The two variable per inequality abstract domain

This article presents the Two Variable Per Inequality abstract domain (TVPI domain for short). This so-called weakly-relational domain is able to express systems of linear inequalities where each inequality has at most two variables. The domain represents a sweet-point in the performance-cost tradeoff between the faster Octagon domain and the more expressive domain of general convex polyhedra. In particular, we detail techniques to closely approximate integral TVPI systems, thereby finessing the problem of excessively growing coefficients, yielding – to our knowledge – the only relational domain that combines linear relations with arbitrary coefficients and strongly polynomial performance.