Described is a technology by which program analysis uses rich invariant templates that may specify an arbitrary Boolean combination of linear inequalities for program verification. Also described is choosing a cut-set that identifies program locations, each of which is associated with an invariant template. The verification generates second-order constraints, converts second-order logic formula based on those constraints into first-order logic formula, then converts the first-order logic formula into a quantifier-free formula, which is then converted into a Boolean satisfiability formula. Off-the-shelf constraint solvers may then be applied to the Boolean satisfiability formula to generate program analysis results. Various templates may be used to convert the second-order logic formula into the first-order logic formula. Further described are interprocedural analysis and the determination of weakest precondition and strongest postcondition with applications to termination analysis, timing bounds analysis, and generation of most-general counterexamples for both termination and safety properties.