  We construct novel thread-modular analyses that track relational information
for potentially overlapping clusters of global variables - given that they are
protected by common mutexes. We provide a framework to systematically increase
the precision of clustered relational analyses by splitting control locations
based on abstractions of local traces. As one instance, we obtain an analysis
of dynamic thread creation and joining. Interestingly, tracking less relational
information for globals may result in higher precision. We consider the class
of 2-decomposable domains that encompasses many weakly relational domains
(e.g., Octagons). For these domains, we prove that maximal precision is
attained already for clusters of globals of sizes at most 2.
