#8883 ⟨a, b | aa=a, abbab=ba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a = a and a ⋅ 1 = a, however a ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a ⋅ a = a and 1 ⋅ a = a, however a ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=a,abbab=ba ab - -
aa=a
aba=ba
bba=bab
babb=ba
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 24636 | ⟨a, b | aa=a, aabbab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24659 | ⟨a, b | aa=a, ababab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24671 | ⟨a, b | aa=a, abbaab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25202 | ⟨a, b | aa=a, abbab=baa⟩ | φ(a) = a, φ(b) = b |