Morphocompletion for #416 ⟨a, b, c | abc=b, caa=1⟩

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

Step 1

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: workMaxLimit

#	Rule
1.	cb ⇒ bcc
2.	abc ⇒ b
3.	cab ⇒ bc
4.	caa ⇒ 1
5.	baa ⇒ ab
6.	abbc ⇒ bab
7.	abbbcc ⇒ babb
8.	babab ⇒ abbbc
9.	abbbbcccc ⇒ babbb
10.	babbab ⇒ abbbbccc
11.	abbbbbcccccccc ⇒ babbbb
12.	babbbab ⇒ abbbbbccccccc
	...

Collecting factors up to length 4 / frequency 4:

[2/0]	ab	21	`lf:12,lp:5,ls:4,rf:8,rp:4,rs:2,re:1,lsrp:3,lprs:1`
[2/1]	cc	14	`lf:11,ls:3,rf:9,rs:3,a:5`
[2/2]	bb	13	`lf:13,rf:15,rs:3,a:4`
[2/3]	ba	11	`lf:7,lp:4,rf:4,rp:4,a:2`
[3/0]	bab	12	`lf:6,lp:3,ls:3,rf:4,rp:4,rs:1,re:1,a:4`
[3/1]	abb	10	`lf:6,lp:4,rf:6,rp:3,rs:1,lprs:1,a:4`
[3/2]	ccc	10	`lf:8,ls:2,rf:6,rs:2,a:8`
[3/3]	bbb	7	`lf:7,rf:9,rs:2,a:6`

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

Step 2

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	cb ⇒ bcc
2.	dc ⇒ b
3.	cd ⇒ bc
4.	dbc ⇒ bd
5.	ab ⇒ d
6.	cad ⇒ b
7.	caa ⇒ 1
8.	bad ⇒ db
9.	baa ⇒ d
10.	dbbc ⇒ bdd
11.	daa ⇒ ad
12.	adb ⇒ dad
13.	bdad ⇒ dbb
14.	dbbbc ⇒ bddd
15.	bddad ⇒ dbbb
16.	dbbbbc ⇒ bdddd
17.	dadad ⇒ addb
18.	bdddad ⇒ dbbbb
19.	dbbbbbc ⇒ bddddd
20.	daddad ⇒ addbb
	...

Collecting factors up to length 6 / frequency 3:

[2/0]	ad	18	`lf:10,lp:1,ls:7,rf:4,rp:3,rs:2,re:1,lsrp:2,lprs:10,a:4`
[2/1]	db	12	`lf:6,lp:5,ls:1,rf:6,rp:4,rs:2,re:1,a:6`
[2/2]	da	11	`lf:8,lp:3,rf:1,rp:1,a:10`
[3/0]	dad	14	`lf:7,lp:2,ls:5,rf:1,rp:1,rs:1,re:1,a:11`
[3/1]	dbb	8	`lf:4,lp:4,rf:4,rp:3,rs:2,re:1,a:11`
[3/2]	bbc	8	`lf:4,ls:4,a:12`
[4/0]	ddad	6	`lf:3,ls:3,a:16`
[4/1]	dbbb	6	`lf:3,lp:3,rf:2,rp:2,rs:1,re:1,a:15`
[4/2]	bbbc	6	`lf:3,ls:3,a:15`
[5/0]	dbbbb	4	`lf:2,lp:2,rf:1,rp:1,rs:1,re:1,a:18`
[5/1]	bbbbc	4	`lf:2,ls:2,a:18`
[5/2]	addad	2	`lf:1,ls:1,a:17`

Considering [length 2 / frequency 0] ad=e.

Step 3

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

Rewriting system is complete. See ⟨a, b, c | abc=b, caa=1⟩.