Morphocompletion for #1719 ⟨a, b | aabbabaab=a⟩

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

Step 1

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: rulesLimit

#	Rule
1.	ababaab ⇒ aabbaba
2.	aaabab ⇒ ababaa
3.	aabbabaab ⇒ a
4.	aabaabab ⇒ aabbabaa
5.	ababaaaab ⇒ aaaabbaba
6.	ababaaabbaba ⇒ aaab
7.	aabbabaaaab ⇒ aabaaabbaba
8.	ababaaabaab ⇒ aaabaabbaba
9.	aabbabaaabbaba ⇒ aabaab
10.	ababaaaaaab ⇒ aaaaaabbaba
11.	ababaaaaabbaba ⇒ aaaaab
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	ab	50	`lf:36,lp:6,ls:8,rf:20,rp:1,rs:3,lsrp:1,lprs:2`
[2/1]	aa	36	`lf:31,lp:5,rf:26,rp:9,rs:2,lprp:3,lprs:2`
[2/2]	ba	31	`lf:28,ls:3,rf:17,rs:5`
[2/3]	bb	6	`lf:6,rf:6`
[3/0]	aba	31	`lf:22,lp:6,ls:3,rf:11,rp:1,rs:5,lprs:4`
[3/1]	aab	26	`lf:16,lp:4,ls:6,rf:12,rp:4,rs:3,lprp:3,lsrp:2,lprs:1`
[3/2]	aaa	16	`lf:15,lp:1,rf:12,rp:5,a:2`
[3/3]	bab	16	`lf:14,ls:2,rf:7`
[4/0]	abab	16	`lf:8,lp:6,ls:2,rf:1,rp:1,lsrp:1,a:1`
[4/1]	baba	15	`lf:12,ls:3,rf:7,rs:5`
[4/2]	aaab	12	`lf:8,lp:1,ls:3,rf:6,rp:2,rs:2,re:1,a:2`
[4/3]	abaa	11	`lf:11,rf:5,rs:2`
[5/0]	ababa	12	`lf:6,lp:6,rf:1,rp:1,a:1`
[5/1]	aabba	9	`lf:6,lp:3,rf:6,rp:2`
[5/2]	babaa	9	`lf:9,rf:2,rs:2`
[5/3]	bbaba	9	`lf:6,ls:3,rf:6,rs:5`
[6/0]	ababaa	12	`lf:6,lp:6,rf:1,rp:1,rs:1,re:1,a:1`
[6/1]	aabbab	9	`lf:6,lp:3,rf:6,rp:2`
[6/2]	abbaba	9	`lf:6,ls:3,rf:6,rs:5`
[6/3]	babaaa	7	`lf:7,a:2`

Considering [length 5 / frequency 0] ababa=c.

Step 2

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	cba ⇒ abc
2.	aa ⇒ cc
3.	aac ⇒ ccc
4.	aabc ⇒ ccbc
5.	cca ⇒ acc
6.	abca ⇒ cbcc
7.	cabba ⇒ ccbbc
8.	cabab ⇒ a
9.	aaba ⇒ cabc
10.	ababa ⇒ c
11.	ababcc ⇒ ca
12.	ccac ⇒ accc
13.	ccabc ⇒ accbc
14.	cbcabcb ⇒ aba
15.	abcac ⇒ cbccc
16.	acabcb ⇒ ca
17.	ccbca ⇒ acbcc
18.	ccbbaba ⇒ cab
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	ab	20	`lf:15,lp:4,ls:1,rf:4,rp:2,rs:1,a:1`
[2/1]	ca	15	`lf:10,lp:2,ls:3,rf:4,rp:4,rs:2,re:2,a:3`
[2/2]	ba	14	`lf:9,ls:5,rf:1,rs:1,a:1`
[2/3]	cc	12	`lf:6,lp:5,ls:1,rf:13,rp:4,rs:7,re:1,lprs:12,a:3`
[2/4]	bc	11	`lf:9,ls:2,rf:8,rs:5,lsrs:2,a:2`
[2/5]	cb	10	`lf:6,lp:2,ls:2,rf:6,rp:2,a:2`
[2/6]	ac	8	`lf:4,lp:1,ls:3,rf:4,rp:4,lsrp:1,a:12`
[3/0]	aba	11	`lf:6,lp:2,ls:3,rf:1,rp:1,rs:1,re:1,a:1`
[3/1]	abc	11	`lf:7,lp:2,ls:2,rf:2,rp:1,rs:2,re:1,a:2`
[3/2]	cab	7	`lf:5,lp:2,rf:2,rp:2,rs:1,re:1,a:3`
[3/3]	bca	6	`lf:4,ls:2,a:14`
[3/4]	bab	5	`lf:4,ls:1,a:1`
[3/5]	cca	4	`lf:2,lp:2,a:15`
[3/6]	cac	4	`lf:2,ls:2,a:14`
[4/0]	abab	6	`lf:3,lp:2,ls:1,a:1`
[4/1]	cbca	4	`lf:2,lp:1,ls:1,a:40`
[4/2]	cabc	4	`lf:3,ls:1,rf:1,rp:1,rs:1,re:1,a:4`
[4/3]	baba	4	`lf:2,ls:2,a:1`
[4/4]	abcb	4	`lf:2,ls:2,a:37`
[4/5]	caba	2	`lf:1,lp:1,a:26`
[4/6]	acab	2	`lf:1,lp:1,a:37`
[5/0]	cabcb	4	`lf:2,ls:2,a:37`
[5/1]	acabc	2	`lf:1,lp:1,a:37`
[5/2]	cbcab	2	`lf:1,lp:1,a:42`
[5/3]	ccbba	2	`lf:1,lp:1,a:3`
[5/4]	ababc	2	`lf:1,lp:1,a:34`
[5/5]	babcc	2	`lf:1,ls:1,a:34`
[5/6]	bbaba	2	`lf:1,ls:1,a:3`

Considering [length 2 / frequency 0] ab=d.

Step 3

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

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