YES

TRS:

  a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y))
  mark(f(X1,X2)) -> a__f(mark(X1),X2)
  mark(g(X)) -> g(mark(X))
  a__f(X1,X2) -> f(X1,X2)

max/plus interpretations on N:

  a__f_A(x1,x2) = max{4, x1, 13}
  a__f#_A(x1,x2) = max{0, 2 + x1, 6}
  g_A(x1) = max{0, 12 + x1}
  g#_A(x1) = max{11, 12}
  mark_A(x1) = max{1, 3 + x1}
  mark#_A(x1) = max{13, 10 + x1}
  f_A(x1,x2) = max{13, x1, -3}
  f#_A(x1,x2) = max{4, -1, 1}

precedence:

  g > a__f > mark > f