Morphocompletion for #645 ⟨a, b | aaabbabba=1⟩

Solved by morph:2/0,4/0. (See Morphocompletion.)

Step 1

Checking up to 20 rules for overlaps.

Reduction order:
- Right-to-left recursive path with deg(a) = 0; deg(b) = 1

Rewriting system is not complete: rulesLimit

#	Rule
1.	bbaaa ⇒ aaabb
2.	aaaabbabb ⇒ 1
3.	bbabba ⇒ abbabb
4.	aaaabbabaaabb ⇒ baaa
5.	aaabbaabbabb ⇒ bba
6.	aaabbaaabbabb ⇒ bbaa
7.	abbabbbba ⇒ bbaabbabb
8.	abbabbbbbba ⇒ bbbbaabbabb
9.	abbabbbbbbbba ⇒ bbbbbbaabbabb
10.	abbabbbbbbbbbba ⇒ bbbbbbbbaabbabb
11.	abbabbbbbbbbbbbba ⇒ bbbbbbbbbbaabbabb
12.	abbabbbbbbbbbbbbbba ⇒ bbbbbbbbbbbbaabbabb
13.	abbabbbbbbbbbbbbbbbba ⇒ bbbbbbbbbbbbbbaabbabb
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	bb	89	`lf:83,lp:2,ls:4,rf:68,rp:9,rs:9,lsrp:2,lprs:2,a:3`
[2/1]	ab	33	`lf:26,lp:7,rf:17,rp:1,a:3`
[2/2]	ba	32	`lf:24,ls:8,rf:18,rp:1,rs:1,a:3`
[2/3]	aa	22	`lf:17,lp:4,ls:1,rf:12,rp:1,rs:2,lsrp:1,lprs:2,a:4`
[3/0]	bbb	56	`lf:56,rf:42,rp:6,a:4`
[3/1]	abb	36	`lf:25,lp:7,ls:4,rf:17,rp:1,rs:9,lprs:7,a:3`
[3/2]	bba	33	`lf:23,lp:2,ls:8,rf:17,rp:3,rs:1,re:1,lsrp:1,a:3`
[3/3]	aaa	14	`lf:9,lp:4,ls:1,rf:2,rp:1,rs:1,lsrp:1,lprs:1,a:12`
[4/0]	bbbb	49	`lf:49,rf:36,rp:6,a:4`
[4/1]	abba	22	`lf:14,lp:7,ls:1,rf:8,rp:1,lsrp:1,a:3`
[4/2]	bbba	14	`lf:7,ls:7,rf:6,a:4`
[4/3]	babb	14	`lf:11,ls:3,rf:8,rs:8,a:3`
[5/0]	bbbbb	42	`lf:42,rf:30,rp:5,a:5`
[5/1]	abbab	18	`lf:11,lp:7,rf:8,rp:1,a:3`
[5/2]	bbabb	15	`lf:11,lp:1,ls:3,rf:8,rs:8,lprs:10,a:3`
[5/3]	bbbba	14	`lf:7,ls:7,rf:6,rp:1,lsrp:1,a:4`
[6/0]	bbbbbb	36	`lf:36,rf:25,rp:5,a:5`
[6/1]	abbabb	20	`lf:10,lp:7,ls:3,rf:8,rp:1,rs:8,re:1,lprs:7,a:3`
[6/2]	bbbbba	12	`lf:6,ls:6,rf:5,a:5`
[6/3]	bbabbb	7	`lf:7,a:4`

Considering [length 2 / frequency 0] bb=c.

Step 2

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = bb
Reduction order:
- Right-to-left recursive path with deg(a) = 0; deg(c) = deg(b) = 1, c < b

Rewriting system is not complete: roundsLimit

#	Rule
1.	caaa ⇒ aaac
2.	aaaacac ⇒ 1
3.	caca ⇒ acac
4.	cb ⇒ bc
5.	aaaacab ⇒ baaaaca
6.	bb ⇒ c
7.	aaacaacac ⇒ ca
8.	aaacaaacac ⇒ caa
9.	acacca ⇒ caacac
10.	caccaa ⇒ aaccac
11.	aaaacabc ⇒ b
12.	aaaacabaaac ⇒ baaa
13.	aaaccaacac ⇒ cca
14.	acaccca ⇒ ccaacac
15.	aaacaacabc ⇒ cab
16.	acacccca ⇒ cccaacac
17.	acaccccca ⇒ ccccaacac
18.	acacccccca ⇒ cccccaacac
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	aa	40	`lf:30,lp:8,ls:2,rf:14,rp:2,rs:2,lsrp:2,lprs:2,a:7`
[2/1]	ac	39	`lf:29,lp:5,ls:5,rf:16,rp:1,rs:8,lprs:5,a:6`
[2/2]	ca	36	`lf:27,lp:3,ls:6,rf:17,rp:4,rs:3,re:1,lsrp:1,a:6`
[2/3]	cc	17	`lf:17,rf:12,rp:5,a:7`
[2/4]	ab	5	`lf:4,ls:1,rf:1,rs:1,a:14`
[2/5]	bc	4	`lf:2,ls:2,rf:1,rp:1,rs:1,re:1,a:3`
[2/6]	ba	1	`lf:1,rf:2,rp:2,a:35`
[3/0]	aaa	24	`lf:15,lp:8,ls:1,rf:4,rp:1,rs:1,lsrp:10,lprs:1,a:13`
[3/1]	aca	23	`lf:17,lp:5,ls:1,rf:7,rp:1,rs:1,lsrp:10,a:6`
[3/2]	cac	17	`lf:11,lp:2,ls:4,rf:7,rs:7,lprs:11,a:6`
[3/3]	aac	14	`lf:13,ls:1,rf:8,rp:1,rs:1,a:7`
[3/4]	cca	12	`lf:7,ls:5,rf:6,rp:2,rs:1,re:1,lsrp:1,a:7`
[3/5]	ccc	10	`lf:10,rf:6,rp:3,a:8`
[3/6]	caa	8	`lf:6,lp:1,ls:1,rf:6,rp:2,rs:1,re:1,a:7`
[4/0]	acac	18	`lf:9,lp:5,ls:4,rf:6,rp:1,rs:6,re:1,lprs:5,a:6`
[4/1]	aaac	15	`lf:10,lp:4,ls:1,rf:2,rp:1,rs:1,re:1,a:13`
[4/2]	aaca	11	`lf:11,rf:6,rs:1,a:7`
[4/3]	ccca	8	`lf:4,ls:4,rf:3,rp:1,lsrp:1,a:8`
[4/4]	aaaa	8	`lf:4,lp:4,rf:1,a:13`
[4/5]	cacc	7	`lf:6,lp:1,a:7`
[4/6]	cccc	6	`lf:6,rf:3,rp:2,a:9`
[5/0]	aaaca	11	`lf:8,lp:3,rf:1,rs:1,a:13`
[5/1]	acacc	10	`lf:5,lp:5,a:7`
[5/2]	aacac	8	`lf:4,ls:4,rf:5,rs:5,a:7`
[5/3]	aaaac	8	`lf:4,lp:4,rf:1,a:13`
[5/4]	cccca	6	`lf:3,ls:3,rf:2,rp:1,lsrp:1,a:9`
[5/5]	aacab	5	`lf:4,ls:1,a:14`
[5/6]	caccc	4	`lf:4,a:8`

Considering [length 4 / frequency 0] acac=d.

Step 3

Auxiliary generators:
1. c = bb
2. d = acac
Reduction order:
- Right-to-left recursive path with deg(a) = deg(d) = 0, a < d; deg(c) = deg(b) = 1, c < b

Rewriting system is complete. See ⟨a, b | aaabbabba=1⟩.