YES
Input TRS:
      1: minus(x,0()) -> x
      2: minus(s(x),s(y)) -> minus(x,y)
      3: quot(0(),s(y)) -> 0()
      4: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
      5: plus(0(),y) -> y
      6: plus(s(x),y) -> s(plus(x,y))
      7: minus(minus(x,y),z) -> minus(x,plus(y,z))
      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)))))
      14: rand(x) ->= x
      15: rand(x) ->= rand(s(x))
Number of strict rules: 13
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #minus(s(x),s(y)) -> #minus(x,y)
     #2: #plus(s(x),y) -> #plus(x,y)
     #3: #sum(app(l,cons(x,cons(y,k)))) -> #sum(app(l,sum(cons(x,cons(y,k)))))
     #4: #sum(app(l,cons(x,cons(y,k)))) -> #app(l,sum(cons(x,cons(y,k))))
     #5: #sum(app(l,cons(x,cons(y,k)))) -> #sum(cons(x,cons(y,k)))
     #6: #sum(cons(x,cons(y,l))) -> #sum(cons(plus(x,y),l))
     #7: #sum(cons(x,cons(y,l))) -> #plus(x,y)
     #8: #minus(minus(x,y),z) -> #minus(x,plus(y,z))
     #9: #minus(minus(x,y),z) -> #plus(y,z)
     #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)
Number of SCCs: 6, DPs: 7
  SCC { #2 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 0	w: x1
      minus	s: 1
      #plus	s: 1
      rand	s: []	p: 0	w: x1 + 1
      sum	s: []	p: 2	w: 20904
      0 	s: []	p: 1	w: 1
      quot	s: [1]	p: 1	w: max(x1 + 40651)
      nil	s: []	p: 1	w: 20904
      #app	s: [2]	p: 0	w: x2 + 1
      #minus	s: 1
      plus	s: [1,2]	p: 1	w: max(x1 + 10452, x2 + 10453)
      cons	s: []	p: 0	w: 10451
      #quot	s: [2,1]	p: 0	w: max(x1 + 1, x2 + 1)
      #sum	s: []	p: 0	w: 1
      app	s: [2,1]	p: 0	w: x1 + x2 + 10452
    Removed DPs: #2
Number of SCCs: 5, DPs: 6
  SCC { #10 }
POLO(Sum)... succeeded.
      s 	w: x1
      minus	w: x1 + 1
      #plus	w: 0
      rand	w: x1
      sum	w: x1
      0 	w: 1
      quot	w: 1
      nil	w: 32286
      #app	w: x1
      #minus	w: 0
      plus	w: x2 + 1
      cons	w: x1 + x2 + 1
      #quot	w: 0
      #sum	w: 0
      app	w: x1 + x2 + 20163
    Removed DPs: #10
Number of SCCs: 4, DPs: 5
  SCC { #11 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 0	w: x1
      minus	s: 1
      #plus	s: 1
      rand	s: []	p: 0	w: x1 + 1
      sum	s: []	p: 2	w: 26757
      0 	s: []	p: 1	w: 1
      quot	s: [1]	p: 1	w: max(x1 + 40651)
      nil	s: []	p: 1	w: 26757
      #app	s: [2]	p: 0	w: x2 + 1
      #minus	s: 1
      plus	s: [1,2]	p: 1	w: max(x1 + 10452, x2 + 10453)
      cons	s: []	p: 0	w: 10451
      #quot	s: [1]	p: 0	w: max(x1 + 28101)
      #sum	s: []	p: 0	w: 1
      app	s: [2,1]	p: 0	w: x1 + x2 + 10452
    Removed DPs: #11
Number of SCCs: 3, DPs: 4
  SCC { #6 }
POLO(Sum)... succeeded.
      s 	w: x1
      minus	w: x1 + 1
      #plus	w: 0
      rand	w: x1
      sum	w: x1
      0 	w: 1
      quot	w: 1
      nil	w: 32286
      #app	w: 0
      #minus	w: 0
      plus	w: x2 + 1
      cons	w: x1 + x2 + 2
      #quot	w: 0
      #sum	w: x1
      app	w: x1 + x2 + 26016
    Removed DPs: #6
Number of SCCs: 2, DPs: 3
  SCC { #3 }
POLO(Sum)... succeeded.
      s 	w: x1
      minus	w: x1 + 1
      #plus	w: 0
      rand	w: x1
      sum	w: 3
      0 	w: 1
      quot	w: 1
      nil	w: 1
      #app	w: 0
      #minus	w: 0
      plus	w: x2
      cons	w: x2 + 2
      #quot	w: 0
      #sum	w: x1
      app	w: x1 + x2 + 20819
    Removed DPs: #3
Number of SCCs: 1, DPs: 2
  SCC { #1 #8 }
POLO(Sum)... succeeded.
      s 	w: x1
      minus	w: x1 + 8947
      #plus	w: 0
      rand	w: x1
      sum	w: 26287
      0 	w: 1
      quot	w: 1
      nil	w: 1
      #app	w: 0
      #minus	w: x1 + x2
      plus	w: x2 + 8946
      cons	w: x2 + 26286
      #quot	w: 0
      #sum	w: 0
      app	w: x1 + x2 + 17678
    Removed DPs: #8
Number of SCCs: 1, DPs: 1
  SCC { #1 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
      s 	s: [1]	p: 0	w: x1
      minus	s: 1
      #plus	s: 1
      rand	s: []	p: 0	w: x1 + 1
      sum	s: []	p: 2	w: 29041
      0 	s: []	p: 1	w: 1
      quot	s: [1]	p: 1	w: max(x1 + 40651)
      nil	s: []	p: 1	w: 29041
      #app	s: [2]	p: 0	w: x2 + 1
      #minus	s: [1]	p: 1	w: max(x1 + 1)
      plus	s: [1,2]	p: 1	w: max(x1 + 11594, x2 + 11595)
      cons	s: []	p: 0	w: 11593
      #quot	s: [1]	p: 0	w: max(x1 + 28101)
      #sum	s: []	p: 0	w: 1
      app	s: [2,1]	p: 0	w: x1 + x2 + 11594
    Removed DPs: #1
Number of SCCs: 0, DPs: 0