#2890 ⟨a, b | aa=a, babbb=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a = a and a ⋅ 1 = a, however a ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a ⋅ a = a and 1 ⋅ a = a, however a ≠ 1
- 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:aa=a,babbb=a b/a - -
abbbbbbbbbbbb=a
ba=abbbbbbbbb
aa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
6 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 8626 | ⟨a, b | aa=a, baabbb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8902 | ⟨a, b | aa=a, babbb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 15655 | ⟨a, b | aab=ab, babbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24154 | ⟨a, b | aa=a, baaabbb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24699 | ⟨a, b | aa=a, baabbb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25240 | ⟨a, b | aa=a, babbb=aaa⟩ | φ(a) = a, φ(b) = b |