/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 strict:
  f(f(x)) -> x
 weak:
  f(x) -> g(f(g(f(x))))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
             [1 0]  
   [g](x0) = [0 0]x0,
   
             [1 1]     [0]
   [f](x0) = [2 0]x0 + [2]
  orientation:
             [3 1]    [2]         
   f(f(x)) = [2 2]x + [2] >= x = x
   
          [1 1]    [0]    [1 1]                 
   f(x) = [2 0]x + [2] >= [0 0]x = g(f(g(f(x))))
  problem:
   strict:
    
   weak:
    f(x) -> g(f(g(f(x))))
  Qed