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:

Length 2:	[2/0] aa, [2/1] bb
Length 3:	[3/0] bbb, [3/1] bab
Length 4:	[4/0] bbbb, [4/1] baab
Length 5:	[5/0] bbbba, [5/1] bbbbb
Length 6:	[6/0] bbbbbb, [6/1] bbbbba

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:

Length 2:	[2/0] bb
Length 3:	[3/0] bcb
Length 4:	[4/0] bbbb
Length 5:	[5/0] bbbbb
Length 6:	[6/0] bbbbbb
Length 7:	[7/0] bcbbbcb
Length 8:	[8/0] bcbbbbcb
Length 9:	[9/0] cbbbbcbbb
Length 10:	[10/0] bbbbcbbbbc
Length 11:	[11/0] cbbbbcbbbbc
Length 12:	[12/0] cbbbbcbbbbcb
Length 13:	[13/0] bbbcbbcbbbbbb

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⟩.