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{6, x1}
  a__f#_A(x1) = max{6, x1}
  f_A(x1) = max{1, x1}
  f#_A(x1) = max{1, x1}
  a_A = 3
  a#_A = 3
  c_A(x1) = max{0, 1 + x1}
  c#_A(x1) = max{0, 1 + x1}
  g_A(x1) = max{4, x1}
  g#_A(x1) = max{4, x1}
  mark_A(x1) = max{6, x1}
  mark#_A(x1) = max{6, x1}

precedence:

  a = c > mark > a__f > f > g