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. [ABSTRACT FROM AUTHOR]