#7054 ⟨a, b | ab=aa, aaaa=aa⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- 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:
-
a3 ⋅ a = a2 and a ⋅ a = a2, however a3 ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=aa,aaaa=aa ab - -
ab=aa
aaaa=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
15 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 7055 | ⟨a, b | ab=aa, aaaa=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 7058 | ⟨a, b | ab=aa, aaab=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 7059 | ⟨a, b | ab=aa, aaab=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 7062 | ⟨a, b | ab=aa, aaba=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 7063 | ⟨a, b | ab=aa, aaba=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 7066 | ⟨a, b | ab=aa, aabb=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 7067 | ⟨a, b | ab=aa, aabb=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 7070 | ⟨a, b | ab=aa, abaa=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 7071 | ⟨a, b | ab=aa, abaa=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 7074 | ⟨a, b | ab=aa, abab=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 7075 | ⟨a, b | ab=aa, abab=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 7078 | ⟨a, b | ab=aa, abba=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 7079 | ⟨a, b | ab=aa, abba=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 7082 | ⟨a, b | ab=aa, abbb=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 7083 | ⟨a, b | ab=aa, abbb=ab⟩ | φ(a) = a, φ(b) = b |