YES
Input TRS:
      1: +(x,0()) -> x
      2: +(0(),x) -> x
      3: +(s(x),s(y)) -> s(s(+(x,y)))
      4: *(x,0()) -> 0()
      5: *(0(),x) -> 0()
      6: *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
      7: sum(nil()) -> 0()
      8: sum(cons(x,l)) -> +(x,sum(l))
      9: prod(nil()) -> s(0())
      10: prod(cons(x,l)) -> *(x,prod(l))
Number of strict rules: 10
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #*(s(x),s(y)) -> #+(*(x,y),+(x,y))
     #2: #*(s(x),s(y)) -> #*(x,y)
     #3: #*(s(x),s(y)) -> #+(x,y)
     #4: #prod(cons(x,l)) -> #*(x,prod(l))
     #5: #prod(cons(x,l)) -> #prod(l)
     #6: #+(s(x),s(y)) -> #+(x,y)
     #7: #sum(cons(x,l)) -> #+(x,sum(l))
     #8: #sum(cons(x,l)) -> #sum(l)
Number of SCCs: 4, DPs: 4
  SCC { #8 }
POLO(Sum)... succeeded.
      prod	w: 0
      s 	w: 0
      #prod	w: 0
      #* 	w: 0
      sum	w: 0
      0 	w: 0
      nil	w: 0
      cons	w: x2 + 1
      + 	w: 0
      #sum	w: x1
      #+ 	w: 0
      * 	w: 0
    USABLE RULES: { }
    Removed DPs: #8
Number of SCCs: 3, DPs: 3
  SCC { #5 }
POLO(Sum)... succeeded.
      prod	w: 0
      s 	w: 0
      #prod	w: x1
      #* 	w: 0
      sum	w: 0
      0 	w: 0
      nil	w: 0
      cons	w: x2 + 1
      + 	w: 0
      #sum	w: 0
      #+ 	w: 0
      * 	w: 0
    USABLE RULES: { }
    Removed DPs: #5
Number of SCCs: 2, DPs: 2
  SCC { #2 }
POLO(Sum)... succeeded.
      prod	w: 0
      s 	w: x1 + 1
      #prod	w: 0
      #* 	w: x2
      sum	w: 0
      0 	w: 0
      nil	w: 0
      cons	w: 1
      + 	w: 0
      #sum	w: 0
      #+ 	w: 0
      * 	w: 0
    USABLE RULES: { }
    Removed DPs: #2
Number of SCCs: 1, DPs: 1
  SCC { #6 }
POLO(Sum)... succeeded.
      prod	w: 0
      s 	w: x1 + 1
      #prod	w: 0
      #* 	w: 0
      sum	w: 0
      0 	w: 0
      nil	w: 0
      cons	w: 1
      + 	w: 0
      #sum	w: 0
      #+ 	w: x2
      * 	w: 0
    USABLE RULES: { }
    Removed DPs: #6
Number of SCCs: 0, DPs: 0