YES
TRS:
 {f(g(x), g(y)) -> f(p(f(g(x), s(y))), g(s(p(x)))),
         p(0()) -> g(0()),
     g(s(p(x))) -> p(x)}
 DP:
  Strict:
   {f#(g(x), g(y)) -> f#(p(f(g(x), s(y))), g(s(p(x)))),
    f#(g(x), g(y)) -> f#(g(x), s(y)),
    f#(g(x), g(y)) -> p#(x),
    f#(g(x), g(y)) -> p#(f(g(x), s(y))),
    f#(g(x), g(y)) -> g#(s(p(x))),
           p#(0()) -> g#(0())}
  Weak:
  {f(g(x), g(y)) -> f(p(f(g(x), s(y))), g(s(p(x)))),
          p(0()) -> g(0()),
      g(s(p(x))) -> p(x)}
  EDG:
   {(f#(g(x), g(y)) -> p#(x), p#(0()) -> g#(0()))}
   SCCS:
    
    Qed