#5823 ⟨a, b | abaaab=abbba⟩

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Properties
Rewriting system

Properties

Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ba³b = ab³a and a ⋅ b³a = ab³a, however ba³b ≠ b³a
Enveloping group: ⟨a, b | aaabba^-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 = abbba
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.	cb³a ⇒ ab³c	[4]
2.	ab³a ⇒ c	[2]
3.	cba²c ⇒ ab³cb²a	[9]
4.	c(b²a)² ⇒ ca²c	[8]
5.	aba²c ⇒ cb²a	[6]
6.	ca³b ⇒ cb²a	[10]
7.	cba³b ⇒ ab³c	[7]
8.	cb²a³c ⇒ ca²cb²a	[12]
9.	aba³b ⇒ c	[3]
10.	cb²a⁴b ⇒ ca²c	[11]

# ab:abaaab=abbba bc/a abbba=c magic:0
cbbba=abbbc
abbba=c
cbaac=abbbcbba
cbbabba=caac
abaac=cbba
caaab=cbba
cbaaab=abbbc
cbbaaac=caacbba
abaaab=c
cbbaaaab=caac

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