#5379 ⟨a, b | aab=ab, abb=ba⟩
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 ⋅ ab = ab and a ⋅ b = ab, however ab ≠ b
- Not right cancellative, because right multiplication by b is not injective:
-
a2 ⋅ b = ab and a ⋅ b = ab, however a2 ≠ a
- Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=ab,abb=ba b/a - -
abbbbb=abbb
ba=abb
aab=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16159 | ⟨a, b | aab=ab, aabb=ba⟩ | φ(a) = a, φ(b) = b |