#5395 ⟨a, b | aab=ba, 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 = ab2 and a ⋅ b2 = ab2, however ab ≠ b2
- Not right cancellative, because right multiplication by b is not injective:
-
a2 ⋅ b = ab2 and ab ⋅ b = ab2, however a2 ≠ ab
- 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=ba,abb=ba b/a - -
abbbbb=abbbb
ba=abb
aab=abb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16510 | ⟨a, b | aab=ba, abb=aab⟩ | φ(a) = a, φ(b) = b |