#3106 ⟨a, b | ab=a, baaa=ba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- 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:
-
a3 ⋅ a = a2 and a ⋅ a = a2, however a3 ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,baaa=ba ab - -
ab=a
aaaa=aa
baaa=ba
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
14 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 9054 | ⟨a, b | ab=a, baaab=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9058 | ⟨a, b | ab=a, baaba=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9066 | ⟨a, b | ab=a, babaa=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9325 | ⟨a, b | ab=a, baaa=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25002 | ⟨a, b | ab=a, baaabb=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25010 | ⟨a, b | ab=a, baabab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25014 | ⟨a, b | ab=a, baabba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25026 | ⟨a, b | ab=a, babaab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25030 | ⟨a, b | ab=a, bababa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25038 | ⟨a, b | ab=a, babbaa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25545 | ⟨a, b | ab=a, baaab=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25553 | ⟨a, b | ab=a, baaba=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25569 | ⟨a, b | ab=a, babaa=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25855 | ⟨a, b | ab=a, babb=baaa⟩ | φ(a) = a, φ(b) = b |