YES

TRS:

  active(f(f(a()))) -> mark(f(g(f(a()))))
  mark(f(X)) -> active(f(X))
  mark(a()) -> active(a())
  mark(g(X)) -> active(g(mark(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{0, x1}
  active#_A(x1) = max{5, 3}
  f_A(x1) = max{0, -3 + x1}
  f#_A(x1) = max{1, 6 + x1}
  a_A = 5
  a#_A = 2
  mark_A(x1) = max{0, x1}
  mark#_A(x1) = max{8, 4}
  g_A(x1) = max{1, -6}
  g#_A(x1) = max{0, 4}

precedence:

  f > a > mark = g > active