#13219 ⟨a, b | abb=aba, bbb=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 b is not injective:
-
b ⋅ b2a = b4 and b ⋅ b3 = b4, however b2a ≠ b3
- Not right cancellative, because right multiplication by b is not injective:
-
a ⋅ b = b3 and b2 ⋅ b = b3, however a ≠ b2
- 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:abb=aba,bbb=ab b/a - -
bbbbbb=bbbbb
ab=bbb
bbba=bbbb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 13260 | ⟨a, b | bab=aba, bbb=ab⟩ | φ(a) = a, φ(b) = b |