#6501 ⟨a, b | aba=b, aabbb=b⟩
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 b is not injective:
-
b ⋅ a4 = b and b ⋅ 1 = b, however a4 ≠ 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,aabbb=b a/b - -
baaaa=b
ab=baaa
bbb=baa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6509 | ⟨a, b | aba=b, abbab=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 6517 | ⟨a, b | aba=b, baabb=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 6786 | ⟨a, b | aba=b, abbb=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 6792 | ⟨a, b | aba=b, babb=ab⟩ | φ(a) = a, φ(b) = b |