadc ⇒ acaccd
8.	dcaac ⇒ aaccd
9.	aaa ⇒ d
10.	ccaccccaca ⇒ dccb
11.	acaac ⇒ ccd
12.	dcab ⇒ ccaccccd
13.	caab ⇒ abac
14.	ccaccaad ⇒ dcaa
15.	abaab ⇒ c
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	cc	18	`lf:12,lp:6,rf:9,rp:3,a:8`
[2/1]	ca	16	`lf:14,lp:1,ls:1,rf:7,rp:1,rs:2,a:5`
[2/2]	ac	13	`lf:9,lp:1,ls:3,rf:7,rp:1,rs:2,a:5`
[2/3]	aa	11	`lf:9,lp:1,ls:1,rf:3,rp:1,rs:1,a:1`
[2/4]	ab	8	`lf:4,lp:1,ls:3,rf:1,rp:1,lsrp:1,a:1`
[3/0]	cca	15	`lf:9,lp:6,rf:2,rp:2,a:8`
[3/1]	caa	7	`lf:6,lp:1,rf:2,rp:1,rs:1,a:5`
[3/2]	aac	6	`lf:3,ls:3,rf:2,rp:1,rs:1,lsrp:1,a:7`
[3/3]	cac	5	`lf:5,rf:3,a:11`
[3/4]	aab	4	`lf:2,ls:2,a:1`
[4/0]	ccac	9	`lf:5,lp:4,rf:2,rp:2,a:11`
[4/1]	caac	6	`lf:3,ls:3,rf:1,rp:1,rs:1,re:1,a:7`
[4/2]	ccaa	5	`lf:3,lp:2,a:8`
[4/3]	cacc	4	`lf:4,rf:2,a:11`
[4/4]	caad	3	`lf:2,ls:1,a:12`
[5/0]	ccacc	8	`lf:4,lp:4,rf:1,rp:1,a:11`
[5/1]	ccaad	4	`lf:2,lp:1,ls:1,a:12`
[5/2]	caadc	2	`lf:1,ls:1,a:12`
[5/3]	accad	2	`lf:1,ls:1,a:14`
[5/4]	cacca	2	`lf:2,a:14`

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

Step 4

Auxiliary generators:
1. c = abaab
2. d = aaa
3. e = cca
Reduction order:
- Right-to-left recursive path with deg(c) = 0; deg(e) = 1; deg(d) = deg(a) = deg(b) = 2, d < a < b

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