YES

Problem:
 sum(0()) -> 0()
 sum(s(x)) -> +(sqr(s(x)),sum(x))
 sqr(x) -> *(x,x)
 sum(s(x)) -> +(*(s(x),s(x)),sum(x))

Proof:
 DP Processor:
  DPs:
   sum#(s(x)) -> sum#(x)
   sum#(s(x)) -> sqr#(s(x))
  TRS:
   sum(0()) -> 0()
   sum(s(x)) -> +(sqr(s(x)),sum(x))
   sqr(x) -> *(x,x)
   sum(s(x)) -> +(*(s(x),s(x)),sum(x))
  Usable Rule Processor:
   DPs:
    sum#(s(x)) -> sum#(x)
    sum#(s(x)) -> sqr#(s(x))
   TRS:
    
   TDG Processor:
    DPs:
     sum#(s(x)) -> sum#(x)
     sum#(s(x)) -> sqr#(s(x))
    TRS:
     
    graph:
     sum#(s(x)) -> sum#(x) -> sum#(s(x)) -> sqr#(s(x))
     sum#(s(x)) -> sum#(x) -> sum#(s(x)) -> sum#(x)
    CDG Processor:
     DPs:
      sum#(s(x)) -> sum#(x)
      sum#(s(x)) -> sqr#(s(x))
     TRS:
      
     graph:
      
     Qed