The work reported here is part of the PROGRES (PROgrammed Graph Rewriting Systems) project. PROGRES is a very high level multi paradigm language for the specification of complex structured data types and their operations. The data structures are modelled as directed, attributed, node and edge labelled graphs (diane graphs). The basic programming constructs of PROGRES are graph rewriting rules (productions and tests) and derived relations on nodes (paths and restrictions). These basic operations may be combined to build partly imperative, partly rule based, complex graph transformations by special control structures which regard the nondeterministic nature of graph rewriting rules. In order to use PROGRES not only as a specification language but also for building rapid prototypes and even for the derivation of final implementations, we have to be able to execute PROGRES specifications efficiently. The central problem in executing a graph rewriting system is to match the left-hand side..
