#2244 ⟨a, b | ab=aa, baa=aa⟩
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 ⋅ b = a2 and a ⋅ a = a2, however b ≠ a
- Not right cancellative, because right multiplication by a is not injective:
-
ba ⋅ a = a2 and a ⋅ a = a2, however ba ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=aa,baa=aa ab - -
ab=aa
baa=aa
aaaa=aaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
3 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 2245 | ⟨a, b | ab=aa, baa=ab⟩ | φ(a) = a, φ(b) = b |
| 9 | 2248 | ⟨a, b | ab=aa, bab=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 2249 | ⟨a, b | ab=aa, bab=ab⟩ | φ(a) = a, φ(b) = b |