/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(g(x)) -> g(f(f(x)))
  f(h(x)) -> h(g(x))
  f'(s(x),y,y) -> f'(y,x,s(x))
 weak:
  rand(x) -> x
  rand(x) -> rand(s(x))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                [2 0]     [1]
   [rand](x0) = [0 1]x0 + [0],
   
                      [3 0]     [1 0]     [2 0]     [0]
   [f'](x0, x1, x2) = [1 0]x0 + [0 0]x1 + [1 0]x2 + [2],
   
             [1 0]  
   [s](x0) = [0 0]x0,
   
             [2 2]  
   [h](x0) = [0 0]x0,
   
             [1 0]  
   [f](x0) = [0 0]x0,
   
             [1 0]  
   [g](x0) = [0 0]x0
  orientation:
             [1 0]     [1 0]              
   f(g(x)) = [0 0]x >= [0 0]x = g(f(f(x)))
   
             [2 2]     [2 0]           
   f(h(x)) = [0 0]x >= [0 0]x = h(g(x))
   
                  [3 0]    [3 0]    [0]    [3 0]    [3 0]    [0]               
   f'(s(x),y,y) = [1 0]x + [1 0]y + [2] >= [1 0]x + [1 0]y + [2] = f'(y,x,s(x))
   
             [2 0]    [1]         
   rand(x) = [0 1]x + [0] >= x = x
   
             [2 0]    [1]    [2 0]    [1]             
   rand(x) = [0 1]x + [0] >= [0 0]x + [0] = rand(s(x))
  problem:
   strict:
    f(g(x)) -> g(f(f(x)))
    f(h(x)) -> h(g(x))
    f'(s(x),y,y) -> f'(y,x,s(x))
   weak:
    rand(x) -> rand(s(x))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
                 [2 0]  
    [rand](x0) = [0 0]x0,
    
                       [2 1]     [1 1]     [2 0]  
    [f'](x0, x1, x2) = [0 2]x0 + [0 1]x1 + [1 1]x2,
    
              [1 0]     [0]
    [s](x0) = [1 1]x0 + [1],
    
              [2 2]     [2]
    [h](x0) = [0 0]x0 + [0],
    
              [1 0]  
    [f](x0) = [0 0]x0,
    
              [1 1]  
    [g](x0) = [0 0]x0
   orientation:
              [1 1]     [1 0]              
    f(g(x)) = [0 0]x >= [0 0]x = g(f(f(x)))
    
              [2 2]    [2]    [2 2]    [2]          
    f(h(x)) = [0 0]x + [0] >= [0 0]x + [0] = h(g(x))
    
                   [3 1]    [3 1]    [1]    [3 1]    [2 1]    [0]               
    f'(s(x),y,y) = [2 2]x + [1 2]y + [2] >= [2 2]x + [0 2]y + [1] = f'(y,x,s(x))
    
              [2 0]     [2 0]              
    rand(x) = [0 0]x >= [0 0]x = rand(s(x))
   problem:
    strict:
     f(g(x)) -> g(f(f(x)))
     f(h(x)) -> h(g(x))
    weak:
     rand(x) -> rand(s(x))
   Matrix Interpretation Processor: dim=2
    
    interpretation:
                  [1 1]  
     [rand](x0) = [2 2]x0,
     
               [1 0]  
     [s](x0) = [0 0]x0,
     
               [1 0]     [0]
     [h](x0) = [1 0]x0 + [2],
     
               [1 1]  
     [f](x0) = [0 1]x0,
     
               [1 0]  
     [g](x0) = [0 2]x0
    orientation:
               [1 2]     [1 2]              
     f(g(x)) = [0 2]x >= [0 2]x = g(f(f(x)))
     
               [2 0]    [2]    [1 0]    [0]          
     f(h(x)) = [1 0]x + [2] >= [1 0]x + [2] = h(g(x))
     
               [1 1]     [1 0]              
     rand(x) = [2 2]x >= [2 0]x = rand(s(x))
    problem:
     strict:
      f(g(x)) -> g(f(f(x)))
     weak:
      rand(x) -> rand(s(x))
    String Reversal Processor:
     strict:
      g(f(x)) -> f(f(g(x)))
     weak:
      rand(x) -> s(rand(x))
     Matrix Interpretation Processor: dim=2
      
      interpretation:
                    [2 2]     [1]
       [rand](x0) = [3 2]x0 + [2],
       
                 [1 0]     [0]
       [s](x0) = [1 0]x0 + [1],
       
                      [0]
       [f](x0) = x0 + [1],
       
                 [1 1]  
       [g](x0) = [0 2]x0
      orientation:
                 [1 1]    [1]    [1 1]    [0]             
       g(f(x)) = [0 2]x + [2] >= [0 2]x + [2] = f(f(g(x)))
       
                 [2 2]    [1]    [2 2]    [1]             
       rand(x) = [3 2]x + [2] >= [2 2]x + [2] = s(rand(x))
      problem:
       strict:
        
       weak:
        rand(x) -> s(rand(x))
      Qed