  The HOM-problem asks whether the image of a regular tree language under a
given tree homomorphism is again regular. It was recently shown to be decidable
by Godoy, Gim\'enez, Ramos, and \`Alvarez. In this paper, the N-weighted
version of this problem is considered and its decidability is proved. More
precisely, it is decidable in polynomial time whether the image of a regular
N-weighted tree language under a nondeleting, nonerasing tree homomorphism is
regular.
