  We introduce the well structured problem as the question of whether a model
(here a counter machine) is well structured (here for the usual ordering on
integers). We show that it is undecidable for most of the (Presburger-defined)
counter machines except for Affine VASS of dimension one. However, the strong
well structured problem is decidable for all Presburger counter machines. While
Affine VASS of dimension one are not, in general, well structured, we give an
algorithm that computes the set of predecessors of a configuration; as a
consequence this allows to decide the well structured problem for 1-Affine
VASS.
