Testing and debugging the implementation of static analysis is a challenging task, often involving significant manual effort from domain experts in a tedious and unprincipled process. In this work, we propose an approach that greatly improves the automation of this process for static analyzers with configuration options. At the core of our approach is the novel adaptation of the theoretical partial order relations that exist between these options to reason about the correctness of actual results from running the static analyzer with different configurations. This allows for automated testing of static analyzers with clearly defined oracles, followed by automated delta debugging, even in cases where ground truths are not defined over the input programs. To apply this approach to many static analysis tools, we design and implement ECSTATIC, an easy-to-extend, open-source framework. We have integrated four popular static analysis tools, SOOT, WALA, DOOP, and FlowDroid, into ECSTATIC. Our evaluation shows running ECSTATIC detects 74 distinct bugs in the four tools and produces reduced bug-inducing programs to assist debugging. We reported 42 bugs; in all cases where we received responses, the tool developers confirmed the reported tool behavior was unintended. So far, two bugs have been fixed and there are ongoing discussions to fix more.