YES
Time: 0.000888
TRS:
 {    g1(x, x, y, a()) -> h(x, y),
      g1(y, x, x, a()) -> h(x, y),
    f(x, y, w, w, a()) -> g1(x, x, y, w),
  f(x, y, w, a(), a()) -> g1(y, x, x, w),
    f(x, y, a(), w, w) -> g2(y, y, x, w),
  f(x, y, a(), a(), w) -> g2(x, y, y, w),
      g2(x, y, y, a()) -> h(x, y),
      g2(y, y, x, a()) -> h(x, y),
               h(x, x) -> x}
 DP:
  DP:
   {    g1#(x, x, y, a()) -> h#(x, y),
        g1#(y, x, x, a()) -> h#(x, y),
      f#(x, y, w, w, a()) -> g1#(x, x, y, w),
    f#(x, y, w, a(), a()) -> g1#(y, x, x, w),
      f#(x, y, a(), w, w) -> g2#(y, y, x, w),
    f#(x, y, a(), a(), w) -> g2#(x, y, y, w),
        g2#(x, y, y, a()) -> h#(x, y),
        g2#(y, y, x, a()) -> h#(x, y)}
  TRS:
  {    g1(x, x, y, a()) -> h(x, y),
       g1(y, x, x, a()) -> h(x, y),
     f(x, y, w, w, a()) -> g1(x, x, y, w),
   f(x, y, w, a(), a()) -> g1(y, x, x, w),
     f(x, y, a(), w, w) -> g2(y, y, x, w),
   f(x, y, a(), a(), w) -> g2(x, y, y, w),
       g2(x, y, y, a()) -> h(x, y),
       g2(y, y, x, a()) -> h(x, y),
                h(x, x) -> x}
  EDG:
   {(f#(x, y, w, a(), a()) -> g1#(y, x, x, w), g1#(y, x, x, a()) -> h#(x, y))
    (f#(x, y, w, a(), a()) -> g1#(y, x, x, w), g1#(x, x, y, a()) -> h#(x, y))
    (f#(x, y, a(), a(), w) -> g2#(x, y, y, w), g2#(y, y, x, a()) -> h#(x, y))
    (f#(x, y, a(), a(), w) -> g2#(x, y, y, w), g2#(x, y, y, a()) -> h#(x, y))
    (f#(x, y, a(), w, w) -> g2#(y, y, x, w), g2#(x, y, y, a()) -> h#(x, y))
    (f#(x, y, a(), w, w) -> g2#(y, y, x, w), g2#(y, y, x, a()) -> h#(x, y))
    (f#(x, y, w, w, a()) -> g1#(x, x, y, w), g1#(x, x, y, a()) -> h#(x, y))
    (f#(x, y, w, w, a()) -> g1#(x, x, y, w), g1#(y, x, x, a()) -> h#(x, y))}
   SCCS (0):
    
    Qed