#2569 ⟨a, b | abaaab=abba⟩

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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 ⋅ ba³b = ab²a and a ⋅ b²a = ab²a, however ba³b ≠ b²a
Enveloping group: ⟨a, b | aaaba^-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 = abba
Reduction order:
- Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

#	Rule	Proof
1.	cb²a ⇒ ab²c	[4]
2.	ab²a ⇒ c	[2]
3.	cba²c ⇒ ab²cba	[9]
4.	c(ba)² ⇒ ca²c	[8]
5.	aba²c ⇒ cba	[6]
6.	ca³b ⇒ cba	[13]
7.	ca(ac)² ⇒ (cb)²a	[12]
8.	cba³b ⇒ ab²c	[7]
9.	cba³c ⇒ ca²cba	[10]
10.	aba³b ⇒ c	[3]
11.	(ca²)²b ⇒ cbc	[11]
12.	cba⁴b ⇒ ca²c	[14]

# ab:abaaab=abba bc/a abba=c magic:0
cbba=abbc
abba=c
cbaac=abbcba
cbaba=caac
abaac=cba
caaab=cba
caacac=cbcba
cbaaab=abbc
cbaaac=caacba
abaaab=c
caacaab=cbc
cbaaaab=caac