Abstract There are many techniques and tools to prove termination of programs, but up to now these tools were not very powerful for fully automated termination proofs of programs whose termination depends on recursive data structures like lists. We present the first approach that extends powerful techniques for termination analysis of programs (with memory allocation and explicit pointer arithmetic) to lists.

Abstract To (dis)prove termination of programs, uses symbolic execution to transform the program’s code into an integer transition system, which is then analyzed by several backends. The transformation steps in and the tools in the backend only produce sub-proofs in their domains. Hence, we now developed new techniques to automatically combine the essence of these proofs. If non-termination is proved, then they yield an overall witness, which identifies a non-terminating path in the original program.

We present the first approach to deduce lower bounds for innermost runtime complexity of term rewrite systems (TRSs) automatically. Inferring lower runtime bounds is useful to detect bugs and to complement existing techniques that compute upper complexity bounds. The key idea of our approach is to generate suitable families of rewrite sequences of a TRS and to find a relation between the length of such a rewrite sequence and the size of the first term in the sequence. We implemented our approach in the tool AProVE and evaluated it by extensive experiments.