#19278 ⟨a, b | aaa=a, abbba=ab⟩

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 ⋅ a² = a and a ⋅ 1 = a, however a² ≠ 1
• Not right cancellative, because right multiplication by a is not injective:
  • a² ⋅ a = a and 1 ⋅ a = a, however a² ≠ 1

Rewriting system

1

# ab:aaa=a,abbba=ab ab - -
aaa=a
abaa=ab
abba=abab
abbb=aba
ababa=abb
ababb=ab