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