This paper investigates the computational complexity of deciding if a given finite idempotent algebra has a ternary term operation
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.