Input TRS:
    1: |app'|(|app'|(minus(),x),|0|()) -> x
    2: |app'|(|app'|(minus(),|app'|(s(),x)),|app'|(s(),y)) -> |app'|(|app'|(minus(),x),y)
    3: |app'|(|app'|(quot(),|0|()),|app'|(s(),y)) -> |0|()
    4: |app'|(|app'|(quot(),|app'|(s(),x)),|app'|(s(),y)) -> |app'|(s(),|app'|(|app'|(quot(),|app'|(|app'|(minus(),x),y)),|app'|(s(),y)))
    5: |app'|(|app'|(le(),|0|()),y) -> true()
    6: |app'|(|app'|(le(),|app'|(s(),x)),|0|()) -> false()
    7: |app'|(|app'|(le(),|app'|(s(),x)),|app'|(s(),y)) -> |app'|(|app'|(le(),x),y)
    8: |app'|(|app'|(app(),nil()),y) -> y
    9: |app'|(|app'|(app(),|app'|(|app'|(add(),n),x)),y) -> |app'|(|app'|(add(),n),|app'|(|app'|(app(),x),y))
    10: |app'|(|app'|(low(),n),nil()) -> nil()
    11: |app'|(|app'|(low(),n),|app'|(|app'|(add(),m),x)) -> |app'|(|app'|(|app'|(if_low(),|app'|(|app'|(le(),m),n)),n),|app'|(|app'|(add(),m),x))
    12: |app'|(|app'|(|app'|(if_low(),true()),n),|app'|(|app'|(add(),m),x)) -> |app'|(|app'|(add(),m),|app'|(|app'|(low(),n),x))
    13: |app'|(|app'|(|app'|(if_low(),false()),n),|app'|(|app'|(add(),m),x)) -> |app'|(|app'|(low(),n),x)
    14: |app'|(|app'|(high(),n),nil()) -> nil()
    15: |app'|(|app'|(high(),n),|app'|(|app'|(add(),m),x)) -> |app'|(|app'|(|app'|(if_high(),|app'|(|app'|(le(),m),n)),n),|app'|(|app'|(add(),m),x))
    16: |app'|(|app'|(|app'|(if_high(),true()),n),|app'|(|app'|(add(),m),x)) -> |app'|(|app'|(high(),n),x)
    17: |app'|(|app'|(|app'|(if_high(),false()),n),|app'|(|app'|(add(),m),x)) -> |app'|(|app'|(add(),m),|app'|(|app'|(high(),n),x))
    18: |app'|(quicksort(),nil()) -> nil()
    19: |app'|(quicksort(),|app'|(|app'|(add(),n),x)) -> |app'|(|app'|(app(),|app'|(quicksort(),|app'|(|app'|(low(),n),x))),|app'|(|app'|(add(),n),|app'|(quicksort(),|app'|(|app'|(high(),n),x))))
    20: |app'|(|app'|(map(),f),nil()) -> nil()
    21: |app'|(|app'|(map(),f),|app'|(|app'|(add(),x),xs)) -> |app'|(|app'|(add(),|app'|(f,x)),|app'|(|app'|(map(),f),xs))
    22: |app'|(|app'|(filter(),f),nil()) -> nil()
    23: |app'|(|app'|(filter(),f),|app'|(|app'|(add(),x),xs)) -> |app'|(|app'|(|app'|(|app'|(filter2(),|app'|(f,x)),f),x),xs)
    24: |app'|(|app'|(|app'|(|app'|(filter2(),true()),f),x),xs) -> |app'|(|app'|(add(),x),|app'|(|app'|(filter(),f),xs))
    25: |app'|(|app'|(|app'|(|app'|(filter2(),false()),f),x),xs) -> |app'|(|app'|(filter(),f),xs)
Number of strict rules: 25
Direct Order(PosReal,>,Poly) ... failed.
Freezing |app'|
1: |app'|❆2_minus(x,|0|()) -> x
2: |app'|❆2_minus(|app'|❆1_s(x),|app'|❆1_s(y)) -> |app'|❆2_minus(x,y)
3: |app'|❆2_quot(|0|(),|app'|❆1_s(y)) -> |0|()
4: |app'|❆2_quot(|app'|❆1_s(x),|app'|❆1_s(y)) -> |app'|❆1_s(|app'|❆2_quot(|app'|❆2_minus(x,y),|app'|❆1_s(y)))
5: |app'|❆2_le(|0|(),y) -> true()
6: |app'|❆2_le(|app'|❆1_s(x),|0|()) -> false()
7: |app'|❆2_le(|app'|❆1_s(x),|app'|❆1_s(y)) -> |app'|❆2_le(x,y)
8: |app'|❆2_app(nil(),y) -> y
9: |app'|❆2_app(|app'|❆2_add(n,x),y) -> |app'|❆2_add(n,|app'|❆2_app(x,y))
10: |app'|❆2_low(n,nil()) -> nil()
11: |app'|❆2_low(n,|app'|❆2_add(m,x)) -> |app'|❆3_if_low(|app'|❆2_le(m,n),n,|app'|❆2_add(m,x))
12: |app'|❆3_if_low(true(),n,|app'|❆2_add(m,x)) -> |app'|❆2_add(m,|app'|❆2_low(n,x))
13: |app'|❆3_if_low(false(),n,|app'|❆2_add(m,x)) -> |app'|❆2_low(n,x)
14: |app'|❆2_high(n,nil()) -> nil()
15: |app'|❆2_high(n,|app'|❆2_add(m,x)) -> |app'|❆3_if_high(|app'|❆2_le(m,n),n,|app'|❆2_add(m,x))
16: |app'|❆3_if_high(true(),n,|app'|❆2_add(m,x)) -> |app'|❆2_high(n,x)
17: |app'|❆3_if_high(false(),n,|app'|❆2_add(m,x)) -> |app'|❆2_add(m,|app'|❆2_high(n,x))
18: |app'|❆1_quicksort(nil()) -> nil()
19: |app'|❆1_quicksort(|app'|❆2_add(n,x)) -> |app'|❆2_app(|app'|❆1_quicksort(|app'|❆2_low(n,x)),|app'|❆2_add(n,|app'|❆1_quicksort(|app'|❆2_high(n,x))))
20: |app'|❆2_map(f,nil()) -> nil()
21: |app'|❆2_map(f,|app'|❆2_add(x,xs)) -> |app'|❆2_add(|app'|(f,x),|app'|❆2_map(f,xs))
22: |app'|❆2_filter(f,nil()) -> nil()
23: |app'|❆2_filter(f,|app'|❆2_add(x,xs)) -> |app'|❆4_filter2(|app'|(f,x),f,x,xs)
24: |app'|❆4_filter2(true(),f,x,xs) -> |app'|❆2_add(x,|app'|❆2_filter(f,xs))
25: |app'|❆4_filter2(false(),f,x,xs) -> |app'|❆2_filter(f,xs)
26: |app'|(le(),_1) ->= |app'|❆1_le(_1)
27: |app'|(|app'|❆1_le(_1),_2) ->= |app'|❆2_le(_1,_2)
28: |app'|(quot(),_1) ->= |app'|❆1_quot(_1)
29: |app'|(|app'|❆1_quot(_1),_2) ->= |app'|❆2_quot(_1,_2)
30: |app'|(high(),_1) ->= |app'|❆1_high(_1)
31: |app'|(|app'|❆1_high(_1),_2) ->= |app'|❆2_high(_1,_2)
32: |app'|(add(),_1) ->= |app'|❆1_add(_1)
33: |app'|(|app'|❆1_add(_1),_2) ->= |app'|❆2_add(_1,_2)
34: |app'|(s(),_1) ->= |app'|❆1_s(_1)
35: |app'|(filter(),_1) ->= |app'|❆1_filter(_1)
36: |app'|(|app'|❆1_filter(_1),_2) ->= |app'|❆2_filter(_1,_2)
37: |app'|(if_low(),_1) ->= |app'|❆1_if_low(_1)
38: |app'|(|app'|❆1_if_low(_1),_2) ->= |app'|❆2_if_low(_1,_2)
39: |app'|(|app'|❆2_if_low(_1,_2),_3) ->= |app'|❆3_if_low(_1,_2,_3)
40: |app'|(map(),_1) ->= |app'|❆1_map(_1)
41: |app'|(|app'|❆1_map(_1),_2) ->= |app'|❆2_map(_1,_2)
42: |app'|(minus(),_1) ->= |app'|❆1_minus(_1)
43: |app'|(|app'|❆1_minus(_1),_2) ->= |app'|❆2_minus(_1,_2)
44: |app'|(quicksort(),_1) ->= |app'|❆1_quicksort(_1)
45: |app'|(if_high(),_1) ->= |app'|❆1_if_high(_1)
46: |app'|(|app'|❆1_if_high(_1),_2) ->= |app'|❆2_if_high(_1,_2)
47: |app'|(|app'|❆2_if_high(_1,_2),_3) ->= |app'|❆3_if_high(_1,_2,_3)
48: |app'|(filter2(),_1) ->= |app'|❆1_filter2(_1)
49: |app'|(|app'|❆1_filter2(_1),_2) ->= |app'|❆2_filter2(_1,_2)
50: |app'|(|app'|❆2_filter2(_1,_2),_3) ->= |app'|❆3_filter2(_1,_2,_3)
51: |app'|(|app'|❆3_filter2(_1,_2,_3),_4) ->= |app'|❆4_filter2(_1,_2,_3,_4)
52: |app'|(app(),_1) ->= |app'|❆1_app(_1)
53: |app'|(|app'|❆1_app(_1),_2) ->= |app'|❆2_app(_1,_2)
54: |app'|(low(),_1) ->= |app'|❆1_low(_1)
55: |app'|(|app'|❆1_low(_1),_2) ->= |app'|❆2_low(_1,_2)
Number of strict rules: 25
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #|app'|❆2_minus(|app'|❆1_s(x),|app'|❆1_s(y)) -> #|app'|❆2_minus(x,y)
   #2: #|app'|(|app'|❆1_minus(_1),_2) ->? #|app'|❆2_minus(_1,_2)
   #3: #|app'|(|app'|❆1_quot(_1),_2) ->? #|app'|❆2_quot(_1,_2)
   #4: #|app'|(|app'|❆1_map(_1),_2) ->? #|app'|❆2_map(_1,_2)
   #5: #|app'|(|app'|❆2_if_high(_1,_2),_3) ->? #|app'|❆3_if_high(_1,_2,_3)
   #6: #|app'|(|app'|❆1_app(_1),_2) ->? #|app'|❆2_app(_1,_2)
   #7: #|app'|(|app'|❆1_low(_1),_2) ->? #|app'|❆2_low(_1,_2)
   #8: #|app'|(|app'|❆3_filter2(_1,_2,_3),_4) ->? #|app'|❆4_filter2(_1,_2,_3,_4)
   #9: #|app'|❆3_if_low(false(),n,|app'|❆2_add(m,x)) -> #|app'|❆2_low(n,x)
   #10: #|app'|❆2_app(|app'|❆2_add(n,x),y) -> #|app'|❆2_app(x,y)
   #11: #|app'|❆2_low(n,|app'|❆2_add(m,x)) -> #|app'|❆3_if_low(|app'|❆2_le(m,n),n,|app'|❆2_add(m,x))
   #12: #|app'|❆2_low(n,|app'|❆2_add(m,x)) -> #|app'|❆2_le(m,n)
   #13: #|app'|❆4_filter2(true(),f,x,xs) -> #|app'|❆2_filter(f,xs)
   #14: #|app'|❆2_filter(f,|app'|❆2_add(x,xs)) -> #|app'|❆4_filter2(|app'|(f,x),f,x,xs)
   #15: #|app'|❆2_filter(f,|app'|❆2_add(x,xs)) -> #|app'|(f,x)
   #16: #|app'|❆3_if_low(true(),n,|app'|❆2_add(m,x)) -> #|app'|❆2_low(n,x)
   #17: #|app'|(|app'|❆1_high(_1),_2) ->? #|app'|❆2_high(_1,_2)
   #18: #|app'|❆4_filter2(false(),f,x,xs) -> #|app'|❆2_filter(f,xs)
   #19: #|app'|❆2_le(|app'|❆1_s(x),|app'|❆1_s(y)) -> #|app'|❆2_le(x,y)
   #20: #|app'|(|app'|❆2_if_low(_1,_2),_3) ->? #|app'|❆3_if_low(_1,_2,_3)
   #21: #|app'|(quicksort(),_1) ->? #|app'|❆1_quicksort(_1)
   #22: #|app'|(|app'|❆1_le(_1),_2) ->? #|app'|❆2_le(_1,_2)
   #23: #|app'|❆3_if_high(false(),n,|app'|❆2_add(m,x)) -> #|app'|❆2_high(n,x)
   #24: #|app'|❆1_quicksort(|app'|❆2_add(n,x)) -> #|app'|❆2_app(|app'|❆1_quicksort(|app'|❆2_low(n,x)),|app'|❆2_add(n,|app'|❆1_quicksort(|app'|❆2_high(n,x))))
   #25: #|app'|❆1_quicksort(|app'|❆2_add(n,x)) -> #|app'|❆1_quicksort(|app'|❆2_low(n,x))
   #26: #|app'|❆1_quicksort(|app'|❆2_add(n,x)) -> #|app'|❆2_low(n,x)
   #27: #|app'|❆1_quicksort(|app'|❆2_add(n,x)) -> #|app'|❆1_quicksort(|app'|❆2_high(n,x))
   #28: #|app'|❆1_quicksort(|app'|❆2_add(n,x)) -> #|app'|❆2_high(n,x)
   #29: #|app'|(|app'|❆1_filter(_1),_2) ->? #|app'|❆2_filter(_1,_2)
   #30: #|app'|❆2_map(f,|app'|❆2_add(x,xs)) -> #|app'|(f,x)
   #31: #|app'|❆2_map(f,|app'|❆2_add(x,xs)) -> #|app'|❆2_map(f,xs)
   #32: #|app'|❆3_if_high(true(),n,|app'|❆2_add(m,x)) -> #|app'|❆2_high(n,x)
   #33: #|app'|❆2_high(n,|app'|❆2_add(m,x)) -> #|app'|❆3_if_high(|app'|❆2_le(m,n),n,|app'|❆2_add(m,x))
   #34: #|app'|❆2_high(n,|app'|❆2_add(m,x)) -> #|app'|❆2_le(m,n)
   #35: #|app'|❆2_quot(|app'|❆1_s(x),|app'|❆1_s(y)) -> #|app'|❆2_quot(|app'|❆2_minus(x,y),|app'|❆1_s(y))
   #36: #|app'|❆2_quot(|app'|❆1_s(x),|app'|❆1_s(y)) -> #|app'|❆2_minus(x,y)
Number of SCCs: 8, DPs: 21, edges: 36
	SCC { #19 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: 0
|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
     s()	weight: 0
|app'|❆1_map(x1)	weight: 0
|app'|❆1_minus(x1)	weight: 0
 minus()	weight: 0
|app'|❆2_add(x1,x2)	weight: 0
|app'|❆1_quicksort(x1)	weight: 0
if_high()	weight: 0
|app'|❆1_if_high(x1)	weight: 0
#|app'|❆2_le(x1,x2)	weight: x2
|app'|❆2_if_high(x1,x2)	weight: 0
|app'|❆2_filter(x1,x2)	weight: 0
#|app'|❆2_low(x1,x2)	weight: 0
#|app'|❆3_if_low(x1,x2,x3)	weight: 0
 false()	weight: 0
|app'|(x1,x2)	weight: 0
|app'|❆1_filter2(x1)	weight: 0
#|app'|❆2_app(x1,x2)	weight: 0
#|app'|❆3_if_high(x1,x2,x3)	weight: 0
|app'|❆3_if_high(x1,x2,x3)	weight: 0
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
|app'|❆2_low(x1,x2)	weight: 0
quicksort()	weight: 0
  true()	weight: 0
|app'|❆1_quot(x1)	weight: 0
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: 0
#|app'|❆2_quot(x1,x2)	weight: 0
|app'|❆2_quot(x1,x2)	weight: 0
  quot()	weight: 0
  high()	weight: 0
|app'|❆2_filter2(x1,x2)	weight: 0
|app'|❆1_le(x1)	weight: 0
|app'|❆1_if_low(x1)	weight: 0
|app'|❆2_map(x1,x2)	weight: 0
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: 0
|app'|❆1_app(x1)	weight: 0
|app'|❆2_high(x1,x2)	weight: 0
#|app'|❆2_high(x1,x2)	weight: 0
   map()	weight: 0
|app'|❆2_minus(x1,x2)	weight: 0
|app'|❆3_if_low(x1,x2,x3)	weight: 0
|app'|❆1_filter(x1)	weight: 0
   low()	weight: 0
#|app'|❆2_minus(x1,x2)	weight: 0
|app'|❆1_s(x1)	weight: (/ 1 2) + x1
|app'|❆2_if_low(x1,x2)	weight: 0
#|app'|❆1_quicksort(x1)	weight: 0
   add()	weight: 0
filter()	weight: 0
|app'|❆2_app(x1,x2)	weight: 0
if_low()	weight: 0
|app'|❆1_high(x1)	weight: 0
|app'|❆1_add(x1)	weight: 0
|app'|❆1_low(x1)	weight: 0
#|app'|❆2_map(x1,x2)	weight: 0
   app()	weight: 0
    Usable rules: { }
    Removed DPs: #19
Number of SCCs: 7, DPs: 20, edges: 35
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: 0
|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
     s()	weight: 0
|app'|❆1_map(x1)	weight: 0
|app'|❆1_minus(x1)	weight: 0
 minus()	weight: 0
|app'|❆2_add(x1,x2)	weight: 0
|app'|❆1_quicksort(x1)	weight: 0
if_high()	weight: 0
|app'|❆1_if_high(x1)	weight: 0
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆2_if_high(x1,x2)	weight: 0
|app'|❆2_filter(x1,x2)	weight: 0
#|app'|❆2_low(x1,x2)	weight: 0
#|app'|❆3_if_low(x1,x2,x3)	weight: 0
 false()	weight: 0
|app'|(x1,x2)	weight: 0
|app'|❆1_filter2(x1)	weight: 0
#|app'|❆2_app(x1,x2)	weight: 0
#|app'|❆3_if_high(x1,x2,x3)	weight: 0
|app'|❆3_if_high(x1,x2,x3)	weight: 0
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
|app'|❆2_low(x1,x2)	weight: 0
quicksort()	weight: 0
  true()	weight: 0
|app'|❆1_quot(x1)	weight: 0
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: 0
#|app'|❆2_quot(x1,x2)	weight: 0
|app'|❆2_quot(x1,x2)	weight: 0
  quot()	weight: 0
  high()	weight: 0
|app'|❆2_filter2(x1,x2)	weight: 0
|app'|❆1_le(x1)	weight: 0
|app'|❆1_if_low(x1)	weight: 0
|app'|❆2_map(x1,x2)	weight: 0
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: 0
|app'|❆1_app(x1)	weight: 0
|app'|❆2_high(x1,x2)	weight: 0
#|app'|❆2_high(x1,x2)	weight: 0
   map()	weight: 0
|app'|❆2_minus(x1,x2)	weight: 0
|app'|❆3_if_low(x1,x2,x3)	weight: 0
|app'|❆1_filter(x1)	weight: 0
   low()	weight: 0
#|app'|❆2_minus(x1,x2)	weight: x2
|app'|❆1_s(x1)	weight: (/ 1 2) + x1
|app'|❆2_if_low(x1,x2)	weight: 0
#|app'|❆1_quicksort(x1)	weight: 0
   add()	weight: 0
filter()	weight: 0
|app'|❆2_app(x1,x2)	weight: 0
if_low()	weight: 0
|app'|❆1_high(x1)	weight: 0
|app'|❆1_add(x1)	weight: 0
|app'|❆1_low(x1)	weight: 0
#|app'|❆2_map(x1,x2)	weight: 0
   app()	weight: 0
    Usable rules: { }
    Removed DPs: #1
Number of SCCs: 6, DPs: 19, edges: 34
	SCC { #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: 0
|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
     s()	weight: 0
|app'|❆1_map(x1)	weight: 0
|app'|❆1_minus(x1)	weight: 0
 minus()	weight: 0
|app'|❆2_add(x1,x2)	weight: (/ 1 2) + x2
|app'|❆1_quicksort(x1)	weight: 0
if_high()	weight: 0
|app'|❆1_if_high(x1)	weight: 0
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆2_if_high(x1,x2)	weight: 0
|app'|❆2_filter(x1,x2)	weight: 0
#|app'|❆2_low(x1,x2)	weight: 0
#|app'|❆3_if_low(x1,x2,x3)	weight: 0
 false()	weight: 0
|app'|(x1,x2)	weight: 0
|app'|❆1_filter2(x1)	weight: 0
#|app'|❆2_app(x1,x2)	weight: x1
#|app'|❆3_if_high(x1,x2,x3)	weight: 0
|app'|❆3_if_high(x1,x2,x3)	weight: 0
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
|app'|❆2_low(x1,x2)	weight: 0
quicksort()	weight: 0
  true()	weight: 0
|app'|❆1_quot(x1)	weight: 0
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: 0
#|app'|❆2_quot(x1,x2)	weight: 0
|app'|❆2_quot(x1,x2)	weight: 0
  quot()	weight: 0
  high()	weight: 0
|app'|❆2_filter2(x1,x2)	weight: 0
|app'|❆1_le(x1)	weight: 0
|app'|❆1_if_low(x1)	weight: 0
|app'|❆2_map(x1,x2)	weight: 0
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: 0
|app'|❆1_app(x1)	weight: 0
|app'|❆2_high(x1,x2)	weight: 0
#|app'|❆2_high(x1,x2)	weight: 0
   map()	weight: 0
|app'|❆2_minus(x1,x2)	weight: 0
|app'|❆3_if_low(x1,x2,x3)	weight: 0
|app'|❆1_filter(x1)	weight: 0
   low()	weight: 0
#|app'|❆2_minus(x1,x2)	weight: 0
|app'|❆1_s(x1)	weight: (/ 1 2)
|app'|❆2_if_low(x1,x2)	weight: 0
#|app'|❆1_quicksort(x1)	weight: 0
   add()	weight: 0
filter()	weight: 0
|app'|❆2_app(x1,x2)	weight: 0
if_low()	weight: 0
|app'|❆1_high(x1)	weight: 0
|app'|❆1_add(x1)	weight: 0
|app'|❆1_low(x1)	weight: 0
#|app'|❆2_map(x1,x2)	weight: 0
   app()	weight: 0
    Usable rules: { }
    Removed DPs: #10
Number of SCCs: 5, DPs: 18, edges: 33
	SCC { #35 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: 0
|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
     s()	weight: 0
|app'|❆1_map(x1)	weight: 0
|app'|❆1_minus(x1)	weight: 0
 minus()	weight: 0
|app'|❆2_add(x1,x2)	weight: (/ 1 4)
|app'|❆1_quicksort(x1)	weight: 0
if_high()	weight: 0
|app'|❆1_if_high(x1)	weight: 0
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆2_if_high(x1,x2)	weight: 0
|app'|❆2_filter(x1,x2)	weight: 0
#|app'|❆2_low(x1,x2)	weight: 0
#|app'|❆3_if_low(x1,x2,x3)	weight: 0
 false()	weight: 0
|app'|(x1,x2)	weight: 0
|app'|❆1_filter2(x1)	weight: 0
#|app'|❆2_app(x1,x2)	weight: 0
#|app'|❆3_if_high(x1,x2,x3)	weight: 0
|app'|❆3_if_high(x1,x2,x3)	weight: 0
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
|app'|❆2_low(x1,x2)	weight: 0
quicksort()	weight: 0
  true()	weight: 0
|app'|❆1_quot(x1)	weight: 0
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: 0
#|app'|❆2_quot(x1,x2)	weight: x1
|app'|❆2_quot(x1,x2)	weight: 0
  quot()	weight: 0
  high()	weight: 0
|app'|❆2_filter2(x1,x2)	weight: 0
|app'|❆1_le(x1)	weight: 0
|app'|❆1_if_low(x1)	weight: 0
|app'|❆2_map(x1,x2)	weight: 0
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: 0
|app'|❆1_app(x1)	weight: 0
|app'|❆2_high(x1,x2)	weight: 0
#|app'|❆2_high(x1,x2)	weight: 0
   map()	weight: 0
|app'|❆2_minus(x1,x2)	weight: (/ 1 4) + x1
|app'|❆3_if_low(x1,x2,x3)	weight: 0
|app'|❆1_filter(x1)	weight: 0
   low()	weight: 0
#|app'|❆2_minus(x1,x2)	weight: 0
|app'|❆1_s(x1)	weight: (/ 1 2) + x1
|app'|❆2_if_low(x1,x2)	weight: 0
#|app'|❆1_quicksort(x1)	weight: 0
   add()	weight: 0
filter()	weight: 0
|app'|❆2_app(x1,x2)	weight: 0
if_low()	weight: 0
|app'|❆1_high(x1)	weight: 0
|app'|❆1_add(x1)	weight: 0
|app'|❆1_low(x1)	weight: 0
#|app'|❆2_map(x1,x2)	weight: 0
   app()	weight: 0
    Usable rules: { 1 2 }
    Removed DPs: #35
Number of SCCs: 4, DPs: 17, edges: 32
	SCC { #25 #27 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: 0
|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
     s()	weight: 0
|app'|❆1_map(x1)	weight: 0
|app'|❆1_minus(x1)	weight: 0
 minus()	weight: 0
|app'|❆2_add(x1,x2)	weight: (/ 1 2) + x1 + x2
|app'|❆1_quicksort(x1)	weight: 0
if_high()	weight: 0
|app'|❆1_if_high(x1)	weight: 0
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆2_if_high(x1,x2)	weight: 0
|app'|❆2_filter(x1,x2)	weight: 0
#|app'|❆2_low(x1,x2)	weight: 0
#|app'|❆3_if_low(x1,x2,x3)	weight: 0
 false()	weight: 0
|app'|(x1,x2)	weight: 0
|app'|❆1_filter2(x1)	weight: 0
#|app'|❆2_app(x1,x2)	weight: 0
#|app'|❆3_if_high(x1,x2,x3)	weight: 0
|app'|❆3_if_high(x1,x2,x3)	weight: (/ 1 4) + x3
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
|app'|❆2_low(x1,x2)	weight: (/ 1 4) + x2
quicksort()	weight: 0
  true()	weight: 0
|app'|❆1_quot(x1)	weight: 0
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: (/ 1 4)
#|app'|❆2_quot(x1,x2)	weight: x1
|app'|❆2_quot(x1,x2)	weight: 0
  quot()	weight: 0
  high()	weight: 0
|app'|❆2_filter2(x1,x2)	weight: 0
|app'|❆1_le(x1)	weight: 0
|app'|❆1_if_low(x1)	weight: 0
|app'|❆2_map(x1,x2)	weight: 0
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: 0
|app'|❆1_app(x1)	weight: 0
|app'|❆2_high(x1,x2)	weight: (/ 1 4) + x2
#|app'|❆2_high(x1,x2)	weight: 0
   map()	weight: 0
|app'|❆2_minus(x1,x2)	weight: (/ 1 4) + x1
|app'|❆3_if_low(x1,x2,x3)	weight: (/ 1 4) + x3
|app'|❆1_filter(x1)	weight: 0
   low()	weight: 0
#|app'|❆2_minus(x1,x2)	weight: 0
|app'|❆1_s(x1)	weight: (/ 1 4) + x1
|app'|❆2_if_low(x1,x2)	weight: 0
#|app'|❆1_quicksort(x1)	weight: x1
   add()	weight: 0
filter()	weight: 0
|app'|❆2_app(x1,x2)	weight: 0
if_low()	weight: 0
|app'|❆1_high(x1)	weight: 0
|app'|❆1_add(x1)	weight: 0
|app'|❆1_low(x1)	weight: 0
#|app'|❆2_map(x1,x2)	weight: 0
   app()	weight: 0
    Usable rules: { 10..17 }
    Removed DPs: #25 #27
Number of SCCs: 3, DPs: 15, edges: 28
	SCC { #9 #11 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: 0
|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
     s()	weight: 0
|app'|❆1_map(x1)	weight: 0
|app'|❆1_minus(x1)	weight: 0
 minus()	weight: 0
|app'|❆2_add(x1,x2)	weight: (/ 1 2) + x1 + x2
|app'|❆1_quicksort(x1)	weight: 0
if_high()	weight: 0
|app'|❆1_if_high(x1)	weight: 0
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆2_if_high(x1,x2)	weight: 0
|app'|❆2_filter(x1,x2)	weight: 0
#|app'|❆2_low(x1,x2)	weight: (/ 1 4) + x2
#|app'|❆3_if_low(x1,x2,x3)	weight: x3
 false()	weight: 0
|app'|(x1,x2)	weight: 0
|app'|❆1_filter2(x1)	weight: 0
#|app'|❆2_app(x1,x2)	weight: 0
#|app'|❆3_if_high(x1,x2,x3)	weight: 0
|app'|❆3_if_high(x1,x2,x3)	weight: (/ 1 4) + x3
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
|app'|❆2_low(x1,x2)	weight: (/ 1 4) + x2
quicksort()	weight: 0
  true()	weight: 0
|app'|❆1_quot(x1)	weight: 0
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: (/ 1 4)
#|app'|❆2_quot(x1,x2)	weight: x1
|app'|❆2_quot(x1,x2)	weight: 0
  quot()	weight: 0
  high()	weight: 0
|app'|❆2_filter2(x1,x2)	weight: 0
|app'|❆1_le(x1)	weight: 0
|app'|❆1_if_low(x1)	weight: 0
|app'|❆2_map(x1,x2)	weight: 0
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: 0
|app'|❆1_app(x1)	weight: 0
|app'|❆2_high(x1,x2)	weight: (/ 1 4) + x2
#|app'|❆2_high(x1,x2)	weight: 0
   map()	weight: 0
|app'|❆2_minus(x1,x2)	weight: (/ 1 4) + x1
|app'|❆3_if_low(x1,x2,x3)	weight: (/ 1 4) + x3
|app'|❆1_filter(x1)	weight: 0
   low()	weight: 0
#|app'|❆2_minus(x1,x2)	weight: 0
|app'|❆1_s(x1)	weight: (/ 1 4) + x1
|app'|❆2_if_low(x1,x2)	weight: 0
#|app'|❆1_quicksort(x1)	weight: x1
   add()	weight: 0
filter()	weight: 0
|app'|❆2_app(x1,x2)	weight: 0
if_low()	weight: 0
|app'|❆1_high(x1)	weight: 0
|app'|❆1_add(x1)	weight: 0
|app'|❆1_low(x1)	weight: 0
#|app'|❆2_map(x1,x2)	weight: 0
   app()	weight: 0
    Usable rules: { }
    Removed DPs: #9 #11 #16
Number of SCCs: 2, DPs: 12, edges: 24
	SCC { #23 #32 #33 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: 0
|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
     s()	weight: 0
|app'|❆1_map(x1)	weight: 0
|app'|❆1_minus(x1)	weight: 0
 minus()	weight: 0
|app'|❆2_add(x1,x2)	weight: (/ 1 2) + x1 + x2
|app'|❆1_quicksort(x1)	weight: 0
if_high()	weight: 0
|app'|❆1_if_high(x1)	weight: 0
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆2_if_high(x1,x2)	weight: 0
|app'|❆2_filter(x1,x2)	weight: 0
#|app'|❆2_low(x1,x2)	weight: (/ 1 4)
#|app'|❆3_if_low(x1,x2,x3)	weight: 0
 false()	weight: 0
|app'|(x1,x2)	weight: 0
|app'|❆1_filter2(x1)	weight: 0
#|app'|❆2_app(x1,x2)	weight: 0
#|app'|❆3_if_high(x1,x2,x3)	weight: x3
|app'|❆3_if_high(x1,x2,x3)	weight: (/ 1 4) + x3
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: 0
|app'|❆2_low(x1,x2)	weight: (/ 1 4) + x2
quicksort()	weight: 0
  true()	weight: 0
|app'|❆1_quot(x1)	weight: 0
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: (/ 1 4)
#|app'|❆2_quot(x1,x2)	weight: x1
|app'|❆2_quot(x1,x2)	weight: 0
  quot()	weight: 0
  high()	weight: 0
|app'|❆2_filter2(x1,x2)	weight: 0
|app'|❆1_le(x1)	weight: 0
|app'|❆1_if_low(x1)	weight: 0
|app'|❆2_map(x1,x2)	weight: 0
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: 0
|app'|❆1_app(x1)	weight: 0
|app'|❆2_high(x1,x2)	weight: (/ 1 4) + x2
#|app'|❆2_high(x1,x2)	weight: (/ 1 4) + x2
   map()	weight: 0
|app'|❆2_minus(x1,x2)	weight: (/ 1 4) + x1
|app'|❆3_if_low(x1,x2,x3)	weight: (/ 1 4) + x3
|app'|❆1_filter(x1)	weight: 0
   low()	weight: 0
#|app'|❆2_minus(x1,x2)	weight: 0
|app'|❆1_s(x1)	weight: (/ 1 4) + x1
|app'|❆2_if_low(x1,x2)	weight: 0
#|app'|❆1_quicksort(x1)	weight: x1
   add()	weight: 0
filter()	weight: 0
|app'|❆2_app(x1,x2)	weight: 0
if_low()	weight: 0
|app'|❆1_high(x1)	weight: 0
|app'|❆1_add(x1)	weight: 0
|app'|❆1_low(x1)	weight: 0
#|app'|❆2_map(x1,x2)	weight: 0
   app()	weight: 0
    Usable rules: { 5..7 }
    Removed DPs: #23 #32 #33
Number of SCCs: 1, DPs: 9, edges: 20
	SCC { #4 #8 #13..15 #18 #29..31 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: x1
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: (/ 3 8) + x2
|app'|❆4_filter2(x1,x2,x3,x4)	weight: (/ 3 8) + x1
     s()	weight: 0
|app'|❆1_map(x1)	weight: (/ 3 8) + x1
|app'|❆1_minus(x1)	weight: (/ 3 8)
 minus()	weight: 0
|app'|❆2_add(x1,x2)	weight: (/ 3 8) + x1 + x2
|app'|❆1_quicksort(x1)	weight: (/ 3 8) + x1
if_high()	weight: 0
|app'|❆1_if_high(x1)	weight: (/ 3 8)
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆2_if_high(x1,x2)	weight: (/ 3 8) + x1
|app'|❆2_filter(x1,x2)	weight: (/ 1 2) + x1
#|app'|❆2_low(x1,x2)	weight: (/ 1 8)
#|app'|❆3_if_low(x1,x2,x3)	weight: 0
 false()	weight: 0
|app'|(x1,x2)	weight: (/ 1 4) + x2
|app'|❆1_filter2(x1)	weight: (/ 3 8)
#|app'|❆2_app(x1,x2)	weight: 0
#|app'|❆3_if_high(x1,x2,x3)	weight: 0
|app'|❆3_if_high(x1,x2,x3)	weight: (/ 3 8) + x3
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: (/ 1 8) + x2
|app'|❆2_low(x1,x2)	weight: (/ 3 8) + x2
quicksort()	weight: 0
  true()	weight: 0
|app'|❆1_quot(x1)	weight: (/ 3 8)
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: (/ 3 8)
#|app'|❆2_quot(x1,x2)	weight: x1
|app'|❆2_quot(x1,x2)	weight: (/ 3 8)
  quot()	weight: 0
  high()	weight: 0
|app'|❆2_filter2(x1,x2)	weight: (/ 3 8) + x1
|app'|❆1_le(x1)	weight: (/ 3 8)
|app'|❆1_if_low(x1)	weight: (/ 3 8)
|app'|❆2_map(x1,x2)	weight: (/ 3 8) + x1
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: (/ 1 8) + x1
|app'|❆1_app(x1)	weight: (/ 3 8)
|app'|❆2_high(x1,x2)	weight: (/ 3 8) + x2
#|app'|❆2_high(x1,x2)	weight: (/ 1 8)
   map()	weight: 0
|app'|❆2_minus(x1,x2)	weight: (/ 3 8) + x1
|app'|❆3_if_low(x1,x2,x3)	weight: (/ 3 8) + x3
|app'|❆1_filter(x1)	weight: (/ 3 8) + x1
   low()	weight: 0
#|app'|❆2_minus(x1,x2)	weight: 0
|app'|❆1_s(x1)	weight: (/ 3 8) + x1
|app'|❆2_if_low(x1,x2)	weight: (/ 3 8) + x1
#|app'|❆1_quicksort(x1)	weight: x1
   add()	weight: 0
filter()	weight: 0
|app'|❆2_app(x1,x2)	weight: (/ 7 8)
if_low()	weight: 0
|app'|❆1_high(x1)	weight: (/ 3 8)
|app'|❆1_add(x1)	weight: (/ 3 8)
|app'|❆1_low(x1)	weight: (/ 3 8)
#|app'|❆2_map(x1,x2)	weight: (/ 1 8) + x1
   app()	weight: 0
    Usable rules: { 1..3 10..18 }
    Removed DPs: #4 #8 #15 #29 #30
Number of SCCs: 2, DPs: 4, edges: 5
	SCC { #31 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: (/ 3 8) + x2
|app'|❆4_filter2(x1,x2,x3,x4)	weight: (/ 3 8) + x1
     s()	weight: 0
|app'|❆1_map(x1)	weight: (/ 3 8) + x1
|app'|❆1_minus(x1)	weight: (/ 3 8)
 minus()	weight: 0
|app'|❆2_add(x1,x2)	weight: (/ 3 8) + x1 + x2
|app'|❆1_quicksort(x1)	weight: (/ 3 8) + x1
if_high()	weight: 0
|app'|❆1_if_high(x1)	weight: (/ 3 8)
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆2_if_high(x1,x2)	weight: (/ 3 8) + x1
|app'|❆2_filter(x1,x2)	weight: (/ 1 2) + x1
#|app'|❆2_low(x1,x2)	weight: (/ 1 8)
#|app'|❆3_if_low(x1,x2,x3)	weight: 0
 false()	weight: 0
|app'|(x1,x2)	weight: (/ 1 4) + x2
|app'|❆1_filter2(x1)	weight: (/ 3 8)
#|app'|❆2_app(x1,x2)	weight: 0
#|app'|❆3_if_high(x1,x2,x3)	weight: 0
|app'|❆3_if_high(x1,x2,x3)	weight: (/ 3 8) + x3
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: (/ 1 8)
|app'|❆2_low(x1,x2)	weight: (/ 3 8) + x2
quicksort()	weight: 0
  true()	weight: 0
|app'|❆1_quot(x1)	weight: (/ 3 8)
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: (/ 3 8)
#|app'|❆2_quot(x1,x2)	weight: x1
|app'|❆2_quot(x1,x2)	weight: (/ 3 8)
  quot()	weight: 0
  high()	weight: 0
|app'|❆2_filter2(x1,x2)	weight: (/ 3 8) + x1
|app'|❆1_le(x1)	weight: (/ 3 8)
|app'|❆1_if_low(x1)	weight: (/ 3 8)
|app'|❆2_map(x1,x2)	weight: (/ 3 8) + x1
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: (/ 1 8)
|app'|❆1_app(x1)	weight: (/ 3 8)
|app'|❆2_high(x1,x2)	weight: (/ 3 8) + x2
#|app'|❆2_high(x1,x2)	weight: (/ 1 8)
   map()	weight: 0
|app'|❆2_minus(x1,x2)	weight: (/ 3 8) + x1
|app'|❆3_if_low(x1,x2,x3)	weight: (/ 3 8) + x3
|app'|❆1_filter(x1)	weight: (/ 3 8) + x1
   low()	weight: 0
#|app'|❆2_minus(x1,x2)	weight: 0
|app'|❆1_s(x1)	weight: (/ 3 8) + x1
|app'|❆2_if_low(x1,x2)	weight: (/ 3 8) + x1
#|app'|❆1_quicksort(x1)	weight: x1
   add()	weight: 0
filter()	weight: 0
|app'|❆2_app(x1,x2)	weight: (/ 7 8)
if_low()	weight: 0
|app'|❆1_high(x1)	weight: (/ 3 8)
|app'|❆1_add(x1)	weight: (/ 3 8)
|app'|❆1_low(x1)	weight: (/ 3 8)
#|app'|❆2_map(x1,x2)	weight: (/ 1 8) + x2
   app()	weight: 0
    Usable rules: { }
    Removed DPs: #31
Number of SCCs: 1, DPs: 3, edges: 4
	SCC { #13 #14 #18 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   |0|()	weight: 0
#|app'|(x1,x2)	weight: 0
    le()	weight: 0
|app'|❆3_filter2(x1,x2,x3)	weight: (/ 3 8) + x2
|app'|❆4_filter2(x1,x2,x3,x4)	weight: (/ 3 8) + x1
     s()	weight: 0
|app'|❆1_map(x1)	weight: (/ 3 8) + x1
|app'|❆1_minus(x1)	weight: (/ 3 8)
 minus()	weight: 0
|app'|❆2_add(x1,x2)	weight: (/ 3 8) + x1 + x2
|app'|❆1_quicksort(x1)	weight: (/ 3 8) + x1
if_high()	weight: 0
|app'|❆1_if_high(x1)	weight: (/ 3 8)
#|app'|❆2_le(x1,x2)	weight: 0
|app'|❆2_if_high(x1,x2)	weight: (/ 3 8) + x1
|app'|❆2_filter(x1,x2)	weight: (/ 1 2) + x1
#|app'|❆2_low(x1,x2)	weight: (/ 1 8)
#|app'|❆3_if_low(x1,x2,x3)	weight: 0
 false()	weight: 0
|app'|(x1,x2)	weight: (/ 1 4) + x2
|app'|❆1_filter2(x1)	weight: (/ 3 8)
#|app'|❆2_app(x1,x2)	weight: 0
#|app'|❆3_if_high(x1,x2,x3)	weight: 0
|app'|❆3_if_high(x1,x2,x3)	weight: (/ 3 8) + x3
#|app'|❆4_filter2(x1,x2,x3,x4)	weight: (/ 1 4) + x2 + x4
|app'|❆2_low(x1,x2)	weight: (/ 3 8) + x2
quicksort()	weight: 0
  true()	weight: 0
|app'|❆1_quot(x1)	weight: (/ 3 8)
filter2()	weight: 0
|app'|❆2_le(x1,x2)	weight: (/ 3 8)
#|app'|❆2_quot(x1,x2)	weight: x1
|app'|❆2_quot(x1,x2)	weight: (/ 3 8)
  quot()	weight: 0
  high()	weight: 0
|app'|❆2_filter2(x1,x2)	weight: (/ 3 8) + x1
|app'|❆1_le(x1)	weight: (/ 3 8)
|app'|❆1_if_low(x1)	weight: (/ 3 8)
|app'|❆2_map(x1,x2)	weight: (/ 3 8) + x1
   nil()	weight: 0
#|app'|❆2_filter(x1,x2)	weight: (/ 1 8) + x1 + x2
|app'|❆1_app(x1)	weight: (/ 3 8)
|app'|❆2_high(x1,x2)	weight: (/ 3 8) + x2
#|app'|❆2_high(x1,x2)	weight: (/ 1 8)
   map()	weight: 0
|app'|❆2_minus(x1,x2)	weight: (/ 3 8) + x1
|app'|❆3_if_low(x1,x2,x3)	weight: (/ 3 8) + x3
|app'|❆1_filter(x1)	weight: (/ 3 8) + x1
   low()	weight: 0
#|app'|❆2_minus(x1,x2)	weight: 0
|app'|❆1_s(x1)	weight: (/ 3 8) + x1
|app'|❆2_if_low(x1,x2)	weight: (/ 3 8) + x1
#|app'|❆1_quicksort(x1)	weight: x1
   add()	weight: 0
filter()	weight: 0
|app'|❆2_app(x1,x2)	weight: (/ 7 8)
if_low()	weight: 0
|app'|❆1_high(x1)	weight: (/ 3 8)
|app'|❆1_add(x1)	weight: (/ 3 8)
|app'|❆1_low(x1)	weight: (/ 3 8)
#|app'|❆2_map(x1,x2)	weight: (/ 1 8)
   app()	weight: 0
    Usable rules: { 1..3 10..18 }
    Removed DPs: #13 #14 #18
Number of SCCs: 0, DPs: 0, edges: 0
YES