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Automatic Verification of Sufficient Completeness for Specifications of Complex Data Structures ?

We present a new procedure for testing sufficient completeness for conditional and constrained term rewriting systems in presence of constrained axioms for constructors. Such axioms allow to specify complex data structures like e.g. sets or sorted lists. Our approach is based on tree grammars with constraints, a formalism which permits an exact representation of languages of ground constructor terms in normal form. The procedure is sound and complete and has been successfully used for checking the sufficient completeness of several specifications where related former techniques fail.