Morphocompletion for #7831 ⟨a, b, c | ab=1, cac=aca⟩

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

Step 1

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	ab ⇒ 1
2.	cac ⇒ aca
3.	acaacb ⇒ caac
4.	caaca ⇒ acaac
5.	acaaacb ⇒ ccaac
6.	acaaccb ⇒ caaac
7.	caaaca ⇒ acaacc
8.	acaaaacb ⇒ cccaac
9.	acaaaccb ⇒ ccaaac
10.	acaacccb ⇒ caaaac
11.	caaaaca ⇒ acaaccc
12.	acaaaaacb ⇒ ccccaac
13.	acaaaaccb ⇒ cccaaac
14.	acaaacccb ⇒ ccaaaac
15.	acaaccccb ⇒ caaaaac
16.	caaaaaca ⇒ acaacccc
17.	acaaaaaacb ⇒ cccccaac
18.	acaaaaaccb ⇒ ccccaaac
19.	acaaaacccb ⇒ cccaaaac
20.	acaaaccccb ⇒ ccaaaaac
	...

Collecting factors up to length 4 / frequency 7:

[2/0]	ac	48	`lf:33,lp:14,ls:1,rf:23,rp:5,rs:15,lsrp:10,lprs:14,a:1`
[2/1]	aa	44	`lf:44,rf:34,a:2`
[2/2]	ca	32	`lf:23,lp:5,ls:4,rf:19,rp:4,rs:1,lprs:10,a:1`
[2/3]	cb	28	`lf:14,ls:14,a:4`
[2/4]	cc	16	`lf:16,rf:26,rp:10,rs:3,a:5`
[3/0]	aca	36	`lf:18,lp:14,ls:4,rf:5,rp:5,rs:1,re:1,lsrp:4,a:1`
[3/1]	aaa	26	`lf:26,rf:16,a:5`
[3/2]	caa	22	`lf:18,lp:4,rf:18,rp:4,a:2`
[3/3]	aac	18	`lf:18,rf:18,rs:15,a:2`
[3/4]	ccb	18	`lf:9,ls:9,a:10`
[3/5]	acb	10	`lf:5,ls:5,a:4`
[3/6]	acc	9	`lf:9,rf:3,rs:1,a:5`

Considering [length 2 / frequency 0] ac=d.

Step 2

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

Rewriting system is complete. See ⟨a, b, c | ab=1, cac=aca⟩.