YES

TRS:

  a__f(f(a())) -> a__f(g(f(a())))
  mark(f(X)) -> a__f(mark(X))
  mark(a()) -> a()
  mark(g(X)) -> g(X)
  a__f(X) -> f(X)

max/plus interpretations on N:

  a__f_A(x1) = max{2, 12 + x1}
  a__f#_A(x1) = max{14, 11 + x1}
  f_A(x1) = max{5, 12 + x1}
  f#_A(x1) = max{7, 13}
  a_A = 2
  a#_A = 6
  g_A(x1) = max{6, -9}
  g#_A(x1) = max{0, 1 + x1}
  mark_A(x1) = max{1, 8 + x1}
  mark#_A(x1) = max{15, 8 + x1}

precedence:

  mark > a__f > f > a = g