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

A new notion of generalized rewrite theory suitable for symbolic reasoning and generalizing the standard notion in [3] is motivated and defined. Also, new requirements for symbolic executability of generalized rewrite theories that extend those in [8] for standard rewrite theories, including a generalized notion of coherence, are given. Finally, symbolic executability, including coherence, is b...

At first an introduction to context-sensitive rewrite-systems is given. The main part of this paper deals with the topic how one can prove termination of contextsensitive rewrite-systems. This can be done either by either transforming them into non context-sensitive ones or by extending the existing techniques which are used to prove termination of classic rewrite systems. This is described in ...

Many formal models for in nite-state concurrent systems are equivalent to special classes of rewrite systems. We classify these models by their expressiveness and de ne a hierarchy of classes of rewrite systems. We show that this hierarchy is strict with respect to bisimulation equivalence. The most general and most expressive class of systems in this hierarchy is called Process Rewrite Systems...