#4260 ⟨a, b, c | aab=1, bcaa=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 ⋅ aba = a and a ⋅ 1 = a, however aba ≠ 1
• Not right cancellative, because right multiplication by ab is not injective:
  • aba ⋅ ab = ab and 1 ⋅ ab = ab, however aba ≠ 1

Rewriting system

1

# abc:aab=1,bcaa=c cbad cb=d morph:2/0
cb=d
bc=d
dc=cd
db=bd
cab=da
aac=caa
aab=1
aad=c
dac=cad
dab=bda
daa=c