#19175 ⟨a, b | aba=b, aaabbb=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ a6 = b and b ⋅ 1 = b, however a6 ≠ 1
- 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:aba=b,aaabbb=b a/b - -
baaaaaa=b
ab=baaaaa
bbb=baaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
9 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 19185 | ⟨a, b | aba=b, aabbab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 19203 | ⟨a, b | aba=b, abbaab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 19215 | ⟨a, b | aba=b, baaabb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 19732 | ⟨a, b | aba=b, aabbb=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 19747 | ⟨a, b | aba=b, abbab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 19760 | ⟨a, b | aba=b, baabb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20261 | ⟨a, b | aba=b, aaab=bbb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20296 | ⟨a, b | aba=b, abbb=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20307 | ⟨a, b | aba=b, babb=aab⟩ | φ(a) = a, φ(b) = b |