#3011 ⟨a, b, c | aba=a, aca=c⟩

Contents

1. Properties
2. Rewriting system

Properties

• Sum of relation sides is 8
• Infinite non-cancellative non-commutative monoid
• Element a 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

# abc:aba=a,aca=c abc - -
aba=a
abc=c
aca=c
cba=c
cbc=acc
cca=acc