Non-termination Checking for Imperative Programs

  • Helga Velroyen
  • Philipp Rümmer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4966)


While termination checking tailored to real-world library code or frameworks has received ever-increasing attention during the last years, the complementary question of disproving termination properties as a means of debugging has largely been ignored so far. We present an approach to automatic non-termination checking that relates to termination checking in the same way as symbolic testing does to program verification. Our method is based on the automated generation of invariants that show that terminating states of a program are unreachable from certain initial states. Such initial states are identified using constraint-solving techniques. The method is fully implemented on top of a program verification system and available for download. We give an empirical evaluation of the approach using a collection of non-terminating example programs.


Open Goal Sequent Calculus Dynamic Logic Fibonacci Number Proof Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cook, B., Podelski, A., Rybalchenko, A.: Terminator: Beyond safety. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 415–418. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  2. 2.
    Sondermann, M.: Automatische Terminierungsanalyse von imperativen Programmen. Master’s thesis, RWTH Aachen University, Aachen, Germany (2006)Google Scholar
  3. 3.
    Rümmer, P., Shah, M.A.: Proving programs incorrect using a sequent calculus for Java Dynamic Logic. In: Gurevich, Y., Meyer, B. (eds.) TAP 2007. LNCS, vol. 4454, pp. 41–60. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Fitting, M.C.: First-Order Logic and Automated Theorem Proving, 2nd edn. Springer, New York (1996)zbMATHGoogle Scholar
  5. 5.
    Velroyen, H.: Automatic non-termination analysis of imperative programs. Master’s thesis, Chalmers University of Technology, Aachen Technical University, Göteborg, Sweden and Aachen, Germany (2007)Google Scholar
  6. 6.
    Winskel, G.: The Formal Semantics of Programming Languages. MIT Press, Cambridge (1993)zbMATHGoogle Scholar
  7. 7.
    Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)zbMATHGoogle Scholar
  8. 8.
    Beckert, B., Hähnle, R., Schmitt, P.H. (eds.): Verification of Object-Oriented Software. LNCS (LNAI), vol. 4334. Springer, Heidelberg (2007)Google Scholar
  9. 9.
    Rümmer, P.: A sequent calculus for integer arithmetic with counterexample generation. In: Proceedings of 4th International Verification Workshop (VERIFY 2007). CEUR, vol. 259 (2007),
  10. 10.
    Giese, M.: Incremental closure of free variable tableaux. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 545–560. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  11. 11.
    Gupta, A., Henzinger, T.A., Majumdar, R., Rybalchenko, A., Xu, R.-G.: Proving non-termination. In: Necula, G.C., Wadler, P. (eds.) ACM Symposium on Principles of Programming Languages (POPL), San Francisco, USA, pp. 147–158. ACM, New York (2008)Google Scholar
  12. 12.
    Giesl, J., Schneider-Kamp, P., Thiemann, R.: Aprove 1.2: Automatic termination proofs in the dependency pair framework. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 281–286. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  13. 13.
    Giesl, J., Thiemann, R., Schneider-Kamp, P.: Proving and disproving termination of higher-order functions. In: Gramlich, B. (ed.) FroCos 2005. LNCS (LNAI), vol. 3717, pp. 216–231. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  14. 14.
    Kapur, D.: Automatically generating loop invariants using quantifier elimination. In: Baader, F., Baumgartner, P., Nieuwenhuis, R., Voronkov, A. (eds.) Deduction and Applications. Dagstuhl Seminar Proceedings, Schloss Dagstuhl, Germany, vol. 05431 (2006)Google Scholar
  15. 15.
    Colón, M., Sankaranarayanan, S., Sipma, H.: Linear invariant generation using non-linear constraint solving. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 420–432. Springer, Heidelberg (2003)Google Scholar
  16. 16.
    Bjørner, N., Browne, A., Manna, Z.: Automatic generation of invariants and intermediate assertions. Theor. Comput. Sci. 173(1), 49–87 (1997)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Helga Velroyen
    • 1
  • Philipp Rümmer
    • 2
  1. 1.Department of Computer ScienceRWTH Aachen University of Technology 
  2. 2.Department of Computer Science and EngineeringChalmers University of Technology and Göteborg University 

Personalised recommendations