#16231 ⟨a, b | aab=ba, abab=ba⟩
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 a is not injective:
-
a ⋅ a2b = a2b and a ⋅ ab = a2b, however a2b ≠ ab
- Not right cancellative, because right multiplication by b is not injective:
-
a3 ⋅ b = a2b and a2 ⋅ b = a2b, however a3 ≠ a2
- Reduction order:
- Right-to-left recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=ba,abab=ba reversed:a/b - -
aaab=aab
ba=aab
aabb=aab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16235 | ⟨a, b | aab=ba, abba=ba⟩ | φ(a) = a, φ(b) = b |