Morphocompletion for #3812 ⟨a, b | abbabaaaab=a⟩

Solved by morph:2/1,2/1,2/1,6/0. (See Morphocompletion.)

Step 1

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: rulesLimit

#	Rule
1.	aaaaabbb ⇒ abbabaaa
2.	aabaaaab ⇒ ababaaaa
3.	ababaaaab ⇒ abbabaaaa
4.	abbabaaaab ⇒ a
5.	aaaaababbbab ⇒ abbabaaababa
6.	aaaaabbaaaabbb ⇒ abbabaaababaaa
7.	abbabaaababaaaa ⇒ aaaaab
8.	abbabaaabbabaaaa ⇒ aaaaabb
9.	ababaaaaaaaab ⇒ aabaaababaaaa
10.	abbabaaaaaaaab ⇒ ababaaababaaaa
11.	abbabaaabababbabaaa ⇒ aaaaababbb
	...

Collecting factors up to length 4 / frequency 3:

[2/0]	aa	60	`lf:53,lp:4,ls:3,rf:37,rp:4,rs:6,lsrp:3,lprs:3`
[2/1]	ab	47	`lf:34,lp:7,ls:6,rf:25,rp:6,rs:1,lprp:2,lsrp:4,lprs:1`
[2/2]	ba	26	`lf:26,rf:22,rs:1`
[3/0]	aaa	43	`lf:37,lp:3,ls:3,rf:23,rp:3,rs:6,lsrp:3,lprs:2`
[3/1]	aab	19	`lf:13,lp:1,ls:5,rf:8,rp:1,rs:1,lsrp:1`
[3/2]	aba	19	`lf:17,lp:2,rf:18,rp:2,rs:1`

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

Step 2

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = ab
Reduction order:
- Right-to-left recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1

Rewriting system is not complete: roundsLimit

#	Rule
1.	ab ⇒ c
2.	cbcaaac ⇒ a
3.	ccaaacb ⇒ a
4.	ccaaaccbb ⇒ cbccbcaaa
5.	ccaaacccbbc ⇒ cbccbcaacca
6.	cbcaaaa ⇒ ccaaac
7.	acaaac ⇒ ccaaaa
8.	aaaacbb ⇒ cbcaaa
9.	ccaaacacbb ⇒ cbcacbcaaa
10.	aaaaccbbb ⇒ cbcaacccbcaac
11.	aaaaccbbc ⇒ cbcaacca
12.	aaaacbcbbc ⇒ cbcaacbca
13.	cbcaacccbcaaa ⇒ aaaaccbb
14.	cbcaacbccbcaaa ⇒ aaaacbcbb
15.	cbcaaccaaac ⇒ aaaacb
16.	cbcaaccccaaac ⇒ aaaaccbba
17.	ccaaacaacbb ⇒ cbcaacbcaaa
18.	cbcaaccaaaa ⇒ aaaac
19.	ccaaaccaaac ⇒ acaaaa
20.	ccaaaaaaac ⇒ acaaccaaaa
	...

Collecting factors up to length 5 / frequency 3:

[2/0]	aa	64	`lf:56,lp:4,ls:4,rf:41,rp:5,rs:7,lsrp:3,lprs:1,a:2`
[2/1]	ac	31	`lf:24,lp:1,ls:6,rf:16,rp:2,rs:3,lsrp:2,a:2`
[2/2]	cc	28	`lf:21,lp:7,rf:11,rp:2,a:3`
[3/0]	aaa	38	`lf:30,lp:4,ls:4,rf:21,rp:5,rs:7,lsrp:3,lprs:1,a:2`
[3/1]	aac	28	`lf:22,ls:6,rf:13,rs:3,a:2`
[3/2]	caa	22	`lf:22,rf:15,a:2`
[4/0]	aaac	22	`lf:16,ls:6,rf:6,rs:2,a:2`
[4/1]	caaa	18	`lf:16,ls:2,rf:8,rs:4,a:2`
[4/2]	ccaa	18	`lf:11,lp:7,rf:3,rp:2,a:3`

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

Step 3

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = ab
2. d = ac
Reduction order:
- Right-to-left recursive path with deg(b) = deg(d) = deg(c) = 0, b < d < c; deg(a) = 1

Rewriting system is not complete: roundsLimit

#	Rule
1.	ab ⇒ c
2.	ac ⇒ d
3.	dbcaad ⇒ aa
4.	cbcaad ⇒ a
5.	daadb ⇒ ccaad
6.	dcaadb ⇒ aa
7.	ccaadb ⇒ a
8.	ccaaad ⇒ daadc
9.	dbcaaad ⇒ dcaadc
10.	cbcaaad ⇒ ccaadc
11.	aaadb ⇒ cbcadcaad
12.	adaadc ⇒ dcaaad
13.	dcaaaa ⇒ adaad
14.	ccaaaa ⇒ daad
15.	dbcaaaa ⇒ dcaad
16.	cbcaaaa ⇒ ccaad
17.	cbcadcaaad ⇒ aaadc
18.	ccaadcaad ⇒ daaaa
19.	aaaadc ⇒ dbcadcaaad
20.	adaaaa ⇒ dcaadcaad
	...

Collecting factors up to length 4 / frequency 3:

[2/0]	aa	43	`lf:36,lp:2,ls:5,rf:22,rp:3,rs:3,re:2,a:3`
[2/1]	ad	26	`lf:17,lp:2,ls:7,rf:17,rp:1,rs:9,lprs:2,a:3`
[2/2]	ca	15	`lf:15,rf:12,a:3`
[3/0]	aaa	24	`lf:17,lp:2,ls:5,rf:5,rp:1,rs:1,a:5`
[3/1]	aad	21	`lf:14,ls:7,rf:14,rs:9,a:3`
[3/2]	caa	14	`lf:14,rf:10,a:3`

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

Step 4

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = ab
2. d = ac
3. e = ad
Reduction order:
- Right-to-left recursive path with deg(b) = deg(d) = deg(c) = 0, b < d < c; deg(e) = 1; deg(a) = 2

Rewriting system is not complete: roundsLimit

#	Rule
1.	ab ⇒ c
2.	ad ⇒ e
3.	ac ⇒ d
4.	cbcae ⇒ a
5.	daeb ⇒ ccae
6.	dcaeb ⇒ dbcae
7.	ccaeb ⇒ a
8.	dbcaeb ⇒ d
9.	eaeb ⇒ dcae
10.	ecaeb ⇒ ebcae
11.	ebcaeb ⇒ e
12.	dbcaed ⇒ ae
13.	daec ⇒ ccebcaed
14.	dbcaec ⇒ e
15.	eaec ⇒ dcebcaed
16.	ebcaec ⇒ ae
17.	dbcaee ⇒ ebcaed
18.	aa ⇒ dbcae
19.	dbcaea ⇒ ebcae
20.	aebcae ⇒ ebcaea
	...

Collecting factors up to length 7 / frequency 2:

[2/0]	ae	20	`lf:17,lp:1,ls:2,rf:12,rp:2,rs:8,re:2,a:4`
[2/1]	eb	19	`lf:10,lp:2,ls:7,rf:6,rp:4,lsrp:1,a:6`
[3/0]	aeb	16	`lf:8,lp:1,ls:7,a:6`
[3/1]	cae	14	`lf:12,ls:2,rf:10,rs:6,a:4`
[4/0]	bcae	11	`lf:9,ls:2,rf:8,rs:4,a:4`
[4/1]	caeb	10	`lf:5,ls:5,a:6`
[5/0]	dbcae	10	`lf:5,lp:5,rf:2,rp:2,rs:2,re:2,a:5`
[5/1]	ebcae	6	`lf:3,lp:2,ls:1,rf:6,rp:4,rs:2,re:2,lsrp:10,a:9`
[6/0]	ebcaea	0	`rf:1,rp:1,rs:1,re:1,a:24`
[6/1]	ebcaed	0	`rf:3,rp:1,rs:3,re:1,a:18`

Considering [length 6 / frequency 0] ebcaea=f.

Step 5

Auxiliary generators:
1. c = ab
2. d = ac
3. e = ad
4. f = ebcaea
Reduction order:
- Right-to-left recursive path with deg(b) = deg(d) = deg(c) = 0, b < d < c; deg(e) = 1; deg(f) = 2; deg(a) = 3

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