0.00/0.22	YES
0.00/0.22	Input TRS:
0.00/0.22	    1: minus(x,0()) -> x
0.00/0.22	    2: minus(s(x),s(y)) -> minus(x,y)
0.00/0.22	    3: quot(0(),s(y)) -> 0()
0.00/0.22	    4: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
0.00/0.22	    5: plus(0(),y) -> y
0.00/0.22	    6: plus(s(x),y) -> s(plus(x,y))
0.00/0.22	    7: minus(minus(x,y),z) -> minus(x,plus(y,z))
0.00/0.22	    8: app(nil(),k) -> k
0.00/0.22	    9: app(l,nil()) -> l
0.00/0.22	    10: app(cons(x,l),k) -> cons(x,app(l,k))
0.00/0.22	    11: sum(cons(x,nil())) -> cons(x,nil())
0.00/0.22	    12: sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
0.00/0.22	    13: sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
0.00/0.22	    14: rand(x) ->= x
0.00/0.22	    15: rand(x) ->= rand(s(x))
0.00/0.22	Number of strict rules: 13
0.00/0.22	Direct POLO(bPol) ... failed.
0.00/0.22	Uncurrying ... failed.
0.00/0.22	Dependency Pairs:
0.00/0.22	   #1: #minus(s(x),s(y)) -> #minus(x,y)
0.00/0.22	   #2: #plus(s(x),y) -> #plus(x,y)
0.00/0.22	   #3: #sum(app(l,cons(x,cons(y,k)))) -> #sum(app(l,sum(cons(x,cons(y,k)))))
0.00/0.22	   #4: #sum(app(l,cons(x,cons(y,k)))) -> #app(l,sum(cons(x,cons(y,k))))
0.00/0.22	   #5: #sum(app(l,cons(x,cons(y,k)))) -> #sum(cons(x,cons(y,k)))
0.00/0.22	   #6: #sum(cons(x,cons(y,l))) -> #sum(cons(plus(x,y),l))
0.00/0.22	   #7: #sum(cons(x,cons(y,l))) -> #plus(x,y)
0.00/0.22	   #8: #minus(minus(x,y),z) -> #minus(x,plus(y,z))
0.00/0.22	   #9: #minus(minus(x,y),z) -> #plus(y,z)
0.00/0.22	   #10: #app(cons(x,l),k) -> #app(l,k)
0.00/0.22	   #11: #quot(s(x),s(y)) -> #quot(minus(x,y),s(y))
0.00/0.22	   #12: #quot(s(x),s(y)) -> #minus(x,y)
0.00/0.22	Number of SCCs: 6, DPs: 7
0.00/0.22	  SCC { #2 }
0.00/0.22	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
0.00/0.22	      s 	s: [1]	p: 1	w: x1
0.00/0.22	      minus	s: [1]	p: 0	w: max(x1)
0.00/0.22	      #plus	s: [1]	p: 0	w: max(x1 + 1)
0.00/0.22	      rand	s: []	p: 0	w: x1 + 1
0.00/0.22	      sum	s: []	p: 0	w: 6
0.00/0.22	      0 	s: []	p: 2	w: 1
0.00/0.22	      quot	s: [2,1]	p: 2	w: max(x1 + 2, x2 + 1)
0.00/0.22	      nil	s: []	p: 1	w: 1
0.00/0.22	      #app	s: [2,1]	p: 0	w: x1 + x2
0.00/0.22	      #minus	s: [1,2]	p: 0	w: max(x1, x2)
0.00/0.22	      plus	s: [2,1]	p: 2	w: max(x1, x2)
0.00/0.22	      cons	s: []	p: 0	w: x2 + 4
0.00/0.22	      #quot	s: [1,2]	p: 0	w: max(x1 + 1, x2 + 1)
0.00/0.22	      #sum	s: []	p: 0	w: 1
0.00/0.22	      app	s: [2]	p: 1	w: x1 + x2 + 1
0.00/0.22	    Removed DPs: #2
0.00/0.22	Number of SCCs: 5, DPs: 6
0.00/0.22	  SCC { #10 }
0.00/0.22	POLO(Sum)... succeeded.
0.00/0.22	      s 	w: x1
0.00/0.22	      minus	w: x1 + 1
0.00/0.22	      #plus	w: 0
0.00/0.22	      rand	w: x1
0.00/0.22	      sum	w: 2
0.00/0.22	      0 	w: 1
0.00/0.22	      quot	w: 1
0.00/0.22	      nil	w: 1
0.00/0.22	      #app	w: x1
0.00/0.22	      #minus	w: 0
0.00/0.22	      plus	w: x2 + 1
0.00/0.22	      cons	w: x2 + 1
0.00/0.22	      #quot	w: 0
0.00/0.22	      #sum	w: 0
0.00/0.22	      app	w: x1 + x2 + 1
0.00/0.22	    Removed DPs: #10
0.00/0.22	Number of SCCs: 4, DPs: 5
0.00/0.22	  SCC { #11 }
0.00/0.22	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
0.00/0.22	      s 	s: [1]	p: 2	w: x1
0.00/0.22	      minus	s: [1]	p: 1	w: max(x1)
0.00/0.22	      #plus	s: [1]	p: 0	w: max(x1 + 1)
0.00/0.22	      rand	s: []	p: 0	w: x1 + 1
0.00/0.22	      sum	s: []	p: 0	w: 6
0.00/0.22	      0 	s: []	p: 3	w: 1
0.00/0.22	      quot	s: [2,1]	p: 3	w: max(x1 + 2, x2 + 1)
0.00/0.22	      nil	s: []	p: 1	w: 1
0.00/0.22	      #app	s: [2,1]	p: 0	w: x1 + x2
0.00/0.22	      #minus	s: [1,2]	p: 0	w: max(x1, x2)
0.00/0.22	      plus	s: [2,1]	p: 3	w: max(x1, x2)
0.00/0.22	      cons	s: []	p: 0	w: x2 + 4
0.00/0.22	      #quot	s: [1,2]	p: 0	w: max(x1 + 1, x2 + 1)
0.00/0.22	      #sum	s: []	p: 0	w: 1
0.00/0.22	      app	s: [2]	p: 1	w: x1 + x2 + 1
0.00/0.22	    Removed DPs: #11
0.00/0.22	Number of SCCs: 3, DPs: 4
0.00/0.22	  SCC { #6 }
0.00/0.22	POLO(Sum)... succeeded.
0.00/0.22	      s 	w: x1
0.00/0.22	      minus	w: x1 + 1
0.00/0.22	      #plus	w: 0
0.00/0.22	      rand	w: x1
0.00/0.22	      sum	w: 2
0.00/0.22	      0 	w: 1
0.00/0.22	      quot	w: 1
0.00/0.22	      nil	w: 1
0.00/0.22	      #app	w: 0
0.00/0.22	      #minus	w: 0
0.00/0.22	      plus	w: x2 + 1
0.00/0.22	      cons	w: x2 + 1
0.00/0.22	      #quot	w: 0
0.00/0.22	      #sum	w: x1
0.00/0.22	      app	w: x1 + x2 + 1
0.00/0.22	    Removed DPs: #6
0.00/0.22	Number of SCCs: 2, DPs: 3
0.00/0.22	  SCC { #3 }
0.00/0.22	POLO(Sum)... succeeded.
0.00/0.22	      s 	w: x1
0.00/0.22	      minus	w: x1 + 1
0.00/0.22	      #plus	w: 0
0.00/0.22	      rand	w: x1
0.00/0.22	      sum	w: 3
0.00/0.22	      0 	w: 1
0.00/0.22	      quot	w: 1
0.00/0.22	      nil	w: 1
0.00/0.22	      #app	w: 0
0.00/0.22	      #minus	w: 0
0.00/0.22	      plus	w: x2 + 1
0.00/0.22	      cons	w: x2 + 2
0.00/0.22	      #quot	w: 0
0.00/0.22	      #sum	w: x1
0.00/0.22	      app	w: x1 + x2 + 1
0.00/0.22	    Removed DPs: #3
0.00/0.22	Number of SCCs: 1, DPs: 2
0.00/0.22	  SCC { #1 #8 }
0.00/0.22	POLO(Sum)... succeeded.
0.00/0.22	      s 	w: x1
0.00/0.22	      minus	w: x1 + 2
0.00/0.22	      #plus	w: 0
0.00/0.22	      rand	w: x1
0.00/0.22	      sum	w: 3
0.00/0.22	      0 	w: 1
0.00/0.22	      quot	w: 1
0.00/0.22	      nil	w: 1
0.00/0.22	      #app	w: 0
0.00/0.22	      #minus	w: x1 + x2
0.00/0.22	      plus	w: x2 + 1
0.00/0.22	      cons	w: x2 + 2
0.00/0.22	      #quot	w: 0
0.00/0.22	      #sum	w: 0
0.00/0.22	      app	w: x1 + x2 + 1
0.00/0.22	    Removed DPs: #8
0.00/0.22	Number of SCCs: 1, DPs: 1
0.00/0.22	  SCC { #1 }
0.00/0.22	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
0.00/0.22	      s 	s: [1]	p: 2	w: x1
0.00/0.22	      minus	s: [1]	p: 1	w: max(x1)
0.00/0.22	      #plus	s: [1]	p: 0	w: max(x1 + 1)
0.00/0.22	      rand	s: []	p: 0	w: x1 + 1
0.00/0.22	      sum	s: []	p: 0	w: 6
0.00/0.22	      0 	s: []	p: 3	w: 1
0.00/0.22	      quot	s: [2,1]	p: 3	w: max(x1 + 2, x2 + 1)
0.00/0.22	      nil	s: []	p: 1	w: 1
0.00/0.22	      #app	s: [2,1]	p: 0	w: x1 + x2
0.00/0.22	      #minus	s: [1]	p: 3	w: max(x1)
0.00/0.22	      plus	s: [2,1]	p: 3	w: max(x1, x2)
0.00/0.22	      cons	s: []	p: 0	w: x2 + 4
0.00/0.22	      #quot	s: [1,2]	p: 0	w: max(x1 + 1, x2 + 1)
0.00/0.22	      #sum	s: []	p: 0	w: 1
0.00/0.22	      app	s: [2]	p: 1	w: x1 + x2 + 1
0.00/0.22	    Removed DPs: #1
0.00/0.22	Number of SCCs: 0, DPs: 0
0.00/0.22	EOF