  We study pushdown vector addition systems, which are synchronized products of
pushdown automata with vector addition systems. The question of the boundedness
of the reachability set for this model can be refined into two decision
problems that ask if infinitely many counter values or stack configurations are
reachable, respectively.
  Counter boundedness seems to be the more intricate problem. We show
decidability in exponential time for one-dimensional systems. The proof is via
a small witness property derived from an analysis of derivation trees of
grammar-controlled vector addition systems.
