Morphocompletion for #6270 ⟨a, b, c | aa=1, bcbccb=1⟩

Solved by morph:2/0,3/0. (See Morphocompletion.)

Step 1

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	aa ⇒ 1
2.	cbbc ⇒ bccb
3.	cbccb ⇒ bcbcc
4.	ccbb ⇒ bcbc
5.	bbcbcc ⇒ 1
6.	cbbbcc ⇒ bbcccb
7.	cbcbcbcc ⇒ bcbccccb
8.	cbbbbccc ⇒ bbbccccb
9.	cbbbcbc ⇒ bccbcbb
10.	bbcbcbcbc ⇒ cbb
11.	bccbcbbbc ⇒ bbcccbcbb
12.	cbbbbcbc ⇒ bbcbcbcb
13.	cbbbbcccb ⇒ bbbccbcbc
14.	bbcccbcbbbc ⇒ cbcbb
15.	bbbccbcbcbcb ⇒ cbbbbc
	...

Collecting factors up to length 4 / frequency 4:

[2/0]	cb	38	`lf:27,lp:8,ls:3,rf:20,rp:3,rs:5,lsrp:1,lprs:5,a:2`
[2/1]	bc	35	`lf:28,lp:1,ls:6,rf:21,rp:5,rs:3,lsrp:2,a:2`
[2/2]	bb	29	`lf:24,lp:4,ls:1,rf:14,rp:5,rs:4,lprs:2,a:10`
[2/3]	cc	18	`lf:13,lp:1,ls:4,rf:14,rs:1,a:2`
[3/0]	cbc	20	`lf:15,lp:2,ls:3,rf:10,rp:1,rs:2,a:2`
[3/1]	bbc	18	`lf:12,lp:3,ls:3,rf:6,rp:3,rs:1,lsrp:1,a:15`
[3/2]	cbb	16	`lf:9,lp:6,ls:1,rf:5,rp:2,rs:4,re:1,lprs:1,a:10`
[3/3]	bcb	14	`lf:13,ls:1,rf:10,rp:3,rs:1,a:2`

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

Step 2

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	aa ⇒ 1
2.	ddcd ⇒ c
3.	cdcd ⇒ ddcc
4.	ddddcc ⇒ ccd
5.	bdcd ⇒ 1
6.	bdcc ⇒ dcd
7.	bdddcc ⇒ cd
8.	dbc ⇒ bcd
9.	dbdd ⇒ b
10.	dbdc ⇒ 1
11.	cb ⇒ d
12.	cdb ⇒ bdc
13.	cddb ⇒ bdddddc
14.	bbdc ⇒ dbd
15.	bbdddc ⇒ db
16.	bbdddddc ⇒ ddbd
17.	dbb ⇒ bbdddd
18.	dbdb ⇒ bbdd
	...

Collecting factors up to length 6 / frequency 3:

[2/0]	dd	17	`lf:14,lp:2,ls:1,rf:10,rp:2,rs:2,a:4`
[2/1]	db	16	`lf:8,lp:5,ls:3,rf:3,rp:2,rs:1,re:1,a:8`
[2/2]	dc	14	`lf:10,ls:4,rf:4,rp:1,rs:2,a:3`
[3/0]	bdc	8	`lf:4,lp:2,ls:2,rf:1,rp:1,rs:1,re:1,a:3`
[3/1]	ddc	8	`lf:5,lp:1,ls:2,rf:2,rp:1,rs:1,a:4`
[3/2]	ddd	8	`lf:7,lp:1,rf:5,rs:1,a:18`
[4/0]	dddc	6	`lf:4,ls:2,rf:1,rs:1,a:18`
[4/1]	bbdd	4	`lf:2,lp:2,rf:2,rp:2,rs:1,re:1,a:17`
[4/2]	bddd	4	`lf:3,lp:1,rf:2,rp:1,a:18`
[5/0]	bbddd	4	`lf:2,lp:2,rf:1,rp:1,a:18`
[5/1]	bdddc	4	`lf:2,lp:1,ls:1,a:20`
[5/2]	dddcc	4	`lf:2,ls:2,a:20`

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

Step 3

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

Rewriting system is complete. See ⟨a, b, c | aa=1, bcbccb=1⟩.