YES
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 POLO(bPol) ... failed.
Uncurrying 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 POLO(bPol) ... 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
  SCC { #2..4 #6 #8 #9 }
POLO(Sum)... succeeded.
      #app^3_if	w: 0
      app^1_cons	w: 0
      #app^2_takeWhile	w: x1 + x2
      app^1_dropWhile	w: x1 + 1
      app^1_takeWhile	w: x1 + 39
      true	w: 0
      takeWhile	w: 0
      app^2_takeWhile	w: 0
      if	w: 0
      nil	w: 0
      #app^2_dropWhile	w: x1 + x2
      #app	w: x1 + x2
      cons	w: 0
      app^2_dropWhile	w: 0
      app^2_if	w: 0
      app^3_if	w: 0
      dropWhile	w: 0
      app^2_cons	w: x1 + x2 + 1
      app^1_if	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #2..4 #6 #8 #9
Number of SCCs: 0, DPs: 0