/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:
 f(f(a())) -> c(n__f(n__g(n__f(n__a()))))
 f(X) -> n__f(X)
 g(X) -> n__g(X)
 a() -> n__a()
 activate(n__f(X)) -> f(activate(X))
 activate(n__g(X)) -> g(activate(X))
 activate(n__a()) -> a()
 activate(X) -> X

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                         [1]
   [activate](x0) = x0 + [0]
                         [0],
   
             [1 0 0]  
   [g](x0) = [0 0 0]x0
             [0 0 0]  ,
   
             [1 0 0]  
   [c](x0) = [0 0 0]x0
             [0 0 0]  ,
   
                [1 0 0]  
   [n__g](x0) = [0 0 0]x0
                [0 0 0]  ,
   
                [1 0 0]  
   [n__f](x0) = [0 0 0]x0
                [0 0 0]  ,
   
            [0]
   [n__a] = [0]
            [0],
   
             [1 0 0]  
   [f](x0) = [0 0 0]x0
             [0 0 0]  ,
   
         [1]
   [a] = [0]
         [0]
  orientation:
               [1]    [0]                              
   f(f(a())) = [0] >= [0] = c(n__f(n__g(n__f(n__a()))))
               [0]    [0]                              
   
          [1 0 0]     [1 0 0]           
   f(X) = [0 0 0]X >= [0 0 0]X = n__f(X)
          [0 0 0]     [0 0 0]           
   
          [1 0 0]     [1 0 0]           
   g(X) = [0 0 0]X >= [0 0 0]X = n__g(X)
          [0 0 0]     [0 0 0]           
   
         [1]    [0]         
   a() = [0] >= [0] = n__a()
         [0]    [0]         
   
                       [1 0 0]    [1]    [1 0 0]    [1]                 
   activate(n__f(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = f(activate(X))
                       [0 0 0]    [0]    [0 0 0]    [0]                 
   
                       [1 0 0]    [1]    [1 0 0]    [1]                 
   activate(n__g(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = g(activate(X))
                       [0 0 0]    [0]    [0 0 0]    [0]                 
   
                      [1]    [1]      
   activate(n__a()) = [0] >= [0] = a()
                      [0]    [0]      
   
                     [1]         
   activate(X) = X + [0] >= X = X
                     [0]         
  problem:
   f(X) -> n__f(X)
   g(X) -> n__g(X)
   activate(n__f(X)) -> f(activate(X))
   activate(n__g(X)) -> g(activate(X))
   activate(n__a()) -> a()
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                     [1 1 0]  
    [activate](x0) = [0 0 1]x0
                     [0 1 0]  ,
    
                   [1]
    [g](x0) = x0 + [1]
                   [1],
    
                      [0]
    [n__g](x0) = x0 + [1]
                      [1],
    
                 [1 1 0]     [0]
    [n__f](x0) = [0 0 1]x0 + [1]
                 [0 1 0]     [1],
    
             [0]
    [n__a] = [1]
             [0],
    
              [1 1 0]     [1]
    [f](x0) = [0 0 1]x0 + [1]
              [0 1 0]     [1],
    
          [0]
    [a] = [0]
          [0]
   orientation:
           [1 1 0]    [1]    [1 1 0]    [0]          
    f(X) = [0 0 1]X + [1] >= [0 0 1]X + [1] = n__f(X)
           [0 1 0]    [1]    [0 1 0]    [1]          
    
               [1]        [0]          
    g(X) = X + [1] >= X + [1] = n__g(X)
               [1]        [1]          
    
                        [1 1 1]    [1]    [1 1 1]    [1]                 
    activate(n__f(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = f(activate(X))
                        [0 0 1]    [1]    [0 0 1]    [1]                 
    
                        [1 1 0]    [1]    [1 1 0]    [1]                 
    activate(n__g(X)) = [0 0 1]X + [1] >= [0 0 1]X + [1] = g(activate(X))
                        [0 1 0]    [1]    [0 1 0]    [1]                 
    
                       [1]    [0]      
    activate(n__a()) = [0] >= [0] = a()
                       [1]    [0]      
   problem:
    activate(n__f(X)) -> f(activate(X))
    activate(n__g(X)) -> g(activate(X))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                      [1 0 1]  
     [activate](x0) = [0 0 0]x0
                      [0 0 0]  ,
     
               [1 0 0]  
     [g](x0) = [0 0 0]x0
               [0 0 0]  ,
     
                  [1 0 0]     [1]
     [n__g](x0) = [0 0 0]x0 + [0]
                  [0 0 1]     [0],
     
                  [1 0 0]     [0]
     [n__f](x0) = [0 0 0]x0 + [0]
                  [0 0 1]     [1],
     
               [1 0 0]  
     [f](x0) = [0 0 0]x0
               [0 0 0]  
    orientation:
                         [1 0 1]    [1]    [1 0 1]                  
     activate(n__f(X)) = [0 0 0]X + [0] >= [0 0 0]X = f(activate(X))
                         [0 0 0]    [0]    [0 0 0]                  
     
                         [1 0 1]    [1]    [1 0 1]                  
     activate(n__g(X)) = [0 0 0]X + [0] >= [0 0 0]X = g(activate(X))
                         [0 0 0]    [0]    [0 0 0]                  
    problem:
     
    Qed