/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 strict:
  f(x) -> s(x)
  f(s(s(x))) -> s(f(f(x)))
 weak:
  rand(x) -> x
  rand(x) -> rand(s(x))

Proof:
 String Reversal Processor:
  strict:
   f(x) -> s(x)
   s(s(f(x))) -> f(f(s(x)))
  weak:
   rand(x) -> x
   rand(x) -> s(rand(x))
  Arctic Interpretation Processor:
   dimension: 2
   interpretation:
                 [4 4]  
    [rand](x0) = [1 1]x0,
    
                
    [s](x0) = x0,
    
              [0  -&]  
    [f](x0) = [0  0 ]x0
   orientation:
           [0  -&]             
    f(x) = [0  0 ]x >= x = s(x)
    
                 [0  -&]     [0  -&]              
    s(s(f(x))) = [0  0 ]x >= [0  0 ]x = f(f(s(x)))
    
              [4 4]          
    rand(x) = [1 1]x >= x = x
    
              [4 4]     [4 4]              
    rand(x) = [1 1]x >= [1 1]x = s(rand(x))
   problem:
    strict:
     f(x) -> s(x)
     s(s(f(x))) -> f(f(s(x)))
    weak:
     rand(x) -> s(rand(x))
   Matrix Interpretation Processor: dim=5
    
    interpretation:
                  [1 0 0 0 0]  
                  [0 0 0 0 0]  
     [rand](x0) = [0 0 0 0 0]x0
                  [0 1 0 0 0]  
                  [0 0 0 0 0]  ,
     
               [1 0 1 0 0]  
               [0 0 1 0 1]  
     [s](x0) = [0 1 0 0 1]x0
               [0 0 0 0 0]  
               [0 1 1 0 0]  ,
     
               [1 0 1 0 0]     [0]
               [0 0 1 0 1]     [1]
     [f](x0) = [0 1 0 0 1]x0 + [0]
               [0 0 0 0 0]     [0]
               [0 1 1 0 0]     [1]
    orientation:
            [1 0 1 0 0]    [0]    [1 0 1 0 0]        
            [0 0 1 0 1]    [1]    [0 0 1 0 1]        
     f(x) = [0 1 0 0 1]x + [0] >= [0 1 0 0 1]x = s(x)
            [0 0 0 0 0]    [0]    [0 0 0 0 0]        
            [0 1 1 0 0]    [1]    [0 1 1 0 0]        
     
                  [1 2 3 0 2]    [2]    [1 2 3 0 2]    [0]             
                  [0 2 3 0 3]    [3]    [0 2 3 0 3]    [2]             
     s(s(f(x))) = [0 3 2 0 3]x + [2] >= [0 3 2 0 3]x + [2] = f(f(s(x)))
                  [0 0 0 0 0]    [0]    [0 0 0 0 0]    [0]             
                  [0 3 3 0 2]    [3]    [0 3 3 0 2]    [2]             
     
               [1 0 0 0 0]     [1 0 0 0 0]              
               [0 0 0 0 0]     [0 0 0 0 0]              
     rand(x) = [0 0 0 0 0]x >= [0 0 0 0 0]x = s(rand(x))
               [0 1 0 0 0]     [0 0 0 0 0]              
               [0 0 0 0 0]     [0 0 0 0 0]              
    problem:
     strict:
      f(x) -> s(x)
     weak:
      rand(x) -> s(rand(x))
    String Reversal Processor:
     strict:
      f(x) -> s(x)
     weak:
      rand(x) -> rand(s(x))
     Arctic Interpretation Processor:
      dimension: 3
      interpretation:
                    [0  -& 2 ]  
       [rand](x0) = [-& -& -&]x0
                    [-& -& 0 ]  ,
       
                 [0  -& 2 ]  
       [s](x0) = [2  1  1 ]x0
                 [-& -& 0 ]  ,
       
                 [1 0 3]  
       [f](x0) = [3 2 2]x0
                 [0 0 3]  
      orientation:
              [1 0 3]     [0  -& 2 ]        
       f(x) = [3 2 2]x >= [2  1  1 ]x = s(x)
              [0 0 3]     [-& -& 0 ]        
       
                 [0  -& 2 ]     [0  -& 2 ]              
       rand(x) = [-& -& -&]x >= [-& -& -&]x = rand(s(x))
                 [-& -& 0 ]     [-& -& 0 ]              
      problem:
       strict:
        
       weak:
        rand(x) -> rand(s(x))
      Qed