#9149 ⟨a, b | aa=a, abab=bbb⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element ab2 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:
- Right-to-left recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=a,abab=bbb reversed:a/b - -
aa=a
bbb=abab
babab=ababb
ababbab=ababb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 25159 | ⟨a, b | aa=a, aabab=bbb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25183 | ⟨a, b | aa=a, abaab=bbb⟩ | φ(a) = a, φ(b) = b |