Morphocompletion for #4107 ⟨a, b | bab=aaa, bbbb=1⟩

Solved by morph:3/0,10/0. (See Morphocompletion.)

Step 1

Checking up to 80 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	aaaab ⇒ baaaa
2.	bab ⇒ aaa
3.	abaab ⇒ bbaaaaaaa
4.	aaabbaaa ⇒ baab
5.	bbbaaa ⇒ ab
6.	aaabbb ⇒ ba
7.	aaabbaabaaaa ⇒ baabaaab
8.	bbbb ⇒ 1
9.	bbbaabaaaa ⇒ abaaab
10.	aaabbaabbaaaa ⇒ baabaaabb
11.	aaabbaabaaabaaaa ⇒ baabaaabaaab
12.	bbbaabbaaaa ⇒ abaaabb
13.	bbbaabaaabaaaa ⇒ abaaabaaab
14.	aaabbaabbaaba ⇒ baabaaabaaabb
15.	aaabbaabbaaabaaaa ⇒ baabbaabb
16.	aaabbaabaaabaaabaaaa ⇒ baabaaabaaabaaab
17.	bbbaabbaaba ⇒ abaaabaaabb
18.	bbbaabbaaabaaaa ⇒ abbaabb
19.	bbbaabaaabaaabaaaa ⇒ abaaabaaabaaab
20.	abaaabbaabbb ⇒ bbbaabbaaaba
21.	aaabbaabbbaaba ⇒ baabbaabbb
22.	aaabbaabbaabbaaaa ⇒ baabaaabbaabb
23.	aaabbaabbaaabaaabaaaa ⇒ baabbaabbaaab
24.	aaabbaabaaabbaaba ⇒ baabaaabaaabaaabb
25.	aaabbaabaaabaaabaaabaaaa ⇒ baabaaabaaabaaabaaab
26.	bbbaabbbaaba ⇒ abbaabbb
27.	bbbaabbaabbaaaa ⇒ abaaabbaabb
28.	bbbaabbaaabaaabaaaa ⇒ abbaabbaaab
29.	bbbaabaaabbaaba ⇒ abaaabaaabaaabb
30.	bbbaabaaabaaabaaabaaaa ⇒ abaaabaaabaaabaaab
31.	abbaabbaabbb ⇒ bbbaabbaaabaaaba
32.	aaabbaabbaabbaab ⇒ baabaaabaaabbaabbaaa
33.	aaabbaabbaabbaaabaaaa ⇒ baabaaabbaabbaaab
34.	aaabbaabbaaabbaaba ⇒ baabbaabbaaabb
35.	aaabbaabbaaabaaabaaabaaaa ⇒ baabbaabbaaabaaab
36.	aaabbaabaaabaaabbaaba ⇒ baabaaabaaabaaabaaabb
37.	bbbaabbaabbaab ⇒ abaaabaaabbaabbaaa
38.	bbbaabbaabbaaabaaaa ⇒ abaaabbaabbaaab
39.	bbbaabbaaabbaaba ⇒ abbaabbaaabb
40.	bbbaabbaaabaaabaaabaaaa ⇒ abbaabbaaabaaab
41.	bbbaabaaabaaabbaaba ⇒ abaaabaaabaaabaaabb
42.	bbbaabaaabaaabaaabaaabaaaa ⇒ abaaabaaabaaabaaabaaab
43.	abbaabbbaabbb ⇒ bbbaabbbaabba
44.	abaaabaaabbaabbaaabb ⇒ bbaaabbaabbaaabaaaba
45.	aabbbaabbaaabaaabaaaba ⇒ baabaaabbaabbaaabb
46.	aaabbaabbbaabbaab ⇒ baabbaabbbaabbaaa
47.	aaabbaabbbaabbaaaba ⇒ baabbaaabbaabbb
48.	aaabbaabbaabbaaabaaabaaaa ⇒ baabaaabbaabbaaabaaab
49.	aaabbaabbaaabaaabbaaba ⇒ baabbaabbaaabaaabb
50.	aaabbaabaaabbaabbaab ⇒ baabaaabaaabaaabbaabbaaa
51.	bbbaabbbaabbaab ⇒ abbaabbbaabbaaa
52.	bbbaabbbaabbaaaba ⇒ abbaaabbaabbb
53.	bbbaabbaabbbaaba ⇒ abaaabbaabbaaabb
54.	bbbaabbaabbaaabaaabaaaa ⇒ abaaabbaabbaaabaaab
55.	bbbaabbaaabaaabbaaba ⇒ abbaabbaaabaaabb
56.	bbbaabbaaabaaabaaabaaabaaaa ⇒ abbaabbaaabaaabaaab
57.	bbbaabaaabbaabbaab ⇒ abaaabaaabaaabbaabbaaa
58.	bbbaabaaabaaabaaabbaaba ⇒ abaaabaaabaaabaaabaaabb
59.	abbaabbaaabbaabbb ⇒ bbbaabbaaabbaabba
60.	abbaabaaabbaabbaaabb ⇒ bbbaabbaabbaaabaaaba
61.	abaaabbaabbaabbaaabb ⇒ bbaaabbaabbaaabaaabaaaba
62.	aaabbaabbaabbaaabbaaba ⇒ baabaaabbaabbaaabaaabb
63.	aaabbaabbaaabbaabbaab ⇒ baabbaabbaaabbaabbaaa
64.	bbbaabbaabbaaabbaaba ⇒ abaaabbaabbaaabaaabb
65.	bbbaabbaaabbaabbaab ⇒ abbaabbaaabbaabbaaa
66.	bbbaabbaaabaaabaaabbaaba ⇒ abbaabbaaabaaabaaabb
67.	abbaabbbaabbaabbb ⇒ bbbaabbaaabbaabbaaaba
68.	abbaabbaabbaabbaaabb ⇒ bbbaabbaabbaaabaaabaaaba
69.	aabbbaabbbaabbbaab ⇒ baabbbaabbbaabbbaa
70.	aabbbaabbbaabbaaabba ⇒ baabbbaabbbaabbb
71.	aabbbaabbaaabbaabbaaaba ⇒ baabbaabbbaabbaaabb
72.	aaabbaabbbaabbaaabbaab ⇒ baabbaaabbaabbbaabbaaa
73.	bbbaabbbaabbbaabba ⇒ abbbaabbbaabbb
74.	bbbaabbbaabbaaabbaab ⇒ abbaaabbaabbbaabbaaa
75.	bbbaabbaabbbaabbaab ⇒ abaaabbaabbaaabbaabbaaa
76.	bbbaabbaaabbaabbaaabaaaba ⇒ abbaaabaaabbaabbaaabb
77.	bbbaabbaaabaaabbaabbaab ⇒ abbaabbaaabaaabbaabbaaa
78.	bbbaabbaabbbaabbaaabaaaba ⇒ abbaabbaaabbaabbaaabb
79.	abbbaabbbaabbbaabbb ⇒ bbbaabbbaabbbaabbba
80.	abbaabbbaabbaaabbaabbb ⇒ bbbaabbaaabbaabbbaabba
	...

Collecting factors up to length 7 / frequency 2:

[2/0]	bb	28571	`lf:278,lp:36,ls:13,rf:201,rp:12,rs:31,lsrp:11,lprs:17,a:1`
[2/1]	ba	11629	`lf:291,lp:1,ls:25,rf:268,rp:31,rs:12,re:1,lsrp:11`
[3/0]	bbb	10163	`lf:71,lp:36,ls:9,rf:32,rp:9,rs:6,lsrp:7,lprs:3,a:1`
[3/1]	aba	9247	`lf:96,lp:4,ls:23,rf:99,rp:18,rs:7,lsrp:6,lprs:3,a:7`
[4/0]	aaaa	10057	`lf:25,lp:1,ls:24,rf:5,rs:2,lprs:10,a:2`
[4/1]	aaab	8297	`lf:117,lp:26,ls:1,rf:135,rs:18,lprs:8,a:2`
[5/0]	aaabb	7160	`lf:58,lp:26,ls:4,rf:51,rs:21,lprs:7,a:3`
[5/1]	baaba	4081	`lf:34,ls:17,rf:15,rp:15,lsrp:4,a:8`
[6/0]	abbaab	3172	`lf:88,lp:7,ls:12,rf:53,rp:12,lsrp:3,a:9`
[6/1]	aabbaa	215	`lf:124,rf:91,a:5`

Considering [length 3 / frequency 0] bbb=c.

Step 2

Checking up to 80 rules for overlaps.

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

Rewriting system is not complete: wordLimit

#	Rule
1.	aaaac ⇒ caaaa
2.	caaac ⇒ a
3.	acc ⇒ caacaaa
4.	aaacaac ⇒ cca
5.	ccca ⇒ aaac
6.	caacaacaaa ⇒ ac
7.	aaacacaacaaa ⇒ ccac
8.	cccc ⇒ 1
9.	caacacaacaaaaaaa ⇒ acac
10.	caacaacacaaaa ⇒ acaac
11.	acacaacaac ⇒ caacaacaca
12.	acaacaacaac ⇒ caacaacaaca
13.	aaacacacaacaaaaaaa ⇒ ccacac
14.	aaacacaacacaaaa ⇒ ccacaac
15.	caacacacaacaaaaaaaaaaa ⇒ acacac
16.	caacacaacacaaaaaaaa ⇒ acacaac
17.	caacaacacacaaaa ⇒ acaacac
18.	caacaacacaacaaaa ⇒ acaacaac
19.	caacaacaacaca ⇒ aacaacaac
20.	acacaacacaacaaa ⇒ caacaacacac
21.	acaacaacacaacaaa ⇒ caacaacaacac
22.	aacaacaacacaca ⇒ ccacaacaac
23.	aacaacaacacaaca ⇒ ccaacaacaac
24.	aaacacacacaacaaaaaaaaaaa ⇒ ccacacac
25.	aaacacacaacacaaaaaaaa ⇒ ccacacaac
26.	aaacacaacacacaaaa ⇒ ccacaacac
27.	caacacacacaacaaaaaaaaaaaaaaa ⇒ acacacac
28.	caacacacaacacaaaaaaaaaaaa ⇒ acacacaac
29.	caacacaacacacaaaaaaaa ⇒ acacaacac
30.	caacaacacacacaaaa ⇒ acaacacac
31.	caacaacacacaacaaaa ⇒ acaacacaac
32.	caacaacacaacacaaaa ⇒ acaacaacac
33.	acacacaacacaac ⇒ caacacaacacaca
34.	acacaacacacaacaaaaaaa ⇒ caacaacacacac
35.	acacaacacaacacaaaa ⇒ caacaacacacaac
36.	aaacacacacaacacaaaaaaaaaaaa ⇒ ccacacacaac
37.	aaacacacaacacacaaaaaaaa ⇒ ccacacaacac
38.	aaacacaacacacacaaaa ⇒ ccacaacacac
39.	aaacacaacacacaacaaaa ⇒ ccacaacacaac
40.	cacaacaacacacaca ⇒ acacaacacaac
41.	cacaacaacacaacaca ⇒ acaacaacacaac
42.	caacacacaacacacaaaaaaaaaaaa ⇒ acacacaacac
43.	caacacaacacacacaaaaaaaa ⇒ acacaacacac
44.	caacaacacacacacaaaa ⇒ acaacacacac
45.	caacaacacacacaacaaaa ⇒ acaacacacaac
46.	caacaacacacaacacaaaa ⇒ acaacacaacac
47.	caacaacacaacacaca ⇒ aacacaacacaac
48.	acacacaacacacaacaaa ⇒ caacacaacacacac
49.	acacaacacaacacacaaaa ⇒ caacaacacacaacac
50.	acacaacacaacacaac ⇒ caacacaacacaacaca
51.	acaacaacacaacacaaca ⇒ ccacaacaacacaac
52.	aacaacacaacacacacaaaaa ⇒ ccacacaacacaac
53.	aaacacacaacacacacaaaaaaaa ⇒ ccacacaacacac
54.	aaacacaacacacacacaaaa ⇒ ccacaacacacac
55.	aaacacaacacacacaacaaaa ⇒ ccacaacacacaac
56.	aaacacaacacacaacacaaaa ⇒ ccacaacacaacac
57.	aaacacaacacaacacaca ⇒ ccaacacaacacaac
58.	cacaacaacacacaacaca ⇒ acaacacaacacaac
59.	caacaacacacacacacaaaa ⇒ acaacacacacac
60.	caacaacacacacacaacaaaa ⇒ acaacacacacaac
61.	caacaacacacacaacacaaaa ⇒ acaacacacaacac
62.	caacaacacacaacacacaaaa ⇒ acaacacaacacac
63.	caacaacacaacacaacaca ⇒ aacaacacaacacaac
64.	aacaacacaacacacacaca ⇒ ccacacaacacacaac
65.	b ⇒ ccc
	...

Collecting factors up to length 14 / frequency 1:

[2/0]	ac	7673	`lf:327,lp:12,ls:7,rf:246,rp:25,rs:55,re:1,lprs:7,a:10`
[3/0]	aca	7560	`lf:319,lp:11,ls:11,rf:191,rp:24,rs:4,lsrp:3,lprs:4,a:14`
[4/0]	caac	14288	`lf:126,lp:25,ls:5,rf:96,rp:11,rs:25,lsrp:4,lprs:10,a:14`
[5/0]	acaca	4268	`lf:164,lp:8,ls:9,rf:76,rp:8,rs:3,lsrp:1,lprs:3,a:20`
[6/0]	cacaac	3139	`lf:65,lp:3,ls:2,rf:49,rs:20,lprs:3,a:20`
[7/0]	caacaac	4075	`lf:28,lp:17,ls:2,rf:17,rp:7,rs:4,lsrp:2,lprs:2,a:19`
[8/0]	acaacaca	1119	`lf:66,ls:4,rf:37,rp:10,rs:2,lsrp:1,a:22`
[9/0]	caacacaac	2062	`lf:23,lp:4,ls:2,rf:20,rp:3,rs:10,lsrp:2,a:21`
[10/0]	caacaacaac	10010	`lf:2,lp:1,ls:1,rf:3,rp:2,rs:1,lsrp:10,a:39`
[11/0]	aacacaacaca	36	`lf:23,ls:2,rf:9,rp:1,rs:1,a:24`
[12/0]	caacacaacaca	32	`lf:15,lp:3,ls:2,rf:8,rp:3,rs:1,a:25`
[13/0]	acaacaacacaac	1012	`lf:4,lp:2,rf:2,rp:1,rs:2,re:1,lprs:1,a:40`

Considering [length 10 / frequency 0] caacaacaac=d.

Step 3

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

Rewriting system is complete. See ⟨a, b | bab=aaa, bbbb=1⟩.