Input TRS:
    1: sum(0()) -> 0()
    2: sum(s(x)) -> +(sum(x),s(x))
    3: sum1(0()) -> 0()
    4: sum1(s(x)) -> s(+(sum1(x),+(x,x)))
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #sum(s(x)) -> #sum(x)
   #2: #sum1(s(x)) -> #sum1(x)
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
   sum(x1)	weight: 0
     0()	weight: 0
#sum1(x1)	weight: x1
     +(x1,x2)	weight: 0
 #sum(x1)	weight: 0
  sum1(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 1 2) + x1
   sum(x1)	weight: 0
     0()	weight: 0
#sum1(x1)	weight: 0
     +(x1,x2)	weight: 0
 #sum(x1)	weight: x1
  sum1(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 0, DPs: 0, edges: 0
YES