#4276 ⟨a, b | abaabbaba=ab⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-commutative monoid

Rewriting system

Format:	Pretty Plain
Word to reduce:
	Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Reduction strategy:	Leftmost Rightmost
Path to normal form:	1 1

Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Auxiliary generators:
1. abb=c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

#	Rule	Proof
1.	c²aba² ⇒ c	[17]
2.	(ca)²b ⇒ c²aba	[14]
3.	cac²b ⇒ c²abc	[22]
4.	ab² ⇒ c	[2]
5.	abcaba² ⇒ ab	[13]
6.	abcabac ⇒ cb	[6]
7.	abacab ⇒ abcaba	[5]
8.	abac²b ⇒ (abc)²	[16]
9.	cb² ⇒ c²abac	[7]
10.	c(ba)² ⇒ abcab	[8]
11.	cbabc ⇒ abc²b	[10]
12.	cbcaba² ⇒ cb	[18]
13.	cbacab ⇒ cbcaba	[19]
14.	cbac²b ⇒ cbcabc	[23]
15.	c²(ab)² ⇒ cac²	[21]
16.	c²abcb ⇒ cac³abac	[24]
17.	c²abacb ⇒ cbcabac	[9]
18.	abc(ab)² ⇒ abac²	[15]
19.	(abc)²b ⇒ abac³abac	[26]
20.	ab(cab)²a ⇒ cbab	[11]
21.	(abc)³ ⇒ (cb)²	[12]
22.	cbc(ab)² ⇒ cbac²	[25]
23.	cbcabcb ⇒ cbac³abac	[27]
24.	cbcabacb ⇒ (c²aba)²c	[20]

# ab:abaabbaba=ab ac/b abb=c morph:3/0
ccabaa=c
cacab=ccaba
caccb=ccabc
abb=c
abcabaa=ab
abcabac=cb
abacab=abcaba
abaccb=abcabc
cbb=ccabac
cbaba=abcab
cbabc=abccb
cbcabaa=cb
cbacab=cbcaba
cbaccb=cbcabc
ccabab=cacc
ccabcb=cacccabac
ccabacb=cbcabac
abcabab=abacc
abcabcb=abacccabac
abcabcaba=cbab
abcabcabc=cbcb
cbcabab=cbacc
cbcabcb=cbacccabac
cbcabacb=ccabaccabac