  This article is concerned with automated complexity analysis of term rewrite
systems. Since these systems underlie much of declarative programming, time
complexity of functions defined by rewrite systems is of particular interest.
Among other results, we present a variant of the dependency pair method for
analysing runtime complexities of term rewrite systems automatically. The
established results significantly extent previously known techniques: we give
examples of rewrite systems subject to our methods that could previously not
been analysed automatically. Furthermore, the techniques have been implemented
in the Tyrolean Complexity Tool. We provide ample numerical data for assessing
the viability of the method.
