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