Rewrite systems on free data structures have limited expressive power since semantic data structures like sets or multisets cannot be modeled elegantly. In this work we define a class of rewrite systems that allows the use of semantic data structures. Additionally, built-in natural numbers, including (dis)equality, ordering, and divisibility constraints, are supported. The rewrite mechanism is a combination of normalized equational rewriting with evaluation of conditions and validity checking of instantiated constraints. The framework is highly expressive and allows modeling of algorithms in a natural way.

Termination is one of the most important properties of conditional normalized equational rewriting. For this it is not sufficient to only show well-foundedness of the rewrite relation, but it also has to be ensured that evaluation of the conditions does not loop. The notion of operational termination is a way to capture these properties. In this work we show that it is possible to transform a conditional constrained equational rewrite system into an unconditional one such that termination of the latter implies operational termination of the former. Methods for showing termination of unconditional constrained equational rewrite system are presented in a companion paper.