YES
TRS:
 {g(c(x, s(y))) -> g(c(s(x), y)),
           f(x) -> x,
  f(c(s(x), y)) -> f(c(x, s(y))),
        f(f(x)) -> f(d(f(x)))}
 DP:
  Strict:
   {g#(c(x, s(y))) -> g#(c(s(x), y)),
    f#(c(s(x), y)) -> f#(c(x, s(y))),
          f#(f(x)) -> f#(d(f(x)))}
  Weak:
  {g(c(x, s(y))) -> g(c(s(x), y)),
            f(x) -> x,
   f(c(s(x), y)) -> f(c(x, s(y))),
         f(f(x)) -> f(d(f(x)))}
  EDG:
   {(g#(c(x, s(y))) -> g#(c(s(x), y)), g#(c(x, s(y))) -> g#(c(s(x), y)))
    (f#(c(s(x), y)) -> f#(c(x, s(y))), f#(c(s(x), y)) -> f#(c(x, s(y))))}
   SCCS:
    Scc:
     {f#(c(s(x), y)) -> f#(c(x, s(y)))}
    Scc:
     {g#(c(x, s(y))) -> g#(c(s(x), y))}
    SCC:
     Strict:
      {f#(c(s(x), y)) -> f#(c(x, s(y)))}
     Weak:
     {g(c(x, s(y))) -> g(c(s(x), y)),
               f(x) -> x,
      f(c(s(x), y)) -> f(c(x, s(y))),
            f(f(x)) -> f(d(f(x)))}
     POLY:
      Argument Filtering:
       pi(d) = [], pi(f#) = 0, pi(f) = [], pi(s) = [0], pi(c) = [0], pi(g) = []
      Usable Rules:
       {}
      Interpretation:
       [c](x0) = x0 + 1,
       [s](x0) = x0 + 1
      Strict:
       {}
      Weak:
       {g(c(x, s(y))) -> g(c(s(x), y)),
                 f(x) -> x,
        f(c(s(x), y)) -> f(c(x, s(y))),
              f(f(x)) -> f(d(f(x)))}
      Qed
    SCC:
     Strict:
      {g#(c(x, s(y))) -> g#(c(s(x), y))}
     Weak:
     {g(c(x, s(y))) -> g(c(s(x), y)),
               f(x) -> x,
      f(c(s(x), y)) -> f(c(x, s(y))),
            f(f(x)) -> f(d(f(x)))}
     POLY:
      Argument Filtering:
       pi(d) = [], pi(f) = [], pi(s) = [0], pi(c) = 1, pi(g#) = 0, pi(g) = []
      Usable Rules:
       {}
      Interpretation:
       [s](x0) = x0 + 1
      Strict:
       {}
      Weak:
       {g(c(x, s(y))) -> g(c(s(x), y)),
                 f(x) -> x,
        f(c(s(x), y)) -> f(c(x, s(y))),
              f(f(x)) -> f(d(f(x)))}
      Qed