#3018 ⟨a, b | aa=a, abab=bb⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element b 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,abab=bb ab - -
aa=a
abb=bb
abab=bb
bbab=bbb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 8861 | ⟨a, b | aa=a, aabab=bb⟩ | φ(a) = a, φ(b) = b |
| 10 | 8873 | ⟨a, b | aa=a, abaab=bb⟩ | φ(a) = a, φ(b) = b |
| 11 | 24610 | ⟨a, b | aa=a, aaabab=bb⟩ | φ(a) = a, φ(b) = b |
| 11 | 24622 | ⟨a, b | aa=a, aabaab=bb⟩ | φ(a) = a, φ(b) = b |
| 11 | 24649 | ⟨a, b | aa=a, abaaab=bb⟩ | φ(a) = a, φ(b) = b |