#3435 ⟨a, b, c | ba=ac, aaa=a⟩

Contents

1. Properties
2. Rewriting system

Properties

• Sum of relation sides is 8
• Infinite non-cancellative non-commutative monoid
• Element b has infinite order
• Not left cancellative, because left multiplication by a is not injective:
  • a ⋅ a² = a and a ⋅ 1 = a, however a² ≠ 1
• Not right cancellative, because right multiplication by a is not injective:
  • a² ⋅ a = a and 1 ⋅ a = a, however a² ≠ 1

Rewriting system

1

# abc:ba=ac,aaa=a abdc caa=d morph:3/1
ac=ad
ba=ad
dc=dd
ca=da
aaa=a
daa=d