YES

TRS:

  active(f(f(a()))) -> mark(f(g(f(a()))))
  mark(f(X)) -> active(f(mark(X)))
  mark(a()) -> active(a())
  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{1, x1}
  active#_A(x1) = max{2, 18}
  f_A(x1) = max{26, 16 + x1}
  f#_A(x1) = max{19, 5 + x1}
  a_A = 17
  a#_A = 20
  mark_A(x1) = max{11, 10 + x1}
  mark#_A(x1) = max{17, 4 + x1}
  g_A(x1) = max{18, -50 + x1}
  g#_A(x1) = max{0, 1 + x1}

precedence:

  f > mark > a > active > g