Morphocompletion for #555 ⟨a, b | abbba=bab⟩

Solved by morph:2/1,2/1,2/0. (See Morphocompletion.)

Step 1

Checking up to 20 rules for overlaps.

Reduction order:
- Left-to-right shortlex with b < a

Rewriting system is not complete: rulesLimit

#	Rule
1.	abbba ⇒ bab
2.	abbbbab ⇒ babbbba
3.	aabbbbbab ⇒ babbbbbaa
4.	bbbabbbbaa ⇒ abbbbbab
5.	ababbbbbab ⇒ babbbbbaba
6.	abbabbbbbab ⇒ babbbbbabba
7.	babbbbbaabba ⇒ aabbbbbbab
8.	abbbbbabbbba ⇒ babbbbbabb
9.	babbbbbababba ⇒ ababbbbbbab
10.	abbbbbbabbbba ⇒ babbbbbabbb
	...

Collecting factors up to length 7 / frequency 3:

[2/0]	bb	49	`lf:48,lp:1,rf:41,rs:2`
[2/1]	ab	31	`lf:21,lp:6,ls:4,rf:18,rp:2,rs:4,lprs:1`
[2/2]	ba	27	`lf:20,lp:2,ls:5,rf:19,rp:7,rs:3,lsrp:3`
[3/0]	bbb	33	`lf:32,lp:1,rf:29,rs:1`
[3/1]	bba	21	`lf:16,ls:5,rf:10,rs:2`
[3/2]	abb	20	`lf:15,lp:5,rf:12,rp:1,rs:1,lprs:1`
[4/0]	bbbb	19	`lf:19,rf:19,a:1`
[4/1]	bbba	17	`lf:13,lp:1,ls:3,rf:9,rs:1`
[4/2]	abbb	16	`lf:12,lp:4,rf:10,rp:1,rs:1,lprs:1`
[5/0]	abbbb	14	`lf:11,lp:3,rf:9,rp:1,a:1`
[5/1]	bbbab	13	`lf:8,lp:1,ls:4,rf:7,rs:3,lprs:1,a:1`
[5/2]	bbbba	13	`lf:11,ls:2,rf:9,rs:1,a:1`
[6/0]	bbbbab	11	`lf:7,ls:4,rf:7,rs:3,a:1`
[6/1]	abbbbb	9	`lf:7,lp:2,rf:8,rp:1,a:3`
[6/2]	babbbb	9	`lf:7,lp:2,rf:7,rp:6,a:1`

Considering [length 2 / frequency 1] ab=c.

Step 2

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = ab
Reduction order:
- Left-to-right shortlex with b < a < c

Rewriting system is not complete: roundsLimit

#	Rule
1.	ab ⇒ c
2.	cbba ⇒ bc
3.	cbbc ⇒ bcb
4.	bcbbba ⇒ cbbbc
5.	cbbbcb ⇒ bcbbbc
6.	ccbbba ⇒ acbbbc
7.	cbcbbbc ⇒ bcbbbba
8.	bbcbbbca ⇒ cbbbbc
9.	bbcbbbcc ⇒ cbbbbcb
10.	bcbbbbaa ⇒ acbbbbc
11.	bcbbbbca ⇒ ccbbbbc
12.	acbbbbcb ⇒ bcbbbbac
13.	ccbbbbaa ⇒ aacbbbbc
14.	ccbbbbcb ⇒ bcbbbbcc
15.	ccbbbbca ⇒ accbbbbc
16.	bcbbbbcba ⇒ cbcbbbbc
17.	acbcbbbbc ⇒ bcbbbbcca
18.	cbacbbbbc ⇒ bcbbbbbaa
19.	cbcbbbbcb ⇒ bcbbbbcbc
20.	cbccbbbbc ⇒ bcbbbbbca
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	bb	51	`lf:49,lp:2,rf:50,a:2`
[2/1]	cb	40	`lf:29,lp:7,ls:4,rf:21,rp:4,rs:2,lprs:1,a:2`
[2/2]	bc	33	`lf:24,lp:4,ls:5,rf:26,rp:10,rs:11,re:1,lsrp:5,lprs:4,a:2`
[2/3]	cc	11	`lf:6,lp:4,ls:1,rf:4,rp:1,rs:1,lprs:1,a:6`
[2/4]	ba	11	`lf:7,ls:4,rf:3,rs:1,a:2`
[3/0]	bbb	28	`lf:28,rf:33,a:4`
[3/1]	bbc	23	`lf:16,lp:2,ls:5,rf:14,rs:9,lprs:1,a:3`
[3/2]	cbb	22	`lf:19,lp:3,rf:17,rp:3,a:2`
[3/3]	bcb	22	`lf:14,lp:4,ls:4,rf:12,rp:9,rs:2,re:1,lsrp:4,a:3`
[3/4]	ccb	9	`lf:5,lp:4,rf:2,rp:1,a:6`
[4/0]	cbbb	18	`lf:17,lp:1,rf:17,rp:3,a:4`
[4/1]	bbbc	17	`lf:13,ls:4,rf:14,rs:9,a:4`
[4/2]	bcbb	13	`lf:9,lp:4,rf:9,rp:8,a:4`
[4/3]	bbcb	13	`lf:7,lp:2,ls:4,rf:2,rs:1,lprs:1,a:5`
[4/4]	bbbb	11	`lf:11,rf:16,a:7`
[5/0]	bcbbb	13	`lf:9,lp:4,rf:9,rp:8,a:4`
[5/1]	bbbbc	12	`lf:9,ls:3,rf:11,rs:6,a:9`
[5/2]	cbbbb	11	`lf:11,rf:14,rp:2,a:7`
[5/3]	ccbbb	9	`lf:5,lp:4,rf:2,rp:1,a:6`
[5/4]	bbbcb	9	`lf:5,ls:4,rf:2,rs:1,a:5`

Considering [length 2 / frequency 1] cb=d.

Step 3

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = ab
2. d = cb
Reduction order:
- Left-to-right shortlex with b < a < c < d

Rewriting system is not complete: roundsLimit

#	Rule
1.	ab ⇒ c
2.	cb ⇒ d
3.	dba ⇒ bc
4.	dbc ⇒ bd
5.	dbd ⇒ bdb
6.	bdbba ⇒ dbbc
7.	bdbbc ⇒ dbbd
8.	cdbba ⇒ adbbc
9.	cdbbc ⇒ adbbd
10.	dbbdb ⇒ bdbbd
11.	ddbba ⇒ adbbd
12.	ddbbc ⇒ cdbbd
13.	bdbbba ⇒ cdbbd
14.	bdbbbc ⇒ ddbbd
15.	bdbbda ⇒ dbbbc
16.	bdbbdc ⇒ dbbbd
17.	cdbbba ⇒ acdbbd
18.	cdbbbc ⇒ addbbd
19.	cdbbda ⇒ adbbbc
20.	cdbbdc ⇒ adbbbd
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	db	24	`lf:19,lp:4,ls:1,rf:16,rp:4,rs:1,lprs:10,a:3`
[2/1]	bd	19	`lf:12,lp:6,ls:1,rf:14,rp:3,rs:12,re:1,lsrp:10,lprs:4,a:4`
[2/2]	bb	19	`lf:19,rf:19,a:6`
[2/3]	cd	12	`lf:6,lp:6,rf:3,rp:2,a:9`
[2/4]	bc	12	`lf:6,ls:6,rf:5,rp:1,rs:5,re:1,a:3`
[3/0]	dbb	16	`lf:15,lp:1,rf:15,rp:4,a:6`
[3/1]	bdb	14	`lf:7,lp:6,ls:1,rf:2,rp:2,rs:1,re:1,lsrp:1,a:5`
[3/2]	cdb	12	`lf:6,lp:6,rf:3,rp:2,a:9`
[3/3]	bbc	10	`lf:5,ls:5,rf:4,rs:4,a:6`
[3/4]	bba	10	`lf:5,ls:5,a:6`
[4/0]	cdbb	12	`lf:6,lp:6,rf:3,rp:2,a:9`
[4/1]	bdbb	12	`lf:6,lp:6,rf:1,rp:1,a:6`
[4/2]	dbbd	6	`lf:5,lp:1,rf:9,rp:1,rs:9,re:1,lprs:10,a:7`
[4/3]	dbbc	6	`lf:3,ls:3,rf:2,rp:1,rs:2,re:1,a:6`
[4/4]	dbba	6	`lf:3,ls:3,a:6`
[5/0]	dbbdc	4	`lf:2,ls:2,a:17`
[5/1]	dbbda	4	`lf:2,ls:2,a:16`
[5/2]	dbbbc	4	`lf:2,ls:2,rf:2,rp:1,rs:2,re:1,a:14`
[5/3]	dbbba	4	`lf:2,ls:2,a:11`
[5/4]	cdbbd	4	`lf:2,lp:2,rf:3,rp:2,rs:3,re:2,a:11`

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

Step 4

Auxiliary generators:
1. c = ab
2. d = cb
3. e = db
Reduction order:
- Left-to-right shortlex with b < a < c < d < e

Rewriting system is complete. See ⟨a, b | abbba=bab⟩.