Modularity of Termination and Confluence in Combinations of Rewrite Systems with lambda_omega

We prove that termination and confluence are modular properties in combinations of the typed λ-calculus of order Ω with (first or higher order) term rewrite systems, provided that the first order rewrite system is conservative (non-duplicating) and the higher order rewrite system satisfies some suitable conditions (the general schema) and does not introduce critical pairs.

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