#9260 ⟨a, b | ab=a, aaaa=baa⟩
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:
-
a4 ⋅ a = a3 and a2 ⋅ a = a3, however a4 ≠ a2
- 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,aaaa=baa a/b - -
aaaaa=aaa
baa=aaaa
ab=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
6 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 25416 | ⟨a, b | ab=a, aaaab=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25424 | ⟨a, b | ab=a, aaaba=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25440 | ⟨a, b | ab=a, aabaa=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25472 | ⟨a, b | ab=a, abaaa=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25828 | ⟨a, b | ab=a, baab=aaaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25837 | ⟨a, b | ab=a, baba=aaaa⟩ | φ(a) = a, φ(b) = b |