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We address the problem of checking state reachability for programs running under Total Store Order (TSO). The problem has been shown to be decidable but the cost is prohibitive, namely non-primitive recursive. We propose here to give up completeness. Our contribution is a new algorithm for TSO reachability: it uses the standard SC semantics and introduces the TSO semantics lazily and only where needed. At the heart of our algorithm is an iterative refinement of the program of interest. If thearXiv:1501.02683v1 fatcat:adu677ebovbfdi7f2bbrrm4leq