Morphocompletion for #1515 ⟨a, b | abababbaba=1⟩

Solved by morph:2/0,4/0. (See Morphocompletion.)

Step 1

Checking up to 20 rules for overlaps.

Reduction order:
- Left-to-right shortlex with a < b

Rewriting system is not complete: rulesLimit

#	Rule
1.	babaab ⇒ abbaba
2.	abbabaa ⇒ aababab
3.	babbaba ⇒ abababb
4.	baababab ⇒ abababba
5.	aabbbabaa ⇒ aabababab
6.	aabababbab ⇒ 1
7.	baabaabbaba ⇒ abababbaaab
8.	babaaababab ⇒ abbabababaa
9.	babaaabbaba ⇒ aabababbaab
10.	babbaabbaba ⇒ abababbbaab
11.	aababababababb ⇒ baba
12.	aaabababbbbabaa ⇒ aabab
	...

Collecting factors up to length 7 / frequency 4:

[2/0]	ba	51	`lf:40,lp:7,ls:4,rf:28,rp:1,rs:3,lprs:2,a:1`
[2/1]	ab	43	`lf:38,lp:1,ls:4,rf:34,rp:6,rs:6,lsrp:3,lprs:1,a:1`
[2/2]	aa	24	`lf:17,lp:4,ls:3,rf:9,rp:4,rs:1,lprp:2,lsrp:3,a:10`
[2/3]	bb	14	`lf:13,ls:1,rf:8,rs:1,a:1`
[3/0]	bab	34	`lf:26,lp:5,ls:3,rf:21,rp:1,rs:3,a:1`
[3/1]	aba	28	`lf:24,ls:4,rf:21,rp:4,rs:2,lsrp:3,a:1`
[3/2]	baa	15	`lf:10,lp:2,ls:3,rf:4,rs:1,a:17`
[3/3]	aab	15	`lf:11,lp:3,ls:1,rf:7,rp:4,rs:3,lprp:1,a:10`
[4/0]	baba	25	`lf:18,lp:3,ls:4,rf:13,rp:1,rs:2,re:1,lprs:1,a:1`
[4/1]	abab	15	`lf:13,ls:2,rf:18,rp:4,rs:3,lsrp:1,a:1`
[4/2]	abaa	10	`lf:7,ls:3,rf:1,rs:1,a:19`
[4/3]	bbab	9	`lf:8,ls:1,rf:2,a:1`
[5/0]	babaa	12	`lf:6,lp:3,ls:3,rf:1,rs:1,lprs:1,a:19`
[5/1]	bbaba	11	`lf:7,ls:4,rf:2,rs:1,a:1`
[5/2]	babab	10	`lf:8,ls:2,rf:10,rs:2,a:1`
[5/3]	abbab	8	`lf:6,lp:1,ls:1,rf:2,rp:2,a:1`
[6/0]	abbaba	10	`lf:5,lp:1,ls:4,rf:2,rp:2,rs:1,re:1,a:1`
[6/1]	ababab	10	`lf:8,ls:2,rf:9,rp:4,rs:2,lsrp:1,a:1`
[6/2]	aababa	7	`lf:5,lp:2,rf:3,rp:3,a:10`
[6/3]	bbabaa	6	`lf:3,ls:3,a:21`

Considering [length 2 / frequency 0] ba=c.

Step 2

Checking up to 20 rules for overlaps.

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

Rewriting system is not complete: roundsLimit

#	Rule
1.	ccaccc ⇒ a
2.	cccbcc ⇒ b
3.	ccaca ⇒ aaccc
4.	ccacca ⇒ acaccc
5.	accbcc ⇒ 1
6.	caccb ⇒ accbc
7.	ccab ⇒ abcc
8.	ccacb ⇒ acbcc
9.	ba ⇒ c
10.	bcca ⇒ accb
11.	cccbca ⇒ bcaccc
12.	cccbb ⇒ bcbcc
13.	cccbcb ⇒ bccbcc
14.	aaccb ⇒ ccac
15.	accbca ⇒ caccc
16.	accbb ⇒ cbcc
17.	accbcb ⇒ ccbcc
	...

Collecting factors up to length 6 / frequency 7:

[2/0]	cc	37	`lf:25,lp:9,ls:3,rf:19,rp:2,rs:10,lprs:7,a:2`
[2/1]	cb	18	`lf:13,ls:5,rf:7,rp:1,rs:1,a:2`
[2/2]	ca	17	`lf:11,lp:1,ls:5,rf:4,rp:1,lsrp:1,a:16`
[2/3]	ac	14	`lf:10,lp:4,rf:9,rp:4,rs:1,a:2`
[2/4]	bc	8	`lf:7,lp:1,rf:10,rp:3,rs:1,a:2`
[2/5]	bb	4	`lf:2,ls:2,a:4`
[2/6]	ab	2	`lf:1,ls:1,rf:1,rp:1,lsrp:1,a:24`
[3/0]	cca	14	`lf:7,lp:5,ls:2,rf:1,rp:1,a:16`
[3/1]	ccb	12	`lf:10,ls:2,rf:4,rp:1,rs:1,a:2`
[3/2]	acc	12	`lf:8,lp:4,rf:6,rp:2,a:2`
[3/3]	ccc	10	`lf:5,lp:4,ls:1,rf:4,rs:4,lprs:1,a:3`
[3/4]	cbc	6	`lf:6,rf:6,rp:1,rs:1,a:2`
[3/5]	bcc	6	`lf:3,lp:1,ls:2,rf:7,rp:1,rs:6,a:2`
[3/6]	cac	6	`lf:5,lp:1,rf:4,rp:1,rs:1,a:17`
[4/0]	accb	12	`lf:6,lp:4,ls:2,rf:2,rp:2,rs:1,re:1,lsrp:10,a:2`
[4/1]	cccb	8	`lf:4,lp:4,a:3`
[4/2]	ccac	8	`lf:4,lp:4,rf:1,rp:1,rs:1,re:1,a:22`
[4/3]	ccbc	6	`lf:6,rf:3,rp:1,rs:1,a:2`
[4/4]	ccbb	4	`lf:2,ls:2,a:4`
[4/5]	cbcb	4	`lf:2,ls:2,a:5`
[4/6]	cbca	4	`lf:2,ls:2,a:19`
[5/0]	accbc	6	`lf:3,lp:3,rf:1,rp:1,rs:1,re:1,a:2`
[5/1]	cccbc	6	`lf:3,lp:3,a:3`
[5/2]	ccbcb	4	`lf:2,ls:2,a:5`
[5/3]	ccbca	4	`lf:2,ls:2,a:19`
[5/4]	ccbcc	4	`lf:2,ls:2,rf:2,rp:1,rs:2,re:1,a:2`
[5/5]	ccacc	4	`lf:2,lp:2,a:22`
[5/6]	cacca	2	`lf:1,ls:1,a:28`

Considering [length 4 / frequency 0] accb=d.

Step 3

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

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