YES
TRS:
 {f(g(x), g(y)) -> h(g(y), x, g(y)),
   f(g(x), a()) -> f(x, g(a())),
   f(a(), g(y)) -> g(g(y)),
  h(g(x), y, z) -> f(y, h(x, y, z)),
   h(a(), y, z) -> z}
 DP:
  Strict:
   {f#(g(x), g(y)) -> h#(g(y), x, g(y)),
     f#(g(x), a()) -> f#(x, g(a())),
    h#(g(x), y, z) -> f#(y, h(x, y, z)),
    h#(g(x), y, z) -> h#(x, y, z)}
  Weak:
  {f(g(x), g(y)) -> h(g(y), x, g(y)),
    f(g(x), a()) -> f(x, g(a())),
    f(a(), g(y)) -> g(g(y)),
   h(g(x), y, z) -> f(y, h(x, y, z)),
    h(a(), y, z) -> z}
  EDG:
   {(h#(g(x), y, z) -> h#(x, y, z), h#(g(x), y, z) -> h#(x, y, z))
    (h#(g(x), y, z) -> h#(x, y, z), h#(g(x), y, z) -> f#(y, h(x, y, z)))
    (f#(g(x), g(y)) -> h#(g(y), x, g(y)), h#(g(x), y, z) -> h#(x, y, z))
    (f#(g(x), g(y)) -> h#(g(y), x, g(y)), h#(g(x), y, z) -> f#(y, h(x, y, z)))
    (h#(g(x), y, z) -> f#(y, h(x, y, z)), f#(g(x), g(y)) -> h#(g(y), x, g(y)))
    (h#(g(x), y, z) -> f#(y, h(x, y, z)), f#(g(x), a()) -> f#(x, g(a())))
    (f#(g(x), a()) -> f#(x, g(a())), f#(g(x), g(y)) -> h#(g(y), x, g(y)))}
   SCCS:
    Scc:
     {f#(g(x), g(y)) -> h#(g(y), x, g(y)),
       f#(g(x), a()) -> f#(x, g(a())),
      h#(g(x), y, z) -> f#(y, h(x, y, z)),
      h#(g(x), y, z) -> h#(x, y, z)}
    SCC:
     Strict:
      {f#(g(x), g(y)) -> h#(g(y), x, g(y)),
        f#(g(x), a()) -> f#(x, g(a())),
       h#(g(x), y, z) -> f#(y, h(x, y, z)),
       h#(g(x), y, z) -> h#(x, y, z)}
     Weak:
     {f(g(x), g(y)) -> h(g(y), x, g(y)),
       f(g(x), a()) -> f(x, g(a())),
       f(a(), g(y)) -> g(g(y)),
      h(g(x), y, z) -> f(y, h(x, y, z)),
       h(a(), y, z) -> z}
     SPSC:
      Simple Projection:
       pi(h#) = 1, pi(f#) = 0
      Strict:
       {f#(g(x), g(y)) -> h#(g(y), x, g(y)),
        h#(g(x), y, z) -> f#(y, h(x, y, z)),
        h#(g(x), y, z) -> h#(x, y, z)}
      EDG:
       {(h#(g(x), y, z) -> h#(x, y, z), h#(g(x), y, z) -> h#(x, y, z))
        (h#(g(x), y, z) -> h#(x, y, z), h#(g(x), y, z) -> f#(y, h(x, y, z)))
        (f#(g(x), g(y)) -> h#(g(y), x, g(y)), h#(g(x), y, z) -> f#(y, h(x, y, z)))
        (f#(g(x), g(y)) -> h#(g(y), x, g(y)), h#(g(x), y, z) -> h#(x, y, z))
        (h#(g(x), y, z) -> f#(y, h(x, y, z)), f#(g(x), g(y)) -> h#(g(y), x, g(y)))}
       SCCS:
        Scc:
         {f#(g(x), g(y)) -> h#(g(y), x, g(y)),
          h#(g(x), y, z) -> f#(y, h(x, y, z)),
          h#(g(x), y, z) -> h#(x, y, z)}
        SCC:
         Strict:
          {f#(g(x), g(y)) -> h#(g(y), x, g(y)),
           h#(g(x), y, z) -> f#(y, h(x, y, z)),
           h#(g(x), y, z) -> h#(x, y, z)}
         Weak:
         {f(g(x), g(y)) -> h(g(y), x, g(y)),
           f(g(x), a()) -> f(x, g(a())),
           f(a(), g(y)) -> g(g(y)),
          h(g(x), y, z) -> f(y, h(x, y, z)),
           h(a(), y, z) -> z}
         SPSC:
          Simple Projection:
           pi(h#) = 1, pi(f#) = 0
          Strict:
           {h#(g(x), y, z) -> f#(y, h(x, y, z)),
            h#(g(x), y, z) -> h#(x, y, z)}
          EDG:
           {(h#(g(x), y, z) -> h#(x, y, z), h#(g(x), y, z) -> h#(x, y, z))
            (h#(g(x), y, z) -> h#(x, y, z), h#(g(x), y, z) -> f#(y, h(x, y, z)))}
           SCCS:
            Scc:
             {h#(g(x), y, z) -> h#(x, y, z)}
            SCC:
             Strict:
              {h#(g(x), y, z) -> h#(x, y, z)}
             Weak:
             {f(g(x), g(y)) -> h(g(y), x, g(y)),
               f(g(x), a()) -> f(x, g(a())),
               f(a(), g(y)) -> g(g(y)),
              h(g(x), y, z) -> f(y, h(x, y, z)),
               h(a(), y, z) -> z}
             SPSC:
              Simple Projection:
               pi(h#) = 0
              Strict:
               {}
              Qed