#4253 ⟨a, b | abaaabbba=ab⟩

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

#	Rule	Proof
1.	c²a ⇒ cac	[12]
2.	(ca)² ⇒ ca²c	[9]
3.	ca²ca ⇒ c	[6]
4.	abca ⇒ abac	[10]
5.	abaca ⇒ aba²c	[7]
6.	aba²ca ⇒ ab	[3]
7.	cb ⇒ aba²c²	[4]
8.	ab²ca ⇒ ab²ac	[11]
9.	ab²aca ⇒ ab²a²c	[8]
10.	ab²a²ca ⇒ ab²	[5]
11.	ab³ ⇒ c	[2]

# ab:abaaabbba=ab ac/b abbb=c morph:4/0
cca=cac
caca=caac
caaca=c
abca=abac
abaca=abaac
abaaca=ab
cb=abaacc
abbca=abbac
abbaca=abbaac
abbaaca=abb
abbb=c