#964 ⟨a, b | aa=a, abb=ba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- 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 ⋅ 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 recursive path with deg(b) = 0; deg(a) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=a,abb=ba b/a - -
abbbb=abb
ba=abb
aa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
7 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 3013 | ⟨a, b | aa=a, aabb=ba⟩ | φ(a) = a, φ(b) = b |
| 9 | 3143 | ⟨a, b | aa=a, baa=abb⟩ | φ(a) = a, φ(b) = b |
| 10 | 8853 | ⟨a, b | aa=a, aaabb=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9138 | ⟨a, b | aa=a, aabb=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24601 | ⟨a, b | aa=a, aaaabb=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25142 | ⟨a, b | aa=a, aaabb=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25687 | ⟨a, b | aa=a, baaa=aabb⟩ | φ(a) = a, φ(b) = b |