#1645 ⟨a, b | aab=ba, bbb=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ b2 = b and b ⋅ 1 = b, however b2 ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
b2 ⋅ b = b and 1 ⋅ b = b, however b2 ≠ 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:aab=ba,bbb=b reversed:a/b - -
aaaaaaaab=aab
ba=aab
bbb=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 19788 | ⟨a, b | aaa=a, aaab=bba⟩ | φ(a) = b, φ(b) = a |