  In this paper, we prove that the set of all $F$-pure thresholds on a fixed
germ of a strongly $F$-regular pair satisfies the ascending chain condition. As
a corollary, we verify the ascending chain condition for the set of all
$F$-pure thresholds on smooth varieties or, more generally, on varieties with
tame quotient singularities, which is an affirmative answer to a conjecture
given by Blickle, Musta\c{t}\v{a} and Smith.
