#6746 ⟨a, b | aba=a, abba=ab⟩

Contents

1. Properties
2. Rewriting system

Properties

• Sum of relation sides is 10
• 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

# ab:aba=a,abba=ab acb abb=c morph:3/1
ca=ab
cb=cc
aba=a
abc=c
abb=c