#8986 ⟨a, b | ab=a, aaaaa=ba⟩
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 = a and a ⋅ 1 = a, however b ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a5 ⋅ a = a2 and a ⋅ a = a2, however a5 ≠ a
- Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,aaaaa=ba a/b - -
aaaaaa=aa
ba=aaaaa
ab=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
6 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 24866 | ⟨a, b | ab=a, aaaaab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24870 | ⟨a, b | ab=a, aaaaba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24878 | ⟨a, b | ab=a, aaabaa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24894 | ⟨a, b | ab=a, aabaaa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24926 | ⟨a, b | ab=a, abaaaa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25409 | ⟨a, b | ab=a, aaaaa=bab⟩ | φ(a) = a, φ(b) = b |