Morphocompletion for #4865 ⟨a, b | abbaabba=bab⟩

Solved by morph:2/0,2/1,2/1,2/0,2/1,2/0. (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.	abbabab ⇒ bababba
2.	abbaabba ⇒ bab
3.	abbaabbbab ⇒ babbbaabba
4.	abbbabbabbab ⇒ babbabbabbba
5.	abbbababbaba ⇒ bbababbabaab
6.	bababbabaabba ⇒ abbabbab
7.	abbbbababbaba ⇒ bbababbabaabb
8.	bbababbabaaabba ⇒ ababbabbab
9.	bbababbabaababba ⇒ abbabbabbab
10.	bbababbabaaaabba ⇒ aababbabbab
	...

Collecting factors up to length 3 / frequency 2:

[2/0]	ab	46	`lf:37,lp:6,ls:3,rf:31,rp:3,rs:6,lprs:2`
[2/1]	ba	46	`lf:38,lp:1,ls:7,rf:30,rp:4,rs:3,lsrp:1`

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

Step 2

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	ab ⇒ c
2.	bccba ⇒ cbcc
3.	cbccb ⇒ bccbc
4.	acbcc ⇒ cccba
5.	bccbca ⇒ ccbcc
6.	cbacbc ⇒ bcb
7.	cbacba ⇒ bc
8.	accbcc ⇒ cccbca
9.	bccbcca ⇒ cccbcc
10.	cbcccbc ⇒ bcbcb
11.	cbcccba ⇒ bcbc
12.	acccbcc ⇒ cccbcca
13.	bcbbacba ⇒ cbacbbc
14.	bccbccca ⇒ ccccbcc
15.	cbbccbcc ⇒ bccbcccb
16.	cbacbbcb ⇒ bcbbacbc
17.	acbacbbc ⇒ ccbbacba
18.	accccbcc ⇒ cccbccca
19.	cccbcacbc ⇒ acbcbcb
20.	cccbcacba ⇒ acbcbc
	...

Collecting factors up to length 3 / frequency 2:

[2/0]	cb	40	`lf:31,lp:7,ls:2,rf:26,rp:2,rs:4,lprs:3,a:2`
[2/1]	cc	35	`lf:28,lp:2,ls:5,rf:26,rp:8,rs:4,lsrp:4,a:4`

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

Step 3

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	cc ⇒ d
2.	dc ⇒ cd
3.	ab ⇒ c
4.	bdba ⇒ cbd
5.	cbdb ⇒ bdbc
6.	dbdb ⇒ bdbd
7.	acbd ⇒ cdba
8.	bdbca ⇒ dbd
9.	bdbda ⇒ cdbd
10.	cdbca ⇒ adbd
11.	ddbca ⇒ cadbd
12.	acbcd ⇒ cdbac
13.	acdbd ⇒ cdbda
14.	bdbcda ⇒ ddbd
15.	bdbdda ⇒ cddbd
16.	cbcdba ⇒ bcbc
17.	cbacbc ⇒ bcb
18.	cbacba ⇒ bc
19.	dbacbc ⇒ cbcb
20.	dbacba ⇒ cbc
	...

Collecting factors up to length 3 / frequency 2:

[2/0]	db	19	`lf:14,lp:3,ls:2,rf:11,rp:1,a:5`
[2/1]	bd	18	`lf:11,lp:5,ls:2,rf:11,rp:2,rs:8,lprs:5,a:7`

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

Step 4

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	bd ⇒ e
2.	cc ⇒ d
3.	dc ⇒ cd
4.	ae ⇒ cd
5.	ab ⇒ c
6.	eba ⇒ ce
7.	bee ⇒ eeb
8.	bcd ⇒ ec
9.	cee ⇒ eec
10.	ceb ⇒ ebc
11.	cde ⇒ eea
12.	dee ⇒ eed
13.	deb ⇒ ee
14.	eeca ⇒ dde
15.	ebca ⇒ de
16.	bace ⇒ ecba
17.	cdba ⇒ ace
18.	cdde ⇒ eeda
19.	ddba ⇒ cace
20.	cbacba ⇒ bc
	...

Collecting factors up to length 3 / frequency 2:

[2/0]	ba	11	`lf:6,lp:1,ls:4,rf:1,rs:1,lprs:1,a:4`
[2/1]	de	8	`lf:4,lp:2,ls:2,rf:2,rp:1,rs:2,re:1,a:14`

Considering [length 2 / frequency 0] ba=f.

Step 5

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	fe ⇒ ec
2.	bc ⇒ fb
3.	bd ⇒ e
4.	ba ⇒ f
5.	ce ⇒ ef
6.	cc ⇒ d
7.	dc ⇒ cd
8.	ae ⇒ cd
9.	af ⇒ ca
10.	ab ⇒ c
11.	eff ⇒ de
12.	fff ⇒ ea
13.	ffb ⇒ e
14.	bee ⇒ eeb
15.	bef ⇒ fbe
16.	cde ⇒ eea
17.	dee ⇒ eed
18.	def ⇒ eea
19.	deb ⇒ ee
20.	cfcf ⇒ fb
	...

Collecting factors up to length 3 / frequency 2:

[2/0]	de	8	`lf:4,lp:3,ls:1,rf:1,rp:1,rs:1,re:1,a:19`
[2/1]	ff	8	`lf:4,lp:2,ls:2,a:10`

Considering [length 2 / frequency 1] ff=g.

Step 6

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = ab
2. d = cc
3. e = bd
4. f = ba
5. g = ff
Reduction order:
- Left-to-right shortlex with e < f < b < c < g < d < a

Rewriting system is not complete: roundsLimit

#	Rule
1.	fe ⇒ ec
2.	ff ⇒ g
3.	fg ⇒ ea
4.	bc ⇒ fb
5.	bd ⇒ e
6.	ba ⇒ f
7.	ce ⇒ ef
8.	cc ⇒ d
9.	ge ⇒ ed
10.	gf ⇒ ea
11.	gb ⇒ e
12.	de ⇒ eg
13.	dc ⇒ cd
14.	ae ⇒ cd
15.	af ⇒ ca
16.	ab ⇒ c
17.	ag ⇒ da
18.	eca ⇒ gg
19.	beg ⇒ ee
20.	cfcf ⇒ fb
	...

Collecting factors up to length 3 / frequency 1:

[2/0]	cf	4	`lf:2,lp:1,ls:1,a:6`

Considering [length 2 / frequency 0] cf=h.

Step 7

Auxiliary generators:
1. c = ab
2. d = cc
3. e = bd
4. f = ba
5. g = ff
6. h = cf
Reduction order:
- Left-to-right recursive path with deg(h) = 0; deg(e) = deg(f) = deg(b) = deg(c) = deg(g) = deg(d) = deg(a) = 1, e < f < b < c < g < d < a

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