Morphocompletion for #22860 ⟨a, b | aaa=1, bbbbb=aba⟩

Solved by morph:2/0,12/0. (See Morphocompletion.)

Step 1

Checking up to 80 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	bbbbbba ⇒ abbbbbb
2.	aabbbbb ⇒ ba
3.	aba ⇒ bbbbb
4.	abba ⇒ bbbbbabbbbb
5.	babbba ⇒ abbbbbabbbbbbbbbbb
6.	bbbbbaa ⇒ ab
7.	bbbbbabbbbbabbbbb ⇒ abbba
8.	aaa ⇒ 1
9.	aabbbabbbbbb ⇒ babbbba
10.	aabbbbabbbbbb ⇒ babbbbba
11.	babbbbaa ⇒ aabbbbab
12.	bbbbbabbbbabbbbbabbbbbbbbbbbbbbbbb ⇒ abbbabbbba
13.	bbbbbabbbbbabbbbabbbbbb ⇒ abbbabbbbba
14.	aabbbabbbbabbbbbb ⇒ babbbbabbbba
15.	aabbbabbbbbabbbbbb ⇒ babbbbabbbbba
16.	aabbbbabbbbabbbbbb ⇒ babbbbbabbbba
17.	aabbbbabbbbbabbbbbb ⇒ babbbbbabbbbba
18.	bbbbbabbbbabbbbbabbbbabbbbbbbbbbbbbbbbbb ⇒ abbbabbbbabbbbba
19.	bbbbbabbbbbabbbbabbbbabbbbbb ⇒ abbbabbbbbabbbba
20.	bbbbbabbbbbabbbbabbbbbabbbbbb ⇒ abbbabbbbbabbbbba
21.	aabbbaabbbab ⇒ babbbbabbbbbabbbbba
22.	aabbbabbbbabbbbabbbbbb ⇒ babbbbabbbbabbbba
23.	aabbbabbbbabbbbbabbbbbb ⇒ babbbbabbbbabbbbba
24.	aabbbabbbbbabbbbabbbbbb ⇒ babbbbabbbbbabbbba
25.	aabbbbaabbbab ⇒ baabbbaa
26.	aabbbbaabbbbab ⇒ baabbbbaa
27.	aabbbbabbbbabbbbabbbbbb ⇒ babbbbbabbbbabbbba
28.	aabbbbabbbbabbbbbabbbbbb ⇒ babbbbbabbbbabbbbba
29.	aabbbbabbbbbabbbbabbbbbb ⇒ babbbbbabbbbbabbbba
30.	babbbbabbbbabbbbbabbbbba ⇒ abbbbbabbbbbabbbbabbbbab
31.	bbbbaabbbbaabbba ⇒ abbbaabbbbaabbbb
32.	bbbbaabbbbaabbbba ⇒ abbbbaabbbbaabbbb
33.	bbbbaabbbbabbbbabbbbab ⇒ abbbabbbbabbbbbabbbbba
34.	bbbbaabbbbabbbbbabbbbab ⇒ abbbaabbbaa
35.	bbbbaabbbbabbbbbabbbbbab ⇒ abbbaabbbbaa
36.	bbbbbabbbbbabbbbabbbbabbbbabbbbbb ⇒ abbbabbbbbabbbbabbbba
37.	bbbbbabbbbbabbbbabbbbabbbbbabbbbbb ⇒ abbbabbbbbabbbbabbbbba
38.	bbbbbabbbbbabbbbabbbbbabbbbabbbbbb ⇒ abbbabbbbbabbbbbabbbba
39.	aabbbaabbbbabbbbab ⇒ babbbbbabbbbabbbbbabbbbba
40.	aabbbabbbbabbbbabbbbabbbbbb ⇒ babbbbabbbbabbbbabbbba
41.	aabbbabbbbabbbbabbbbbabbbbbb ⇒ babbbbabbbbabbbbabbbbba
42.	aabbbabbbbabbbbbabbbbabbbbbb ⇒ babbbbabbbbabbbbbabbbba
43.	aabbbabbbbbabbbbabbbbabbbbbb ⇒ babbbbabbbbbabbbbabbbba
44.	aabbbabbbbbabbbbabbbbbabbbbbb ⇒ babbbbabbbbbabbbbabbbbba
45.	aabbbbabbbbabbbbabbbbabbbbbb ⇒ babbbbbabbbbabbbbabbbba
46.	aabbbbabbbbabbbbabbbbbabbbbbb ⇒ babbbbbabbbbabbbbabbbbba
47.	aabbbbabbbbabbbbbabbbbabbbbbb ⇒ babbbbbabbbbabbbbbabbbba
48.	aabbbbabbbbbabbbbabbbbabbbbbb ⇒ babbbbbabbbbbabbbbabbbba
49.	aabbbbabbbbbabbbbabbbbbabbbbbb ⇒ babbbbbabbbbbabbbbabbbbba
50.	baabbbaabbbaa ⇒ aabbbbabbbbbabbbbbabbbbab
51.	baabbbaabbbbaa ⇒ aabbbbaabbbaab
52.	baabbbabbbbabbbbbabbbbba ⇒ aabbbbabbbbbabbbbabbbbab
53.	baabbbbaabbbbaa ⇒ aabbbbaabbbbaab
54.	babbbbabbbbbabbbbabbbbbabbbbba ⇒ abbbbbabbbbbabbbbabbbbbabbbbab
55.	bbbbaabbbbabbbbabbbbbabbbbab ⇒ abbbabbbbbabbbbabbbbbabbbbba
56.	aabbbaabbbaabbba ⇒ babbbbabbbbbabbbbbabbbbabbbbbabbbbb
57.	aabbbaabbbbabbbbbabbbbab ⇒ babbbbbabbbbbabbbbabbbbbabbbbba
58.	aabbbabbbbabbbbabbbbabbbbabbbbbb ⇒ babbbbabbbbabbbbabbbbabbbba
59.	aabbbabbbbabbbbabbbbabbbbbabbbbbb ⇒ babbbbabbbbabbbbabbbbabbbbba
60.	aabbbabbbbabbbbabbbbbabbbbabbbbbb ⇒ babbbbabbbbabbbbabbbbbabbbba
61.	aabbbabbbbabbbbbabbbbabbbbabbbbbb ⇒ babbbbabbbbabbbbbabbbbabbbba
62.	aabbbabbbbabbbbbabbbbabbbbbabbbbbb ⇒ babbbbabbbbabbbbbabbbbabbbbba
63.	aabbbabbbbbabbbbabbbbabbbbabbbbbb ⇒ babbbbabbbbbabbbbabbbbabbbba
64.	aabbbabbbbbabbbbabbbbabbbbbabbbbbb ⇒ babbbbabbbbbabbbbabbbbabbbbba
65.	aabbbabbbbbabbbbabbbbbabbbbabbbbbb ⇒ babbbbabbbbbabbbbabbbbbabbbba
66.	aabbbbaabbbaabbba ⇒ baabbbaabbbbabbbbbabbbbb
67.	aabbbbaabbbaabbbbab ⇒ baabbbbaabbbaa
68.	aabbbbabbbbabbbbabbbbabbbbabbbbbb ⇒ babbbbbabbbbabbbbabbbbabbbba
69.	aabbbbabbbbabbbbabbbbabbbbbabbbbbb ⇒ babbbbbabbbbabbbbabbbbabbbbba
70.	aabbbbabbbbabbbbabbbbbabbbbabbbbbb ⇒ babbbbbabbbbabbbbabbbbbabbbba
71.	aabbbbabbbbabbbbbabbbbabbbbabbbbbb ⇒ babbbbbabbbbabbbbbabbbbabbbba
72.	baabbbabbbbbabbbbabbbbbabbbbba ⇒ aabbbbabbbbbabbbbabbbbbabbbbab
73.	bbbaabbbbaabbbaabbbba ⇒ abbbaabbbbaabbbaabbbb
74.	bbbbaabbbaabbbbabbbbbabbbba ⇒ abbbaabbbaabbbbabbbbbabbbbb
75.	bbbbaabbbaabbbbabbbbbabbbbbab ⇒ abbbaabbbbaabbbaa
76.	aabbbaabbbbabbbbbabbbbbabbbbab ⇒ baabbbaabbbbabbbbbabbbbba
	...

Collecting factors up to length 7 / frequency 2:

[2/0]	aa	7186	`lf:86,lp:45,ls:6,rf:37,rp:6,rs:6,lsrp:4,lprs:3`
[2/1]	bb	6933	`lf:1038,lp:20,ls:44,rf:819,rp:2,rs:10,lprs:5,a:1`
[3/0]	bab	6473	`lf:212,lp:4,ls:12,rf:201,rp:38,rs:6,lsrp:3,lprs:3,a:5`
[3/1]	bbb	6385	`lf:738,lp:20,ls:44,rf:571,rp:2,rs:10,lprs:5,a:1`
[4/0]	bbbb	4837	`lf:439,lp:19,ls:44,rf:323,rp:2,rs:10,lprs:4,a:1`
[4/1]	baab	2072	`lf:35,lp:5,rf:25,rp:5,rs:2,lprs:2,a:15`
[5/0]	bbbba	2489	`lf:213,lp:8,ls:8,rf:212,rs:48,lprs:2,a:3`
[5/1]	bbbbb	1348	`lf:182,lp:11,ls:44,rf:101,rp:2,rs:7,re:1,lprs:1,a:1`
[6/0]	bbbbbb	10118	`lf:66,lp:1,ls:42,rf:7,rs:2,lprs:10,a:4`
[6/1]	bbbbba	4198	`lf:72,lp:10,ls:5,rf:87,rp:1,rs:23,lprs:4,a:3`

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

Step 2

Checking up to 80 rules for overlaps.

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

Rewriting system is not complete: wordLimit

#	Rule
1.	bbbbbbc ⇒ cbbbbbb
2.	ccb ⇒ bbbbbc
3.	cbbbbcbbbbb ⇒ bc
4.	cbbbbbc ⇒ b
5.	bcc ⇒ cbbbbb
6.	bcbc ⇒ cbbbcbbbbbbbbbbb
7.	bbbbbcbbbcbbbbb ⇒ cbc
8.	bbbbbcbbbbc ⇒ cb
9.	ccc ⇒ 1
10.	cbbbbcbbcbbbbbb ⇒ bcbbbc
11.	cbbbbcbbbcbbbbbb ⇒ bcbbbbc
12.	bcbbcbbbbc ⇒ cbbbbcbbcb
13.	bcbbbcbbbbc ⇒ cbbbbcbbbcb
14.	bcbbbbcbbbbc ⇒ cbbbbcbbbbcb
15.	bbbbbcbbbcbbcbbbbbb ⇒ cbcbbbc
16.	cbbbbcbbcbbcbbbbbb ⇒ bcbbbcbbc
17.	cbbbbcbbbbcbbbcb ⇒ bbbbcbbbbc
18.	a ⇒ cc
	...

Collecting factors up to length 14 / frequency 1:

[2/0]	bb	1168	`lf:97,lp:4,ls:6,rf:56,rp:2,rs:3,lprs:1,a:8`
[3/0]	bcb	3048	`lf:24,lp:4,ls:1,rf:13,rp:3,rs:3,lprs:3,a:12`
[4/0]	bbbb	1075	`lf:38,lp:4,ls:6,rf:22,rp:2,rs:3,lprs:1,a:8`
[5/0]	bbbbb	1041	`lf:16,lp:4,ls:6,rf:11,rp:1,rs:3,lprs:1,a:8`
[6/0]	bbbbbb	10019	`lf:5,lp:1,ls:4,rf:7,rs:2,lprs:10,a:14`
[7/0]	bcbbbcb	1011	`lf:5,lp:1,ls:1,rf:2,rp:1,rs:1,lprs:1,a:16`
[8/0]	bcbbbbcb	1005	`lf:2,lp:1,rf:1,rs:1,lprs:1,a:20`
[9/0]	cbbbbcbbb	12	`lf:5,lp:3,rf:2,rp:2,a:15`
[10/0]	bbbbcbbbbc	10	`lf:3,ls:2,rf:2,rp:1,rs:1,re:1,a:12`
[11/0]	cbbbbcbbbbc	10006	`lf:2,lp:1,ls:1,rf:1,rp:1,lsrp:10,a:20`
[12/0]	cbbbbcbbbbcb	6	`lf:1,lp:1,rf:1,rp:1,rs:1,re:1,a:20`
[13/0]	bbbcbbcbbbbbb	4	`lf:2,ls:2,a:22`

Considering [length 12 / frequency 0] cbbbbcbbbbcb=d.

Step 3

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

Rewriting system is complete. See ⟨a, b | aaa=1, bbbbb=aba⟩.