#2101 ⟨a, b | aba=a, babb=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 left cancellative, because left multiplication by b is not injective:
-
b ⋅ b = b and b ⋅ 1 = b, however b ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
b ⋅ b = b and 1 ⋅ b = b, however b ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aba=a,babb=b ab - -
bb=b
aba=a
bab=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 14828 | ⟨a, b | abba=a, babbb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 14830 | ⟨a, b | abba=a, bbabb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 19149 | ⟨a, b | aba=a, bababb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 19151 | ⟨a, b | aba=a, babbab=b⟩ | φ(a) = a, φ(b) = b |