YES

TRS:

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

max/plus interpretations on N:

  a__f_A(x1) = max{2, 3 + x1}
  a__f#_A(x1) = max{15, 2 + x1}
  f_A(x1) = max{0, 3 + x1}
  f#_A(x1) = max{10, 12}
  a_A = 4
  a#_A = 11
  c_A(x1) = max{4, -8 + x1}
  c#_A(x1) = max{0, 1}
  g_A(x1) = max{3, 1 + x1}
  g#_A(x1) = max{13, 15}
  mark_A(x1) = max{0, x1}
  mark#_A(x1) = max{16, 14 + x1}

precedence:

  mark > a__f > f > a = c = g