#56 ⟨a, b | aa=a, ab=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 6
- 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,ab=b ab - -
aa=a
ab=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 7 | 238 | ⟨a, b | aa=a, aab=b⟩ | φ(a) = a, φ(b) = b |
| 8 | 883 | ⟨a, b | aa=a, aaab=b⟩ | φ(a) = a, φ(b) = b |
| 9 | 2859 | ⟨a, b | aa=a, aaaab=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 8571 | ⟨a, b | aa=a, aaaaab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 24047 | ⟨a, b | aa=a, aaaaaab=b⟩ | φ(a) = a, φ(b) = b |