YES
Input TRS:
AC symbols: plus
      1: minus(x,0()) -> x
      2: minus(s(x),s(y)) -> minus(x,y)
      3: minus(minus(x,y),z) -> minus(x,plus(y,z))
      4: quot(0(),s(y)) -> 0()
      5: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
      6: plus(0(),y) -> y
      7: plus(s(x),y) -> s(plus(x,y))
      8: app(nil(),k) -> k
      9: app(l,nil()) -> l
      10: app(cons(x,l),k) -> cons(x,app(l,k))
      11: sum(cons(x,nil())) -> cons(x,nil())
      12: sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
      13: sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
Number of strict rules: 13
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #minus(s(x),s(y)) -> #minus(x,y)
     #2: #sum(app(l,cons(x,cons(y,k)))) -> #sum(app(l,sum(cons(x,cons(y,k)))))
     #3: #sum(app(l,cons(x,cons(y,k)))) -> #app(l,sum(cons(x,cons(y,k))))
     #4: #sum(app(l,cons(x,cons(y,k)))) -> #sum(cons(x,cons(y,k)))
     #5: #sum(cons(x,cons(y,l))) -> #sum(cons(plus(x,y),l))
     #6: #sum(cons(x,cons(y,l))) -> #plus(x,y)
     #7: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #8: #plus(x,plus(y,z)) ->= #plus(x,y)
     #9: #plus(s(x),y) -> #plus(x,y)
     #10: #app(cons(x,l),k) -> #app(l,k)
     #11: #quot(s(x),s(y)) -> #quot(minus(x,y),s(y))
     #12: #quot(s(x),s(y)) -> #minus(x,y)
     #13: #minus(minus(x,y),z) -> #minus(x,plus(y,z))
     #14: #minus(minus(x,y),z) -> #plus(y,z)
Number of SCCs: 6, DPs: 9
  SCC { #10 }
POLO(Sum)... succeeded.
      s 	w: 0
      minus	w: 0
      #plus	w: 0
      sum	w: 0
      0 	w: 0
      quot	w: 0
      nil	w: 0
      #app	w: x1
      #minus	w: 0
      plus	w: 0
      cons	w: x2 + 1
      #quot	w: 0
      #sum	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #10
Number of SCCs: 5, DPs: 8
  SCC { #11 }
POLO(Sum)... succeeded.
      s 	w: x1 + 2
      minus	w: x1 + 1
      #plus	w: 0
      sum	w: 0
      0 	w: 1
      quot	w: 0
      nil	w: 0
      #app	w: 0
      #minus	w: 0
      plus	w: x1 + x2 + 23676
      cons	w: 1
      #quot	w: x1
      #sum	w: 0
      app	w: 0
    USABLE RULES: { 1..3 }
    Removed DPs: #11
Number of SCCs: 4, DPs: 7
  SCC { #5 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      minus	w: x1 + 1
      #plus	w: 0
      sum	w: 0
      0 	w: 1
      quot	w: 0
      nil	w: 0
      #app	w: 0
      #minus	w: 0
      plus	w: x1 + x2 + 1
      cons	w: x1 + x2 + 2
      #quot	w: x1
      #sum	w: x1
      app	w: 0
    USABLE RULES: { 1..3 6 7 14 }
    Removed DPs: #5
Number of SCCs: 3, DPs: 6
  SCC { #2 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      minus	w: x1 + 1
      #plus	w: 0
      sum	w: 3
      0 	w: 1
      quot	w: 0
      nil	w: 1
      #app	w: 0
      #minus	w: 0
      plus	w: x1 + x2 + 6996
      cons	w: x2 + 2
      #quot	w: x1
      #sum	w: x1
      app	w: x1 + x2 + 28382
    USABLE RULES: { 1..3 6..12 14 }
    Removed DPs: #2
Number of SCCs: 2, DPs: 5
  SCC { #1 #13 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      minus	w: x1 + x2 + 1
      #plus	w: 0
      sum	w: 2
      0 	w: 35231
      quot	w: 0
      nil	w: 1
      #app	w: 0
      #minus	w: x1
      plus	w: x1 + x2 + 1
      cons	w: x2 + 1
      #quot	w: 0
      #sum	w: x1
      app	w: x1 + x2 + 28382
    USABLE RULES: { 1 8..12 }
    Removed DPs: #1 #13
Number of SCCs: 1, DPs: 3
  SCC { #7..9 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      minus	w: x1 + x2 + 1
      #plus	w: x1 + x2
      sum	w: 2
      0 	w: 46572
      quot	w: 0
      nil	w: 1
      #app	w: 0
      #minus	w: 0
      plus	w: x1 + x2 + 1
      cons	w: x2 + 1
      #quot	w: 0
      #sum	w: x1
      app	w: x1 + x2 + 42632
    USABLE RULES: { 1 6..12 14 }
    Removed DPs: #8 #9
Number of SCCs: 1, DPs: 1
  SCC { #7 }
only weak rules.
Number of SCCs: 0, DPs: 0
Next Dependency Pairs:
     #15: #plus(plus(0(),y),_1) -> #plus(y,_1)
     #16: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
     #17: #plus(x,plus(y,z)) ->= #plus(x,y)
     #18: #plus(plus(s(x),y),_1) -> #plus(s(plus(x,y)),_1)
Number of SCCs: 1, DPs: 4
  SCC { #15..18 }
POLO(Sum)... succeeded.
      s 	w: x1 + 1
      minus	w: x1 + x2 + 9726
      #plus	w: x1 + x2
      sum	w: 2
      0 	w: 32869
      quot	w: 0
      nil	w: 1
      #app	w: 0
      #minus	w: 0
      plus	w: x1 + x2 + 1
      cons	w: x2 + 1
      #quot	w: 0
      #sum	w: x1
      app	w: x1 + x2 + 3287
    USABLE RULES: { 1 6..12 14 }
    Removed DPs: #15 #17
Number of SCCs: 1, DPs: 2
  SCC { #16 #18 }
POLO(Sum)... succeeded.
      s 	w: 1
      minus	w: x1 + 9726
      #plus	w: x1 + x2
      sum	w: 36230
      0 	w: 32869
      quot	w: 0
      nil	w: 1
      #app	w: 0
      #minus	w: 0
      plus	w: x1 + x2 + 1
      cons	w: x2 + 36229
      #quot	w: 0
      #sum	w: x1
      app	w: x1 + x2 + 1
    USABLE RULES: { 1 6..12 14 }
    Removed DPs: #18
Number of SCCs: 1, DPs: 1
  SCC { #16 }
only weak rules.
Number of SCCs: 0, DPs: 0