A Path Order for Rewrite Systems that Compute Exponential Time Functions (Technical Report)

In this paper we present a new path order for rewrite systems, the exponential path order EPOSTAR. Suppose a term rewrite system is compatible with EPOSTAR, then the runtime complexity of this rewrite system is bounded from above by an exponential function. Furthermore, the class of function computed by a rewrite system compatible with EPOSTAR equals the class of functions computable in exponential time on a Turing maschine.