#6950 ⟨a, b | ab=aa, aaaaa=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 10
- 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:
-
a4 ⋅ a = a and 1 ⋅ a = a, however a4 ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=aa,aaaaa=a ab - -
ab=aa
aaaaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
15 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 6952 | ⟨a, b | ab=aa, aaaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6954 | ⟨a, b | ab=aa, aaaba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6956 | ⟨a, b | ab=aa, aaabb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6958 | ⟨a, b | ab=aa, aabaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6960 | ⟨a, b | ab=aa, aabab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6962 | ⟨a, b | ab=aa, aabba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6964 | ⟨a, b | ab=aa, aabbb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6966 | ⟨a, b | ab=aa, abaaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6968 | ⟨a, b | ab=aa, abaab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6970 | ⟨a, b | ab=aa, ababa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6972 | ⟨a, b | ab=aa, ababb=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6974 | ⟨a, b | ab=aa, abbaa=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6976 | ⟨a, b | ab=aa, abbab=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6978 | ⟨a, b | ab=aa, abbba=a⟩ | φ(a) = a, φ(b) = b |
| 10 | 6980 | ⟨a, b | ab=aa, abbbb=a⟩ | φ(a) = a, φ(b) = b |