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)

linear polynomial interpretations on N:

  a__f_A(x1,x2) = x1 + 2
  a__f#_A(x1,x2) = x1 + 1
  g_A(x1) = x1 + 2
  g#_A(x1) = 2
  mark_A(x1) = x1 + 1
  mark#_A(x1) = x1 + 1
  f_A(x1,x2) = x1 + 2
  f#_A(x1,x2) = 0

precedence:

  a__f > f > mark > g