Using rippling to prove the termination of algorithms

Abstract

When proving theorems by explicit induction the used induction orderings are synthesized from the recursion orderings underlying the definition principles for functions and predicates. In order to guarantee the soundness of a generated induction scheme the well-foundedness of the used recursion orderings has to be proved. In this paper we present a method to synthesize appropriate measure functions in order to prove the termination of algorithms. We use Walthers' estimation-calculus as a "black-box procedure'; in these explicit proofs. Thus, we inherit both, the flexibility of an explicit representation of the termination proof as well as the in-built knowledge concerning the count ordering.