  While the problem of computing the genus of a knot is now fairly well
understood, no algorithm is known for its four-dimensional variants, both in
the smooth and in the topological locally flat category. In this article, we
investigate a class of knots and links called Hopf arborescent links, which are
obtained as the boundaries of some iterated plumbings of Hopf bands. We show
that for such links, computing the genus defects, which measure how much the
four-dimensional genera differ from the classical genus, is decidable. Our
proof is non-constructive, and is obtained by proving that Seifert surfaces of
Hopf arborescent links under a relation of minors defined by containment of
their Seifert surfaces form a well-quasi-order.
