#2352 ⟨a, b | abbabba=aab⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ (b²a)² = a²b and a ⋅ ab = a²b, however (b²a)² ≠ ab
Enveloping group: ⟨a, b | aabba^-1b^-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 = aab
Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = deg(c) = 1, a < c
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	a²b ⇒ c	[2]
2.	cb²a ⇒ ab²c	[4]
3.	a(b²a)² ⇒ c	[3]
4.	(ab²)²c ⇒ cab	[5]
5.	ab²cab ⇒ cb²c	[8]
6.	c(ab)² ⇒ a(b²c)²	[12]
7.	cab³a ⇒ cb²c	[7]
8.	cbab²a ⇒ ac	[6]
9.	cbab²c ⇒ acab	[9]
10.	cbcab ⇒ acb²c	[11]
11.	cb²cab ⇒ cab³c	[10]
12.	cab³cab ⇒ a(b²c)³	[13]

# ab:abbabba=aab b/ac aab=c magic:0
aab=c
cbba=abbc
abbabba=c
abbabbc=cab
abbcab=cbbc
cabab=abbcbbc
cabbba=cbbc
cbabba=ac
cbabbc=acab
cbcab=acbbc
cbbcab=cabbbc
cabbbcab=abbcbbcbbc