  We apply the 'almost good reduction' (AGR) criterion, which has been
introduced in our previous (arXiv:1206.4456 and arXiv:1209.0223), to several
classes of discrete integrable equations. We verify our conjecture that AGR
plays the same role for maps of the plane define over simple finite fields as
the notion of the singularity confinement does. We first prove that q-discrete
analogues of the Painlev\'e III and IV equations have AGR. We next prove that
the Hietarinta-Viallet equation, a non-integrable chaotic system also has AGR.
