YES
Input TRS:
      1: app(app(.(),1()),x) -> x
      2: app(app(.(),x),1()) -> x
      3: app(app(.(),app(i(),x)),x) -> 1()
      4: app(app(.(),x),app(i(),x)) -> 1()
      5: app(app(.(),app(i(),y)),app(app(.(),y),z)) -> z
      6: app(app(.(),y),app(app(.(),app(i(),y)),z)) -> z
      7: app(app(.(),app(app(.(),x),y)),z) -> app(app(.(),x),app(app(.(),y),z))
      8: app(i(),1()) -> 1()
      9: app(i(),app(i(),x)) -> x
      10: app(i(),app(app(.(),x),y)) -> app(app(.(),app(i(),y)),app(i(),x))
      11: app(app(map(),f),nil()) -> nil()
      12: app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
      13: app(app(filter(),f),nil()) -> nil()
      14: app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
      15: app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
      16: app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)
Number of strict rules: 16
Direct POLO(bPol) ... failed.
Uncurrying app
      1: app^2_.(1(),x) -> x
      2: app^2_.(x,1()) -> x
      3: app^2_.(app^1_i(x),x) -> 1()
      4: app^2_.(x,app^1_i(x)) -> 1()
      5: app^2_.(app^1_i(y),app^2_.(y,z)) -> z
      6: app^2_.(y,app^2_.(app^1_i(y),z)) -> z
      7: app^2_.(app^2_.(x,y),z) -> app^2_.(x,app^2_.(y,z))
      8: app^1_i(1()) -> 1()
      9: app^1_i(app^1_i(x)) -> x
      10: app^1_i(app^2_.(x,y)) -> app^2_.(app^1_i(y),app^1_i(x))
      11: app^2_map(f,nil()) -> nil()
      12: app^2_map(f,app^2_cons(x,xs)) -> app^2_cons(app(f,x),app^2_map(f,xs))
      13: app^2_filter(f,nil()) -> nil()
      14: app^2_filter(f,app^2_cons(x,xs)) -> app^4_filter2(app(f,x),f,x,xs)
      15: app^4_filter2(true(),f,x,xs) -> app^2_cons(x,app^2_filter(f,xs))
      16: app^4_filter2(false(),f,x,xs) -> app^2_filter(f,xs)
      17: app(cons(),_1) ->= app^1_cons(_1)
      18: app(app^1_cons(_1),_2) ->= app^2_cons(_1,_2)
      19: app(filter(),_1) ->= app^1_filter(_1)
      20: app(app^1_filter(_1),_2) ->= app^2_filter(_1,_2)
      21: app(map(),_1) ->= app^1_map(_1)
      22: app(app^1_map(_1),_2) ->= app^2_map(_1,_2)
      23: app(filter2(),_1) ->= app^1_filter2(_1)
      24: app(app^1_filter2(_1),_2) ->= app^2_filter2(_1,_2)
      25: app(app^2_filter2(_1,_2),_3) ->= app^3_filter2(_1,_2,_3)
      26: app(app^3_filter2(_1,_2,_3),_4) ->= app^4_filter2(_1,_2,_3,_4)
      27: app(.(),_1) ->= app^1_.(_1)
      28: app(app^1_.(_1),_2) ->= app^2_.(_1,_2)
      29: app(i(),_1) ->= app^1_i(_1)
Number of strict rules: 16
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #app(i(),_1) ->? #app^1_i(_1)
     #2: #app^2_map(f,app^2_cons(x,xs)) -> #app(f,x)
     #3: #app^2_map(f,app^2_cons(x,xs)) -> #app^2_map(f,xs)
     #4: #app^2_filter(f,app^2_cons(x,xs)) -> #app^4_filter2(app(f,x),f,x,xs)
     #5: #app^2_filter(f,app^2_cons(x,xs)) -> #app(f,x)
     #6: #app(app^1_filter(_1),_2) ->? #app^2_filter(_1,_2)
     #7: #app^2_.(app^2_.(x,y),z) -> #app^2_.(x,app^2_.(y,z))
     #8: #app^2_.(app^2_.(x,y),z) -> #app^2_.(y,z)
     #9: #app^1_i(app^2_.(x,y)) -> #app^2_.(app^1_i(y),app^1_i(x))
     #10: #app^1_i(app^2_.(x,y)) -> #app^1_i(y)
     #11: #app^1_i(app^2_.(x,y)) -> #app^1_i(x)
     #12: #app(app^1_.(_1),_2) ->? #app^2_.(_1,_2)
     #13: #app(app^1_map(_1),_2) ->? #app^2_map(_1,_2)
     #14: #app(app^3_filter2(_1,_2,_3),_4) ->? #app^4_filter2(_1,_2,_3,_4)
     #15: #app^4_filter2(false(),f,x,xs) -> #app^2_filter(f,xs)
     #16: #app^4_filter2(true(),f,x,xs) -> #app^2_filter(f,xs)
Number of SCCs: 3, DPs: 13
  SCC { #10 #11 }
POLO(Sum)... succeeded.
      1 	w: 0
      #app^2_.	w: 0
      app^1_cons	w: 0
      #app^2_map	w: 0
      app^2_filter2	w: 0
      app^4_filter2	w: 0
      #app^1_i	w: x1
      false	w: 0
      app^2_.	w: x1 + x2 + 1
      app^1_i	w: 0
      app^1_filter2	w: 0
      true	w: 0
      filter2	w: 0
      #app^4_filter2	w: 0
      nil	w: 0
      #app	w: 0
      map	w: 0
      app^1_filter	w: 0
      . 	w: 0
      i 	w: 0
      app^1_.	w: 0
      cons	w: 0
      filter	w: 0
      app^3_filter2	w: 0
      app^2_filter	w: 0
      app^1_map	w: 0
      app^2_cons	w: 0
      app^2_map	w: 0
      #app^2_filter	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #10 #11
Number of SCCs: 2, DPs: 11
  SCC { #7 #8 }
POLO(Sum)... succeeded.
      1 	w: 7760
      #app^2_.	w: x1
      app^1_cons	w: 0
      #app^2_map	w: 0
      app^2_filter2	w: 0
      app^4_filter2	w: 0
      #app^1_i	w: 0
      false	w: 0
      app^2_.	w: x1 + x2 + 1
      app^1_i	w: 7758
      app^1_filter2	w: 0
      true	w: 0
      filter2	w: 0
      #app^4_filter2	w: 0
      nil	w: 0
      #app	w: 0
      map	w: 0
      app^1_filter	w: 0
      . 	w: 0
      i 	w: 0
      app^1_.	w: 0
      cons	w: 0
      filter	w: 0
      app^3_filter2	w: 0
      app^2_filter	w: 0
      app^1_map	w: 0
      app^2_cons	w: 0
      app^2_map	w: 0
      #app^2_filter	w: 0
      app	w: 0
    USABLE RULES: { }
    Removed DPs: #7 #8
Number of SCCs: 1, DPs: 9
  SCC { #2..6 #13..16 }
POLO(Sum)... succeeded.
      1 	w: 30617
      #app^2_.	w: 0
      app^1_cons	w: x1 + 2
      #app^2_map	w: x2
      app^2_filter2	w: x1 + x2 + 2
      app^4_filter2	w: x3 + x4 + 33958
      #app^1_i	w: 0
      false	w: 1
      app^2_.	w: x1 + 2
      app^1_i	w: x1 + 30614
      app^1_filter2	w: x1 + 2
      true	w: 1
      filter2	w: 1
      #app^4_filter2	w: x4 + 28101
      nil	w: 1145
      #app	w: x2 + 28102
      map	w: 1
      app^1_filter	w: x1 + 2
      . 	w: 1
      i 	w: 1
      app^1_.	w: x1 + 2
      cons	w: 1
      filter	w: 1
      app^3_filter2	w: x1 + x2 + x3 + 2
      app^2_filter	w: x2 + 5855
      app^1_map	w: x1 + 2
      app^2_cons	w: x1 + x2 + 28103
      app^2_map	w: x1 + 1144
      #app^2_filter	w: x2
      app	w: 1
    USABLE RULES: { 13..16 }
    Removed DPs: #2..6 #13..16
Number of SCCs: 0, DPs: 0