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