YES
Input TRS:
      1: app(app(twice(),f),x) -> app(f,app(f,x))
      2: app(app(map(),f),nil()) -> nil()
      3: app(app(map(),f),app(app(cons(),h),t)) -> app(app(cons(),app(f,h)),app(app(map(),f),t))
      4: app(app(fmap(),nil()),x) -> nil()
      5: app(app(fmap(),app(app(cons(),f),t_f())),x) -> app(app(cons(),app(f,x)),app(app(fmap(),t_f()),x))
Number of strict rules: 5
Direct POLO(bPol) ... failed.
Uncurrying app
      1: app^2_twice(f,x) -> app(f,app(f,x))
      2: app^2_map(f,nil()) -> nil()
      3: app^2_map(f,app^2_cons(h,t)) -> app^2_cons(app(f,h),app^2_map(f,t))
      4: app^2_fmap(nil(),x) -> nil()
      5: app^2_fmap(app^2_cons(f,t_f()),x) -> app^2_cons(app(f,x),app^2_fmap(t_f(),x))
      6: app(fmap(),_1) ->= app^1_fmap(_1)
      7: app(app^1_fmap(_1),_2) ->= app^2_fmap(_1,_2)
      8: app(cons(),_1) ->= app^1_cons(_1)
      9: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
      10: app(twice(),_1) ->= app^1_twice(_1)
      11: app(app^1_twice(_1),_2) ->= app^2_twice(_1,_2)
      12: app(map(),_1) ->= app^1_map(_1)
      13: app(app^1_map(_1),_2) ->= app^2_map(_1,_2)
Number of strict rules: 5
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2)
     #2: #app(app^1_twice(_1),_2) ->? #app^2_twice(_1,_2)
     #3: #app(app^1_fmap(_1),_2) ->? #app^2_fmap(_1,_2)
     #4: #app^2_fmap(app^2_cons(f,t_f()),x) -> #app(f,x)
     #5: #app^2_fmap(app^2_cons(f,t_f()),x) -> #app^2_fmap(t_f(),x)
     #6: #app^2_map(f,app^2_cons(h,t)) -> #app(f,h)
     #7: #app^2_map(f,app^2_cons(h,t)) -> #app^2_map(f,t)
     #8: #app^2_twice(f,x) -> #app(f,app(f,x))
     #9: #app^2_twice(f,x) -> #app(f,x)
Number of SCCs: 1, DPs: 8
  SCC { #1..4 #6..9 }
POLO(Sum)... succeeded.
      t_f	w: 1
      app^1_twice	w: x1 + 31757
      app^1_cons	w: x1 + 38553
      #app^2_map	w: x1 + 1
      twice	w: 31755
      #app^2_twice	w: x1 + 31756
      fmap	w: 6135
      app^2_twice	w: 31759
      app^1_fmap	w: x1 + 6137
      nil	w: 6
      #app	w: x1
      map	w: 1
      cons	w: 38551
      #app^2_fmap	w: x1
      app^2_fmap	w: x1 + x2 + 6139
      app^1_map	w: x1 + 3
      app^2_cons	w: x1 + x2 + 38555
      app^2_map	w: x1 + 5
      app	w: x1 + x2 + 1
    USABLE RULES: { }
    Removed DPs: #1..4 #6 #8 #9
Number of SCCs: 1, DPs: 1
  SCC { #7 }
POLO(Sum)... succeeded.
      t_f	w: 2998
      app^1_twice	w: x1 + 14683
      app^1_cons	w: x1 + 42209
      #app^2_map	w: x2 + 1
      twice	w: 14681
      #app^2_twice	w: 31756
      fmap	w: 1
      app^2_twice	w: 31759
      app^1_fmap	w: x1 + 3
      nil	w: 6
      #app	w: 0
      map	w: 1
      cons	w: 42207
      #app^2_fmap	w: 0
      app^2_fmap	w: x1 + x2 + 5
      app^1_map	w: x1 + 3
      app^2_cons	w: x1 + x2 + 42211
      app^2_map	w: x1 + 5
      app	w: x1 + x2 + 1
    USABLE RULES: { }
    Removed DPs: #7
Number of SCCs: 0, DPs: 0