#16314 ⟨a, b | aab=bb, baba=ab⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element a has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ b4 = b2 and b ⋅ b = b2, however b4 ≠ b
- Not right cancellative, because right multiplication by b is not injective:
-
a ⋅ b = b3 and b2 ⋅ b = b3, however a ≠ b2
- Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aab=bb,baba=ab b/a - -
bbbbb=bb
ab=bbb
bba=bbbb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 16449 | ⟨a, b | aba=bb, aabb=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16453 | ⟨a, b | aba=bb, abab=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16457 | ⟨a, b | aba=bb, abba=ab⟩ | φ(a) = a, φ(b) = b |
| 11 | 16464 | ⟨a, b | aba=bb, baab=ab⟩ | φ(a) = a, φ(b) = b |