The paper presents a new schematization of innnite families of terms called the primal grammars, based on the notion of primitive recursive rewrite systems. This schematization is presented by a generating term and a canonical rewrite system. It is proved that the class of primal grammars covers completely the class of crossed rewrite systems. This proof contains a construction of a primal gram...

This paper is concerned with methods that automatically prove termination of term rewrite systems. The aim of dummy elimination, a method to prove termination introduced by Ferreira and Zantema, is to transform a given rewrite system into a rewrite system whose termination is easier to prove. We show that dummy elimination is subsumed by the more recent dependency pair method of Arts and Giesl....

The uniform first-order theory of ground tree rewrite graphs is the set of all pairs consisting of a ground tree rewrite system and a first-order sentence that holds in the graph defined by the ground tree rewrite system. We prove that the complexity of the uniform first-order theory of ground tree rewrite graphs is in ATIME(2 poly(n) , O(n)). Providing a matching lower bound, we show that ther...

The use of automata techniques to prove the termination of string rewrite systems and left-linear term rewrite systems is advocated by Geser et al. in a recent sequence of papers. We extend their work to non-left-linear rewrite systems. The key to this extension is the introduction of so-called raise rules and the use of tree automata that are not quite deterministic. Furthermore, we present ne...

The reachability problem for ground associative-commutative (AC) rewrite systems is decidable. We show that ground AC rewrite systems are equivalent to Process Rewrite Systems (PRS) for which reach-ability is decidable 4]. However, the decidability proofs for PRS are cumbersome and thus we present a simpler and more readable proof in the framework of ground AC rewrite systems. Moreover, we show...

Right-(ground or variable) rewrite systems (RGV systems for short) are term rewrite systems where all right hand sides of rules are restricted to be either ground or a variable. We define a minimal rewrite extensionR of the rewrite relation induced by a RGV system R. This extension admits a rewrite closure presentation, which can be effectively constructed from R. The rewrite closure is used to...