An algorithm, permitting us to extract iterations belonging to synchronization-free slices and to generate code enumerating sources of such slices and iterations of each slice in lexicographical order is presented. Synchronization-free slices can be executed independently preserving the lexicographic order of iterations in each slice. Our approach requires exact dependence analysis and based on operations on relations and sets. To describe and implement the algorithms, the dependence analysis by Pugh and Wonnacott was chosen where dependences are found in the form of tuple relations. The proposed algorithms have been implemented and verified by means of the Omega project software. Presburger arithmetic limitations are discussed. Results of experiments are presented. Tasks for future research are outlined.
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