Strict Functionals for Termination Proofs

A semantical method to prove termination of higher order rewrite systems (HRS) is presented. Its main tool is the notion of a strict functional, which is a variant of Gandy's notion of a hereditarily monotonic functional [1]. The main advantage of the method is that it makes it possible to transfer ones intuitions about why an HRS should be terminating into a proof: one has to nd a \strict" interpretation of the constants involved in such a way that the left hand side of any rewrite rule gets a bigger value than the right hand side. The applicability of the method is demonstrated in three examples.