Size-Change Termination Analysis in k-Bits

Size-change termination analysis is a simple and powerful technique successfully applied for a variety of programming paradigms. A main advantage is that termination for size-change graphs is decidable and based on simple linear ranking functions. A main disadvantage is that the size-change termination problem is PSPACE-complete. Proving size change termination may have to consider exponentially many size change graphs. This paper is concerned with the representation of large sets of size-change graphs. The approach is constraint based and the novelty is that sets of size-change graphs are represented as disjunctions of size-change constraints. A constraint solver to facilitate size-change termination analysis is obtained by interpreting size-change constraints over a sufficiently large but finite non-negative integer domain. A Boolean kbit modeling of size change graphs using binary decision diagrams leads to a concise representation. Experimental evaluation indicates that the 2-bit representation facilitates an efficient implementation which is guaranteed complete for our entire benchmark suite.