In the context of file systems like those of Unix, path resolution is the operation that given a character string denoting an access path, determines the target object (a file, a directory, etc.) designated by this path. This operation is not trivial because of the presence of symbolic links. Indeed, the presence of such links may induce infinite loops in the resolution process. We consider a path resolution algorithm that always terminates, detecting if it enters an infinite loop and reports a resolution failure in such a case. We propose a formal specification of path resolution and we formally prove that our algorithm terminates on any input, and is correct and complete with respect to our formal specification.