#5181 ⟨a, b | aab=ba, babb=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 ⋅ a = b and b ⋅ 1 = b, however a ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
a2 ⋅ b = b and 1 ⋅ b = b, however a2 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=ba,babb=b ab - -
ba=b
aab=b
bbb=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
8 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 5185 | ⟨a, b | aab=ba, bbab=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5187 | ⟨a, b | aab=ba, bbba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15688 | ⟨a, b | aab=ba, aabbb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15712 | ⟨a, b | aab=ba, baabb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15718 | ⟨a, b | aab=ba, babba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15724 | ⟨a, b | aab=ba, bbaab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15730 | ⟨a, b | aab=ba, bbbaa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15856 | ⟨a, b | aba=ab, aabbb=b⟩ | φ(a) = a, φ(b) = b |