#20926 ⟨a, b | ab=aa, aaaa=bba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- 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:
-
b2 ⋅ a = a4 and a3 ⋅ a = a4, however b2 ≠ a3
- 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=aa,aaaa=bba a/b - -
aaaaa=aaaa
ab=aa
bba=aaaa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
7 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20934 | ⟨a, b | ab=aa, aaab=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20942 | ⟨a, b | ab=aa, aaba=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20950 | ⟨a, b | ab=aa, aabb=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20958 | ⟨a, b | ab=aa, abaa=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20966 | ⟨a, b | ab=aa, abab=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20974 | ⟨a, b | ab=aa, abba=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 20982 | ⟨a, b | ab=aa, abbb=bba⟩ | φ(a) = a, φ(b) = b |