#1016 ⟨a, b | ab=a, bba=aa⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a2 ⋅ a = a2 and a ⋅ a = a2, however a2 ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,bba=aa ab - -
ab=a
aaa=aa
bba=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
19 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 3124 | ⟨a, b | ab=a, bbab=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 3188 | ⟨a, b | ab=a, bba=aab⟩ | φ(a) = a, φ(b) = b |
| 9 | 3189 | ⟨a, b | ab=a, bba=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9092 | ⟨a, b | ab=a, bbabb=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9286 | ⟨a, b | ab=a, aabb=bba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9302 | ⟨a, b | ab=a, abab=bba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9310 | ⟨a, b | ab=a, abba=bba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9361 | ⟨a, b | ab=a, bbab=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9362 | ⟨a, b | ab=a, bbab=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25080 | ⟨a, b | ab=a, bbabbb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25466 | ⟨a, b | ab=a, aabbb=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25498 | ⟨a, b | ab=a, ababb=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25514 | ⟨a, b | ab=a, abbab=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25522 | ⟨a, b | ab=a, abbba=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25621 | ⟨a, b | ab=a, bbabb=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25622 | ⟨a, b | ab=a, bbabb=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25873 | ⟨a, b | ab=a, bbab=aabb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25875 | ⟨a, b | ab=a, bbab=abab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25876 | ⟨a, b | ab=a, bbab=abba⟩ | φ(a) = a, φ(b) = b |