/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 f(f(x)) -> f(x)
 f(s(x)) -> f(x)
 g(s(0())) -> g(f(s(0())))

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