Morphocompletion for #3040 ⟨a, b, c | aba=b, bcb=c⟩

Solved by morph:3/3. (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; deg(c) = 2

Rewriting system is not complete: roundsLimit

#	Rule
1.	bba ⇒ abb
2.	aba ⇒ b
3.	bcb ⇒ c
4.	bcabb ⇒ cba
5.	bcaabb ⇒ cbaa
6.	bcaaabb ⇒ cbaaa
7.	bcaaaabb ⇒ cbaaaa
8.	bcaaaaabb ⇒ cbaaaaa
9.	bcaaaaaabb ⇒ cbaaaaaa
10.	bcc ⇒ ccb
11.	bcac ⇒ cbacbb
12.	bcabc ⇒ cbacb
13.	bcaac ⇒ cbaacbb
14.	bcaabc ⇒ cbaacb
15.	bcaaac ⇒ cbaaacbb
16.	bcaaabc ⇒ cbaaacb
17.	bcaaaac ⇒ cbaaaacbb
18.	bcaaaabc ⇒ cbaaaacb
19.	bcaaaaac ⇒ cbaaaaacbb
20.	bcaaaaabc ⇒ cbaaaaacb
	...

Collecting factors up to length 4 / frequency 7:

[2/0]	bc	46	`lf:23,lp:18,ls:5,a:1`
[2/1]	aa	35	`lf:35,rf:35,rs:5,a:6`
[2/2]	ca	16	`lf:16,a:4`
[2/3]	bb	14	`lf:7,lp:1,ls:6,rf:6,rs:6,lprs:10,a:2`
[2/4]	ab	13	`lf:12,lp:1,rf:1,rp:1`
[2/5]	ac	10	`lf:5,ls:5,rf:10,a:5`
[2/6]	ba	4	`lf:2,ls:2,rf:16,rs:1`
[3/0]	bca	32	`lf:16,lp:16,a:4`
[3/1]	aaa	22	`lf:22,rf:22,rs:4,a:8`
[3/2]	caa	13	`lf:13,a:6`
[3/3]	abb	12	`lf:6,ls:6,rf:1,rp:1,rs:1,re:1,a:2`
[3/4]	abc	10	`lf:5,ls:5,a:5`
[3/5]	aab	9	`lf:9,a:6`
[3/6]	aac	8	`lf:4,ls:4,rf:8,a:7`

Considering [length 3 / frequency 3] abb=d.

Step 2

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

Rewriting system is complete. See ⟨a, b, c | aba=b, bcb=c⟩.