Completeness of Combinations of Conditional Constructor Systems

In this paper we extend the divide and conquer technique of Middeldorp and Toyama for establishing (semi-)completeness of constructor systems to conditional constructor systems. We show that both completeness (i.e. the combination of confluence and strong normalisation) and semi-completeness (confluence plus weak normalisation) are decomposable properties of conditional constructor systems without extra variables in the conditions of the rewrite rules.