0.00/0.43	YES
0.00/0.44	Input TRS:
0.00/0.44	    1: minus(x,0()) -> x
0.00/0.44	    2: minus(s(x),s(y)) -> minus(x,y)
0.00/0.44	    3: quot(0(),s(y)) -> 0()
0.00/0.44	    4: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y)))
0.00/0.44	    5: le(0(),y) -> true()
0.00/0.44	    6: le(s(x),0()) -> false()
0.00/0.44	    7: le(s(x),s(y)) -> le(x,y)
0.00/0.44	    8: app(nil(),y) -> y
0.00/0.44	    9: app(add(n,x),y) -> add(n,app(x,y))
0.00/0.44	    10: low(n,nil()) -> nil()
0.00/0.44	    11: low(n,add(m,x)) -> if_low(le(m,n),n,add(m,x))
0.00/0.44	    12: if_low(true(),n,add(m,x)) -> add(m,low(n,x))
0.00/0.44	    13: if_low(false(),n,add(m,x)) -> low(n,x)
0.00/0.44	    14: high(n,nil()) -> nil()
0.00/0.44	    15: high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x))
0.00/0.44	    16: if_high(true(),n,add(m,x)) -> high(n,x)
0.00/0.44	    17: if_high(false(),n,add(m,x)) -> add(m,high(n,x))
0.00/0.44	    18: quicksort(nil()) -> nil()
0.00/0.44	    19: quicksort(add(n,x)) -> app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))
0.00/0.44	    20: rand(x) ->= x
0.00/0.44	    21: rand(x) ->= rand(s(x))
0.00/0.44	Number of strict rules: 19
0.00/0.44	Direct POLO(bPol) ... failed.
0.00/0.44	Uncurrying ... failed.
0.00/0.44	Dependency Pairs:
0.00/0.44	   #1: #minus(s(x),s(y)) -> #minus(x,y)
0.00/0.44	   #2: #if_low(false(),n,add(m,x)) -> #low(n,x)
0.00/0.44	   #3: #app(add(n,x),y) -> #app(x,y)
0.00/0.44	   #4: #low(n,add(m,x)) -> #if_low(le(m,n),n,add(m,x))
0.00/0.44	   #5: #low(n,add(m,x)) -> #le(m,n)
0.00/0.44	   #6: #if_low(true(),n,add(m,x)) -> #low(n,x)
0.00/0.44	   #7: #le(s(x),s(y)) -> #le(x,y)
0.00/0.44	   #8: #if_high(false(),n,add(m,x)) -> #high(n,x)
0.00/0.44	   #9: #quicksort(add(n,x)) -> #app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))
0.00/0.44	   #10: #quicksort(add(n,x)) -> #quicksort(low(n,x))
0.00/0.44	   #11: #quicksort(add(n,x)) -> #low(n,x)
0.00/0.44	   #12: #quicksort(add(n,x)) -> #quicksort(high(n,x))
0.00/0.44	   #13: #quicksort(add(n,x)) -> #high(n,x)
0.00/0.44	   #14: #if_high(true(),n,add(m,x)) -> #high(n,x)
0.00/0.44	   #15: #high(n,add(m,x)) -> #if_high(le(m,n),n,add(m,x))
0.00/0.44	   #16: #high(n,add(m,x)) -> #le(m,n)
0.00/0.44	   #17: #quot(s(x),s(y)) -> #quot(minus(x,y),s(y))
0.00/0.44	   #18: #quot(s(x),s(y)) -> #minus(x,y)
0.00/0.44	Number of SCCs: 7, DPs: 12
0.00/0.44	  SCC { #1 }
0.00/0.44	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
0.00/0.44	      le	s: []	p: 4	w: max(x1 + 5, x2 + 6)
0.00/0.44	      s 	s: [1]	p: 1	w: x1
0.00/0.44	      #le	s: []	p: 0	w: max(x1)
0.00/0.44	      minus	s: 1
0.00/0.44	      if_high	s: []	p: 2	w: max(x2 + 2, x3)
0.00/0.44	      #quicksort	s: []	p: 0	w: 1
0.00/0.44	      #high	s: [2]	p: 0	w: max(x2)
0.00/0.44	      false	s: []	p: 1	w: 4
0.00/0.44	      #if_high	s: [3,2]	p: 0	w: max(x2, x3)
0.00/0.44	      quicksort	s: [1]	p: 2	w: x1
0.00/0.44	      true	s: []	p: 1	w: 0
0.00/0.44	      rand	s: []	p: 0	w: x1 + 1
0.00/0.44	      0 	s: []	p: 0	w: 4
0.00/0.44	      quot	s: 1
0.00/0.44	      high	s: []	p: 2	w: max(x1 + 2, x2)
0.00/0.44	      nil	s: []	p: 1	w: 1
0.00/0.44	      #app	s: []	p: 0	w: max(x2)
0.00/0.44	      #minus	s: [2]	p: 2	w: max(x2)
0.00/0.44	      low	s: []	p: 3	w: max(x1 + 2, x2)
0.00/0.44	      add	s: []	p: 2	w: max(x1 + 3, x2)
0.00/0.44	      #quot	s: []	p: 0	w: max(x1 + 1)
0.00/0.44	      if_low	s: []	p: 3	w: max(x2 + 2, x3)
0.00/0.44	      #if_low	s: [1,2,3]	p: 0	w: max(x1, x2 + 1, x3)
0.00/0.44	      #low	s: []	p: 0	w: max(x2)
0.00/0.44	      app	s: [2]	p: 2	w: max(x1, x2)
0.00/0.44	    Removed DPs: #1
0.00/0.44	Number of SCCs: 6, DPs: 11
0.00/0.44	  SCC { #3 }
0.00/0.44	POLO(Sum)... POLO(max)... QLPOS... succeeded.
0.00/0.44	      le	s: []	p: 5
0.00/0.44	      s 	s: 1
0.00/0.44	      #le	s: [1]	p: 0
0.00/0.44	      minus	s: [1,2]	p: 3
0.00/0.44	      if_high	s: 3
0.00/0.44	      #quicksort	s: []	p: 0
0.00/0.44	      #high	s: []	p: 0
0.00/0.44	      false	s: []	p: 2
0.00/0.44	      #if_high	s: [1,2]	p: 0
0.00/0.44	      quicksort	s: [1]	p: 7
0.00/0.44	      true	s: []	p: 0
0.00/0.44	      rand	s: [1]	p: 0
0.00/0.44	      0 	s: []	p: 2
0.00/0.44	      quot	s: []	p: 2
0.00/0.44	      high	s: 2
0.00/0.44	      nil	s: []	p: 7
0.00/0.44	      #app	s: 1
0.00/0.44	      #minus	s: []	p: 0
0.00/0.44	      low	s: 2
0.00/0.44	      add	s: [1,2]	p: 5
0.00/0.44	      #quot	s: []	p: 0
0.00/0.44	      if_low	s: 3
0.00/0.44	      #if_low	s: []	p: 0
0.00/0.44	      #low	s: []	p: 0
0.00/0.44	      app	s: [2,1]	p: 6
0.00/0.44	    Removed DPs: #3
0.00/0.44	Number of SCCs: 5, DPs: 10
0.00/0.44	  SCC { #7 }
0.00/0.44	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
0.00/0.44	      le	s: []	p: 4	w: max(x1 + 5, x2 + 6)
0.00/0.44	      s 	s: [1]	p: 1	w: x1
0.00/0.44	      #le	s: [1,2]	p: 2	w: max(x1, x2 + 1)
0.00/0.44	      minus	s: 1
0.00/0.44	      if_high	s: []	p: 2	w: max(x2 + 2, x3)
0.00/0.44	      #quicksort	s: []	p: 0	w: 1
0.00/0.44	      #high	s: [2]	p: 0	w: max(x2)
0.00/0.44	      false	s: []	p: 1	w: 4
0.00/0.44	      #if_high	s: [3,2]	p: 0	w: max(x2, x3)
0.00/0.44	      quicksort	s: [1]	p: 2	w: x1
0.00/0.44	      true	s: []	p: 1	w: 0
0.00/0.44	      rand	s: []	p: 0	w: x1 + 1
0.00/0.44	      0 	s: []	p: 0	w: 4
0.00/0.44	      quot	s: 1
0.00/0.44	      high	s: []	p: 2	w: max(x1 + 2, x2)
0.00/0.44	      nil	s: []	p: 1	w: 1
0.00/0.44	      #app	s: []	p: 0	w: max(x2)
0.00/0.44	      #minus	s: [2]	p: 2	w: max(x2)
0.00/0.44	      low	s: []	p: 3	w: max(x1 + 2, x2)
0.00/0.44	      add	s: []	p: 2	w: max(x1 + 3, x2)
0.00/0.44	      #quot	s: []	p: 0	w: max(x1 + 1)
0.00/0.44	      if_low	s: []	p: 3	w: max(x2 + 2, x3)
0.00/0.44	      #if_low	s: [1,2,3]	p: 0	w: max(x1, x2 + 1, x3)
0.00/0.44	      #low	s: []	p: 0	w: max(x2)
0.00/0.44	      app	s: [2]	p: 2	w: max(x1, x2)
0.00/0.44	    Removed DPs: #7
0.00/0.44	Number of SCCs: 4, DPs: 9
0.00/0.44	  SCC { #17 }
0.00/0.44	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded.
0.00/0.44	      le	s: []	p: 4	w: max(x1 + 5, x2 + 6)
0.00/0.44	      s 	s: [1]	p: 1	w: x1
0.00/0.44	      #le	s: [1,2]	p: 2	w: max(x1, x2 + 1)
0.00/0.44	      minus	s: 1
0.00/0.44	      if_high	s: []	p: 2	w: max(x2 + 2, x3)
0.00/0.44	      #quicksort	s: []	p: 0	w: 1
0.00/0.44	      #high	s: [2]	p: 0	w: max(x2)
0.00/0.44	      false	s: []	p: 1	w: 4
0.00/0.44	      #if_high	s: [3,2]	p: 0	w: max(x2, x3)
0.00/0.44	      quicksort	s: [1]	p: 2	w: x1
0.00/0.44	      true	s: []	p: 1	w: 0
0.00/0.44	      rand	s: []	p: 0	w: x1 + 1
0.00/0.44	      0 	s: []	p: 0	w: 4
0.00/0.44	      quot	s: 1
0.00/0.44	      high	s: []	p: 2	w: max(x1 + 2, x2)
0.00/0.44	      nil	s: []	p: 1	w: 1
0.00/0.44	      #app	s: []	p: 0	w: max(x2)
0.00/0.44	      #minus	s: [2]	p: 2	w: max(x2)
0.00/0.44	      low	s: []	p: 3	w: max(x1 + 2, x2)
0.00/0.44	      add	s: []	p: 2	w: max(x1 + 3, x2)
0.00/0.44	      #quot	s: [2,1]	p: 1	w: max(x1 + 1, x2)
0.00/0.44	      if_low	s: []	p: 3	w: max(x2 + 2, x3)
0.00/0.44	      #if_low	s: [1,2,3]	p: 0	w: max(x1, x2 + 1, x3)
0.00/0.44	      #low	s: []	p: 0	w: max(x2)
0.00/0.44	      app	s: [2]	p: 2	w: max(x1, x2)
0.00/0.44	    Removed DPs: #17
0.00/0.44	Number of SCCs: 3, DPs: 8
0.00/0.44	  SCC { #10 #12 }
0.00/0.44	POLO(Sum)... POLO(max)... QLPOS... succeeded.
0.00/0.44	      le	s: []	p: 5
0.00/0.44	      s 	s: 1
0.00/0.44	      #le	s: [2]	p: 0
0.00/0.44	      minus	s: 1
0.00/0.44	      if_high	s: 3
0.00/0.44	      #quicksort	s: [1]	p: 0
0.00/0.44	      #high	s: []	p: 0
0.00/0.44	      false	s: []	p: 2
0.00/0.44	      #if_high	s: [1,2]	p: 0
0.00/0.44	      quicksort	s: [1]	p: 7
0.00/0.44	      true	s: []	p: 0
0.00/0.44	      rand	s: [1]	p: 0
0.00/0.44	      0 	s: []	p: 2
0.00/0.44	      quot	s: []	p: 2
0.00/0.44	      high	s: 2
0.00/0.44	      nil	s: []	p: 7
0.00/0.44	      #app	s: 1
0.00/0.44	      #minus	s: []	p: 0
0.00/0.44	      low	s: 2
0.00/0.44	      add	s: [1,2]	p: 5
0.00/0.44	      #quot	s: []	p: 1
0.00/0.44	      if_low	s: 3
0.00/0.44	      #if_low	s: []	p: 0
0.00/0.44	      #low	s: []	p: 0
0.00/0.44	      app	s: [2,1]	p: 6
0.00/0.44	    Removed DPs: #10 #12
0.00/0.44	Number of SCCs: 2, DPs: 6
0.00/0.44	  SCC { #8 #14 #15 }
0.00/0.44	POLO(Sum)... POLO(max)... QLPOS... succeeded.
0.00/0.44	      le	s: []	p: 5
0.00/0.44	      s 	s: 1
0.00/0.44	      #le	s: [2]	p: 0
0.00/0.44	      minus	s: 1
0.00/0.44	      if_high	s: 3
0.00/0.44	      #quicksort	s: [1]	p: 0
0.00/0.44	      #high	s: [2]	p: 2
0.00/0.44	      false	s: []	p: 1
0.00/0.44	      #if_high	s: [1,3]	p: 2
0.00/0.44	      quicksort	s: [1]	p: 7
0.00/0.44	      true	s: []	p: 3
0.00/0.44	      rand	s: [1]	p: 0
0.00/0.44	      0 	s: []	p: 4
0.00/0.44	      quot	s: []	p: 4
0.00/0.44	      high	s: 2
0.00/0.44	      nil	s: []	p: 7
0.00/0.44	      #app	s: 1
0.00/0.44	      #minus	s: []	p: 0
0.00/0.44	      low	s: 2
0.00/0.44	      add	s: [1,2]	p: 5
0.00/0.44	      #quot	s: []	p: 1
0.00/0.44	      if_low	s: 3
0.00/0.44	      #if_low	s: []	p: 0
0.00/0.44	      #low	s: []	p: 0
0.00/0.44	      app	s: [2,1]	p: 6
0.00/0.44	    Removed DPs: #8 #14 #15
0.00/0.44	Number of SCCs: 1, DPs: 3
0.00/0.44	  SCC { #2 #4 #6 }
0.00/0.44	POLO(Sum)... POLO(max)... QLPOS... succeeded.
0.00/0.44	      le	s: []	p: 5
0.00/0.44	      s 	s: 1
0.00/0.44	      #le	s: [2]	p: 0
0.00/0.44	      minus	s: 1
0.00/0.44	      if_high	s: 3
0.00/0.44	      #quicksort	s: [1]	p: 0
0.00/0.44	      #high	s: [2]	p: 2
0.00/0.44	      false	s: []	p: 1
0.00/0.44	      #if_high	s: [1,3]	p: 2
0.00/0.44	      quicksort	s: [1]	p: 7
0.00/0.44	      true	s: []	p: 3
0.00/0.44	      rand	s: [1]	p: 0
0.00/0.44	      0 	s: []	p: 4
0.00/0.44	      quot	s: []	p: 4
0.00/0.44	      high	s: 2
0.00/0.44	      nil	s: []	p: 7
0.00/0.44	      #app	s: 1
0.00/0.44	      #minus	s: []	p: 0
0.00/0.44	      low	s: 2
0.00/0.44	      add	s: [1,2]	p: 5
0.00/0.44	      #quot	s: []	p: 1
0.00/0.44	      if_low	s: 3
0.00/0.44	      #if_low	s: [3]	p: 6
0.00/0.44	      #low	s: [2]	p: 6
0.00/0.44	      app	s: [2,1]	p: 6
0.00/0.44	    Removed DPs: #6
0.00/0.44	Number of SCCs: 1, DPs: 2
0.00/0.44	  SCC { #2 #4 }
0.00/0.44	POLO(Sum)... POLO(max)... QLPOS... succeeded.
0.00/0.44	      le	s: []	p: 5
0.00/0.44	      s 	s: 1
0.00/0.44	      #le	s: [2]	p: 0
0.00/0.44	      minus	s: 1
0.00/0.44	      if_high	s: 3
0.00/0.44	      #quicksort	s: [1]	p: 0
0.00/0.44	      #high	s: [2]	p: 2
0.00/0.44	      false	s: []	p: 1
0.00/0.44	      #if_high	s: [1,3]	p: 2
0.00/0.44	      quicksort	s: [1]	p: 7
0.00/0.44	      true	s: []	p: 3
0.00/0.44	      rand	s: [1]	p: 0
0.00/0.44	      0 	s: []	p: 4
0.00/0.44	      quot	s: []	p: 4
0.00/0.44	      high	s: 2
0.00/0.44	      nil	s: []	p: 7
0.00/0.44	      #app	s: 1
0.00/0.44	      #minus	s: []	p: 0
0.00/0.44	      low	s: 2
0.00/0.44	      add	s: [1,2]	p: 5
0.00/0.44	      #quot	s: []	p: 1
0.00/0.44	      if_low	s: 3
0.00/0.44	      #if_low	s: [3]	p: 5
0.00/0.44	      #low	s: [2]	p: 5
0.00/0.44	      app	s: [2,1]	p: 6
0.00/0.44	    Removed DPs: #2
0.00/0.44	Number of SCCs: 0, DPs: 0
0.00/0.44	EOF