#5393 ⟨a, b | aab=ba, aba=bb⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a5b = a5b and a ⋅ a4b = a5b, however a5b ≠ a4b
- Not right cancellative, because right multiplication by b is not injective:
-
b ⋅ b = a3b and a3 ⋅ b = a3b, however b ≠ a3
- 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,aba=bb reversed:a/b - -
aaaaaab=aaaaab
ba=aab
bb=aaab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16216 | ⟨a, b | aab=ba, aaab=bb⟩ | φ(a) = a, φ(b) = b |