#64 ⟨a, b | aa=1, aaaa=1⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 6
- Isomorphic to ℤ2 ∗ ℕ
- Infinite cancellative non-commutative monoid
- Element ab has infinite order
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=1,aaaa=1 ab - -
aa=1
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
42 total
| Σ | # | Presentation | Mapping |
|---|
| 6 | 84 | ⟨a, b | aa=1, aaa=a⟩ | φ(a) = a, φ(b) = 1 |
| 6 | 87 | ⟨a, b | aa=1, aab=b⟩ | φ(a) = a, φ(b) = 1 |
| 8 | 491 | ⟨a, b | aaa=a, aaaa=1⟩ | φ(a) = a, φ(b) = 1 |
| 8 | 1024 | ⟨a, b | aa=1, aaaaaa=1⟩ | φ(a) = a, φ(b) = 1 |
| 8 | 1096 | ⟨a, b | aa=1, aaaaa=a⟩ | φ(a) = a, φ(b) = 1 |
| 8 | 1099 | ⟨a, b | aa=1, aaaab=b⟩ | φ(a) = a, φ(b) = 1 |
| 8 | 1105 | ⟨a, b | aa=1, aabaa=b⟩ | φ(a) = a, φ(b) = 1 |
| 8 | 1168 | ⟨a, b | aa=1, aaaa=aa⟩ | φ(a) = a, φ(b) = 1 |
| 8 | 1172 | ⟨a, b | aa=1, aaab=ab⟩ | φ(a) = a, φ(b) = 1 |
| 8 | 1177 | ⟨a, b | aa=1, aaba=ba⟩ | φ(a) = a, φ(b) = 1 |
| 8 | 1182 | ⟨a, b | aa=1, aabb=bb⟩ | φ(a) = a, φ(b) = 1 |
| 8 | 1196 | ⟨a, b | aa=1, baab=bb⟩ | φ(a) = a, φ(b) = 1 |
| 8 | 1246 | ⟨a, b | aa=1, baa=aab⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 5422 | ⟨a, b | aaaa=1, aaaaaa=1⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 5966 | ⟨a, b | aaa=a, aaaaaa=1⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9384 | ⟨a, b | aa=1, aaaaaaaa=1⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9656 | ⟨a, b | aa=1, aaaaaaa=a⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9659 | ⟨a, b | aa=1, aaaaaab=b⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9665 | ⟨a, b | aa=1, aaaabaa=b⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9928 | ⟨a, b | aa=1, aaaaaa=aa⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9932 | ⟨a, b | aa=1, aaaaab=ab⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9937 | ⟨a, b | aa=1, aaaaba=ba⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9942 | ⟨a, b | aa=1, aaaabb=bb⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9944 | ⟨a, b | aa=1, aaabaa=ab⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9962 | ⟨a, b | aa=1, aabaab=bb⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9973 | ⟨a, b | aa=1, aabbaa=bb⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10030 | ⟨a, b | aa=1, baaaab=bb⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10200 | ⟨a, b | aa=1, aaaaa=aaa⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10207 | ⟨a, b | aa=1, aaaab=aab⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10210 | ⟨a, b | aa=1, aaaab=baa⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10216 | ⟨a, b | aa=1, aaaba=aba⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10225 | ⟨a, b | aa=1, aaabb=abb⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10231 | ⟨a, b | aa=1, aabaa=aab⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10241 | ⟨a, b | aa=1, aabab=bab⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10250 | ⟨a, b | aa=1, aabba=bba⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10259 | ⟨a, b | aa=1, aabbb=bbb⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10263 | ⟨a, b | aa=1, abaab=abb⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10308 | ⟨a, b | aa=1, baaab=bab⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10317 | ⟨a, b | aa=1, baabb=bbb⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10478 | ⟨a, b | aa=1, abaa=aaab⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10505 | ⟨a, b | aa=1, baab=aabb⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 10523 | ⟨a, b | aa=1, bbaa=aabb⟩ | φ(a) = a, φ(b) = 1 |