We consider the framework of regular hedge model checking where configurations are represented by trees of arbitrary arities, sets of configurations are represented by regular hedge automata, and the dynamic of a system is modelled by a term rewriting system. We consider the problem of computing the transitive closure R*(L) of a hedge automaton L and a (not necessarily structure preserving) term rewriting system R. This construction is not possible in general. Therefore, we present a semi-algorithm that computes, in case of termination, an over-approximation of this reachability set. We show that our procedure computes the exact reachability set in many practical applications. We have successfully applied our technique to compute transitive closures for some mutual exclusion protocols defined on arbitrary width tree topologies, as well as for two interesting XML applications.