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This paper reports on the automated verification of the total correctness (partial correctness and termination) of the Deutsch-Schorr-Waite (DSW) algorithm. DSW is an algorithm for traversing a binary tree without the use of a stack by means of destructive pointer manipulation. Prior approaches to the verification of the algorithm involved applications of theorem provers or hand-written proofs. TVLA's abstract-interpretation approach made possible the automatic symbolic exploration of all memory configurations that can arise. With the introduction of a few simple core and instrumentation relations, TVLA was able to establish the partial correctness and termination of DSW.