#3072 ⟨a, b | ab=a, aaaa=aa⟩
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,aaaa=aa ab - -
ab=a
aaaa=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
27 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 8988 | ⟨a, b | ab=a, aaaab=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 8992 | ⟨a, b | ab=a, aaaba=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9000 | ⟨a, b | ab=a, aabaa=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9016 | ⟨a, b | ab=a, abaaa=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9257 | ⟨a, b | ab=a, aaaa=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9258 | ⟨a, b | ab=a, aaaa=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 24872 | ⟨a, b | ab=a, aaaabb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24880 | ⟨a, b | ab=a, aaabab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24884 | ⟨a, b | ab=a, aaabba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24896 | ⟨a, b | ab=a, aabaab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24900 | ⟨a, b | ab=a, aababa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24908 | ⟨a, b | ab=a, aabbaa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24928 | ⟨a, b | ab=a, abaaab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24932 | ⟨a, b | ab=a, abaaba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24940 | ⟨a, b | ab=a, ababaa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24956 | ⟨a, b | ab=a, abbaaa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25413 | ⟨a, b | ab=a, aaaab=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25414 | ⟨a, b | ab=a, aaaab=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25421 | ⟨a, b | ab=a, aaaba=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25422 | ⟨a, b | ab=a, aaaba=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25437 | ⟨a, b | ab=a, aabaa=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25438 | ⟨a, b | ab=a, aabaa=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25469 | ⟨a, b | ab=a, abaaa=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25470 | ⟨a, b | ab=a, abaaa=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25795 | ⟨a, b | ab=a, aabb=aaaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25802 | ⟨a, b | ab=a, abab=aaaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25807 | ⟨a, b | ab=a, abba=aaaa⟩ | φ(a) = a, φ(b) = b |