#994 ⟨a, b | ab=a, aaa=ba⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- 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 recursive path with deg(a) = 0; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,aaa=ba a/b - -
aaaa=aa
ba=aaa
ab=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
34 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 3078 | ⟨a, b | ab=a, aaab=ba⟩ | φ(a) = a, φ(b) = b |
| 9 | 3082 | ⟨a, b | ab=a, aaba=ba⟩ | φ(a) = a, φ(b) = b |
| 9 | 3090 | ⟨a, b | ab=a, abaa=ba⟩ | φ(a) = a, φ(b) = b |
| 9 | 3182 | ⟨a, b | ab=a, bab=aaa⟩ | φ(a) = a, φ(b) = b |
| 10 | 8998 | ⟨a, b | ab=a, aaabb=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9006 | ⟨a, b | ab=a, aabab=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9010 | ⟨a, b | ab=a, aabba=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9022 | ⟨a, b | ab=a, abaab=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9026 | ⟨a, b | ab=a, ababa=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9034 | ⟨a, b | ab=a, abbaa=ba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9269 | ⟨a, b | ab=a, aaab=bab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9277 | ⟨a, b | ab=a, aaba=bab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9293 | ⟨a, b | ab=a, abaa=bab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9344 | ⟨a, b | ab=a, babb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24890 | ⟨a, b | ab=a, aaabbb=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24906 | ⟨a, b | ab=a, aababb=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24914 | ⟨a, b | ab=a, aabbab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24918 | ⟨a, b | ab=a, aabbba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24938 | ⟨a, b | ab=a, abaabb=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24946 | ⟨a, b | ab=a, ababab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24950 | ⟨a, b | ab=a, ababba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24962 | ⟨a, b | ab=a, abbaab=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24966 | ⟨a, b | ab=a, abbaba=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24974 | ⟨a, b | ab=a, abbbaa=ba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25433 | ⟨a, b | ab=a, aaabb=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25449 | ⟨a, b | ab=a, aabab=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25457 | ⟨a, b | ab=a, aabba=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25481 | ⟨a, b | ab=a, abaab=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25489 | ⟨a, b | ab=a, ababa=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25505 | ⟨a, b | ab=a, abbaa=bab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25588 | ⟨a, b | ab=a, babbb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25848 | ⟨a, b | ab=a, babb=aaab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25849 | ⟨a, b | ab=a, babb=aaba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25851 | ⟨a, b | ab=a, babb=abaa⟩ | φ(a) = a, φ(b) = b |