Abstract

We present simple techniques for deciding the satisfiability of lexicographic path ordering constraints under two different semantics: solutions built over the given signature and solutions in extended signatures. For both cases we give the first NP algorithms, which is optimal as we prove the problems to be NP-complete. We discuss the efficient applicability of the techniques in practice, where, as far as we know, their simply exponential bound improves upon the existing methods, and describe some optimizations. Keywords: Automatic theorem proving. 1 Terminology Let F and X be sets of function symbols and variables respectively, and let ØF be a total ordering on F (the precedence). We sometimes write pairs (F ; ØF ). The lexicographic path ordering (LPO) generated by ØF , denoted Ø F lpo , is a total simplification ordering on T (F). It is defined as follows: s = f(s 1 ; : : : ; s m ) Ø F lpo g(t 1 ; : : : ; t n ) = t if 1. s i F lpo t, for some i with 1 i m or 2. f ØF g...

Citations

48	Solving symbolic ordering constraints - Comon - 1990
47	Theorem proving with ordering constrained clauses - Nieuwenhuis, Rubio - 1992
35	Satisfiability of systems of ordinal notations with the subterm ordering is decidable - Jouannaud, Okada - 1991