#5400 ⟨a, b | aab=ba, bab=ba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ ab2 = a2b and a ⋅ ab = a2b, however ab2 ≠ ab
- Not right cancellative, because right multiplication by b is not injective:
-
a2b ⋅ b = a2b and a2 ⋅ b = a2b, however a2b ≠ a2
- Reduction order:
- Right-to-left recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=ba,bab=ba reversed:a/b - -
aaaaaab=aaaab
ba=aab
aabb=aab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16223 | ⟨a, b | aab=ba, aabb=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 16513 | ⟨a, b | aab=ba, bab=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16541 | ⟨a, b | aba=ab, bba=aba⟩ | φ(a) = b, φ(b) = a |