Morphocompletion for #2361 ⟨a, b | abbbbba=bab⟩

Solved by morph:2/1,2/1,2/1,2/1,2/0. (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.	abbbbba ⇒ bab
2.	abbbbbbab ⇒ babbbbbba
3.	aabbbbbbbab ⇒ babbbbbbbaa
4.	ababbbbbbbab ⇒ babbbbbbbaba
5.	bbbbbabbbbbbaa ⇒ abbbbbbbab
6.	babbabbbbbbbab ⇒ bbabbbbbbbabba
7.	aabbabbbbbbbab ⇒ babbbbbbbababa
8.	babbbbbbbaabbbba ⇒ aabbbbbbbbab
9.	abbbbbbbabbbbbba ⇒ babbbbbbbabb
	...

Collecting factors up to length 3, frequency 2:

Length 2:	[2/0] bb, [2/1] ab

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.	cbbbba ⇒ bc
3.	cbbbbc ⇒ bcb
4.	bcbbbbba ⇒ cbbbbbc
5.	cbbbbbcb ⇒ bcbbbbbc
6.	ccbbbbba ⇒ acbbbbbc
7.	bcbbbbbbaa ⇒ acbbbbbbc
8.	bcbbbbbbca ⇒ ccbbbbbbc
9.	acbbbbbbcb ⇒ bcbbbbbbac
10.	ccbbbbbbaa ⇒ aacbbbbbbc
11.	ccbbbbbbcb ⇒ bcbbbbbbcc
12.	ccbbbbbbca ⇒ accbbbbbbc
13.	bcbbbbbbcba ⇒ cbcbbbbbbc
14.	acbcbbbbbbc ⇒ bcbbbbbbcca
15.	cbbbcbbbbbc ⇒ bcbbbbbba
16.	cbcbbbbbbcb ⇒ bcbbbbbbcbc
17.	bbbbcbbbbbca ⇒ cbbbbbbc
18.	bbbbcbbbbbcc ⇒ cbbbbbbcb
19.	bcbbbbbbcbca ⇒ ccbcbbbbbbc
20.	bcbbbbbbccaa ⇒ acccbbbbbbc
	...

Collecting factors up to length 5, frequency 2:

Length 2:	[2/0] bb, [2/1] cb
Length 3:	[3/0] bbb, [3/1] bcb
Length 4:	[4/0] bbbb, [4/1] cbbb

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.	dbbba ⇒ bc
4.	dbbbc ⇒ bd
5.	dbbbd ⇒ bdb
6.	bdbbbba ⇒ dbbbbc
7.	bdbbbbc ⇒ dbbbbd
8.	cdbbbba ⇒ adbbbbc
9.	cdbbbbc ⇒ adbbbbd
10.	dbbbbdb ⇒ bdbbbbd
11.	ddbbbba ⇒ adbbbbd
12.	ddbbbbc ⇒ cdbbbbd
13.	dbdbbbbd ⇒ bdbbbbba
14.	bdbbbbbaa ⇒ adbbbbbc
15.	bdbbbbbac ⇒ adbbbbbd
16.	bdbbbbbca ⇒ cdbbbbbc
17.	bdbbbbbcc ⇒ cdbbbbbd
18.	bdbbbbbda ⇒ ddbbbbbc
19.	dbbdbbbbd ⇒ bdbbbbbc
20.	bbbdbbbbda ⇒ dbbbbbc
	...

Collecting factors up to length 3, frequency 2:

Length 2:	[2/0] bb, [2/1] db

Considering [length 2 / frequency 1] db=e.

Step 4

Checking up to 20 rules for overlaps.

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 not complete: roundsLimit

#	Rule
1.	ab ⇒ c
2.	cb ⇒ d
3.	db ⇒ e
4.	ebba ⇒ bc
5.	ebbc ⇒ bd
6.	ebbd ⇒ be
7.	ebbe ⇒ beb
8.	bebbba ⇒ ebbbc
9.	bebbbc ⇒ ebbbd
10.	bebbbd ⇒ ebbbe
11.	cebbba ⇒ aebbbc
12.	cebbbc ⇒ aebbbd
13.	cebbbd ⇒ aebbbe
14.	debbba ⇒ aebbbd
15.	debbbc ⇒ aebbbe
16.	debbbd ⇒ cebbbe
17.	ebbbeb ⇒ bebbbe
18.	eebbba ⇒ aebbbe
19.	eebbbc ⇒ cebbbe
20.	eebbbd ⇒ debbbe
	...

Collecting factors up to length 3, frequency 2:

Length 2:	[2/0] bb, [2/1] eb

Considering [length 2 / frequency 1] eb=f.

Step 5

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	ab ⇒ c
2.	cb ⇒ d
3.	db ⇒ e
4.	eb ⇒ f
5.	fba ⇒ bc
6.	fbc ⇒ bd
7.	fbd ⇒ be
8.	fbe ⇒ bf
9.	fbf ⇒ bfb
10.	bfbba ⇒ fbbc
11.	bfbbc ⇒ fbbd
12.	bfbbd ⇒ fbbe
13.	bfbbe ⇒ fbbf
14.	cfbba ⇒ afbbc
15.	cfbbc ⇒ afbbd
16.	cfbbd ⇒ afbbe
17.	cfbbe ⇒ afbbf
18.	dfbba ⇒ afbbd
19.	dfbbc ⇒ afbbe
20.	dfbbd ⇒ afbbf
	...

Collecting factors up to length 3, frequency 2:

Length 2:	[2/0] fb, [2/1] bb

Considering [length 2 / frequency 0] fb=g.

Step 6

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

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