#2590 ⟨a, b | ababab=aaab⟩

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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 = a³b and a ⋅ a²b = a³b, however b(ab)² ≠ a²b
Not right cancellative, because right multiplication by b is not injective:
- a(ba)² ⋅ b = a³b and a³ ⋅ b = a³b, however a(ba)² ≠ a³
Enveloping group: ⟨a, b | aabb⟩

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

# ab:ababab=aaab b/ca aaab=c magic:0
abc=cab
aac=cabab
aaab=c
ababab=c

Up:	Monoids with two generators and one relation
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