Program termination analysis in polynomial time

In an earlier work with Neil D.~Jones, we proposed the ``size-change principle'' for program termination: An infinite computation is \emph{impossible}, if it would imply that some data decrease in size infinitely. Such a property can be deduced from program analysis information in the form of \emph{size-change graphs}. A set of size-change graphs with the desired property is said to satisfy \emph{size-change termination} (SCT). There are many examples of practical programs whose termination can be verified by creating size-change graphs and testing them for SCT. While SCT is decidable, it has high worst-case complexity (complete for \sctext{pspace}). In this paper, we formulate an efficient approach to verify practical instances of SCT. Our procedure has worst-case complexity cubic in the input size. Its effectiveness is demonstrated empirically using a test-suite of over 90 programs