#798 ⟨a, b, c | ab=a, bacc=1⟩

Contents

1. Properties
2. Rewriting system
3. Isomorphic instances

Properties

• Sum of relation sides is 7
• Infinite non-cancellative non-commutative monoid
• Element a has infinite order
• Not left cancellative, because left multiplication by a is not injective:
  • a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
• Not right cancellative, because right multiplication by ac² is not injective:
  • ac²b ⋅ ac² = ac² and 1 ⋅ ac² = ac², however ac²b ≠ 1

Rewriting system

1

# abc:ab=a,bacc=1 abc - -
ab=a
aacc=a
bacc=1

Isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.