Morphocompletion for #17663 ⟨a, b | aaaa=1, abbba=bb⟩

Solved by morph:6/0,7/0. (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.	bbbbba ⇒ abbbbb
2.	abbba ⇒ bb
3.	bbaa ⇒ ababbb
4.	bbbaba ⇒ aabb
5.	aaabb ⇒ bbba
6.	abababbb ⇒ bba
7.	aaaa ⇒ 1
8.	aaababbbbb ⇒ bbbabbbba
9.	ababaabbbbb ⇒ bbabba
10.	abababbabbbbb ⇒ bbabbbba
11.	bababababb ⇒ bb
12.	babababbabb ⇒ aaababb
13.	bbabaaa ⇒ abababbabbb
14.	bbabababa ⇒ ababababb
15.	bbabbababa ⇒ abababbabb
16.	aaabaabb ⇒ bbbabbaba
17.	aaababbabbbbb ⇒ bbbabbbbabba
18.	aaababbbbabbbbb ⇒ bbbabbbbabbbba
19.	ababaababbbbb ⇒ bbabbaba
20.	ababaabbabbbbb ⇒ bbabbabba
21.	ababaabbbbabbbbb ⇒ bbabbabbbba
22.	abababaabb ⇒ bbababa
23.	abababbababbb ⇒ bbabaa
24.	abababbabbabbbbb ⇒ bbabbbbabba
25.	baababababb ⇒ ababababbab
26.	babababbababb ⇒ aaabababb
27.	bbababbababab ⇒ bbababaaa
28.	aaabaababbbbb ⇒ bbbabbababbbba
29.	aaababbababbbbb ⇒ bbbabbbbabbaba
30.	ababaabaabbbbb ⇒ bbabbabaa
31.	ababaababbabbbbb ⇒ bbabbababba
32.	ababaabbababbbbb ⇒ bbabbabbaba
33.	ababaabbabbabbbbb ⇒ bbabbabbabba
34.	abababbabaabbbbb ⇒ bbabaabba
35.	abababbababbabbbbb ⇒ bbabaabbbba
36.	baaababababb ⇒ abababaababbbb
37.	bababaababbbbabb ⇒ aaabaababb
38.	babababaababb ⇒ ababb
39.	babababbabaabb ⇒ aaababaabb
40.	babababbabababb ⇒ aaababababb
41.	bbabaabaaa ⇒ abababbababbabbb
42.	bbabaabababa ⇒ abababbabababb
43.	bbabaabbababa ⇒ abababbababbabb
44.	bbabababbababa ⇒ abababaababb
45.	bbabbabaababa ⇒ ababaababbabb
46.	aaabaaababb ⇒ bababaabbbbabb
47.	aaabaabaabb ⇒ bbbabbababbaba
48.	ababaabaababbbbb ⇒ bbabbabaaba
49.	ababaabaabbabbbbb ⇒ bbabbabaabba
50.	ababaabbabaabbbbb ⇒ bbabbabbabaa
51.	abababaaababb ⇒ bbababbababa
52.	abababaabaabb ⇒ bbabababbaba
53.	abababaababbabb ⇒ baabbababa
54.	abababbabaababbbbb ⇒ bbabaabbaba
55.	abababbababaabb ⇒ bbabaababa
56.	abababbababbababbb ⇒ bbabaabaa
57.	baabababaababbb ⇒ ababababbabaa
58.	bababaababaabbbb ⇒ aaabaabababb
59.	bababaabababbabb ⇒ aaababbababa
60.	babababaabababb ⇒ abababb
61.	babababbabaababb ⇒ aaababaababb
62.	bbabaababbababab ⇒ bbabaababaaa
63.	bbababaabbababab ⇒ bbababaabaaa
64.	aaabaaabababb ⇒ bababaabaabbbb
65.	ababaabaabaabbbbb ⇒ bbabbabaabaa
66.	babababaaabababb ⇒ aabababb
67.	babababaabaababbb ⇒ abaababbb
68.	babababaababaabb ⇒ ababaabb
69.	aaabaaababaabb ⇒ bababaabaabbabb
70.	abababaaababaabb ⇒ bbababaaababa
71.	abababaabaaababb ⇒ baaababbababa
72.	abababaabaabaabb ⇒ baaabababbaba
	...

Collecting factors up to length 7 / frequency 2:

[2/0]	bb	45493	`lf:192,lp:14,ls:56,rf:162,rp:38,rs:29,re:2,lprp:3,lsrp:34,lprs:11,lsrs:17,a:1`
[2/1]	ba	1563	`lf:276,lp:17,ls:9,rf:223,rp:6,rs:32,lprs:1,a:1`
[3/0]	aba	18399	`lf:207,lp:28,ls:7,rf:125,rp:16,rs:16,lsrp:6,lprs:12,a:6`
[3/1]	bbb	6170	`lf:84,lp:2,ls:28,rf:41,rp:8,rs:7,lsrp:5,lprs:1,lsrs:1,a:1`
[4/0]	baba	1250	`lf:129,lp:14,ls:7,rf:82,rp:3,rs:15,lprs:1,a:6`
[4/1]	bbbb	1092	`lf:50,lp:1,ls:23,rf:15,rs:3,lprs:1,a:4`
[5/0]	ababa	12180	`lf:84,lp:28,ls:6,rf:42,rp:13,rs:7,lsrp:6,lprs:6,a:8`
[5/1]	bbbbb	10048	`lf:23,lp:1,ls:22,rf:1,rs:1,lprs:10,a:4`
[6/0]	bababa	1089	`lf:43,lp:14,ls:5,rf:19,rp:3,rs:5,lprs:1,a:12`
[6/1]	ababab	96	`lf:44,lp:16,ls:3,rf:22,rp:11,a:8`

Considering [length 6 / frequency 0] bababa=c.

Step 2

Checking up to 80 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	bbbbbc ⇒ cbbbbb
2.	cbbbc ⇒ bb
3.	bbcc ⇒ cbcbbb
4.	bbbcbc ⇒ ccbb
5.	cccbb ⇒ bbbc
6.	cbcbcbbb ⇒ bbc
7.	bbcbcbcb ⇒ bccc
8.	cbcbccbbbbb ⇒ bbcbbc
9.	bcccc ⇒ cbcbcbcbb
10.	bcbcbcbc ⇒ cbcbcbcb
11.	bcbcbcbbc ⇒ cccbc
12.	ccccbc ⇒ bc
13.	cccbccbb ⇒ bbbcbbcbc
14.	cbcbcbccbb ⇒ bbcbcbc
15.	bccbcbcbcb ⇒ bc
16.	cccbccc ⇒ bcbcbccbbb
17.	bcccbcbcbcb ⇒ bcc
18.	abb ⇒ bbc
19.	acbb ⇒ cbcbcbcbb
20.	abc ⇒ cbcbcbbc
21.	accbb ⇒ bbcbcbc
22.	acbc ⇒ ccbcbcbcb
23.	accbc ⇒ cbcbcbccbc
24.	accbcbb ⇒ bcccbcbcbc
25.	accbcbbb ⇒ bcc
26.	acccbc ⇒ cbcbcbcccbc
27.	accbccbb ⇒ bcccbcbc
28.	baccbc ⇒ cbc
29.	bacccbc ⇒ ccbc
30.	bba ⇒ bccc
31.	cba ⇒ bac
32.	bca ⇒ bccbcbcb
33.	bcca ⇒ bcccbcbcb
34.	bccca ⇒ bbcbcb
35.	bababa ⇒ c
36.	caaa ⇒ babab
37.	aaaa ⇒ 1
	...

Collecting factors up to length 14 / frequency 1:

[2/0]	bb	19086	`lf:28,lp:5,ls:11,rf:25,rp:9,rs:7,re:1,lsrp:16,lprs:3,lsrs:1,a:17`
[3/0]	cbc	5105	`lf:32,lp:3,ls:8,rf:43,rp:8,rs:10,re:1,lsrp:4,lprs:1,lsrs:4,a:21`
[4/0]	ccbc	1033	`lf:12,ls:5,rf:9,rp:2,rs:4,re:1,lsrp:1,lsrs:3,a:108`
[5/0]	bbbbb	10006	`lf:2,lp:1,ls:1,rf:1,rs:1,lprs:10,a:79`
[6/0]	cbcbcb	38	`lf:9,lp:2,ls:3,rf:14,rp:6,rs:4,a:21`
[7/0]	cbcbcbc	10019	`lf:4,lp:1,ls:1,rf:7,rp:5,rs:1,lsrp:10,a:110`
[8/0]	cbcbcbcb	14	`lf:2,ls:2,rf:4,rp:3,rs:2,re:1,a:131`
[9/0]	bcccbcbcb	8	`lf:1,lp:1,rf:2,rp:2,rs:1,re:1,a:212`
[10/0]	bcccbcbcbc	6	`lf:1,lp:1,rf:1,rp:1,rs:1,re:1,a:212`
[11/0]	cbcbcbcccbc	4	`rf:1,rp:1,rs:1,re:1,a:274`

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

Step 3

Auxiliary generators:
1. c = bababa
2. d = cbcbcbc
Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(d) = 1; deg(c) = 2; deg(a) = 3

Rewriting system is complete. See ⟨a, b | aaaa=1, abbba=bb⟩.