#16540 ⟨a, b | aba=ab, bba=aaa⟩

Contents

1. Properties
2. Rewriting system

Properties

• Sum of relation sides is 11
• Infinite non-cancellative non-commutative monoid
• Element b has infinite order
• Not left cancellative, because left multiplication by a is not injective:
  • a ⋅ ab = ab and a ⋅ b = ab, however ab ≠ b
• Not right cancellative, because right multiplication by b is not injective:
  • a² ⋅ b = ab and a ⋅ b = ab, however a² ≠ a

Rewriting system

1

# ab:aba=ab,bba=aaa ab - -
aab=ab
aba=ab
bba=aaa
aaaa=abb
abbb=ab