  In this paper, we prove that the set of all $F$-pure thresholds of ideals
with fixed embedding dimension satisfies the ascending chain condition. As a
corollary, given an integer $d$, we verify the ascending chain condition for
the set of all $F$-pure thresholds on all $d$-dimensional normal l.c.i.
varieties. In the process of proving these results, we also show the
rationality of $F$-pure thresholds of ideals on non-strongly $F$-regular pairs.
