  Given a log canonical pair $(X, \Delta)$, we show that $K_X+\Delta$ is nef
assuming there is no non-constant map from the affine line with values in the
open strata of the stratification induced by the non-klt locus of $(X,
\Delta)$. This implies a generalization of the Cone Theorem where each
$K_X+\Delta$-negative extremal ray is spanned by a rational curve that is the
closure of a copy of the affine line contained in one of the open strata of
$\mathrm{Nklt}(X, \Delta)$. Moreover, we give a criterion of Nakai type to
determine when under the above condition $K_X+\Delta$ is ample and we prove
some partial results in the case of arbitrary singularities.
