The Size-Change Termination Principle on Non-Well founded Data Types

Despite its simplicity, the size-change termination principle (SCT), presented by Lee, Jones and Ben-Amram in [LJB01], is surprisingly strong and is able to show termination for a large class of programs. A significant limitation for its use, however, is the fact that the SCT requires data types to be well-founded, and that all mechanisms used to determine termination must involve decreases in these global, well-founded partial orders. In the following, I will present an extension of the size-change principle that allows for non-well founded data types, and a realization of this principle for integer data types. The extended size-change principle is realized through combining abstract interpretation over the domain of convex polyhedra with the use of size-change graphs. In the cases when data types arewell founded, the method handles every case that is handled by LJB size-change termination. The method has been implemented in a subject language independent shared library, as well as in the ANSI C specializer C-MixII, for a subset of its internal language Core-C.