#2230 ⟨a, b | ab=aa, aaa=ba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b = a2 and a ⋅ a = a2, however b ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
b ⋅ a = a3 and a2 ⋅ a = a3, however b ≠ a2
- Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=aa,aaa=ba a/b - -
aaaa=aaa
ba=aaa
ab=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 2234 | ⟨a, b | ab=aa, aab=ba⟩ | φ(a) = a, φ(b) = b |
| 9 | 2238 | ⟨a, b | ab=aa, aba=ba⟩ | φ(a) = a, φ(b) = b |
| 9 | 2242 | ⟨a, b | ab=aa, abb=ba⟩ | φ(a) = a, φ(b) = b |