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