Relative termination

Abstract

"Relative termination" is a property that generalizes both termination and "termination modulo". In order to prove that a term rewrite system relatively terminates, one may reuse the common termination quasiorderings. Further proof methods become available by the cooperation property. Relative termination sets up new proof techniques for termination and confluence. The usefulness of the notion of relative termination is finally demonstrated by a proof of completeness for "reduced narrowing" and "normal narrowing", two attractive variants of the narrowing procedure.