YES

Problem:
 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)

Proof:
 WPO Processor:
  algebra: Max
  weight function:
   w0 = 0
   w(f) = w(a__f) = 7
   w(g) = 6
   w(mark) = 0
  status function:
   st(f) = [0, 1]
   st(mark) = [0]
   st(a__f) = [0, 1]
   st(g) = [0]
  subterm penalty function:
   sp(g, 0) = 4
   sp(f, 1) = sp(f, 0) = sp(mark, 0) = sp(a__f, 1) = sp(a__f, 0) = 0
  precedence:
   mark > a__f > f ~ g
  problem:
   
  Qed