  Program behavior may depend on parameters, which are either configured before
compilation time, or provided at run-time, e.g., by sensors or other input
devices. Parametric program analysis explores how different parameter settings
may affect the program behavior.
  In order to infer invariants depending on parameters, we introduce parametric
strategy iteration. This algorithm determines the precise least solution of
systems of integer equations depending on surplus parameters. Conceptually, our
algorithm performs ordinary strategy iteration on the given integer system for
all possible parameter settings in parallel. This is made possible by means of
region trees to represent the occurring piecewise affine functions. We indicate
that each required operation on these trees is polynomial-time if only
constantly many parameters are involved.
  Parametric strategy iteration for systems of integer equations allows to
construct parametric integer interval analysis as well as parametric analysis
of differences of integer variables. It thus provides a general technique to
realize precise parametric program analysis if numerical properties of integer
variables are of concern.
