#2425 ⟨a, b | aaabaa=abaa⟩

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Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a²ba² = aba² and a ⋅ ba² = aba², however a²ba² ≠ ba²
Not right cancellative, because right multiplication by a is not injective:
- a³ba ⋅ a = aba² and aba ⋅ a = aba², however a³ba ≠ aba
Enveloping group is isomorphic to ℤ₂ ∗ ℤ

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 = abaa
Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# ab:aaabaa=abaa ac/b abaa=c magic:0
aac=c
abc=cc
abaa=c
abac=cac
cbc=cacc
cbaa=cac
cbac=cacac

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