Morphocompletion for #6271 ⟨a, b, c | aa=1, bccbbc=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) = 0; deg(b) = deg(c) = 1, b < c

Rewriting system is not complete: roundsLimit

#	Rule
1.	aa ⇒ 1
2.	cbbc ⇒ bccb
3.	ccbb ⇒ bcbc
4.	bccbb ⇒ bbcbc
5.	cbccb ⇒ bcbcc
6.	bbcbcc ⇒ 1
7.	bcbccb ⇒ 1
8.	cbbbcc ⇒ bbcccb
9.	cbbbcbc ⇒ bccbcbb
10.	cbbbccb ⇒ bccbbbc
11.	cbbbbcbc ⇒ bccbbbcb
12.	cbbbcbcc ⇒ cb
13.	cbcbcbcc ⇒ bcbccccb
14.	bbcbcbcbc ⇒ cbb
15.	bccbbbcbc ⇒ cbb
16.	cbbbbbcbcc ⇒ cbbb
17.	bbcccbcbbbc ⇒ cbcbb
18.	bccbcbbbcbc ⇒ cbcbb
	...

Collecting factors up to length 4 / frequency 4:

[2/0]	bc	45	`lf:34,lp:4,ls:7,rf:18,rp:7,rs:3,lsrp:3,lprs:1,a:2`
[2/1]	cb	44	`lf:32,lp:9,ls:3,rf:20,rp:6,rs:5,re:1,lprp:2,lprs:5,a:2`
[2/2]	bb	32	`lf:27,lp:3,ls:2,rf:13,rp:2,rs:6,lsrp:1,lprs:2,a:2`
[2/3]	cc	20	`lf:14,lp:1,ls:5,rf:10,rs:1,a:2`
[3/0]	cbc	24	`lf:17,lp:2,ls:5,rf:7,rp:2,rs:2,lsrp:1,a:4`
[3/1]	cbb	21	`lf:12,lp:7,ls:2,rf:8,rp:3,rs:5,re:2,lprp:1,lprs:1,a:2`
[3/2]	bcc	20	`lf:12,lp:3,ls:5,rf:7,rp:4,rs:1,a:2`
[3/3]	bbc	18	`lf:13,lp:3,ls:2,rf:4,rp:2,rs:1,a:2`

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

Step 2

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	aa ⇒ 1
2.	dbdd ⇒ b
3.	ddcd ⇒ c
4.	dbb ⇒ bbdddd
5.	dbdb ⇒ bbdd
6.	bc ⇒ d
7.	bddc ⇒ 1
8.	dbdc ⇒ bdcd
9.	cb ⇒ bddddddc
10.	cbdd ⇒ 1
11.	dcb ⇒ cbd
12.	dcdb ⇒ cdbd
13.	dcddb ⇒ cddbd
14.	ddcc ⇒ cdcd
15.	cbb ⇒ bdddd
16.	cbdb ⇒ bdd
17.	cbdc ⇒ dcd
18.	ccbd ⇒ ddc
	...

Collecting factors up to length 6 / frequency 3:

[2/0]	db	16	`lf:8,lp:4,ls:4,rf:2,a:8`
[2/1]	dc	14	`lf:8,lp:3,ls:3,rf:5,rp:1,rs:2,lsrp:1,a:4`
[2/2]	cb	11	`lf:6,lp:4,ls:1,rf:1,rp:1,lsrp:10,a:4`
[3/0]	cbd	8	`lf:4,lp:3,ls:1,rf:1,rp:1,rs:1,re:1,a:4`
[3/1]	ddc	6	`lf:3,lp:2,ls:1,rf:2,rp:1,rs:2,re:1,a:13`
[3/2]	dcd	6	`lf:3,lp:2,ls:1,rf:3,rp:1,rs:3,re:1,a:7`
[4/0]	cddb	2	`lf:1,ls:1,rf:1,rp:1,lsrp:10,a:21`
[4/1]	dcdd	2	`lf:1,lp:1,a:21`
[4/2]	cdcd	0	`rf:1,rp:1,rs:1,re:1,a:19`
[5/0]	cddbd	0	`rf:1,rp:1,rs:1,re:1,a:21`
[5/1]	bbddd	0	`rf:1,rp:1,a:20`
[5/2]	ddddc	0	`rf:1,rs:1,a:25`

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

Step 3

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

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