#5731 ⟨a, b | aabbaa=aabba⟩

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1. Properties
2. 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 ⋅ ab²a² = a²b²a and a ⋅ ab²a = a²b²a, however ab²a² ≠ ab²a
• Not right cancellative, because right multiplication by a is not injective:
  • a²b²a ⋅ a = a²b²a and a²b² ⋅ a = a²b²a, however a²b²a ≠ a²b²
• Enveloping group is isomorphic to ℤ

Rewriting system

1

# ab:aabbaa=aabba abc aabba=c magic:0
ca=c
cbba=cc
cbbc=ccc
aabba=c
aabbc=cc