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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [activate](x0) = 4x0 + 2,
   
   [g](x0) = x0 + 4,
   
   [n__f](x0) = 2x0 + 1,
   
   [n__a] = 2,
   
   [f](x0) = 2x0 + 1,
   
   [a] = 4
  orientation:
   f(f(a())) = 19 >= 19 = f(g(n__f(n__a())))
   
   f(X) = 2X + 1 >= 2X + 1 = n__f(X)
   
   a() = 4 >= 2 = n__a()
   
   activate(n__f(X)) = 8X + 6 >= 8X + 5 = f(activate(X))
   
   activate(n__a()) = 10 >= 4 = a()
   
   activate(X) = 4X + 2 >= X = X
  problem:
   f(f(a())) -> f(g(n__f(n__a())))
   f(X) -> n__f(X)
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]  
    [g](x0) = [0 0 0]x0
              [0 0 0]  ,
    
                 [1 0 1]     [0]
    [n__f](x0) = [0 0 0]x0 + [0]
                 [0 0 0]     [1],
    
             [0]
    [n__a] = [0]
             [0],
    
              [1 0 1]     [0]
    [f](x0) = [0 0 0]x0 + [1]
              [0 0 0]     [1],
    
          [0]
    [a] = [0]
          [0]
   orientation:
                [1]    [0]                     
    f(f(a())) = [1] >= [1] = f(g(n__f(n__a())))
                [1]    [1]                     
    
           [1 0 1]    [0]    [1 0 1]    [0]          
    f(X) = [0 0 0]X + [1] >= [0 0 0]X + [0] = n__f(X)
           [0 0 0]    [1]    [0 0 0]    [1]          
   problem:
    f(X) -> n__f(X)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                  [1 0 0]  
     [n__f](x0) = [0 0 0]x0
                  [0 0 0]  ,
     
               [1 0 0]     [1]
     [f](x0) = [0 0 0]x0 + [0]
               [0 0 1]     [0]
    orientation:
            [1 0 0]    [1]    [1 0 0]           
     f(X) = [0 0 0]X + [0] >= [0 0 0]X = n__f(X)
            [0 0 1]    [0]    [0 0 0]           
    problem:
     
    Qed