/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 strict:
  f(x,0()) -> s(x)
  g(x) -> h(x,gen())
  h(0(),x) -> f(x,x)
  a() -> b()
 weak:
  gen() -> s(gen())

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
           [0]
   [gen] = [0]
           [0],
   
                 [1 0 0]     [1 1 2]     [1]
   [f](x0, x1) = [1 0 2]x0 + [1 2 0]x1 + [0]
                 [0 0 2]     [0 0 0]     [1],
   
             [2 2 2]     [0]
   [g](x0) = [0 2 0]x0 + [1]
             [2 2 3]     [0],
   
                 [1 0 1]     [2 1 2]     [0]
   [h](x0, x1) = [0 2 0]x0 + [2 3 2]x1 + [1]
                 [1 0 2]     [0 0 2]     [0],
   
         [1]
   [0] = [3]
         [1],
   
         [0]
   [b] = [0]
         [0],
   
         [0]
   [a] = [0]
         [2],
   
             [1 0 0]  
   [s](x0) = [0 0 2]x0
             [0 0 0]  
  orientation:
              [1 0 0]    [7]    [1 0 0]        
   f(x,0()) = [1 0 2]x + [7] >= [0 0 2]x = s(x)
              [0 0 2]    [1]    [0 0 0]        
   
          [2 2 2]    [0]    [1 0 1]    [0]             
   g(x) = [0 2 0]x + [1] >= [0 2 0]x + [1] = h(x,gen())
          [2 2 3]    [0]    [1 0 2]    [0]             
   
              [2 1 2]    [2]    [2 1 2]    [1]         
   h(0(),x) = [2 3 2]x + [7] >= [2 2 2]x + [0] = f(x,x)
              [0 0 2]    [3]    [0 0 2]    [1]         
   
         [0]    [0]      
   a() = [0] >= [0] = b()
         [2]    [0]      
   
           [0]    [0]           
   gen() = [0] >= [0] = s(gen())
           [0]    [0]           
  problem:
   strict:
    g(x) -> h(x,gen())
    a() -> b()
   weak:
    gen() -> s(gen())
  Matrix Interpretation Processor: dim=5
   
   interpretation:
            [0]
            [0]
    [gen] = [0]
            [0]
            [0],
    
              [1 0 0 1 0]     [0]
              [0 1 1 0 0]     [1]
    [g](x0) = [0 0 0 0 0]x0 + [0]
              [0 0 0 0 0]     [0]
              [0 0 0 0 0]     [1],
    
                  [1 0 0 0 0]     [1 0 0 0 0]  
                  [0 0 0 0 0]     [0 0 0 0 0]  
    [h](x0, x1) = [0 0 0 0 0]x0 + [0 0 0 0 0]x1
                  [0 0 0 0 0]     [0 0 0 0 0]  
                  [0 0 0 0 0]     [0 0 0 0 0]  ,
    
          [0]
          [0]
    [b] = [0]
          [0]
          [0],
    
          [1]
          [0]
    [a] = [0]
          [0]
          [0],
    
              [1 0 0 0 0]  
              [0 0 0 0 0]  
    [s](x0) = [0 0 0 0 0]x0
              [0 0 0 0 0]  
              [0 0 0 0 0]  
   orientation:
           [1 0 0 1 0]    [0]    [1 0 0 0 0]              
           [0 1 1 0 0]    [1]    [0 0 0 0 0]              
    g(x) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x = h(x,gen())
           [0 0 0 0 0]    [0]    [0 0 0 0 0]              
           [0 0 0 0 0]    [1]    [0 0 0 0 0]              
    
          [1]    [0]      
          [0]    [0]      
    a() = [0] >= [0] = b()
          [0]    [0]      
          [0]    [0]      
    
            [0]    [0]           
            [0]    [0]           
    gen() = [0] >= [0] = s(gen())
            [0]    [0]           
            [0]    [0]           
   problem:
    strict:
     g(x) -> h(x,gen())
    weak:
     gen() -> s(gen())
   Matrix Interpretation Processor: dim=5
    
    interpretation:
             [0]
             [0]
     [gen] = [0]
             [0]
             [1],
     
               [1 1 0 0 0]     [1]
               [1 0 0 0 0]     [0]
     [g](x0) = [0 0 0 0 0]x0 + [0]
               [0 0 0 0 0]     [1]
               [0 0 0 0 0]     [1],
     
                   [1 0 0 0 0]     [1 0 0 0 0]  
                   [0 0 0 0 0]     [0 0 0 0 0]  
     [h](x0, x1) = [0 0 0 0 0]x0 + [0 0 0 0 0]x1
                   [0 0 0 0 0]     [0 0 0 0 1]  
                   [0 0 0 0 0]     [0 0 0 0 0]  ,
     
               [1 0 0 0 0]     [0]
               [0 0 0 0 0]     [0]
     [s](x0) = [0 0 0 0 0]x0 + [0]
               [0 0 0 0 0]     [0]
               [0 0 0 0 0]     [1]
    orientation:
            [1 1 0 0 0]    [1]    [1 0 0 0 0]    [0]             
            [1 0 0 0 0]    [0]    [0 0 0 0 0]    [0]             
     g(x) = [0 0 0 0 0]x + [0] >= [0 0 0 0 0]x + [0] = h(x,gen())
            [0 0 0 0 0]    [1]    [0 0 0 0 0]    [1]             
            [0 0 0 0 0]    [1]    [0 0 0 0 0]    [0]             
     
             [0]    [0]           
             [0]    [0]           
     gen() = [0] >= [0] = s(gen())
             [0]    [0]           
             [1]    [1]           
    problem:
     strict:
      
     weak:
      gen() -> s(gen())
    Qed