#1257 ⟨a, b | ababa=aaba⟩

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Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ (ba)² = a²ba and a ⋅ aba = a²ba, however (ba)² ≠ aba
Not right cancellative, because right multiplication by a is not injective:
- (ab)² ⋅ a = a²ba and a²b ⋅ a = a²ba, however (ab)² ≠ a²b
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 = aaba
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:ababa=aaba b/ca aaba=c magic:0
cbc=cc
ac=cba
abc=cba
cbaba=caba
aaba=c
ababa=c

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