MAYBE
Trs:
 {f(x, y, a(), a(), w) -> g2(x, y, y, w),
    f(x, y, a(), w, w) -> g2(y, y, x, w),
  f(x, y, w, a(), a()) -> g1(y, x, x, w),
    f(x, y, w, w, a()) -> g1(x, x, y, w),
      g1(y, x, x, a()) -> h(x, y),
      g1(x, x, y, a()) -> h(x, y),
      g2(y, y, x, a()) -> h(x, y),
      g2(x, y, y, a()) -> h(x, y),
               h(x, x) -> x}
 Comment:
  We consider a duplicating trs.
  FAIL:
   Open