#9162 ⟨a, b | aa=a, abbb=bba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element ba 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,abbb=bba b/a - -
abbbbbbbbb=abbbbbb
bba=abbb
aa=a
ababbb=abbb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 25174 | ⟨a, b | aa=a, aabbb=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25712 | ⟨a, b | aa=a, bbaa=abbb⟩ | φ(a) = a, φ(b) = b |