Conditional Rewrite Rule Systems with Built-In Arithmetic and Induction

Conditional rewriting systems, conditions being the formulae of decidable theories, are investigated. A practical search space-free decision procedure for the related class of unquantified logical theories is described. The procedure is based on cooperating conditional reductions, case splittings and decision algorithms, and is able to perform certain forms of inductive inferences. Completeness and termination of the procedure are proved.

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