Morphocompletion for #4283 ⟨a, b | ababaaaab=aa⟩

Solved by morph:2/1,5/0,3/0. (See Morphocompletion.)

Step 1

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: rulesLimit

#	Rule
1.	ababaaaaa ⇒ aaabaaaab
2.	ababaaaab ⇒ aa
3.	aaaaaabbabaaaaa ⇒ aaaaaabaabaaaab
4.	aaaaaabbabaaaab ⇒ aaaaaaba
5.	aaaaaababbabaaaab ⇒ aaaaaababa
6.	aaabaaaabbabaaaab ⇒ aaabaaaaba
7.	aaabaaaababbabaaaab ⇒ aaabaaaababa
8.	aaabaaaabaabbabaaaab ⇒ aaabaaaabaaba
	...

Collecting factors up to length 7 / frequency 3:

[2/0]	aa	65	`lf:57,lp:6,ls:2,rf:41,rp:8,rs:1,re:1,lprp:6,lsrp:2`
[2/1]	ab	36	`lf:28,lp:2,ls:6,rf:16,rs:2,lprs:1`
[2/2]	ba	22	`lf:22,rf:14,rs:5`
[3/0]	aaa	47	`lf:39,lp:6,ls:2,rf:26,rp:7,lprp:6,lsrp:2`
[3/1]	aab	22	`lf:16,ls:6,rf:14,rs:2`
[3/2]	aba	18	`lf:16,lp:2,rf:14,rs:5`
[4/0]	aaaa	27	`lf:22,lp:3,ls:2,rf:14,rp:3,lprp:3,lsrp:1`
[4/1]	aaab	24	`lf:15,lp:3,ls:6,rf:12,rp:4,rs:2,lprp:3,lsrp:3`
[4/2]	abaa	12	`lf:12,rf:7`
[5/0]	aaaab	18	`lf:12,ls:6,rf:8,rs:2`
[5/1]	aaaaa	13	`lf:8,lp:3,ls:2,rf:6,rp:3,lprp:3,lsrp:1,a:1`
[5/2]	baaaa	11	`lf:11,rf:5`
[6/0]	baaaab	15	`lf:9,ls:6,rf:5,rs:2`
[6/1]	abaaaa	11	`lf:11,rf:5`
[6/2]	babaaa	8	`lf:8`

Considering [length 2 / frequency 1] ab=c.

Step 2

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = ab
Reduction order:
- Right-to-left recursive path with deg(c) = 0; deg(a) = 1; deg(b) = 2

Rewriting system is not complete: pendingRulesLimit

#	Rule
1.	ccaaac ⇒ aa
2.	aacaaac ⇒ ccaaaaa
3.	ccaccaaaaa ⇒ aaaaac
4.	ccaaaaaaaac ⇒ aacaccaaaaa
5.	ccaccaaaaccaaaaa ⇒ aaaaacacaaac
6.	ccaaaaacaccaaaaa ⇒ aacaaaaaaaac
7.	ab ⇒ c
8.	aaaaacb ⇒ ccaccaaaac
9.	aaaaaccb ⇒ ccaccccaccaaaac
10.	aaaaacccb ⇒ ccaccccaccccaccaaaac
11.	aaaaacacb ⇒ ccaccaccaccaaaac
12.	aaaaaccacb ⇒ ccaccccaccaccaccaaaac
13.	aaaaacaccb ⇒ ccaccaccaccccaccaaaac
14.	aaaaacaacb ⇒ ccaccaaccaccaaaac
15.	aaaaaccaacb ⇒ ccaccccaccaaccaccaaaac
16.	aaaaacaaaacb ⇒ ccaccaaaaccaccaaaac
17.	aaaaacacaaacb ⇒ ccaccaaaaccaaaac
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	aa	92	`lf:78,lp:11,ls:3,rf:66,rp:5,rs:3,re:1,lsrp:3,lprs:1,a:2`
[2/1]	ac	30	`lf:27,ls:3,rf:47,rs:13,a:2`
[2/2]	cb	20	`lf:10,ls:10,a:7`
[2/3]	cc	20	`lf:15,lp:5,rf:53,rp:11,a:2`
[2/4]	ca	19	`lf:19,rf:45,a:2`
[3/0]	aaa	68	`lf:55,lp:10,ls:3,rf:43,rp:2,rs:2,lsrp:2,a:2`
[3/1]	aac	24	`lf:20,lp:1,ls:3,rf:20,rp:2,rs:13,lsrp:1,a:2`
[3/2]	cca	16	`lf:11,lp:5,rf:41,rp:11,a:2`
[3/3]	acb	14	`lf:7,ls:7,a:7`
[3/4]	caa	12	`lf:12,rf:18,a:2`
[4/0]	aaaa	48	`lf:35,lp:10,ls:3,rf:25,rp:2,rs:2,lsrp:2,a:3`
[4/1]	aaac	20	`lf:17,ls:3,rf:16,rs:13,a:2`
[4/2]	ccaa	11	`lf:8,lp:3,rf:16,rp:1,a:2`
[4/3]	aacb	10	`lf:5,ls:5,a:7`
[4/4]	caaa	10	`lf:10,rf:16,a:2`
[5/0]	aaaaa	31	`lf:18,lp:10,ls:3,rf:8,rp:2,rs:2,lsrp:2,a:3`
[5/1]	aaaac	15	`lf:14,ls:1,rf:15,rs:12,a:4`
[5/2]	ccaaa	10	`lf:7,lp:3,rf:14,rp:1,a:2`
[5/3]	caaaa	7	`lf:7,rf:15,a:3`
[5/4]	aaacb	6	`lf:3,ls:3,a:7`

Considering [length 5 / frequency 0] aaaaa=d.

Step 3

Checking up to 20 rules for overlaps.

Auxiliary generators:
1. c = ab
2. d = aaaaa
Reduction order:
- Right-to-left recursive path with deg(c) = 0; deg(d) = deg(a) = 1, d < a; deg(b) = 2

Rewriting system is not complete: roundsLimit

#	Rule
1.	ccaccd ⇒ dc
2.	da ⇒ ad
3.	ccaccad ⇒ dca
4.	ccaaac ⇒ aa
5.	ccaccaad ⇒ dcaa
6.	ccaaadc ⇒ aacaccd
7.	dcaaac ⇒ aaaccd
8.	ccdcaaadc ⇒ aacdcaccd
9.	ccaccaaad ⇒ dcaaa
10.	aaaaa ⇒ d
11.	aacaaac ⇒ ccd
12.	aaaccdcaccd ⇒ dcaaadc
13.	aacaccdcaccd ⇒ ccaaaddc
14.	ccaccaaaad ⇒ dcaaaa
15.	aacaaadc ⇒ ccdcaccd
16.	aadcaaadc ⇒ dccdcaccd
17.	db ⇒ aaaac
18.	dcb ⇒ ccaccaaaac
19.	dccb ⇒ ccaccccaccaaaac
20.	ab ⇒ c
	...

Collecting factors up to length 6 / frequency 5:

[2/0]	aa	37	`lf:30,lp:6,ls:1,rf:24,rp:5,rs:4,re:1,a:2`
[2/1]	cc	26	`lf:18,lp:8,rf:16,rp:5,a:3`
[2/2]	ca	19	`lf:19,rf:15,rs:1,a:3`
[2/3]	ac	18	`lf:15,ls:3,rf:13,rs:3,a:3`
[2/4]	dc	18	`lf:11,lp:3,ls:4,rf:12,rp:7,rs:3,re:1,lsrp:1,a:7`
[3/0]	cca	18	`lf:11,lp:7,rf:6,rp:3,a:3`
[3/1]	aaa	17	`lf:14,lp:2,ls:1,rf:12,rp:2,rs:2,a:2`
[3/2]	aac	13	`lf:7,lp:3,ls:3,rf:6,rp:2,rs:3,a:3`
[3/3]	aad	12	`lf:8,lp:1,ls:3,rf:2,a:9`
[3/4]	caa	10	`lf:10,rf:7,rs:1,a:3`
[4/0]	aadc	10	`lf:5,lp:1,ls:4,rf:1,rs:1,a:9`
[4/1]	ccac	10	`lf:5,lp:5,rf:3,rp:2,a:8`
[4/2]	caaa	9	`lf:9,rf:6,rs:1,a:3`
[4/3]	aaad	8	`lf:6,ls:2,rf:2,a:9`
[4/4]	aaac	8	`lf:4,lp:1,ls:3,rf:4,rp:1,rs:3,lsrp:1,a:3`
[5/0]	ccacc	10	`lf:5,lp:5,rf:3,rp:2,a:8`
[5/1]	aaadc	8	`lf:4,ls:4,rf:1,rs:1,a:9`
[5/2]	caccd	7	`lf:4,ls:3,rf:4,rs:4,a:8`
[5/3]	caaad	6	`lf:5,ls:1,rf:2,a:9`
[5/4]	caaac	6	`lf:3,ls:3,a:3`

Considering [length 3 / frequency 0] cca=e.

Step 4

Auxiliary generators:
1. c = ab
2. d = aaaaa
3. e = cca
Reduction order:
- Right-to-left recursive path with deg(c) = deg(e) = 0, c < e; deg(d) = deg(a) = 1, d < a; deg(b) = 2

Rewriting system is complete. See ⟨a, b | ababaaaab=aa⟩.