#963 ⟨a, b | aa=a, abb=ab⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- 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,abb=ab ab - -
aa=a
abb=ab
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
9 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 3012 | ⟨a, b | aa=a, aabb=ab⟩ | φ(a) = a, φ(b) = b |
| 9 | 3140 | ⟨a, b | aa=a, abb=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 8852 | ⟨a, b | aa=a, aaabb=ab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9121 | ⟨a, b | aa=a, aaab=abb⟩ | φ(a) = a, φ(b) = b |
| 10 | 9135 | ⟨a, b | aa=a, aabb=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24600 | ⟨a, b | aa=a, aaaabb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25125 | ⟨a, b | aa=a, aaaab=abb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25139 | ⟨a, b | aa=a, aaabb=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25664 | ⟨a, b | aa=a, aabb=aaab⟩ | φ(a) = a, φ(b) = b |