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This paper discusses effective processing of subsequence matching under time warping in time-series databases. Time warping is a transformation that enables finding of sequences with similar patterns even when they are of different lengths. Through a preliminary experiment, we first point out that Naive-Scan, a basic method for processing of subsequence matching under time warping, has its performance bottleneck in the CPU processing step. For optimizing this step, in this paper, we propose a novel method that eliminates all possible redundant calculations. It is verified that this method is not only an optimal one for processing Naive-Scan, but also does not incur any false dismissals. Our experimental results showed that the proposed method can make great improvement in performance of subsequence matching under time warping. Especially, Naive-Scan, which has been known to show the worst performance, performs much better than LB-Scan as well as ST-Filter in all the cases by employing the proposed method for CPU processing. This result is interesting and valuable in that the performance inversion among Naive-Scan, LB-Scan, and ST-Filter has occurred by optimizing the CPU processing step, which is their common performance bottleneck.