#1810 ⟨a, b, c | aba=ab, acc=1⟩

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 d is not injective:
  • d ⋅ a = d and d ⋅ 1 = d, however a ≠ 1
• Not right cancellative, because right multiplication by c² is not injective:
  • c²a ⋅ c² = c² and 1 ⋅ c² = c², however c²a ≠ 1

Rewriting system

1

# abc:aba=ab,acc=1 adbc ab=d morph:2/1
ab=d
da=d
db=dd
acc=1
dcc=d