#20924 ⟨a, b | ab=aa, aaaa=baa⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b = a2 and a ⋅ a = a2, however b ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
ba ⋅ a = a4 and a3 ⋅ a = a4, however ba ≠ a3
- Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=aa,aaaa=baa a/b - -
aaaaa=aaaa
baa=aaaa
ab=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
15 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20925 | ⟨a, b | ab=aa, aaaa=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20932 | ⟨a, b | ab=aa, aaab=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20933 | ⟨a, b | ab=aa, aaab=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20940 | ⟨a, b | ab=aa, aaba=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20941 | ⟨a, b | ab=aa, aaba=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20948 | ⟨a, b | ab=aa, aabb=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20949 | ⟨a, b | ab=aa, aabb=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20956 | ⟨a, b | ab=aa, abaa=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20957 | ⟨a, b | ab=aa, abaa=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20964 | ⟨a, b | ab=aa, abab=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20965 | ⟨a, b | ab=aa, abab=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20972 | ⟨a, b | ab=aa, abba=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20973 | ⟨a, b | ab=aa, abba=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 20980 | ⟨a, b | ab=aa, abbb=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 20981 | ⟨a, b | ab=aa, abbb=bab⟩ | φ(a) = a, φ(b) = b |