Input TRS:
    1: app(nil(),k) -> k
    2: app(l,nil()) -> l
    3: app(cons(x,l),k) -> cons(x,app(l,k))
    4: sum(cons(x,nil())) -> cons(x,nil())
    5: sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
    6: sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
    7: plus(0(),y) -> y
    8: plus(s(x),y) -> s(plus(x,y))
    9: sum(plus(cons(0(),x),cons(y,l))) -> pred(sum(cons(s(x),cons(y,l))))
    10: pred(cons(s(x),nil())) -> cons(x,nil())
    11: cons(x,cons(y,l)) ->= cons(y,cons(x,l))
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... removes: 1 3 5 10 7 9 2
     s(x1)	weight: (/ 1 64) + x1
  pred(x1)	weight: x1
   sum(x1)	weight: x1
     0()	weight: (/ 37761 64)
   nil()	weight: (/ 1 64)
  plus(x1,x2)	weight: (/ 3 64) + x2 + x1
  cons(x1,x2)	weight: (/ 1 16) + x2 + x1
   app(x1,x2)	weight: (/ 2222337 64) + 2 * x2 + 2 * x1
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 8
     s(x1)	weight: (/ 1 8) + x1
  pred(x1)	weight: x1
   sum(x1)	weight: x1
     0()	weight: (/ 4721 8)
   nil()	weight: (/ 1 8)
  plus(x1,x2)	weight: (/ 118133 4) + x2 + 2 * x1
  cons(x1,x2)	weight: (/ 236265 8) + x2 + x1
   app(x1,x2)	weight: (/ 277793 8) + 2 * x2 + 2 * x1
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #sum(app(l,cons(x,cons(y,k)))) -> #sum(app(l,sum(cons(x,cons(y,k)))))
   #2: #sum(app(l,cons(x,cons(y,k)))) -> #sum(cons(x,cons(y,k)))
Number of SCCs: 0, DPs: 0, edges: 0
YES