#20181 ⟨a, b | aba=a, aaaa=bbb⟩

Contents

1. Properties
2. Rewriting system

Properties

• Sum of relation sides is 11
• Infinite non-cancellative non-commutative monoid
• Element a²b²a has infinite order
• Not left cancellative, because left multiplication by a is not injective:
  • a ⋅ ba = a and a ⋅ 1 = a, however ba ≠ 1
• Not right cancellative, because right multiplication by a is not injective:
  • ab ⋅ a = a and 1 ⋅ a = a, however ab ≠ 1

Rewriting system

1

# ab:aba=a,aaaa=bbb b/a - -
bbbbbbbbbb=bbb
abbb=bbbbbbbbb
bbba=bbbbbbbbb
aba=a
aaaa=bbb