#992 ⟨a, b | ab=a, aaa=aa⟩
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:
-
a2 ⋅ a = a2 and a ⋅ a = a2, however a2 ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,aaa=aa ab - -
ab=a
aaa=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
55 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 3076 | ⟨a, b | ab=a, aaab=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 3080 | ⟨a, b | ab=a, aaba=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 3088 | ⟨a, b | ab=a, abaa=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 3172 | ⟨a, b | ab=a, aab=aaa⟩ | φ(a) = a, φ(b) = b |
| 9 | 3173 | ⟨a, b | ab=a, aba=aaa⟩ | φ(a) = a, φ(b) = b |
| 10 | 8996 | ⟨a, b | ab=a, aaabb=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9004 | ⟨a, b | ab=a, aabab=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9008 | ⟨a, b | ab=a, aabba=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9020 | ⟨a, b | ab=a, abaab=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9024 | ⟨a, b | ab=a, ababa=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9032 | ⟨a, b | ab=a, abbaa=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9265 | ⟨a, b | ab=a, aaab=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9266 | ⟨a, b | ab=a, aaab=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9273 | ⟨a, b | ab=a, aaba=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9274 | ⟨a, b | ab=a, aaba=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9280 | ⟨a, b | ab=a, aabb=aaa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9289 | ⟨a, b | ab=a, abaa=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9290 | ⟨a, b | ab=a, abaa=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9296 | ⟨a, b | ab=a, abab=aaa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9304 | ⟨a, b | ab=a, abba=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24888 | ⟨a, b | ab=a, aaabbb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24904 | ⟨a, b | ab=a, aababb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24912 | ⟨a, b | ab=a, aabbab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24916 | ⟨a, b | ab=a, aabbba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24936 | ⟨a, b | ab=a, abaabb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24944 | ⟨a, b | ab=a, ababab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24948 | ⟨a, b | ab=a, ababba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24960 | ⟨a, b | ab=a, abbaab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24964 | ⟨a, b | ab=a, abbaba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 24972 | ⟨a, b | ab=a, abbbaa=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25429 | ⟨a, b | ab=a, aaabb=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25430 | ⟨a, b | ab=a, aaabb=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25445 | ⟨a, b | ab=a, aabab=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25446 | ⟨a, b | ab=a, aabab=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25453 | ⟨a, b | ab=a, aabba=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25454 | ⟨a, b | ab=a, aabba=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25460 | ⟨a, b | ab=a, aabbb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25477 | ⟨a, b | ab=a, abaab=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25478 | ⟨a, b | ab=a, abaab=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25485 | ⟨a, b | ab=a, ababa=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25486 | ⟨a, b | ab=a, ababa=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25492 | ⟨a, b | ab=a, ababb=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25501 | ⟨a, b | ab=a, abbaa=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25502 | ⟨a, b | ab=a, abbaa=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25508 | ⟨a, b | ab=a, abbab=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25516 | ⟨a, b | ab=a, abbba=aaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25796 | ⟨a, b | ab=a, aabb=aaab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25797 | ⟨a, b | ab=a, aabb=aaba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25801 | ⟨a, b | ab=a, abaa=aabb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25803 | ⟨a, b | ab=a, abab=aaab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25804 | ⟨a, b | ab=a, abab=aaba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25806 | ⟨a, b | ab=a, abab=abaa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25808 | ⟨a, b | ab=a, abba=aaab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25809 | ⟨a, b | ab=a, abba=aaba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25811 | ⟨a, b | ab=a, abba=abaa⟩ | φ(a) = a, φ(b) = b |