#1971 ⟨a, b | aababbaa=ba⟩

Quick links

Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by a is not injective:
- a²bab²a ⋅ a = ba and b ⋅ a = ba, however a²bab²a ≠ b
Enveloping group: ⟨a, b | aababbab^-1⟩

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

Auxiliary generators:
1. c = ba
Reduction order:
- Right-to-left recursive path with deg(c) = 0; deg(a) = deg(b) = 1, a < b
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	ba ⇒ c	[2]
2.	b²c ⇒ cacbc²	[8]
3.	cacbca ⇒ bc	[5]
4.	a²cbc² ⇒ bc	[6]
5.	(cac)²bc² ⇒ bc²bca	[9]
6.	cac(bc)² ⇒ bcacbc²	[11]
7.	a²cbca ⇒ c	[4]
8.	a²c²acbc² ⇒ c²bca	[12]
9.	a²c(bc)² ⇒ cacbc²	[10]

# ab:aababbaa=ba reversed:c/ab ba=c magic:0
ba=c
bbc=cacbcc
cacbca=bc
aacbcc=bc
caccacbcc=bccbca
cacbcbc=bcacbcc
aacbca=c
aaccacbcc=ccbca
aacbcbc=cacbcc

Up:	Monoids with two generators and one relation
Prev:	#1970 ⟨a, b \| aababbaa=ab⟩
Next:	#1972 ⟨a, b \| aababbaa=bb⟩