YES

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

Proof:
 DP Processor:
  DPs:
   active#(f(f(X))) -> g#(f(X))
   active#(f(f(X))) -> f#(g(f(X)))
   active#(f(f(X))) -> c#(f(g(f(X))))
   active#(f(f(X))) -> mark#(c(f(g(f(X)))))
   active#(c(X)) -> d#(X)
   active#(c(X)) -> mark#(d(X))
   active#(h(X)) -> d#(X)
   active#(h(X)) -> c#(d(X))
   active#(h(X)) -> mark#(c(d(X)))
   mark#(f(X)) -> mark#(X)
   mark#(f(X)) -> f#(mark(X))
   mark#(f(X)) -> active#(f(mark(X)))
   mark#(c(X)) -> active#(c(X))
   mark#(g(X)) -> active#(g(X))
   mark#(d(X)) -> active#(d(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)
   c#(mark(X)) -> c#(X)
   c#(active(X)) -> c#(X)
   g#(mark(X)) -> g#(X)
   g#(active(X)) -> g#(X)
   d#(mark(X)) -> d#(X)
   d#(active(X)) -> d#(X)
   h#(mark(X)) -> h#(X)
   h#(active(X)) -> h#(X)
  TRS:
   active(f(f(X))) -> mark(c(f(g(f(X)))))
   active(c(X)) -> mark(d(X))
   active(h(X)) -> mark(c(d(X)))
   mark(f(X)) -> active(f(mark(X)))
   mark(c(X)) -> active(c(X))
   mark(g(X)) -> active(g(X))
   mark(d(X)) -> active(d(X))
   mark(h(X)) -> active(h(mark(X)))
   f(mark(X)) -> f(X)
   f(active(X)) -> f(X)
   c(mark(X)) -> c(X)
   c(active(X)) -> c(X)
   g(mark(X)) -> g(X)
   g(active(X)) -> g(X)
   d(mark(X)) -> d(X)
   d(active(X)) -> d(X)
   h(mark(X)) -> h(X)
   h(active(X)) -> h(X)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [h#](x0) = 4x0 + 10,
    
    [d#](x0) = x0,
    
    [mark#](x0) = 4x0 + 4,
    
    [c#](x0) = 8x0 + 5,
    
    [f#](x0) = 8x0,
    
    [g#](x0) = x0,
    
    [active#](x0) = 2x0 + 1,
    
    [h](x0) = 2x0 + 6,
    
    [d](x0) = 0,
    
    [mark](x0) = 2x0 + 1,
    
    [c](x0) = x0 + 2,
    
    [g](x0) = 0,
    
    [active](x0) = x0 + 1,
    
    [f](x0) = 4x0 + 4
   orientation:
    active#(f(f(X))) = 32X + 41 >= 4X + 4 = g#(f(X))
    
    active#(f(f(X))) = 32X + 41 >= 0 = f#(g(f(X)))
    
    active#(f(f(X))) = 32X + 41 >= 37 = c#(f(g(f(X))))
    
    active#(f(f(X))) = 32X + 41 >= 28 = mark#(c(f(g(f(X)))))
    
    active#(c(X)) = 2X + 5 >= X = d#(X)
    
    active#(c(X)) = 2X + 5 >= 4 = mark#(d(X))
    
    active#(h(X)) = 4X + 13 >= X = d#(X)
    
    active#(h(X)) = 4X + 13 >= 5 = c#(d(X))
    
    active#(h(X)) = 4X + 13 >= 12 = mark#(c(d(X)))
    
    mark#(f(X)) = 16X + 20 >= 4X + 4 = mark#(X)
    
    mark#(f(X)) = 16X + 20 >= 16X + 8 = f#(mark(X))
    
    mark#(f(X)) = 16X + 20 >= 16X + 17 = active#(f(mark(X)))
    
    mark#(c(X)) = 4X + 12 >= 2X + 5 = active#(c(X))
    
    mark#(g(X)) = 4 >= 1 = active#(g(X))
    
    mark#(d(X)) = 4 >= 1 = active#(d(X))
    
    mark#(h(X)) = 8X + 28 >= 4X + 4 = mark#(X)
    
    mark#(h(X)) = 8X + 28 >= 8X + 14 = h#(mark(X))
    
    mark#(h(X)) = 8X + 28 >= 8X + 17 = active#(h(mark(X)))
    
    f#(mark(X)) = 16X + 8 >= 8X = f#(X)
    
    f#(active(X)) = 8X + 8 >= 8X = f#(X)
    
    c#(mark(X)) = 16X + 13 >= 8X + 5 = c#(X)
    
    c#(active(X)) = 8X + 13 >= 8X + 5 = c#(X)
    
    g#(mark(X)) = 2X + 1 >= X = g#(X)
    
    g#(active(X)) = X + 1 >= X = g#(X)
    
    d#(mark(X)) = 2X + 1 >= X = d#(X)
    
    d#(active(X)) = X + 1 >= X = d#(X)
    
    h#(mark(X)) = 8X + 14 >= 4X + 10 = h#(X)
    
    h#(active(X)) = 4X + 14 >= 4X + 10 = h#(X)
    
    active(f(f(X))) = 16X + 21 >= 13 = mark(c(f(g(f(X)))))
    
    active(c(X)) = X + 3 >= 1 = mark(d(X))
    
    active(h(X)) = 2X + 7 >= 5 = mark(c(d(X)))
    
    mark(f(X)) = 8X + 9 >= 8X + 9 = active(f(mark(X)))
    
    mark(c(X)) = 2X + 5 >= X + 3 = active(c(X))
    
    mark(g(X)) = 1 >= 1 = active(g(X))
    
    mark(d(X)) = 1 >= 1 = active(d(X))
    
    mark(h(X)) = 4X + 13 >= 4X + 9 = active(h(mark(X)))
    
    f(mark(X)) = 8X + 8 >= 4X + 4 = f(X)
    
    f(active(X)) = 4X + 8 >= 4X + 4 = f(X)
    
    c(mark(X)) = 2X + 3 >= X + 2 = c(X)
    
    c(active(X)) = X + 3 >= X + 2 = c(X)
    
    g(mark(X)) = 0 >= 0 = g(X)
    
    g(active(X)) = 0 >= 0 = g(X)
    
    d(mark(X)) = 0 >= 0 = d(X)
    
    d(active(X)) = 0 >= 0 = d(X)
    
    h(mark(X)) = 4X + 8 >= 2X + 6 = h(X)
    
    h(active(X)) = 2X + 8 >= 2X + 6 = h(X)
   problem:
    DPs:
     
    TRS:
     active(f(f(X))) -> mark(c(f(g(f(X)))))
     active(c(X)) -> mark(d(X))
     active(h(X)) -> mark(c(d(X)))
     mark(f(X)) -> active(f(mark(X)))
     mark(c(X)) -> active(c(X))
     mark(g(X)) -> active(g(X))
     mark(d(X)) -> active(d(X))
     mark(h(X)) -> active(h(mark(X)))
     f(mark(X)) -> f(X)
     f(active(X)) -> f(X)
     c(mark(X)) -> c(X)
     c(active(X)) -> c(X)
     g(mark(X)) -> g(X)
     g(active(X)) -> g(X)
     d(mark(X)) -> d(X)
     d(active(X)) -> d(X)
     h(mark(X)) -> h(X)
     h(active(X)) -> h(X)
   Qed