#282 ⟨a, b | ab=b, bb=ab⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 7
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ b = b and b ⋅ 1 = b, however b ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
a ⋅ b = b and 1 ⋅ b = b, however a ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=b,bb=ab ab - -
ab=b
bb=b
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
10 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 1625 | ⟨a, b | aab=ab, abb=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5133 | ⟨a, b | aab=ab, aabb=b⟩ | φ(a) = a, φ(b) = b |
| 10 | 5137 | ⟨a, b | aab=ab, abab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12460 | ⟨a, b | aabb=ab, abbb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12521 | ⟨a, b | abab=ab, abbb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12619 | ⟨a, b | baab=ab, babb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 12621 | ⟨a, b | baab=ab, bbab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15616 | ⟨a, b | aab=ab, aaabb=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15620 | ⟨a, b | aab=ab, aabab=b⟩ | φ(a) = a, φ(b) = b |
| 11 | 15628 | ⟨a, b | aab=ab, abaab=b⟩ | φ(a) = a, φ(b) = b |