Proving Termination of Nonlinear Command Sequences

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We describe a simple and efficient algorithm for proving the termination of a class of loops with nonlinear assignments to variables. The method is based on divergence testing for each variable in the cone-of-influence of the loop’s condition. The analysis allows us to automatically prove the termination of loops that cannot be handled using previous techniques. We also describe a method for integrating our nonlinear termination proving technique into a larger termination proving framework that depends on linear reasoning.


Domagoj Babic, Byron Cook, Alan J. Hu, Zvonimir Rakamaric
Proving Termination of Nonlinear Command Sequences
Formal Aspects of Computing (FAC), 25(3): 389--403, 2012.


  title = {Proving Termination of Nonlinear Command Sequences},
  author = {Domagoj Babic and Byron Cook and Alan J. Hu and Zvonimir Rakamaric},
  journal = {Formal Aspects of Computing (FAC)},
  publisher = {Springer},
  volume = {25},
  number = {3},
  pages = {389--403},
  month = {May},
  year = {2012}