YES

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)

max/plus interpretations on N:

  active_A(x1) = max{5, x1}
  active#_A(x1) = max{89, 86 + x1}
  f_A(x1) = max{4, 31 + x1}
  f#_A(x1) = max{0, 1}
  mark_A(x1) = max{5, 5 + x1}
  mark#_A(x1) = max{100, 107 + x1}
  c_A(x1) = max{3, -109 + x1}
  c#_A(x1) = max{108, 109}
  g_A(x1) = max{6, 28 + x1}
  g#_A(x1) = max{120, 115 + x1}
  d_A(x1) = max{0, -18}
  d#_A(x1) = max{107, 94}
  h_A(x1) = max{0, 8 + x1}
  h#_A(x1) = max{110, 101 + x1}

precedence:

  h > mark = d > active > c = g > f