#5345 ⟨a, b | aaa=bb, abb=aa⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element ab has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a3 = a2 and a ⋅ a = a2, however a3 ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
a3 ⋅ a = a2 and a ⋅ a = a2, however a3 ≠ a
- 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:aaa=bb,abb=aa a/b - -
aaaa=aa
abaa=baaa
aab=baa
bb=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16045 | ⟨a, b | aaa=bb, aaaa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 16285 | ⟨a, b | aab=bb, aabb=aa⟩ | φ(a) = b, φ(b) = a |
| 11 | 16309 | ⟨a, b | aab=bb, baab=aa⟩ | φ(a) = b, φ(b) = a |