Morphocompletion for #4527 ⟨a, b | aaababba=baa⟩

Solved by morph:2/1,5/1. (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.	aaababba ⇒ baa
2.	aaababbbaa ⇒ babaa
3.	aaababbbbaa ⇒ babbaa
4.	aaababbbabaa ⇒ bababaa
5.	aaababbbbbaa ⇒ babbbaa
6.	aaababbbabbaa ⇒ bababbaa
7.	aaababbbbabaa ⇒ babbabaa
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	aa	33	`lf:20,lp:7,ls:6,rf:7,rs:7,lprs:7,lsrs:6`
[2/1]	bb	18	`lf:18,rf:5`
[2/2]	ba	18	`lf:17,ls:1,rf:16,rp:7,lsrp:1`
[2/3]	ab	17	`lf:17,rf:9`
[3/0]	aaa	14	`lf:7,lp:7`
[3/1]	baa	12	`lf:6,ls:6,rf:7,rp:1,rs:7,re:1,lsrs:6`
[3/2]	bbb	10	`lf:10,rf:1,a:1`
[3/3]	bab	10	`lf:10,rf:9,rp:6`
[4/0]	aaab	14	`lf:7,lp:7`
[4/1]	babb	8	`lf:8,rf:4,rp:3`
[4/2]	bbaa	8	`lf:4,ls:4,rf:3,rs:3,lsrs:3,a:1`
[4/3]	abab	7	`lf:7,rf:2`
[5/0]	aaaba	14	`lf:7,lp:7`
[5/1]	ababb	7	`lf:7,rf:1`
[5/2]	aabab	7	`lf:7`
[5/3]	babbb	6	`lf:6,rf:1,rp:1,a:1`
[6/0]	aaabab	14	`lf:7,lp:7`
[6/1]	aababb	7	`lf:7`
[6/2]	ababbb	6	`lf:6,a:1`
[6/3]	bbbbaa	4	`lf:2,ls:2,a:3`

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

Step 2

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: pendingRulesLimit

#	Rule
1.	aaabaca ⇒ baa
2.	cb ⇒ bc
3.	bb ⇒ c
4.	aaabaccaa ⇒ bacaa
5.	aaababcaa ⇒ babaa
6.	aaabacccaa ⇒ baccaa
7.	aaabaccacaa ⇒ bacacaa
8.	aaababccaa ⇒ babcaa
9.	aaababcacaa ⇒ babacaa
10.	aaabaccabaa ⇒ bacabaa
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	aa	38	`lf:23,lp:8,ls:7,rf:8,rs:8,lprs:8,lsrs:7,a:2`
[2/1]	ab	12	`lf:12,rf:4,a:2`
[2/2]	ca	11	`lf:10,ls:1,rf:7,a:2`
[2/3]	ba	9	`lf:9,rf:11,rp:8,a:2`
[2/4]	ac	7	`lf:7,rf:6,a:2`
[2/5]	cc	6	`lf:6,rf:1,a:6`
[2/6]	bc	3	`lf:3,rf:2,rp:1,rs:1,re:1,a:3`
[3/0]	aaa	16	`lf:8,lp:8,a:2`
[3/1]	caa	12	`lf:6,ls:6,rf:5,rs:5,lsrs:5,a:4`
[3/2]	aba	9	`lf:9,rf:3,a:2`
[3/3]	aab	8	`lf:8,a:2`
[3/4]	bac	5	`lf:5,rf:5,rp:4,a:2`
[3/5]	cca	5	`lf:5,rf:1,a:6`
[3/6]	acc	4	`lf:4,rf:1,a:6`
[4/0]	aaab	16	`lf:8,lp:8,a:2`
[4/1]	aaba	8	`lf:8,a:2`
[4/2]	ccaa	6	`lf:3,ls:3,rf:1,rs:1,lsrs:1,a:6`
[4/3]	abac	5	`lf:5,rf:1,a:2`
[4/4]	bacc	4	`lf:4,rf:1,rp:1,a:6`
[4/5]	acaa	4	`lf:2,ls:2,rf:3,rs:3,lsrs:2,a:6`
[4/6]	babc	3	`lf:3,rf:1,rp:1,a:4`
[5/0]	aaaba	16	`lf:8,lp:8,a:2`
[5/1]	aabac	5	`lf:5,a:2`
[5/2]	abacc	4	`lf:4,a:6`
[5/3]	cacaa	4	`lf:2,ls:2,rf:1,rs:1,lsrs:1,a:9`
[5/4]	ababc	3	`lf:3,a:4`
[5/5]	bacca	3	`lf:3,rf:1,rp:1,a:6`
[5/6]	aabab	3	`lf:3,a:4`

Considering [length 5 / frequency 1] aabac=d.

Step 3

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

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