Solving Disequations modulo some Class of Rewrite Systems

. This paper gives a procedure for solving disequations modulo equational theories, and to decide existence of solutions. For this, we assume that the equational theory is specified by a confluent and constructor-based rewrite system, and that four additional restrictions are satisfied. The procedure represents the possibly infinite set of solutions thanks to a grammar, and decides existence of solutions thanks to an emptiness test. As a consequence, checking whether a linear equality is an inductive theorem is decidable, if assuming moreover sufficient completeness. 1 Introduction The problem that consists in solving symbolic equations modulo a theory is called equational unification. A lot of work has already studied this subject in a theoretical way to know when the problem can be decided, as well as in a practical way to find efficient algorithms that solve the problem. Another interesting problem consists in solving the negation of equations, called disequations, i.e. in finding ..