It is part of the tradition and folklore of automated reasoning that the intractability of Cooper's decision procedure for Presburger integer arithmetic makes is too expensive for practical use. More than 25 years of work has resulted in numerous approximate procedures via rational arithmetic, all of which are incomplete and restricted to the quantifier-free fragment. In this paper we report on an experiment which strongly questions this tradition. We measured the performance of procedures due to Hodes, Cooper (and heuristic variants thereof which detect counterexamples), across a corpus of 10 000 randomly generated quantifierfree Presburger formulae. The results are startling: a variant of Cooper's procedure outperforms Hodes' procedure on both valid and invalid formulae, and is fast enough for practical use. These results contradict much perceived wisdom that decision procedures for integer arithmetic are too expensive to use in practice. 1 Introduction A decis..
