This paper investigates the computational complexity of deciding if a given
finite idempotent algebra has a ternary term operation $m$ that satisfies the
minority equations $m(y,x,x) \approx m(x,y,x) \approx m(x,x,y) \approx y$. We
show that a common polynomial-time approach to testing for this type of
condition will not work in this case and that this decision problem lies in the
class NP.