YES
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))
Number of strict rules: 8
Direct POLO(bPol) ... removes: 1 5 7 2
      s 	w: x1 + 1
      sum	w: x1
      0 	w: 30613
      nil	w: 1
      plus	w: x1 + x2 + 1
      cons	w: x1 + x2 + 32287
      app	w: x1 + x2 + 10451
Number of strict rules: 4
Direct POLO(bPol) ... removes: 3
      s 	w: x1 + 15922
      sum	w: x1
      0 	w: 8946
      nil	w: 1
      plus	w: x1 + x2 + 1
      cons	w: x1 + x2 + 1
      app	w: 2 * x1 + x2 + 10451
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Uncurrying sum
      4: sum^1_cons(x,nil()) -> cons(x,nil())
      6: sum^1_app(l,cons(x,cons(y,k))) -> sum^1_app(l,sum^1_cons(x,cons(y,k)))
      8: plus(s(x),y) -> s(plus(x,y))
      9: sum(cons(_1,_2)) ->= sum^1_cons(_1,_2)
      10: sum(app(_1,_2)) ->= sum^1_app(_1,_2)
Number of strict rules: 3
Direct POLO(bPol) ... removes: 4 8 10 9 6
      sum^1_app	w: 2 * x1 + 2 * x2
      s 	w: x1 + 1
      sum^1_cons	w: x1 + x2 + 18462
      sum	w: 2 * x1 + 7449
      0 	w: 0
      nil	w: 1
      plus	w: 2 * x1 + x2 + 21656
      cons	w: x1 + 2 * x2 + 18460
      app	w: x1 + x2 + 1
Number of strict rules: 0