Morphocompletion for #5246 ⟨a, b | aabbbaa=baab⟩

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

Step 1

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: rulesLimit

#	Rule
1.	aabbbaa ⇒ baab
2.	baabbbbaa ⇒ aabbbbaab
3.	baababbbaa ⇒ aabbbabaab
4.	aaaabbbbaabbb ⇒ baabbbbbaa
5.	aabbbbaabbbbbaa ⇒ bbaabbbbbaab
6.	aabbbbaabbbbbbaa ⇒ bbbaabbbbbaab
7.	baabbbbbaaaa ⇒ aaaabbbbbaab
8.	baabbbbbaabaa ⇒ aabaabbbbbaab
9.	baabbbbbaabbaa ⇒ aabbaabbbbbaab
10.	aabbaabbbabaab ⇒ baabbabbbaa
	...

Collecting factors up to length 4 / frequency 3:

[2/0]	bb	44	`lf:43,ls:1,rf:36,rp:2`
[2/1]	aa	42	`lf:29,lp:5,ls:8,rf:23,rp:5,rs:2,lsrp:5,lprs:2`
[2/2]	ba	27	`lf:22,lp:5,rf:18,rp:3`
[3/0]	baa	32	`lf:20,lp:5,ls:7,rf:16,rp:3,rs:2,lsrp:1`
[3/1]	bbb	29	`lf:28,ls:1,rf:23,rp:1`
[3/2]	aab	22	`lf:17,lp:4,ls:1,rf:19,rp:4,rs:8,lprs:3`

Considering [length 2 / frequency 1] 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(b) = deg(c) = 0, b < c; deg(a) = 1

Rewriting system is not complete: pendingRulesLimit

#	Rule
1.	cbbbc ⇒ bcb
2.	cbbbbcb ⇒ bcbbbbc
3.	ccbbbbbcb ⇒ bcbbbbbcc
4.	bbbcbbbbcc ⇒ cbbbbbcb
5.	cbcbbbbbcb ⇒ bcbbbbbcbc
6.	cbbcbbbbbcb ⇒ bcbbbbbcbbc
7.	bcbbbbbccbbc ⇒ ccbbbbbbcb
8.	cbbbbbcbbbbc ⇒ bcbbbbbcbb
9.	bcbbbbbcbcbbc ⇒ cbcbbbbbbcb
10.	cbbbbbbcbbbbc ⇒ bcbbbbbcbbb
11.	ca ⇒ ac
12.	cbbbac ⇒ bcba
13.	cbbbabcb ⇒ bcbabbbc
14.	cbbbabbcb ⇒ bcbabbbcbbc
15.	cbbbabbbcb ⇒ bcbabbbcbbcbbc
16.	cbbbbbcba ⇒ bbbcbbbbacc
17.	aa ⇒ c
	...

Collecting factors up to length 5 / frequency 3:

[2/0]	bb	64	`lf:63,lp:1,rf:55,rp:1,rs:2,a:2`
[2/1]	cb	48	`lf:30,lp:11,ls:7,rf:26,rp:2,rs:4,lprs:1,a:2`
[2/2]	bc	31	`lf:24,lp:2,ls:5,rf:30,rp:11,rs:6,lsrp:3,a:2`
[3/0]	bbb	41	`lf:40,lp:1,rf:35,rp:1,rs:1,a:2`
[3/1]	cbb	30	`lf:20,lp:10,rf:16,rp:1,rs:1,lprs:1,a:2`
[3/2]	bcb	26	`lf:17,lp:2,ls:7,rf:23,rp:11,rs:4,re:1,lsrp:7,lprs:2,a:2`
[4/0]	cbbb	26	`lf:17,lp:9,rf:11,rp:1,rs:1,lprs:1,a:2`
[4/1]	bbbb	21	`lf:21,rf:20,a:4`
[4/2]	bbbc	19	`lf:15,lp:1,ls:3,rf:13,rp:1,rs:2,a:2`

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

Step 3

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	cb ⇒ d
2.	dbbd ⇒ bdb
3.	dbbc ⇒ bd
4.	bdbbbc ⇒ dbbbd
5.	dbbbdb ⇒ bdbbbd
6.	cdbbbd ⇒ ddbbbc
7.	dbdbbbd ⇒ bdbbbbc
8.	bbdbbbdd ⇒ dbbbbdb
9.	bbdbbbdc ⇒ dbbbbd
10.	bdbbbbdc ⇒ ddbbbbd
11.	bdbbbbcc ⇒ cdbbbbd
12.	ddbbbbdb ⇒ bdbbbbdd
13.	cdbbbbdb ⇒ bdbbbbcd
14.	cddbbbbd ⇒ ddbbbbdc
15.	ca ⇒ ac
16.	dbbad ⇒ bdab
17.	dbbac ⇒ bda
18.	dbbabd ⇒ bdabbbc
19.	dbbbda ⇒ bdbbbac
20.	aa ⇒ c
	...

Collecting factors up to length 4 / frequency 3:

[2/0]	bb	38	`lf:36,lp:2,rf:34,a:3`
[2/1]	db	32	`lf:21,lp:8,ls:3,rf:14,rp:3,rs:2,lprs:1,a:3`
[2/2]	bd	26	`lf:18,lp:3,ls:5,rf:18,rp:10,rs:6,re:1,lsrp:3,lprs:3,a:3`
[3/0]	dbb	24	`lf:17,lp:7,rf:12,rp:3,a:3`
[3/1]	bbd	19	`lf:13,lp:2,ls:4,rf:8,rs:5,lprs:1,a:5`
[3/2]	bbb	17	`lf:17,rf:21,a:7`

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

Step 4

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	db ⇒ e
2.	cb ⇒ d
3.	ebd ⇒ be
4.	ebc ⇒ bd
5.	ebe ⇒ beb
6.	bebbd ⇒ ebbe
7.	bebbc ⇒ ebbd
8.	cebbd ⇒ debbc
9.	cebbe ⇒ debbd
10.	ebbeb ⇒ bebbe
11.	eebbd ⇒ debbe
12.	eebbc ⇒ debbd
13.	bebbbd ⇒ eebbe
14.	bebbbc ⇒ debbe
15.	bebbed ⇒ ebbbe
16.	ca ⇒ ac
17.	ebad ⇒ bdab
18.	ebac ⇒ bda
19.	ebae ⇒ bdabb
20.	aa ⇒ c
	...

Collecting factors up to length 7 / frequency 2:

[2/0]	eb	25	`lf:17,lp:7,ls:1,rf:11,rp:3,rs:1,lprs:10,a:4`
[2/1]	be	16	`lf:9,lp:5,ls:2,rf:9,rp:3,rs:7,re:1,lsrp:10,lprs:4,a:6`
[3/0]	beb	12	`lf:6,lp:5,ls:1,rf:2,rp:2,rs:1,re:1,lsrp:1,a:8`
[3/1]	ebb	11	`lf:10,lp:1,rf:10,rp:3,a:9`
[4/0]	bebb	10	`lf:5,lp:5,rf:1,rp:1,a:9`
[4/1]	ebbd	6	`lf:3,ls:3,rf:3,rp:1,rs:3,re:1,a:9`
[5/0]	bebbb	4	`lf:2,lp:2,a:17`
[5/1]	ebbed	2	`lf:1,ls:1,a:29`

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

Step 5

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

Rewriting system is complete. See ⟨a, b | aabbbaa=baab⟩.