#235 ⟨a, b | aa=a, aaa=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 7
- Isomorphic to ℕ(2 = 1) ∗ ℕ
- Infinite non-cancellative non-commutative monoid
- Element ab has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a = a and a ⋅ 1 = a, however a ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a ⋅ a = a and 1 ⋅ a = a, however a ≠ 1
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=a,aaa=a ab - -
aa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
31 total
| Σ | # | Presentation | Mapping |
|---|
| 8 | 880 | ⟨a, b | aa=a, aaaa=a⟩ | φ(a) = a, φ(b) = 1 |
| 8 | 952 | ⟨a, b | aa=a, aaa=aa⟩ | φ(a) = a, φ(b) = 1 |
| 8 | 956 | ⟨a, b | aa=a, aab=ab⟩ | φ(a) = a, φ(b) = 1 |
| 9 | 1980 | ⟨a, b | aaa=a, aaaa=a⟩ | φ(a) = a, φ(b) = 1 |
| 9 | 2856 | ⟨a, b | aa=a, aaaaa=a⟩ | φ(a) = a, φ(b) = 1 |
| 9 | 3000 | ⟨a, b | aa=a, aaaa=aa⟩ | φ(a) = a, φ(b) = 1 |
| 9 | 3004 | ⟨a, b | aa=a, aaab=ab⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 5022 | ⟨a, b | aaa=aa, aaaa=a⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 8568 | ⟨a, b | aa=a, aaaaaa=a⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 8840 | ⟨a, b | aa=a, aaaaa=aa⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 8844 | ⟨a, b | aa=a, aaaab=ab⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9112 | ⟨a, b | aa=a, aaaa=aaa⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9119 | ⟨a, b | aa=a, aaab=aab⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9128 | ⟨a, b | aa=a, aaba=aba⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9137 | ⟨a, b | aa=a, aabb=abb⟩ | φ(a) = a, φ(b) = 1 |
| 10 | 9168 | ⟨a, b | aa=a, baab=bab⟩ | φ(a) = a, φ(b) = 1 |
| 11 | 14329 | ⟨a, b | aaaa=a, aaaaa=a⟩ | φ(a) = a, φ(b) = 1 |
| 11 | 15401 | ⟨a, b | aaa=aa, aaaaa=a⟩ | φ(a) = a, φ(b) = 1 |
| 11 | 18688 | ⟨a, b | aaa=a, aaaaaa=a⟩ | φ(a) = a, φ(b) = 1 |
| 11 | 19232 | ⟨a, b | aaa=a, aaaaa=aa⟩ | φ(a) = a, φ(b) = 1 |
| 11 | 19776 | ⟨a, b | aaa=a, aaaa=aaa⟩ | φ(a) = a, φ(b) = 1 |
| 11 | 24044 | ⟨a, b | aa=a, aaaaaaa=a⟩ | φ(a) = a, φ(b) = 1 |
| 11 | 24588 | ⟨a, b | aa=a, aaaaaa=aa⟩ | φ(a) = a, φ(b) = 1 |
| 11 | 24592 | ⟨a, b | aa=a, aaaaab=ab⟩ | φ(a) = a, φ(b) = 1 |
| 11 | 25116 | ⟨a, b | aa=a, aaaaa=aaa⟩ | φ(a) = a, φ(b) = 1 |
| 11 | 25123 | ⟨a, b | aa=a, aaaab=aab⟩ | φ(a) = a, φ(b) = 1 |
| 11 | 25132 | ⟨a, b | aa=a, aaaba=aba⟩ | φ(a) = a, φ(b) = 1 |
| 11 | 25141 | ⟨a, b | aa=a, aaabb=abb⟩ | φ(a) = a, φ(b) = 1 |
| 11 | 25148 | ⟨a, b | aa=a, aabaa=aba⟩ | φ(a) = a, φ(b) = 1 |
| 11 | 25224 | ⟨a, b | aa=a, baaab=bab⟩ | φ(a) = a, φ(b) = 1 |
| 11 | 25667 | ⟨a, b | aa=a, abaa=aaba⟩ | φ(a) = a, φ(b) = 1 |