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With the increasing complexity of software systems, the set of testing requirements can become very large. If the set of testing requirements can be naturally decomposed into smaller subsets, one may construct a test set separately to satisfy each subset of testing requirements, and then combine the test sets to form the complete test set. Such an approach is referred to as the union approach. On the other hand, the incremental approach attempts to incrementally expand a test set to satisfy the subsets of testing requirements, one at a time. This paper investigates empirically the effect of the incremental approach as compared to the union approach. Our case study indicates that the incremental approach can result in a significantly smaller test set, particularly when supplemented with the greedy heuristics.