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S1 must be executed sequentially, but S2 has no loop-carried dependence. S2 could be executed in parallel using DOALL Parallelism after performing all calculations needed by S1 in series. However, the speedup is limited if this is done. A better approach is to parallelize such that the S2 corresponding to each S1 executes when said S1 is finished.
Implementing pipelined parallelism results in the following set of loops, where the second loop may execute for an index as soon as the first loop has finished its corresponding index.
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