Regression testing is arguably one of the most important activities in software testing. However, its cost-effectiveness and usefulness can be largely impaired by complex system test cases that are poorly designed (e.g., test cases containing multiple test scenarios combined into a single test case) and that require a large amount of time and resources to run. One way to mitigate this issue is decomposing such system test cases into smaller, separate test cases - -each of them with only one test scenario and with its corresponding assertions - -so that the execution time of the decomposed test cases is lower than the original test cases, while the test effectiveness of the original test cases is preserved. This decomposition can be achieved with program slicing techniques, since test cases are software programs too. However, existing static and dynamic slicing techniques exhibit limitations when (1) the test cases use external resources, (2) code instrumentation is not a viable option, and (3) test execution is expensive. In this paper, we propose a novel approach, called DS3 (Decomposing System teSt caSe), which automatically decomposes a complex system test case into separate test case slices. The idea is to use test case execution logs, obtained from past regression testing sessions, to identify "hidden"dependencies in the slices generated by static slicing. Since logs include run-time information about the system under test, we can use them to extract access and usage of global resources and refine the slices generated by static slicing. We evaluated DS3 in terms of slicing effectiveness and compared it with a vanilla static slicing tool. We also compared the slices obtained by DS3 with the corresponding original system test cases, in terms of test efficiency and effectiveness. The evaluation results on one proprietary system and one open-source system show that DS3 is able to accurately identify the dependencies related to the usage of global resources, which vanilla static slicing misses. Moreover, the generated test case slices are, on average, 3.56 times faster than original system test cases and they exhibit no significant loss in terms of fault detection effectiveness.