Input TRS:
    1: app(app(app(if(),true()),x),y) -> x
    2: app(app(app(if(),true()),x),y) -> y
    3: app(app(takeWhile(),p),nil()) -> nil()
    4: app(app(takeWhile(),p),app(app(cons(),x),xs)) -> app(app(app(if(),app(p,x)),app(app(cons(),x),app(app(takeWhile(),p),xs))),nil())
    5: app(app(dropWhile(),p),nil()) -> nil()
    6: app(app(dropWhile(),p),app(app(cons(),x),xs)) -> app(app(app(if(),app(p,x)),app(app(dropWhile(),p),xs)),app(app(cons(),x),xs))
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... failed.
Freezing app
1: app❆3_if(true(),x,y) -> x
2: app❆3_if(true(),x,y) -> y
3: app❆2_takeWhile(p,nil()) -> nil()
4: app❆2_takeWhile(p,app❆2_cons(x,xs)) -> app❆3_if(app(p,x),app❆2_cons(x,app❆2_takeWhile(p,xs)),nil())
5: app❆2_dropWhile(p,nil()) -> nil()
6: app❆2_dropWhile(p,app❆2_cons(x,xs)) -> app❆3_if(app(p,x),app❆2_dropWhile(p,xs),app❆2_cons(x,xs))
7: app(if(),_1) ->= app❆1_if(_1)
8: app(app❆1_if(_1),_2) ->= app❆2_if(_1,_2)
9: app(app❆2_if(_1,_2),_3) ->= app❆3_if(_1,_2,_3)
10: app(cons(),_1) ->= app❆1_cons(_1)
11: app(app❆1_cons(_1),_2) ->= app❆2_cons(_1,_2)
12: app(dropWhile(),_1) ->= app❆1_dropWhile(_1)
13: app(app❆1_dropWhile(_1),_2) ->= app❆2_dropWhile(_1,_2)
14: app(takeWhile(),_1) ->= app❆1_takeWhile(_1)
15: app(app❆1_takeWhile(_1),_2) ->= app❆2_takeWhile(_1,_2)
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #app❆2_dropWhile(p,app❆2_cons(x,xs)) -> #app❆3_if(app(p,x),app❆2_dropWhile(p,xs),app❆2_cons(x,xs))
   #2: #app❆2_dropWhile(p,app❆2_cons(x,xs)) -> #app(p,x)
   #3: #app❆2_dropWhile(p,app❆2_cons(x,xs)) -> #app❆2_dropWhile(p,xs)
   #4: #app(app❆1_dropWhile(_1),_2) ->? #app❆2_dropWhile(_1,_2)
   #5: #app(app❆2_if(_1,_2),_3) ->? #app❆3_if(_1,_2,_3)
   #6: #app(app❆1_takeWhile(_1),_2) ->? #app❆2_takeWhile(_1,_2)
   #7: #app❆2_takeWhile(p,app❆2_cons(x,xs)) -> #app❆3_if(app(p,x),app❆2_cons(x,app❆2_takeWhile(p,xs)),nil())
   #8: #app❆2_takeWhile(p,app❆2_cons(x,xs)) -> #app(p,x)
   #9: #app❆2_takeWhile(p,app❆2_cons(x,xs)) -> #app❆2_takeWhile(p,xs)
Number of SCCs: 1, DPs: 6, edges: 12
	SCC { #2..4 #6 #8 #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#app❆2_dropWhile(x1,x2)	weight: (/ 1 4) + x1
app❆1_if(x1)	weight: 0
app❆2_takeWhile(x1,x2)	weight: 0
#app❆3_if(x1,x2,x3)	weight: 0
app❆2_dropWhile(x1,x2)	weight: 0
app❆1_takeWhile(x1)	weight: (/ 1 2) + x1
app❆2_if(x1,x2)	weight: 0
  true()	weight: 0
takeWhile()	weight: 0
    if()	weight: 0
   nil()	weight: 0
app❆3_if(x1,x2,x3)	weight: 0
 #app(x1,x2)	weight: x1
app❆1_dropWhile(x1)	weight: (/ 1 2) + x1
#app❆2_takeWhile(x1,x2)	weight: (/ 1 4) + x1
  cons()	weight: 0
app❆2_cons(x1,x2)	weight: (/ 1 4)
app❆1_cons(x1)	weight: 0
dropWhile()	weight: 0
   app(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #2 #4 #6 #8
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#app❆2_dropWhile(x1,x2)	weight: (/ 1 4) + x2
app❆1_if(x1)	weight: 0
app❆2_takeWhile(x1,x2)	weight: 0
#app❆3_if(x1,x2,x3)	weight: 0
app❆2_dropWhile(x1,x2)	weight: 0
app❆1_takeWhile(x1)	weight: (/ 1 2)
app❆2_if(x1,x2)	weight: 0
  true()	weight: 0
takeWhile()	weight: 0
    if()	weight: 0
   nil()	weight: 0
app❆3_if(x1,x2,x3)	weight: 0
 #app(x1,x2)	weight: 0
app❆1_dropWhile(x1)	weight: (/ 1 2)
#app❆2_takeWhile(x1,x2)	weight: (/ 1 4)
  cons()	weight: 0
app❆2_cons(x1,x2)	weight: (/ 1 4) + x2
app❆1_cons(x1)	weight: 0
dropWhile()	weight: 0
   app(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#app❆2_dropWhile(x1,x2)	weight: (/ 1 4)
app❆1_if(x1)	weight: 0
app❆2_takeWhile(x1,x2)	weight: 0
#app❆3_if(x1,x2,x3)	weight: 0
app❆2_dropWhile(x1,x2)	weight: 0
app❆1_takeWhile(x1)	weight: (/ 1 2)
app❆2_if(x1,x2)	weight: 0
  true()	weight: 0
takeWhile()	weight: 0
    if()	weight: 0
   nil()	weight: 0
app❆3_if(x1,x2,x3)	weight: 0
 #app(x1,x2)	weight: 0
app❆1_dropWhile(x1)	weight: (/ 1 2)
#app❆2_takeWhile(x1,x2)	weight: (/ 1 4) + x2
  cons()	weight: 0
app❆2_cons(x1,x2)	weight: (/ 1 4) + x2
app❆1_cons(x1)	weight: 0
dropWhile()	weight: 0
   app(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #9
Number of SCCs: 0, DPs: 0, edges: 0
YES