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