#5535 ⟨a, b | aaabaa=aaaba⟩

Quick links

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 ⋅ a²ba² = a³ba and a ⋅ a²ba = a³ba, however a²ba² ≠ a²ba
• Not right cancellative, because right multiplication by a is not injective:
  • a³ba ⋅ a = a³ba and a³b ⋅ a = a³ba, however a³ba ≠ a³b
• Enveloping group is isomorphic to ℤ

Rewriting system

1

# ab:aaabaa=aaaba acb aaaba=c magic:0
ca=c
cba=cc
cbc=ccc
aaaba=c
aaabc=cc