#9048 ⟨a, b | ab=a, baaaa=aa⟩
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:
-
ba ⋅ a = a2 and a ⋅ a = a2, however ba ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,baaaa=aa ab - -
ab=a
baa=aa
aaaa=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
6 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 24992 | ⟨a, b | ab=a, baaaab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24996 | ⟨a, b | ab=a, baaaba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25004 | ⟨a, b | ab=a, baabaa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25020 | ⟨a, b | ab=a, babaaa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25533 | ⟨a, b | ab=a, baaaa=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25534 | ⟨a, b | ab=a, baaaa=aba⟩ | φ(a) = a, φ(b) = b |