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:
 Arctic Interpretation Processor:
  dimension: 2
  interpretation:
                [0 3]  
   [mark](x0) = [0 3]x0,
   
             [0  -&]  
   [g](x0) = [-& -&]x0,
   
             [0  -&]  
   [h](x0) = [1  1 ]x0,
   
                  [0 0]  
   [active](x0) = [0 0]x0,
   
             [0 2]  
   [f](x0) = [0 3]x0
  orientation:
                  [0 3]     [0 2]                    
   active(f(X)) = [0 3]X >= [0 2]X = mark(g(h(f(X))))
   
                [3 6]     [3 6]                      
   mark(f(X)) = [3 6]X >= [3 6]X = active(f(mark(X)))
   
                [0  -&]     [0  -&]                
   mark(g(X)) = [0  -&]X >= [0  -&]X = active(g(X))
   
                [4 4]     [1 4]                      
   mark(h(X)) = [4 4]X >= [1 4]X = active(h(mark(X)))
   
                [2 5]     [0 2]        
   f(mark(X)) = [3 6]X >= [0 3]X = f(X)
   
                  [2 2]     [0 2]        
   f(active(X)) = [3 3]X >= [0 3]X = f(X)
   
                [0  3 ]     [0  -&]        
   g(mark(X)) = [-& -&]X >= [-& -&]X = g(X)
   
                  [0  0 ]     [0  -&]        
   g(active(X)) = [-& -&]X >= [-& -&]X = g(X)
   
                [0 3]     [0  -&]        
   h(mark(X)) = [1 4]X >= [1  1 ]X = h(X)
   
                  [0 0]     [0  -&]        
   h(active(X)) = [1 1]X >= [1  1 ]X = h(X)
  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(active(X)) -> f(X)
   g(mark(X)) -> g(X)
   g(active(X)) -> g(X)
   h(mark(X)) -> h(X)
   h(active(X)) -> h(X)
  Bounds Processor:
   bound: 2
   enrichment: match
   automaton:
    final states: {13,10,3,11,9,6,1}
    transitions:
     h1(50) -> 51*
     h1(30) -> 31*
     h1(15) -> 16*
     h1(52) -> 53*
     h1(74) -> 75*
     h1(64) -> 65*
     h1(58) -> 59*
     active1(28) -> 29*
     g1(27) -> 28*
     g1(16) -> 17*
     mark1(17) -> 18*
     f1(62) -> 63*
     f1(14) -> 15*
     f1(46) -> 47*
     f1(68) -> 69*
     active2(38) -> 39*
     g2(37) -> 38*
     f50() -> 2*
     f2(40) -> 41*
     mark0(5) -> 1*
     mark0(2) -> 7*
     g0(2) -> 10*
     g0(4) -> 5*
     h0(7) -> 12*
     h0(2) -> 13*
     h0(3) -> 4*
     f0(7) -> 8*
     f0(2) -> 3*
     active0(10) -> 9*
     active0(12) -> 11*
     active0(8) -> 6*
     2 -> 30*
     4 -> 27*
     6 -> 7,14
     7 -> 14*
     8 -> 58,46
     9 -> 7,14
     10 -> 64,62
     11 -> 7,14
     12 -> 74,68
     16 -> 37*
     17 -> 50*
     18 -> 6*
     29 -> 1*
     31 -> 12*
     38 -> 52,40
     39 -> 18,6
     41 -> 8,15
     47 -> 8,15
     51 -> 12*
     53 -> 12*
     59 -> 12*
     63 -> 8,15
     65 -> 12*
     69 -> 8,15
     75 -> 12,68
   problem:
    
   Qed