Abstract
This paper surveys some techniques and tools for achieving reachability analysis over term rewriting systems. The core of those techniques is a generic tree automata completion algorithm used to compute in an exact or approximated way the set of descendants (or reachable terms). This algorithm has been implemented in the \textsf{Timbuk} tool. Furthermore, we show that many classes with regular sets of descendants of the literature corresponds to specific instances of the tree automata completion algorithm and can thus be efficiently computed by \textsf{Timbuk} . An extension of the completion algorithm to conditional term rewriting systems and some applications are also presented.
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