MAYBE
Trs:
 {     mark(g(X)) -> g(mark(X)),
  mark(f(X1, X2)) -> a__f(mark(X1), X2),
    a__f(g(X), Y) -> a__f(mark(X), f(g(X), Y)),
     a__f(X1, X2) -> f(X1, X2)}
 Comment:
  We consider a duplicating trs.
  FAIL:
   Open