  The solving degree of a system of multivariate polynomial equations provides
an upper bound for the complexity of computing the solutions of the system via
Groebner bases methods. In this paper, we consider polynomial systems that are
obtained via Weil restriction of scalars. The latter is an arithmetic
construction which, given a finite Galois field extension $k\hookrightarrow K$,
associates to a system $\mathcal{F}$ defined over $K$ a system
$\mathrm{Weil}(\mathcal{F})$ defined over $k$, in such a way that the solutions
of $\mathcal{F}$ over $K$ and those of $\mathrm{Weil}(\mathcal{F})$ over $k$
are in natural bijection. In this paper, we find upper bounds for the
complexity of solving a polynomial system $\mathrm{Weil}(\mathcal{F})$ obtained
via Weil restriction in terms of algebraic invariants of the system
$\mathcal{F}$.
