#1982 ⟨a, b | aabbaaab=ab⟩

Quick links

1. Properties
2. Rewriting system

Properties

• Presentation has sum-of-sides 10
• Infinite non-cancellative non-commutative monoid
• Not left cancellative, because left multiplication by a is not injective:
  • a ⋅ ab²a³b = ab and a ⋅ b = ab, however ab²a³b ≠ b
• Not right cancellative, because right multiplication by b is not injective:
  • a²b²a³ ⋅ b = ab and a ⋅ b = ab, however a²b²a³ ≠ a
• Enveloping group: ⟨a, b | aaaabb⟩

Rewriting system

1

# ab:aabbaaab=ab ab
abbaab=aabbab
abbaaab=aaabbab
aaaabbab=ab