#5385 ⟨a, b | abbaaab=abaa⟩

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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 shortlex with a < b < c
Auxiliary generators:
1. abaa=c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	aba² ⇒ c	[2]
2.	cba² ⇒ abac	[4]
3.	ca⁴ ⇒ abac²	[10]
4.	(ca)²b ⇒ abac²	[12]
5.	abacab ⇒ ca²	[6]
6.	ab²a²c ⇒ ca²	[18]
7.	cac²a² ⇒ ca³c²	[14]
8.	cbacab ⇒ abaca²	[9]
9.	cb²a²c ⇒ abaca²	[17]
10.	abac²a² ⇒ cac²	[13]
11.	ab²a³b ⇒ c	[3]
12.	ca³cab ⇒ cac²	[19]
13.	cbac²a² ⇒ abacac²	[15]
14.	cb²a³b ⇒ abac	[7]
15.	ca³c²a² ⇒ ab(ac²)²	[16]

# ab:abbaaab=abaa abc abaa=c magic:0
abaa=c
cbaa=abac
caaaa=abacc
cacab=abacc
abacab=caa
abbaac=caa
caccaa=caaacc
cbacab=abacaa
cbbaac=abacaa
abaccaa=cacc
abbaaab=c
caaacab=cacc
cbaccaa=abacacc
cbbaaab=abac
caaaccaa=abaccacc