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:
 Arctic Interpretation Processor:
  dimension: 1
  interpretation:
   [h](x0) = 1x0,
   
   [d](x0) = x0,
   
   [mark](x0) = x0,
   
   [c](x0) = x0,
   
   [g](x0) = x0,
   
   [active](x0) = x0,
   
   [f](x0) = x0
  orientation:
   active(f(f(X))) = X >= X = mark(c(f(g(f(X)))))
   
   active(c(X)) = X >= X = mark(d(X))
   
   active(h(X)) = 1X >= X = mark(c(d(X)))
   
   mark(f(X)) = X >= X = active(f(mark(X)))
   
   mark(c(X)) = X >= X = active(c(X))
   
   mark(g(X)) = X >= X = active(g(X))
   
   mark(d(X)) = X >= X = active(d(X))
   
   mark(h(X)) = 1X >= 1X = active(h(mark(X)))
   
   f(mark(X)) = X >= X = f(X)
   
   f(active(X)) = X >= X = f(X)
   
   c(mark(X)) = X >= X = c(X)
   
   c(active(X)) = X >= X = c(X)
   
   g(mark(X)) = X >= X = g(X)
   
   g(active(X)) = X >= X = g(X)
   
   d(mark(X)) = X >= X = d(X)
   
   d(active(X)) = X >= X = d(X)
   
   h(mark(X)) = 1X >= 1X = h(X)
   
   h(active(X)) = 1X >= 1X = h(X)
  problem:
   active(f(f(X))) -> mark(c(f(g(f(X)))))
   active(c(X)) -> mark(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)
  Bounds Processor:
   bound: 4
   enrichment: match
   automaton:
    final states: {19,8,15,13,3,17,16,14,12,9,7,1}
    transitions:
     d4(156) -> 157*
     h1(40) -> 41*
     h1(82) -> 83*
     h1(214) -> 215*
     h1(194) -> 195*
     h1(174) -> 175*
     h1(206) -> 207*
     h1(196) -> 197*
     h1(166) -> 167*
     h1(96) -> 97*
     h1(98) -> 99*
     h1(88) -> 89*
     h1(190) -> 191*
     h1(90) -> 91*
     f1(80) -> 81*
     f1(202) -> 203*
     f1(132) -> 133*
     f1(107) -> 108*
     f1(72) -> 73*
     f1(74) -> 75*
     f1(64) -> 65*
     f1(186) -> 187*
     f1(66) -> 67*
     f1(38) -> 39*
     f1(210) -> 211*
     active1(30) -> 31*
     active1(32) -> 33*
     d1(20) -> 21*
     c1(29) -> 30*
     c1(108) -> 109*
     mark1(21) -> 22*
     active2(54) -> 55*
     d2(47) -> 48*
     d2(53) -> 54*
     mark2(48) -> 49*
     f70() -> 2*
     active3(60) -> 61*
     mark0(2) -> 10*
     mark0(6) -> 1*
     mark0(8) -> 7*
     d3(59) -> 60*
     d3(150) -> 151*
     c0(5) -> 6*
     c0(2) -> 13*
     g1(124) -> 125*
     g1(126) -> 127*
     g1(116) -> 117*
     g1(106) -> 107*
     g1(118) -> 119*
     g1(110) -> 111*
     f0(10) -> 11*
     f0(2) -> 3*
     f0(4) -> 5*
     f2(182) -> 183*
     f2(162) -> 163*
     f2(144) -> 145*
     f2(146) -> 147*
     f2(178) -> 179*
     f2(168) -> 169*
     f2(140) -> 141*
     g0(2) -> 15*
     g0(3) -> 4*
     c2(134) -> 135*
     d0(2) -> 8*
     mark3(151) -> 152*
     active0(15) -> 14*
     active0(11) -> 9*
     active0(18) -> 17*
     active0(13) -> 12*
     active0(8) -> 16*
     active4(157) -> 158*
     h0(10) -> 18*
     h0(2) -> 19*
     1 -> 9*
     2 -> 40,38,20
     5 -> 29*
     6 -> 88,66
     9 -> 10*
     10 -> 132*
     11 -> 98,80
     12 -> 10*
     13 -> 196,186
     14 -> 10*
     15 -> 206,202
     17 -> 10*
     18 -> 214,210
     20 -> 53*
     21 -> 190,178,32
     22 -> 12*
     29 -> 47*
     30 -> 146,96,74
     31 -> 1*
     33 -> 7*
     39 -> 133,106,126,11
     41 -> 18*
     47 -> 59*
     48 -> 140,82,64
     49 -> 31,1
     54 -> 194,182
     55 -> 22,12
     60 -> 144,90,72
     61 -> 49,31
     65 -> 118,11
     67 -> 133,106,124,11
     73 -> 110,11
     75 -> 116,11
     81 -> 133,106,11
     83 -> 18*
     89 -> 18*
     91 -> 18*
     97 -> 18*
     99 -> 18*
     108 -> 134*
     109 -> 48*
     111 -> 107*
     117 -> 107*
     119 -> 107*
     125 -> 107*
     127 -> 107*
     133 -> 106*
     134 -> 150*
     135 -> 60*
     141 -> 133,106
     145 -> 133,106
     147 -> 133,106
     150 -> 156*
     151 -> 166,162
     152 -> 61,49
     157 -> 174,168
     158 -> 152,61
     163 -> 133,11,80,98,106
     167 -> 18*
     169 -> 133,11,80,98,106
     175 -> 18*
     179 -> 133,11,80,98,106
     183 -> 133,11,80,98,106
     187 -> 133,11,80,98,106
     191 -> 18*
     195 -> 18*
     197 -> 18*
     203 -> 133,11,80,98,106
     207 -> 18*
     211 -> 133,11,80,98,106
     215 -> 18*
   problem:
    
   Qed