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This paper addresses the problem of model-based off-line selection of test cases for testing the conformance of a black-box implementation with respect to a specification, in the context of reactive systems. Efficient solutions to this problem have been proposed for LTS finite-state models, based on the ioco conformance testing theory. In this paper, the approach is extended for infinite-state specifications, modelled as automata extended with variables. When considering the selection of test cases according to test purposes (abstract scenarii focused by test cases), the selection of test cases relies on approximate co-reachability analyses using abstract interpretation and syntactical transformations guided by this analysis, while test execution uses constraint solving.