#5357 ⟨a, b | abababa=aaba⟩

Quick links

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

#	Rule	Proof
1.	cba ⇒ abc	[5]
2.	cbc ⇒ a²c	[11]
3.	cac ⇒ ac²	[12]
4.	a²ba ⇒ c	[2]
5.	a²bc ⇒ abac	[19]
6.	a³c ⇒ abc²	[14]
7.	caba ⇒ abac	[21]
8.	cabc ⇒ abc²	[17]
9.	ca²c ⇒ a²c²	[18]
10.	(ab)²c ⇒ ac	[7]
11.	aba²c ⇒ c²	[16]
12.	a(ba)²c ⇒ a²c	[20]
13.	a(ba)³ ⇒ c	[3]

# ab:abababa=aaba bac aaba=c magic:0
cba=abc
cbc=aac
cac=acc
aaba=c
aabc=abac
aaac=abcc
caba=abac
cabc=abcc
caac=aacc
ababc=ac
abaac=cc
ababac=aac
abababa=c