#7056 ⟨a, b | ab=aa, aaaa=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 ⋅ b = a2 and a ⋅ a = a2, however b ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
b ⋅ a = a4 and a3 ⋅ a = a4, however b ≠ a3
- 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,aaaa=ba a/b - -
aaaaa=aaa
ba=aaaa
ab=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
7 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 7060 | ⟨a, b | ab=aa, aaab=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 7064 | ⟨a, b | ab=aa, aaba=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 7068 | ⟨a, b | ab=aa, aabb=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 7072 | ⟨a, b | ab=aa, abaa=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 7076 | ⟨a, b | ab=aa, abab=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 7080 | ⟨a, b | ab=aa, abba=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 7084 | ⟨a, b | ab=aa, abbb=ba⟩ | φ(a) = a, φ(b) = b |