An Extension of an Automated Termination Method of Recursive Functions

Inductive proofs are commonly used in automated deduction systems or functional programming, such as for instance the ProPre system, for establishing the termination of recursively defined functions. Such proofs deal with the structural orderings of the term algebras that define the domain of the functions. However there exists other interesting functions whose termination requires different underlying orderings. To treat a class of such functions that are not taken into account by systems such as ProPre, we develop termination properties that can be shown automatically. In contrast with the ProPre system that builds formal trees based on inductive proofs, we generate measures that satisfy an extended termination property and well-founded orderings which ensure the termination of the functions.