#2876 ⟨a, b | aa=a, ababb=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element ba has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a = a and a ⋅ 1 = a, however a ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a ⋅ a = a and 1 ⋅ a = a, however a ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=a,ababb=a ab - -
aa=a
ababb=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
10 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 8588 | ⟨a, b | aa=a, aababb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8602 | ⟨a, b | aa=a, abaabb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 8877 | ⟨a, b | aa=a, ababb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 15631 | ⟨a, b | aab=ab, ababb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24066 | ⟨a, b | aa=a, aaababb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24080 | ⟨a, b | aa=a, aabaabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24108 | ⟨a, b | aa=a, abaaabb=a⟩ | φ(a) = a, φ(b) = b |
| 11 | 24627 | ⟨a, b | aa=a, aababb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24653 | ⟨a, b | aa=a, abaabb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25190 | ⟨a, b | aa=a, ababb=aaa⟩ | φ(a) = a, φ(b) = b |