#19523 ⟨a, b | aab=b, aabaa=bb⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ b = ba2 and b ⋅ a2 = ba2, however b ≠ a2
- 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 recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=b,aabaa=bb a/b - -
baaaa=baa
aab=b
bb=baa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20076 | ⟨a, b | aab=b, aabb=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20083 | ⟨a, b | aab=b, abaa=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 20124 | ⟨a, b | aab=b, baab=baa⟩ | φ(a) = a, φ(b) = b |