YES

Problem:
 active(f(X)) -> mark(g(h(f(X))))
 mark(f(X)) -> active(f(mark(X)))
 mark(g(X)) -> active(g(X))
 mark(h(X)) -> active(h(mark(X)))
 f(mark(X)) -> f(X)
 f(active(X)) -> f(X)
 g(mark(X)) -> g(X)
 g(active(X)) -> g(X)
 h(mark(X)) -> h(X)
 h(active(X)) -> h(X)

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