#2073 ⟨a, b | aab=b, baba=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:aab=b,baba=b ab - -
bb=b
aab=b
baa=b
bab=ba
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 12393 | ⟨a, b | aaba=ba, baba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 18981 | ⟨a, b | aab=b, aababa=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 19029 | ⟨a, b | aab=b, baaaba=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 19545 | ⟨a, b | aab=b, ababa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20129 | ⟨a, b | aab=b, baba=aab⟩ | φ(a) = a, φ(b) = b |