  We present a combination of the Mixed-Echelon-Hermite transformation and the
Double-Bounded Reduction for systems of linear mixed arithmetic that preserve
satisfiability and can be computed in polynomial time. Together, the two
transformations turn any system of linear mixed constraints into a bounded
system, i.e., a system for which termination can be achieved easily. Existing
approaches for linear mixed arithmetic, e.g., branch-and-bound and cuts from
proofs, only explore a finite search space after application of our two
transformations. Instead of generating a priori bounds for the variables, e.g.,
as suggested by Papadimitriou, unbounded variables are eliminated through the
two transformations. The transformations orient themselves on the structure of
an input system instead of computing a priori (over-)approximations out of the
available constants. Experiments provide further evidence to the efficiency of
the transformations in practice. We also present a polynomial method for
converting certificates of (un)satisfiability from the transformed to the
original system.
