In this work we investigate the satisfiability problem for the logic XPath( , , =), that includes all downward axes as well as equality and inequality tests. We address this problem in the absence of DTDs and the sibling axis. We prove that this fragment is decidable, and we nail down its complexity, showing the problem to be ExpTime-complete. The result also holds when path expressions allow closure under the Kleene star operator. To obtain these results, we introduce a new automaton model over data trees that captures XPath( , , =) and has an ExpTime emptiness problem. Furthermore, we give the exact complexity of several downward-looking fragments. Categories and Subject Descriptors I.7.2 [Document Preparation]: Markup Languages; H.2.3 [Database Management]: Languages; H.2.3 [Languages]: Query Languages General Terms Algorithms, Languages Keywords XML, XPath, unranked unordered tree, data-tree, infinite alphabet, data values, BIP automaton