#1008 ⟨a, b | ab=a, baa=aa⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 8
- Infinite non-cancellative non-commutative monoid
- Element a 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:
-
ba ⋅ a = a2 and a ⋅ a = a2, however ba ≠ a
- Reduction order:
- Left-to-right shortlex with a < b
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:ab=a,baa=aa ab - -
ab=a
baa=aa
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
34 total
| Σ | # | Presentation | Mapping |
|---|
| 9 | 3108 | ⟨a, b | ab=a, baab=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 3112 | ⟨a, b | ab=a, baba=aa⟩ | φ(a) = a, φ(b) = b |
| 9 | 3179 | ⟨a, b | ab=a, baa=aab⟩ | φ(a) = a, φ(b) = b |
| 9 | 3180 | ⟨a, b | ab=a, baa=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9060 | ⟨a, b | ab=a, baabb=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9068 | ⟨a, b | ab=a, babab=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9072 | ⟨a, b | ab=a, babba=aa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9284 | ⟨a, b | ab=a, aabb=baa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9300 | ⟨a, b | ab=a, abab=baa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9308 | ⟨a, b | ab=a, abba=baa⟩ | φ(a) = a, φ(b) = b |
| 10 | 9329 | ⟨a, b | ab=a, baab=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9330 | ⟨a, b | ab=a, baab=aba⟩ | φ(a) = a, φ(b) = b |
| 10 | 9337 | ⟨a, b | ab=a, baba=aab⟩ | φ(a) = a, φ(b) = b |
| 10 | 9338 | ⟨a, b | ab=a, baba=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25016 | ⟨a, b | ab=a, baabbb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25032 | ⟨a, b | ab=a, bababb=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25040 | ⟨a, b | ab=a, babbab=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25044 | ⟨a, b | ab=a, babbba=aa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25464 | ⟨a, b | ab=a, aabbb=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25496 | ⟨a, b | ab=a, ababb=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25512 | ⟨a, b | ab=a, abbab=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25520 | ⟨a, b | ab=a, abbba=baa⟩ | φ(a) = a, φ(b) = b |
| 11 | 25557 | ⟨a, b | ab=a, baabb=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25558 | ⟨a, b | ab=a, baabb=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25573 | ⟨a, b | ab=a, babab=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25574 | ⟨a, b | ab=a, babab=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25581 | ⟨a, b | ab=a, babba=aab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25582 | ⟨a, b | ab=a, babba=aba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25831 | ⟨a, b | ab=a, baab=aabb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25833 | ⟨a, b | ab=a, baab=abab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25834 | ⟨a, b | ab=a, baab=abba⟩ | φ(a) = a, φ(b) = b |
| 11 | 25840 | ⟨a, b | ab=a, baba=aabb⟩ | φ(a) = a, φ(b) = b |
| 11 | 25842 | ⟨a, b | ab=a, baba=abab⟩ | φ(a) = a, φ(b) = b |
| 11 | 25843 | ⟨a, b | ab=a, baba=abba⟩ | φ(a) = a, φ(b) = b |