#3074 ⟨a, b | ab=a, aaaa=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:
-
a4 ⋅ a = a2 and a ⋅ a = a2, however a4 ≠ 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,aaaa=ba a/b - -
aaaaa=aa
ba=aaaa
ab=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
20 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 8990 | ⟨a, b | ab=a, aaaab=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 8994 | ⟨a, b | ab=a, aaaba=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9002 | ⟨a, b | ab=a, aabaa=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9018 | ⟨a, b | ab=a, abaaa=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9261 | ⟨a, b | ab=a, aaaa=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 24874 | ⟨a, b | ab=a, aaaabb=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24882 | ⟨a, b | ab=a, aaabab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24886 | ⟨a, b | ab=a, aaabba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24898 | ⟨a, b | ab=a, aabaab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24902 | ⟨a, b | ab=a, aababa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24910 | ⟨a, b | ab=a, aabbaa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24930 | ⟨a, b | ab=a, abaaab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24934 | ⟨a, b | ab=a, abaaba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24942 | ⟨a, b | ab=a, ababaa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24958 | ⟨a, b | ab=a, abbaaa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25417 | ⟨a, b | ab=a, aaaab=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25425 | ⟨a, b | ab=a, aaaba=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25441 | ⟨a, b | ab=a, aabaa=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25473 | ⟨a, b | ab=a, abaaa=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25847 | ⟨a, b | ab=a, babb=aaaa⟩ | φ(a) = a, φ(b) = b |