#16230 ⟨a, b | aab=ba, abab=ab⟩
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 ⋅ b2 = ab and a ⋅ b = ab, however b2 ≠ b
- Not right cancellative, because right multiplication by b is not injective:
-
ab ⋅ b = ab and a ⋅ b = ab, however ab ≠ a
- 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=ab reversed:a/b - -
aaab=ab
ba=aab
abb=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16234 | ⟨a, b | aab=ba, abba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16387 | ⟨a, b | aba=ab, aabb=ba⟩ | φ(a) = a, φ(b) = b |