#5071 ⟨a, b | aaabbaa=aaba⟩

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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. aaba=c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	a²ba ⇒ c	[2]
2.	caba ⇒ a²bc	[4]
3.	c(ba)² ⇒ cab²c	[10]
4.	a³b²c ⇒ cba	[7]
5.	ca²b²c ⇒ a²bcba	[11]
6.	cab²a² ⇒ cba	[15]
7.	cab²ac ⇒ cbc	[14]
8.	a³b²a² ⇒ c	[3]
9.	a³b²ac ⇒ a²bc	[8]
10.	ca²b²a² ⇒ a²bc	[17]
11.	ca²b²ac ⇒ cabc	[9]
12.	cba²b²c ⇒ cab²cba	[12]
13.	cba²b²a² ⇒ cab²c	[16]
14.	cba²b²ac ⇒ cbabc	[13]

# ab:aaabbaa=aaba abc aaba=c magic:0
aaba=c
caba=aabc
cbaba=cabbc
aaabbc=cba
caabbc=aabcba
cabbaa=cba
cabbac=cbc
aaabbaa=c
aaabbac=aabc
caabbaa=aabc
caabbac=cabc
cbaabbc=cabbcba
cbaabbaa=cabbc
cbaabbac=cbabc