YES

TRS:

  active(c()) -> mark(f(g(c())))
  active(f(g(X))) -> mark(g(X))
  mark(c()) -> active(c())
  mark(f(X)) -> active(f(X))
  mark(g(X)) -> active(g(X))
  f(mark(X)) -> f(X)
  f(active(X)) -> f(X)
  g(mark(X)) -> g(X)
  g(active(X)) -> g(X)

max/plus interpretations on N:

  active_A(x1) = max{15, -8 + x1}
  active#_A(x1) = max{1, -4 + x1}
  c_A = 22
  c#_A = 0
  mark_A(x1) = max{15, -11 + x1}
  mark#_A(x1) = max{18, -1 + x1}
  f_A(x1) = max{1, -1}
  f#_A(x1) = max{18, 3}
  g_A(x1) = max{19, -3}
  g#_A(x1) = max{2, 14}

precedence:

  active > g > f > mark > c