#1118 ⟨a, b | ababab=aab⟩

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Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b(ab)² = a²b and a ⋅ ab = a²b, however b(ab)² ≠ ab
Not right cancellative, because right multiplication by b is not injective:
- a(ba)² ⋅ b = a²b and a² ⋅ b = a²b, however a(ba)² ≠ a²
Enveloping group is isomorphic to 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 = aab
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.

# ab:ababab=aab bc/a aab=c magic:0
cab=abc
cac=acc
aab=c
aac=abcc
abac=cc
ababc=ac
ababab=c

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