Morphocompletion for #21749 ⟨a, b | aaa=1, abbbbba=b⟩

Solved by morph:3/0,7/0. (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.	aab ⇒ bbbbba
3.	abbbbabbbbb ⇒ ba
4.	abbbbba ⇒ b
5.	baa ⇒ abbbbb
6.	baba ⇒ abbbabbbbbbbbbbb
7.	bbbbbabbbabbbbb ⇒ aba
8.	bbbbbabbbba ⇒ ab
9.	aaa ⇒ 1
10.	abbbabbbabbbbbbbbbbbbbbbbb ⇒ babba
11.	abbbbabbabbbbbb ⇒ babbba
12.	abbbbabbbabbbbbb ⇒ babbbba
13.	babbabbbba ⇒ abbbbabbab
14.	babbbabbbba ⇒ abbbbabbbab
15.	babbbbabbbba ⇒ abbbbabbbbab
16.	bbbbbabbabbbabbbbbbbbbbbbbbbbb ⇒ ababba
17.	bbbbbabbbabbabbbbbb ⇒ ababbba
18.	bbbbbabbbabbbabbbbbb ⇒ ababbbba
19.	abbbabbbabbabbbbbbbbbbbbbbbbbb ⇒ babbabbba
20.	abbbbabbabbabbbbbb ⇒ babbbabba
21.	abbbbabbabbbabbbbbb ⇒ babbbabbba
22.	abbbbabbbabbabbbbbb ⇒ babbbbabba
23.	abbbbabbbabbbabbbbbb ⇒ babbbbabbba
24.	abbbbabbbbabba ⇒ bbabbbbabbbabbbbb
25.	abbbbabbbbabbba ⇒ bbbabbbbabbbabbbbb
26.	babbabbbabbbabbbbbbbbbbb ⇒ abbbbabbabba
27.	babbbabbbabbbabbbbbbbbbbb ⇒ abbbbabbbabba
28.	bbbbabbbbabbbabba ⇒ ababbbbabbbabbbbb
29.	bbbbabbbbabbbabbba ⇒ abbabbbbabbbabbbbb
30.	bbbbbabbabbbabbabbbbbbbbbbbbbbbbbb ⇒ ababbabbba
31.	bbbbbabbbabbabbabbbbbb ⇒ ababbbabba
32.	bbbbbabbbabbabbbabbbbbb ⇒ ababbbabbba
33.	bbbbbabbbabbbabbabbbbbb ⇒ ababbbbabba
34.	bbbbbabbbabbbabbbabbbbbb ⇒ ababbbbabbba
35.	abbbabbbbabbabba ⇒ babbbabbbabbbabbbbb
36.	abbbabbbbabbbabba ⇒ babbbbabbbabbbabbbbb
37.	abbbabbbbabbbabbba ⇒ bbabbbbabbbabbbabbbbb
38.	abbbbabbabbabbabbbbbb ⇒ babbbabbabba
39.	abbbbabbabbabbbabbbbbb ⇒ babbbabbabbba
40.	abbbbabbabbbabbabbbbbb ⇒ babbbabbbabba
41.	abbbbabbabbbabbbabbbbbb ⇒ babbbabbbabbba
42.	abbbbabbbabbabba ⇒ bbabbabbbabbbabbbbb
43.	abbbbabbbabbabbbabbbbbb ⇒ babbbbabbabbba
44.	abbbbabbbabbbabba ⇒ bbabbbabbbabbbabbbbb
45.	abbbbabbbabbbabbbabbbbbb ⇒ babbbbabbbabbba
46.	babbabbabbbabbbabbbbb ⇒ abbbabbbabbabbabbbbbb
47.	babbabbbabbbabbabbbbbbbbbbbb ⇒ abbbbabbabbabbba
48.	babbabbbabbbabbba ⇒ abbbabbbabbbabbab
49.	bbbabbbbabbbabbbabbba ⇒ ababbbbabbbabbbabbbbb
50.	bbbbabbabbabbbabbba ⇒ bbbabbbabbbabbabbab
51.	bbbbabbbbabbabbbabba ⇒ ababbbabbbabbbabbbbb
52.	bbbbbabbbabbabbabbabbbbbb ⇒ ababbbabbabba
53.	bbbbbabbbabbabbabbbabbbbbb ⇒ ababbbabbabbba
54.	bbbbbabbbabbabbbabbabbbbbb ⇒ ababbbabbbabba
55.	bbbbbabbbabbabbbabbbabbbbbb ⇒ ababbbabbbabbba
56.	bbbbbabbbabbbabbabba ⇒ abbabbabbbabbbabbbbb
57.	bbbbbabbbabbbabbabbbabbbbbb ⇒ ababbbbabbabbba
58.	bbbbbabbbabbbabbbabba ⇒ abbabbbabbbabbbabbbbb
59.	bbbbbabbbabbbabbbabbbabbbbbb ⇒ ababbbbabbbabbba
60.	abbabbbbabbbabbabbba ⇒ babbbabbbabbbabbbabbbbb
61.	abbbabbbabbbabbabbabbbbbbb ⇒ babbbabbabbbabbba
62.	abbbabbbbabbabbbabba ⇒ babbbbabbabbbabbbabbbbb
63.	abbbbabbabbabbabbabbbbbb ⇒ babbbabbabbabba
64.	abbbbabbabbabbabbbabbbbbb ⇒ babbbabbabbabbba
65.	abbbbabbabbabbbabbabbbbbb ⇒ babbbabbabbbabba
66.	abbbbabbabbbabbabbabbbbbb ⇒ babbbabbbabbabba
67.	abbbbabbabbbabbabbbabbbbbb ⇒ babbbabbbabbabbba
68.	abbbbabbabbbabbbabbabbbbbb ⇒ babbbabbbabbbabba
69.	abbbbabbbabbabbbabba ⇒ bbabbbabbabbbabbbabbbbb
70.	abbbbabbbabbbabbbabbab ⇒ bbbabbbabbbabbba
71.	babbabbbabbabbbabbba ⇒ abbbabbbabbabbbabbab
72.	babbbabbabbabbbabbba ⇒ babbabbbabbbabbabbab
73.	bbbbbabbbabbbabbbabbbabbab ⇒ abbbabbbabbbabbba
	...

Collecting factors up to length 7 / frequency 2:

[2/0]	ba	8628	`lf:278,lp:12,ls:27,rf:240,rp:27,rs:43,re:1,lprp:1,lsrp:5,lprs:3,a:1`
[2/1]	bb	8340	`lf:798,lp:25,ls:41,rf:447,rp:9,rs:20,lprp:1,lprs:7,lsrs:1,a:1`
[3/0]	bbb	7814	`lf:492,lp:25,ls:41,rf:232,rp:4,rs:20,lprp:1,lprs:7,lsrs:1,a:1`
[3/1]	bab	6493	`lf:250,lp:11,ls:2,rf:197,rp:26,rs:7,lprp:1,lprs:6,a:6`
[4/0]	bbbb	6432	`lf:271,lp:24,ls:41,rf:75,rp:1,rs:20,lprs:6,lsrs:1,a:1`
[4/1]	bbba	2361	`lf:180,lp:1,ls:15,rf:137,rp:3,rs:25,lsrp:2,a:1`
[5/0]	abbba	4264	`lf:113,lp:7,ls:9,rf:108,rp:5,rs:22,lsrp:2,lprs:2,a:8`
[5/1]	bbbbb	3275	`lf:164,lp:20,ls:41,rf:29,rp:1,rs:20,lprs:3,lsrs:1,a:1`
[6/0]	bbbbbb	10152	`lf:102,lp:1,ls:38,rf:8,rs:3,lprs:10,a:4`
[6/1]	abbbba	4103	`lf:41,lp:25,ls:4,rf:25,rp:6,rs:2,lsrp:3,lprs:1,a:6`

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(c) = deg(b) = 0, c < b; deg(a) = 1

Rewriting system is not complete: roundsLimit

#	Rule
1.	bc ⇒ cb
2.	bbb ⇒ c
3.	cca ⇒ acc
4.	ccba ⇒ bacc
5.	ccbba ⇒ bbacc
6.	aac ⇒ cbbabb
7.	aab ⇒ cbba
8.	acbacc ⇒ bab
9.	acbacbb ⇒ ba
10.	acbba ⇒ b
11.	caa ⇒ bbacbb
12.	baa ⇒ acbb
13.	baba ⇒ acacccbb
14.	bbacacccc ⇒ cabab
15.	bbacacccbb ⇒ caba
16.	cbbacacc ⇒ abab
17.	cbbacacbb ⇒ aba
18.	cbbacba ⇒ ab
19.	aaa ⇒ 1
20.	acacacccccc ⇒ babbab
21.	acacacccccbb ⇒ babba
22.	acbacacc ⇒ bacba
23.	acbabbacc ⇒ baca
24.	cacbacba ⇒ acbacbac
25.	bacacba ⇒ acbacab
26.	bacbacba ⇒ acbacbab
27.	babbacba ⇒ acbabbab
28.	bbacacacccc ⇒ cabacba
29.	bbacabacccc ⇒ cababba
30.	bbacabbacccc ⇒ cabaca
31.	bbacbacac ⇒ cacacbabb
32.	bbacbacab ⇒ cacacba
33.	bbacbabbac ⇒ cabbacbabb
34.	bbacbabbab ⇒ cabbacba
35.	cbbacacacc ⇒ abacba
36.	cbbacabacc ⇒ ababba
37.	cbbacabbacc ⇒ abaca
38.	acacabacccccc ⇒ babbabba
39.	acacabbacccccc ⇒ babbaca
40.	acbacacacc ⇒ bacbaca
41.	acbacaba ⇒ bacacacbb
42.	acbacabbacc ⇒ bacbabba
43.	acbacbaca ⇒ cacbacacbb
44.	acbacbabba ⇒ cacacbacb
45.	acbabbacacc ⇒ bacaca
46.	acbabbabbacc ⇒ bacabba
47.	cacacacbacb ⇒ bbacbaca
48.	cacacbaca ⇒ acacbacac
49.	cabacbacacbb ⇒ bbacbabba
50.	bacacacacccc ⇒ acbacabbab
51.	bacacacacccbb ⇒ acbacabba
52.	bacacacba ⇒ acacbabbabb
53.	bacabbacba ⇒ acbabbacab
54.	bacbacacac ⇒ cacacacbab
55.	bacbacacab ⇒ cabbacbaca
56.	bacbacabbac ⇒ cabacbacabb
57.	bacbacabbab ⇒ cabacbaca
58.	cbacbacaca ⇒ acacacbacb
59.	cbacbacabba ⇒ abacbacacbb
60.	bbacacabac ⇒ cabacacabb
61.	bbacacabab ⇒ cabacaca
62.	bbacabacacccc ⇒ cababbaca
63.	cbbacacacacc ⇒ abacbaca
64.	cbbacacaba ⇒ abacacacbb
65.	cbbacacabbacc ⇒ abacbabba
66.	cbbacabacacc ⇒ ababbaca
67.	cbbacababbacc ⇒ ababbabba
68.	cbbacabbacacc ⇒ abacaca
69.	cbbacabbabbacc ⇒ abacabba
70.	acacacabaccb ⇒ babbacaca
71.	acacbacabba ⇒ cacacacbac
72.	acbacacacacc ⇒ bacbacaca
73.	acbacacabacc ⇒ bbacacacbb
74.	acbabbacacacc ⇒ bacacaca
75.	cacacacacbac ⇒ bacbacaca
76.	cabacbacaca ⇒ acbacacacab
77.	cacbacacaca ⇒ acacacacbac
78.	babbacacaca ⇒ acacacabbab
	...

Collecting factors up to length 14 / frequency 1:

[2/0]	cc	12105	`lf:65,lp:3,ls:29,rf:5,rs:3,lprs:12,a:7`
[3/0]	aca	6196	`lf:95,lp:6,ls:6,rf:65,rp:6,rs:18,lsrp:4,lprs:2,a:18`
[4/0]	acba	6113	`lf:42,lp:14,ls:7,rf:37,rp:8,rs:5,lsrp:5,lprs:1,a:10`
[5/0]	acaca	4075	`lf:35,lp:5,ls:4,rf:21,rp:3,rs:7,lsrp:3,lprs:1,a:20`
[6/0]	acbaca	1052	`lf:20,lp:6,ls:2,rf:15,rp:4,rs:5,lprs:1,a:19`
[7/0]	acbacba	20012	`lf:4,lp:2,ls:2,rf:2,rp:2,lsrp:20,a:36`
[8/0]	acacbaca	10006	`lf:2,lp:1,ls:1,rf:1,rp:1,lsrp:10,a:74`
[9/0]	bacbacabb	1007	`lf:3,lp:2,rf:1,rs:1,lprs:1,a:96`
[10/0]	cacacacbac	10	`lf:2,lp:1,ls:1,rf:2,rp:1,rs:2,re:1,a:74`
[11/0]	acacacacbac	6	`lf:1,ls:1,rf:1,rp:1,rs:1,re:1,a:101`
[12/0]	acbabbacacac	2	`lf:1,lp:1,a:83`
[13/0]	cbbacabbabbac	2	`lf:1,lp:1,a:64`

Considering [length 7 / frequency 0] acbacba=d.

Step 3

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

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