YES
Time: 0.000883
TRS:
 {  f(x, 0()) -> s 0(),
  f(s x, s y) -> s f(x, y),
    g(0(), x) -> g(f(x, x), x)}
 DP:
  DP:
   {f#(s x, s y) -> f#(x, y),
      g#(0(), x) -> f#(x, x),
      g#(0(), x) -> g#(f(x, x), x)}
  TRS:
  {  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 (1):
    Scc:
     {f#(s x, s y) -> f#(x, y)}
    SCC (1):
     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#) = 1
      Strict:
       {}
      Qed