#5313 ⟨a, b | aaa=ab, aab=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 = a3 and a ⋅ a2 = a3, however b ≠ a2
- 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:aaa=ab,aab=ba a/b - -
aaaaa=aaaa
ba=aaaa
ab=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 5317 | ⟨a, b | aaa=ab, aba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 15983 | ⟨a, b | aaa=ab, aaaa=ba⟩ | φ(a) = a, φ(b) = b |