Morphocompletion for #5298 ⟨a, b | abaaaba=aaab⟩

Solved by morph:2/0,2/1,3/0,4/0. (See Morphocompletion.)

Step 1

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: rulesLimit

#	Rule
1.	abaaaba ⇒ aaab
2.	aaabaaba ⇒ abaaaaab
3.	ababaaaaab ⇒ aaababa
4.	aaabbaaaba ⇒ aaabaab
5.	aaabbaaaaab ⇒ abaaaaababa
6.	aaababaaaaba ⇒ ababaaaaaaab
7.	aaabbbaaaba ⇒ aaabbaab
8.	aaabbabaaaaab ⇒ abaaaaabba
9.	aaababbaaaba ⇒ aaababaab
10.	aaabaabbaaaba ⇒ abaaaaabab
	...

Collecting factors up to length 4 / frequency 3:

[2/0]	aa	51	`lf:43,lp:8,rf:35,rp:5,lprp:3`
[2/1]	ab	30	`lf:25,lp:2,ls:3,rf:23,rp:5,rs:7,lsrp:2,lprs:1`
[2/2]	ba	29	`lf:22,ls:7,rf:16,rs:3`
[3/0]	aaa	32	`lf:24,lp:8,rf:22,rp:5,lprp:3`
[3/1]	aba	25	`lf:16,lp:2,ls:7,rf:14,rp:5,rs:2,lsrp:3,lprs:1`
[3/2]	aab	22	`lf:19,ls:3,rf:13,rs:6`

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

Step 2

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = aa
Reduction order:
- Left-to-right recursive path with deg(c) = 0; deg(a) = 1; deg(b) = 2

Rewriting system is not complete: roundsLimit

#	Rule
1.	ca ⇒ ac
2.	aa ⇒ c
3.	cbacbc ⇒ ccba
4.	cbacba ⇒ ccb
5.	ccbcbc ⇒ cbaccba
6.	ccbcba ⇒ cbaccb
7.	abacbc ⇒ acba
8.	abacba ⇒ acb
9.	acbcbc ⇒ abaccba
10.	acbcba ⇒ abaccb
11.	cbabaccb ⇒ ccbaba
12.	ccbbacbc ⇒ cbaccb
13.	ccbbacba ⇒ ccbcb
14.	ccbbaccb ⇒ cbaccbaba
15.	ccbabccba ⇒ cbabacccb
16.	ababaccb ⇒ acbaba
17.	acbbacbc ⇒ abaccb
18.	acbbacba ⇒ acbcb
19.	acbbaccb ⇒ abaccbaba
20.	acbabccba ⇒ ababacccb
	...

Collecting factors up to length 5 / frequency 3:

[2/0]	cb	40	`lf:33,lp:3,ls:4,rf:25,rp:5,rs:10,lsrp:1,lprs:1,a:2`
[2/1]	ba	32	`lf:24,ls:8,rf:24,rs:8,a:2`
[2/2]	ac	24	`lf:18,lp:6,rf:15,rp:5,rs:1,re:1,lprp:1,a:2`
[3/0]	cba	24	`lf:13,lp:3,ls:8,rf:13,rp:5,rs:4,lsrp:2,lprs:1,a:2`
[3/1]	ccb	22	`lf:12,lp:6,ls:4,rf:14,rp:4,rs:7,re:1,lprp:1,lsrp:1,lprs:3,a:4`
[3/2]	acb	20	`lf:14,lp:6,rf:4,rp:4,rs:1,re:1,lprp:1,a:2`
[4/0]	acbc	12	`lf:6,lp:2,ls:4,rf:1,rp:1,a:5`
[4/1]	acba	10	`lf:5,lp:1,ls:4,rf:2,rp:2,rs:1,re:1,a:2`
[4/2]	bacb	8	`lf:8,a:2`

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

Step 3

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = aa
2. d = ba
Reduction order:
- Left-to-right recursive path with deg(c) = 0; deg(d) = 1; deg(a) = 2; deg(b) = 3

Rewriting system is not complete: roundsLimit

#	Rule
1.	cddcdc ⇒ ccd
2.	dddcdc ⇒ dcd
3.	addcdc ⇒ acd
4.	ca ⇒ ac
5.	ccda ⇒ cdcdc
6.	dcda ⇒ ddcdc
7.	ccdda ⇒ cddccd
8.	dcdda ⇒ dddccd
9.	ccddda ⇒ cddcdddccd
10.	aa ⇒ c
11.	acda ⇒ adcdc
12.	acdda ⇒ addccd
13.	bc ⇒ da
14.	ba ⇒ d
15.	ccb ⇒ cdcd
16.	dcb ⇒ ddcd
17.	ccdb ⇒ cddcddcd
18.	dcdb ⇒ dddcddcd
19.	acb ⇒ adcd
20.	acdb ⇒ addcddcd
	...

Collecting factors up to length 4 / frequency 3:

[2/0]	dc	17	`lf:10,lp:4,ls:3,rf:21,rp:1,rs:3,lsrp:1,lprs:1,a:3`
[2/1]	cd	15	`lf:14,lp:1,rf:25,rp:5,rs:13,lprs:1,a:3`
[2/2]	da	14	`lf:7,ls:7,rf:1,rp:1,rs:1,re:1,a:5`
[3/0]	dcd	9	`lf:6,lp:3,rf:14,rp:1,rs:7,re:1,lprs:1,a:3`
[3/1]	dda	8	`lf:4,ls:4,a:19`
[3/2]	ccd	8	`lf:4,lp:4,rf:5,rp:1,rs:5,re:1,lprs:2,a:10`

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

Step 4

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = aa
2. d = ba
3. e = dcd
Reduction order:
- Left-to-right recursive path with deg(c) = deg(e) = 0, c < e; deg(d) = 1; deg(a) = 2; deg(b) = 3

Rewriting system is not complete: roundsLimit

#	Rule
1.	edec ⇒ dce
2.	ccd ⇒ cdec
3.	ecd ⇒ dce
4.	ddec ⇒ e
5.	dcd ⇒ e
6.	eddce ⇒ dced
7.	dddce ⇒ ed
8.	acd ⇒ adec
9.	ca ⇒ ac
10.	ea ⇒ dec
11.	eda ⇒ ddeec
12.	aa ⇒ c
13.	bc ⇒ da
14.	ba ⇒ d
15.	eb ⇒ ddee
16.	ccb ⇒ ce
17.	ecb ⇒ ee
18.	dcb ⇒ de
19.	edb ⇒ ddedee
20.	acb ⇒ ae
	...

Collecting factors up to length 7 / frequency 2:

[2/0]	cb	8	`lf:4,ls:4,a:4`
[2/1]	ed	8	`lf:4,lp:4,rf:3,rp:1,rs:2,re:1,lprs:1,a:17`
[3/0]	dec	4	`lf:2,ls:2,rf:3,rp:1,rs:3,re:1,a:15`
[3/1]	dce	4	`lf:2,ls:2,rf:3,rp:3,rs:2,re:2,lsrp:1,a:7`
[4/0]	ddce	4	`lf:2,ls:2,a:21`
[4/1]	dddc	2	`lf:1,lp:1,a:21`
[5/0]	ddede	0	`rf:1,rp:1,a:26`
[5/1]	dedee	0	`rf:1,rs:1,a:26`
[6/0]	ddedee	0	`rf:1,rp:1,rs:1,re:1,a:26`

Considering [length 4 / frequency 0] ddce=f.

Step 5

Auxiliary generators:
1. c = aa
2. d = ba
3. e = dcd
4. f = ddce
Reduction order:
- Left-to-right recursive path with deg(c) = deg(e) = deg(f) = 0, c < e < f; deg(d) = 1; deg(a) = 2; deg(b) = 3

Rewriting system is complete. See ⟨a, b | abaaaba=aaab⟩.