Proving Termination of Unfolding Graph Rewriting for General Safe Recursion

In this paper we present a new termination proof and complexity analysis of unfolding graph rewriting which is a specific kind of infinite graph rewriting expressing the general form of safe recursion. We introduce a termination order over sequences of terms together with an interpretation of term graphs into sequences of terms. Unfolding graph rewrite rules expressing general safe recursion can be successfully embedded into the termination order by the interpretation, yielding the polynomial runtime complexity. Moreover, generalising the definition of unfolding graph rewrite rules for general safe recursion, we propose a new criterion for the polynomial runtime complexity of infinite GRSs and for the polynomial size of normal forms in infinite GRSs.