YES
TRS:
 { f(0()) -> 1(),
  f(s(x)) -> g(f(x)),
  f(s(x)) -> +(f(x), s(f(x))),
     g(x) -> +(x, s(x))}
 DP:
  Strict:
   {f#(s(x)) -> f#(x),
    f#(s(x)) -> g#(f(x))}
  Weak:
  { f(0()) -> 1(),
   f(s(x)) -> g(f(x)),
   f(s(x)) -> +(f(x), s(f(x))),
      g(x) -> +(x, s(x))}
  EDG:
   {(f#(s(x)) -> f#(x), f#(s(x)) -> f#(x))
    (f#(s(x)) -> f#(x), f#(s(x)) -> g#(f(x)))}
   SCCS:
    Scc:
     {f#(s(x)) -> f#(x)}
    SCC:
     Strict:
      {f#(s(x)) -> f#(x)}
     Weak:
     { f(0()) -> 1(),
      f(s(x)) -> g(f(x)),
      f(s(x)) -> +(f(x), s(f(x))),
         g(x) -> +(x, s(x))}
     SPSC:
      Simple Projection:
       pi(f#) = 0
      Strict:
       {}
      Qed