YES

Problem:
 f(X) -> g(n__h(n__f(X)))
 h(X) -> n__h(X)
 f(X) -> n__f(X)
 activate(n__h(X)) -> h(activate(X))
 activate(n__f(X)) -> f(activate(X))
 activate(X) -> X

Proof:
 DP Processor:
  DPs:
   activate#(n__h(X)) -> activate#(X)
   activate#(n__h(X)) -> h#(activate(X))
   activate#(n__f(X)) -> activate#(X)
   activate#(n__f(X)) -> f#(activate(X))
  TRS:
   f(X) -> g(n__h(n__f(X)))
   h(X) -> n__h(X)
   f(X) -> n__f(X)
   activate(n__h(X)) -> h(activate(X))
   activate(n__f(X)) -> f(activate(X))
   activate(X) -> X
  Matrix Interpretation Processor: dim=3
   
   interpretation:
    [activate#](x0) = [1 1 1]x0,
    
    [h#](x0) = [1 0 0]x0,
    
    [f#](x0) = [0 1 0]x0,
    
                     [1 0 1]  
    [activate](x0) = [1 1 0]x0
                     [0 1 1]  ,
    
              [0 1 0]     [1]
    [h](x0) = [0 0 1]x0 + [0]
              [1 0 0]     [1],
    
              [0]
    [g](x0) = [0]
              [1],
    
                 [0 1 0]     [0]
    [n__h](x0) = [0 0 1]x0 + [0]
                 [1 0 0]     [1],
    
                 [0 0 1]     [0]
    [n__f](x0) = [1 0 0]x0 + [1]
                 [0 1 0]     [1],
    
              [0 0 1]     [0]
    [f](x0) = [1 0 0]x0 + [1]
              [0 1 0]     [1]
   orientation:
    activate#(n__h(X)) = [1 1 1]X + [1] >= [1 1 1]X = activate#(X)
    
    activate#(n__h(X)) = [1 1 1]X + [1] >= [1 0 1]X = h#(activate(X))
    
    activate#(n__f(X)) = [1 1 1]X + [2] >= [1 1 1]X = activate#(X)
    
    activate#(n__f(X)) = [1 1 1]X + [2] >= [1 1 0]X = f#(activate(X))
    
           [0 0 1]    [0]    [0]                   
    f(X) = [1 0 0]X + [1] >= [0] = g(n__h(n__f(X)))
           [0 1 0]    [1]    [1]                   
    
           [0 1 0]    [1]    [0 1 0]    [0]          
    h(X) = [0 0 1]X + [0] >= [0 0 1]X + [0] = n__h(X)
           [1 0 0]    [1]    [1 0 0]    [1]          
    
           [0 0 1]    [0]    [0 0 1]    [0]          
    f(X) = [1 0 0]X + [1] >= [1 0 0]X + [1] = n__f(X)
           [0 1 0]    [1]    [0 1 0]    [1]          
    
                        [1 1 0]    [1]    [1 1 0]    [1]                 
    activate(n__h(X)) = [0 1 1]X + [0] >= [0 1 1]X + [0] = h(activate(X))
                        [1 0 1]    [1]    [1 0 1]    [1]                 
    
                        [0 1 1]    [1]    [0 1 1]    [0]                 
    activate(n__f(X)) = [1 0 1]X + [1] >= [1 0 1]X + [1] = f(activate(X))
                        [1 1 0]    [2]    [1 1 0]    [1]                 
    
                  [1 0 1]          
    activate(X) = [1 1 0]X >= X = X
                  [0 1 1]          
   problem:
    DPs:
     
    TRS:
     f(X) -> g(n__h(n__f(X)))
     h(X) -> n__h(X)
     f(X) -> n__f(X)
     activate(n__h(X)) -> h(activate(X))
     activate(n__f(X)) -> f(activate(X))
     activate(X) -> X
   Qed