#2055 ⟨a, b | aab=b, aaab=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not right cancellative, because right multiplication by b is not injective:
-
a ⋅ b = b and 1 ⋅ b = b, however a ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=b,aaab=b ab - -
ab=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
6 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 5129 | ⟨a, b | aab=ab, aaab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 14476 | ⟨a, b | aaab=b, aaaab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15612 | ⟨a, b | aab=ab, aaaab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 18963 | ⟨a, b | aab=b, aaaaab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 19509 | ⟨a, b | aab=b, aaaab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20057 | ⟨a, b | aab=b, aaab=aab⟩ | φ(a) = a, φ(b) = b |