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)
  EDG 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)
   graph:
    f#(mark(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
    f#(mark(X)) -> f#(X) -> f#(active(X)) -> f#(X)
    f#(active(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
    f#(active(X)) -> f#(X) -> f#(active(X)) -> f#(X)
    mark#(h(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    mark#(h(X)) -> mark#(X) -> mark#(f(X)) -> f#(mark(X))
    mark#(h(X)) -> mark#(X) -> mark#(f(X)) -> active#(f(mark(X)))
    mark#(h(X)) -> mark#(X) -> mark#(g(X)) -> active#(g(X))
    mark#(h(X)) -> mark#(X) -> mark#(h(X)) -> mark#(X)
    mark#(h(X)) -> mark#(X) -> mark#(h(X)) -> h#(mark(X))
    mark#(h(X)) -> mark#(X) -> mark#(h(X)) -> active#(h(mark(X)))
    mark#(h(X)) -> h#(mark(X)) -> h#(mark(X)) -> h#(X)
    mark#(h(X)) -> active#(h(mark(X))) ->
    active#(f(X)) -> h#(f(X))
    mark#(h(X)) -> active#(h(mark(X))) ->
    active#(f(X)) -> g#(h(f(X)))
    mark#(h(X)) -> active#(h(mark(X))) ->
    active#(f(X)) -> mark#(g(h(f(X))))
    mark#(f(X)) -> f#(mark(X)) -> f#(mark(X)) -> f#(X)
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> f#(mark(X))
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> active#(f(mark(X)))
    mark#(f(X)) -> mark#(X) -> mark#(g(X)) -> active#(g(X))
    mark#(f(X)) -> mark#(X) -> mark#(h(X)) -> mark#(X)
    mark#(f(X)) -> mark#(X) -> mark#(h(X)) -> h#(mark(X))
    mark#(f(X)) -> mark#(X) -> mark#(h(X)) -> active#(h(mark(X)))
    mark#(f(X)) -> active#(f(mark(X))) ->
    active#(f(X)) -> h#(f(X))
    mark#(f(X)) -> active#(f(mark(X))) ->
    active#(f(X)) -> g#(h(f(X)))
    mark#(f(X)) -> active#(f(mark(X))) -> active#(f(X)) -> mark#(g(h(f(X))))
    g#(mark(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    g#(mark(X)) -> g#(X) -> g#(active(X)) -> g#(X)
    g#(active(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    g#(active(X)) -> g#(X) -> g#(active(X)) -> g#(X)
    h#(mark(X)) -> h#(X) -> h#(mark(X)) -> h#(X)
    h#(mark(X)) -> h#(X) -> h#(active(X)) -> h#(X)
    h#(active(X)) -> h#(X) -> h#(mark(X)) -> h#(X)
    h#(active(X)) -> h#(X) -> h#(active(X)) -> h#(X)
    active#(f(X)) -> mark#(g(h(f(X)))) -> mark#(g(X)) -> active#(g(X))
   SCC Processor:
    #sccs: 4
    #rules: 8
    #arcs: 35/256
    DPs:
     g#(mark(X)) -> g#(X)
     g#(active(X)) -> g#(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:
     dimension: 1
     interpretation:
      [g#](x0) = x0,
      
      [mark](x0) = x0 + 1,
      
      [g](x0) = 0,
      
      [h](x0) = 0,
      
      [active](x0) = x0,
      
      [f](x0) = x0 + 1
     orientation:
      g#(mark(X)) = X + 1 >= X = g#(X)
      
      g#(active(X)) = X >= X = g#(X)
      
      active(f(X)) = X + 1 >= 1 = mark(g(h(f(X))))
      
      mark(f(X)) = X + 2 >= X + 2 = active(f(mark(X)))
      
      mark(g(X)) = 1 >= 0 = active(g(X))
      
      mark(h(X)) = 1 >= 0 = active(h(mark(X)))
      
      f(mark(X)) = X + 2 >= X + 1 = f(X)
      
      f(active(X)) = X + 1 >= X + 1 = f(X)
      
      g(mark(X)) = 0 >= 0 = g(X)
      
      g(active(X)) = 0 >= 0 = g(X)
      
      h(mark(X)) = 0 >= 0 = h(X)
      
      h(active(X)) = 0 >= 0 = h(X)
     problem:
      DPs:
       g#(active(X)) -> g#(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:
      dimension: 1
      interpretation:
       [g#](x0) = x0,
       
       [mark](x0) = 1,
       
       [g](x0) = 0,
       
       [h](x0) = 0,
       
       [active](x0) = x0 + 1,
       
       [f](x0) = 0
      orientation:
       g#(active(X)) = X + 1 >= X = g#(X)
       
       active(f(X)) = 1 >= 1 = mark(g(h(f(X))))
       
       mark(f(X)) = 1 >= 1 = active(f(mark(X)))
       
       mark(g(X)) = 1 >= 1 = active(g(X))
       
       mark(h(X)) = 1 >= 1 = active(h(mark(X)))
       
       f(mark(X)) = 0 >= 0 = f(X)
       
       f(active(X)) = 0 >= 0 = f(X)
       
       g(mark(X)) = 0 >= 0 = g(X)
       
       g(active(X)) = 0 >= 0 = g(X)
       
       h(mark(X)) = 0 >= 0 = h(X)
       
       h(active(X)) = 0 >= 0 = h(X)
      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
    
    DPs:
     mark#(h(X)) -> mark#(X)
     mark#(f(X)) -> mark#(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:
     dimension: 1
     interpretation:
      [mark#](x0) = x0,
      
      [mark](x0) = x0,
      
      [g](x0) = 1,
      
      [h](x0) = x0,
      
      [active](x0) = x0,
      
      [f](x0) = x0 + 1
     orientation:
      mark#(h(X)) = X >= X = mark#(X)
      
      mark#(f(X)) = X + 1 >= X = mark#(X)
      
      active(f(X)) = X + 1 >= 1 = mark(g(h(f(X))))
      
      mark(f(X)) = X + 1 >= X + 1 = active(f(mark(X)))
      
      mark(g(X)) = 1 >= 1 = active(g(X))
      
      mark(h(X)) = X >= X = active(h(mark(X)))
      
      f(mark(X)) = X + 1 >= X + 1 = f(X)
      
      f(active(X)) = X + 1 >= X + 1 = f(X)
      
      g(mark(X)) = 1 >= 1 = g(X)
      
      g(active(X)) = 1 >= 1 = g(X)
      
      h(mark(X)) = X >= X = h(X)
      
      h(active(X)) = X >= X = h(X)
     problem:
      DPs:
       mark#(h(X)) -> mark#(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:
      dimension: 1
      interpretation:
       [mark#](x0) = x0 + 1,
       
       [mark](x0) = x0,
       
       [g](x0) = 0,
       
       [h](x0) = x0 + 1,
       
       [active](x0) = x0,
       
       [f](x0) = 0
      orientation:
       mark#(h(X)) = X + 2 >= X + 1 = mark#(X)
       
       active(f(X)) = 0 >= 0 = mark(g(h(f(X))))
       
       mark(f(X)) = 0 >= 0 = active(f(mark(X)))
       
       mark(g(X)) = 0 >= 0 = active(g(X))
       
       mark(h(X)) = X + 1 >= X + 1 = active(h(mark(X)))
       
       f(mark(X)) = 0 >= 0 = f(X)
       
       f(active(X)) = 0 >= 0 = f(X)
       
       g(mark(X)) = 0 >= 0 = g(X)
       
       g(active(X)) = 0 >= 0 = g(X)
       
       h(mark(X)) = X + 1 >= X + 1 = h(X)
       
       h(active(X)) = X + 1 >= X + 1 = h(X)
      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
    
    DPs:
     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:
     dimension: 1
     interpretation:
      [h#](x0) = x0,
      
      [mark](x0) = x0 + 1,
      
      [g](x0) = 0,
      
      [h](x0) = 0,
      
      [active](x0) = x0,
      
      [f](x0) = x0 + 1
     orientation:
      h#(mark(X)) = X + 1 >= X = h#(X)
      
      h#(active(X)) = X >= X = h#(X)
      
      active(f(X)) = X + 1 >= 1 = mark(g(h(f(X))))
      
      mark(f(X)) = X + 2 >= X + 2 = active(f(mark(X)))
      
      mark(g(X)) = 1 >= 0 = active(g(X))
      
      mark(h(X)) = 1 >= 0 = active(h(mark(X)))
      
      f(mark(X)) = X + 2 >= X + 1 = f(X)
      
      f(active(X)) = X + 1 >= X + 1 = f(X)
      
      g(mark(X)) = 0 >= 0 = g(X)
      
      g(active(X)) = 0 >= 0 = g(X)
      
      h(mark(X)) = 0 >= 0 = h(X)
      
      h(active(X)) = 0 >= 0 = h(X)
     problem:
      DPs:
       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:
      dimension: 1
      interpretation:
       [h#](x0) = x0,
       
       [mark](x0) = 1,
       
       [g](x0) = 0,
       
       [h](x0) = 0,
       
       [active](x0) = x0 + 1,
       
       [f](x0) = 0
      orientation:
       h#(active(X)) = X + 1 >= X = h#(X)
       
       active(f(X)) = 1 >= 1 = mark(g(h(f(X))))
       
       mark(f(X)) = 1 >= 1 = active(f(mark(X)))
       
       mark(g(X)) = 1 >= 1 = active(g(X))
       
       mark(h(X)) = 1 >= 1 = active(h(mark(X)))
       
       f(mark(X)) = 0 >= 0 = f(X)
       
       f(active(X)) = 0 >= 0 = f(X)
       
       g(mark(X)) = 0 >= 0 = g(X)
       
       g(active(X)) = 0 >= 0 = g(X)
       
       h(mark(X)) = 0 >= 0 = h(X)
       
       h(active(X)) = 0 >= 0 = h(X)
      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
    
    DPs:
     f#(mark(X)) -> f#(X)
     f#(active(X)) -> f#(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:
     dimension: 1
     interpretation:
      [f#](x0) = x0,
      
      [mark](x0) = x0 + 1,
      
      [g](x0) = 0,
      
      [h](x0) = 0,
      
      [active](x0) = x0,
      
      [f](x0) = x0 + 1
     orientation:
      f#(mark(X)) = X + 1 >= X = f#(X)
      
      f#(active(X)) = X >= X = f#(X)
      
      active(f(X)) = X + 1 >= 1 = mark(g(h(f(X))))
      
      mark(f(X)) = X + 2 >= X + 2 = active(f(mark(X)))
      
      mark(g(X)) = 1 >= 0 = active(g(X))
      
      mark(h(X)) = 1 >= 0 = active(h(mark(X)))
      
      f(mark(X)) = X + 2 >= X + 1 = f(X)
      
      f(active(X)) = X + 1 >= X + 1 = f(X)
      
      g(mark(X)) = 0 >= 0 = g(X)
      
      g(active(X)) = 0 >= 0 = g(X)
      
      h(mark(X)) = 0 >= 0 = h(X)
      
      h(active(X)) = 0 >= 0 = h(X)
     problem:
      DPs:
       f#(active(X)) -> f#(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:
      dimension: 1
      interpretation:
       [f#](x0) = x0,
       
       [mark](x0) = 1,
       
       [g](x0) = 0,
       
       [h](x0) = 0,
       
       [active](x0) = x0 + 1,
       
       [f](x0) = 0
      orientation:
       f#(active(X)) = X + 1 >= X = f#(X)
       
       active(f(X)) = 1 >= 1 = mark(g(h(f(X))))
       
       mark(f(X)) = 1 >= 1 = active(f(mark(X)))
       
       mark(g(X)) = 1 >= 1 = active(g(X))
       
       mark(h(X)) = 1 >= 1 = active(h(mark(X)))
       
       f(mark(X)) = 0 >= 0 = f(X)
       
       f(active(X)) = 0 >= 0 = f(X)
       
       g(mark(X)) = 0 >= 0 = g(X)
       
       g(active(X)) = 0 >= 0 = g(X)
       
       h(mark(X)) = 0 >= 0 = h(X)
       
       h(active(X)) = 0 >= 0 = h(X)
      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