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