#2228 ⟨a, b | ab=aa, aaa=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:
-
a2 ⋅ a = a2 and a ⋅ a = a2, however a2 ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=aa,aaa=aa ab - -
ab=aa
aaa=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
12 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 2229 | ⟨a, b | ab=aa, aaa=ab⟩ | φ(a) = a, φ(b) = b |
| 9 | 2232 | ⟨a, b | ab=aa, aab=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 2233 | ⟨a, b | ab=aa, aab=ab⟩ | φ(a) = a, φ(b) = b |
| 9 | 2236 | ⟨a, b | ab=aa, aba=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 2237 | ⟨a, b | ab=aa, aba=ab⟩ | φ(a) = a, φ(b) = b |
| 9 | 2240 | ⟨a, b | ab=aa, abb=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 2241 | ⟨a, b | ab=aa, abb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 15946 | ⟨a, b | aaa=aa, aaaa=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16094 | ⟨a, b | aab=aa, aabb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16149 | ⟨a, b | aab=ab, aaab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 16357 | ⟨a, b | aba=aa, abba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16389 | ⟨a, b | aba=ab, abaa=aa⟩ | φ(a) = a, φ(b) = b |