Input TRS:
    1: sum(0()) -> 0()
    2: sum(s(x)) -> +(sqr(s(x)),sum(x))
    3: sqr(x) -> *(x,x)
    4: sum(s(x)) -> +(*(s(x),s(x)),sum(x))
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #sum(s(x)) -> #sqr(s(x))
   #2: #sum(s(x)) -> #sum(x)
   #3: #sum(s(x)) -> #sum(x)
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #2 #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
   sum(x1)	weight: 0
 #sqr(x1)	weight: 0
     0()	weight: 0
   sqr(x1)	weight: 0
     +(x1,x2)	weight: 0
 #sum(x1)	weight: x1
     *(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #2 #3
Number of SCCs: 0, DPs: 0, edges: 0
YES