#5073 ⟨a, b | aaabbaa=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:
- Right-to-left shortlex with b < a < c
Auxiliary generators:
1. abaa=c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	aba² ⇒ c	[2]
2.	abac ⇒ cba²	[4]
3.	(ab)²c ⇒ cab²c	[9]
4.	cab²a² ⇒ abc	[8]
5.	a³b²c ⇒ abc	[15]
6.	ca²b²c ⇒ cbc	[12]
7.	cab²ac ⇒ abcba²	[10]
8.	a³b²a² ⇒ c	[3]
9.	ca²b²a² ⇒ cba²	[7]
10.	cab²abc ⇒ abcab²c	[11]
11.	a³b²ac ⇒ cba²	[17]
12.	ca²b²ac ⇒ cbac	[13]
13.	a³b²abc ⇒ cab²c	[16]
14.	ca²b²abc ⇒ cbabc	[14]

# ab:aaabbaa=abaa reversed:bac abaa=c magic:0
abaa=c
abac=cbaa
ababc=cabbc
cabbaa=abc
aaabbc=abc
caabbc=cbc
cabbac=abcbaa
aaabbaa=c
caabbaa=cbaa
cabbabc=abcabbc
aaabbac=cbaa
caabbac=cbac
aaabbabc=cabbc
caabbabc=cbabc