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)
    Restore Modifier:
     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))
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 2/4
      DPs:
       sum#(s(x)) -> sum#(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))
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [sum#](x0) = x0,
        
        [*](x0, x1) = 0,
        
        [+](x0, x1) = 0,
        
        [sqr](x0) = 0,
        
        [s](x0) = x0 + 1,
        
        [sum](x0) = 0,
        
        [0] = 0
       orientation:
        sum#(s(x)) = x + 1 >= x = sum#(x)
        
        sum(0()) = 0 >= 0 = 0()
        
        sum(s(x)) = 0 >= 0 = +(sqr(s(x)),sum(x))
        
        sqr(x) = 0 >= 0 = *(x,x)
        
        sum(s(x)) = 0 >= 0 = +(*(s(x),s(x)),sum(x))
       problem:
        DPs:
         
        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))
       Qed