YES

Problem:
 app(f(),app(app(cons(),nil()),y)) -> y
 app(f(),app(app(cons(),app(f(),app(app(cons(),nil()),y))),z)) -> app(app(app(copy(),n()),y),z)
 app(app(app(copy(),0()),y),z) -> app(f(),z)
 app(app(app(copy(),app(s(),x)),y),z) -> app(app(app(copy(),x),y),app(app(cons(),app(f(),y)),z))
 app(app(map(),fun),nil()) -> nil()
 app(app(map(),fun),app(app(cons(),x),xs)) -> app(app(cons(),app(fun,x)),app(app(map(),fun),xs))
 app(app(filter(),fun),nil()) -> nil()
 app(app(filter(),fun),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(fun,x)),fun),x),xs)
 app(app(app(app(filter2(),true()),fun),x),xs) -> app(app(cons(),x),app(app(filter(),fun),xs))
 app(app(app(app(filter2(),false()),fun),x),xs) -> app(app(filter(),fun),xs)

Proof:
 Uncurry Processor:
  f1(cons2(nil(),y)) -> y
  f1(cons2(f1(cons2(nil(),y)),z)) -> copy3(n(),y,z)
  copy3(0(),y,z) -> f1(z)
  copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
  map2(fun,nil()) -> nil()
  map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
  filter2(fun,nil()) -> nil()
  filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
  filter24(true(),fun,x,xs) -> cons2(x,filter2(fun,xs))
  filter24(false(),fun,x,xs) -> filter2(fun,xs)
  app(f(),x8) -> f1(x8)
  app(cons1(x7),x8) -> cons2(x7,x8)
  app(cons(),x8) -> cons1(x8)
  app(copy2(x7,x6),x8) -> copy3(x7,x6,x8)
  app(copy1(x7),x8) -> copy2(x7,x8)
  app(copy(),x8) -> copy1(x8)
  app(s(),x8) -> s1(x8)
  app(map1(x7),x8) -> map2(x7,x8)
  app(map(),x8) -> map1(x8)
  app(filter1(x7),x8) -> filter2(x7,x8)
  app(filter(),x8) -> filter1(x8)
  app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
  app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
  app(filter21(x7),x8) -> filter22(x7,x8)
  app(filter2(),x8) -> filter21(x8)
  DP Processor:
   DPs:
    f{1,#}(cons2(f1(cons2(nil(),y)),z)) -> copy{3,#}(n(),y,z)
    copy{3,#}(0(),y,z) -> f{1,#}(z)
    copy{3,#}(s1(x),y,z) -> f{1,#}(y)
    copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
    map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
    map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
    filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
    filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
    filter2{4,#}(true(),fun,x,xs) -> filter{2,#}(fun,xs)
    filter2{4,#}(false(),fun,x,xs) -> filter{2,#}(fun,xs)
    app#(f(),x8) -> f{1,#}(x8)
    app#(copy2(x7,x6),x8) -> copy{3,#}(x7,x6,x8)
    app#(map1(x7),x8) -> map{2,#}(x7,x8)
    app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
    app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
   TRS:
    f1(cons2(nil(),y)) -> y
    f1(cons2(f1(cons2(nil(),y)),z)) -> copy3(n(),y,z)
    copy3(0(),y,z) -> f1(z)
    copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
    map2(fun,nil()) -> nil()
    map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
    filter2(fun,nil()) -> nil()
    filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
    filter24(true(),fun,x,xs) -> cons2(x,filter2(fun,xs))
    filter24(false(),fun,x,xs) -> filter2(fun,xs)
    app(f(),x8) -> f1(x8)
    app(cons1(x7),x8) -> cons2(x7,x8)
    app(cons(),x8) -> cons1(x8)
    app(copy2(x7,x6),x8) -> copy3(x7,x6,x8)
    app(copy1(x7),x8) -> copy2(x7,x8)
    app(copy(),x8) -> copy1(x8)
    app(s(),x8) -> s1(x8)
    app(map1(x7),x8) -> map2(x7,x8)
    app(map(),x8) -> map1(x8)
    app(filter1(x7),x8) -> filter2(x7,x8)
    app(filter(),x8) -> filter1(x8)
    app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
    app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
    app(filter21(x7),x8) -> filter22(x7,x8)
    app(filter2(),x8) -> filter21(x8)
   TDG Processor:
    DPs:
     f{1,#}(cons2(f1(cons2(nil(),y)),z)) -> copy{3,#}(n(),y,z)
     copy{3,#}(0(),y,z) -> f{1,#}(z)
     copy{3,#}(s1(x),y,z) -> f{1,#}(y)
     copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
     map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
     filter2{4,#}(true(),fun,x,xs) -> filter{2,#}(fun,xs)
     filter2{4,#}(false(),fun,x,xs) -> filter{2,#}(fun,xs)
     app#(f(),x8) -> f{1,#}(x8)
     app#(copy2(x7,x6),x8) -> copy{3,#}(x7,x6,x8)
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
     app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
    TRS:
     f1(cons2(nil(),y)) -> y
     f1(cons2(f1(cons2(nil(),y)),z)) -> copy3(n(),y,z)
     copy3(0(),y,z) -> f1(z)
     copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
     map2(fun,nil()) -> nil()
     map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
     filter2(fun,nil()) -> nil()
     filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
     filter24(true(),fun,x,xs) -> cons2(x,filter2(fun,xs))
     filter24(false(),fun,x,xs) -> filter2(fun,xs)
     app(f(),x8) -> f1(x8)
     app(cons1(x7),x8) -> cons2(x7,x8)
     app(cons(),x8) -> cons1(x8)
     app(copy2(x7,x6),x8) -> copy3(x7,x6,x8)
     app(copy1(x7),x8) -> copy2(x7,x8)
     app(copy(),x8) -> copy1(x8)
     app(s(),x8) -> s1(x8)
     app(map1(x7),x8) -> map2(x7,x8)
     app(map(),x8) -> map1(x8)
     app(filter1(x7),x8) -> filter2(x7,x8)
     app(filter(),x8) -> filter1(x8)
     app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
     app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
     app(filter21(x7),x8) -> filter22(x7,x8)
     app(filter2(),x8) -> filter21(x8)
    graph:
     filter2{4,#}(false(),fun,x,xs) -> filter{2,#}(fun,xs) ->
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
     filter2{4,#}(false(),fun,x,xs) -> filter{2,#}(fun,xs) ->
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     filter2{4,#}(true(),fun,x,xs) -> filter{2,#}(fun,xs) ->
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
     filter2{4,#}(true(),fun,x,xs) -> filter{2,#}(fun,xs) ->
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs) ->
     filter2{4,#}(false(),fun,x,xs) -> filter{2,#}(fun,xs)
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs) ->
     filter2{4,#}(true(),fun,x,xs) -> filter{2,#}(fun,xs)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(copy2(x7,x6),x8) -> copy{3,#}(x7,x6,x8)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(f(),x8) -> f{1,#}(x8)
     app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8) ->
     filter2{4,#}(false(),fun,x,xs) -> filter{2,#}(fun,xs)
     app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8) ->
     filter2{4,#}(true(),fun,x,xs) -> filter{2,#}(fun,xs)
     app#(filter1(x7),x8) -> filter{2,#}(x7,x8) ->
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
     app#(filter1(x7),x8) -> filter{2,#}(x7,x8) ->
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     app#(map1(x7),x8) -> map{2,#}(x7,x8) ->
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     app#(map1(x7),x8) -> map{2,#}(x7,x8) ->
     map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
     app#(copy2(x7,x6),x8) -> copy{3,#}(x7,x6,x8) ->
     copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
     app#(copy2(x7,x6),x8) -> copy{3,#}(x7,x6,x8) ->
     copy{3,#}(s1(x),y,z) -> f{1,#}(y)
     app#(copy2(x7,x6),x8) -> copy{3,#}(x7,x6,x8) ->
     copy{3,#}(0(),y,z) -> f{1,#}(z)
     app#(f(),x8) -> f{1,#}(x8) ->
     f{1,#}(cons2(f1(cons2(nil(),y)),z)) -> copy{3,#}(n(),y,z)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(copy2(x7,x6),x8) -> copy{3,#}(x7,x6,x8)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(f(),x8) -> f{1,#}(x8)
     map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs) ->
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs) ->
     map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
     copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z)) ->
     copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
     copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z)) ->
     copy{3,#}(s1(x),y,z) -> f{1,#}(y)
     copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z)) ->
     copy{3,#}(0(),y,z) -> f{1,#}(z)
     copy{3,#}(s1(x),y,z) -> f{1,#}(y) ->
     f{1,#}(cons2(f1(cons2(nil(),y)),z)) -> copy{3,#}(n(),y,z)
     copy{3,#}(0(),y,z) -> f{1,#}(z) ->
     f{1,#}(cons2(f1(cons2(nil(),y)),z)) -> copy{3,#}(n(),y,z)
     f{1,#}(cons2(f1(cons2(nil(),y)),z)) -> copy{3,#}(n(),y,z) ->
     copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
     f{1,#}(cons2(f1(cons2(nil(),y)),z)) -> copy{3,#}(n(),y,z) ->
     copy{3,#}(s1(x),y,z) -> f{1,#}(y)
     f{1,#}(cons2(f1(cons2(nil(),y)),z)) -> copy{3,#}(n(),y,z) -> copy{3,#}(0(),y,z) -> f{1,#}(z)
    SCC Processor:
     #sccs: 2
     #rules: 13
     #arcs: 36/225
     DPs:
      filter2{4,#}(false(),fun,x,xs) -> filter{2,#}(fun,xs)
      filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
      app#(map1(x7),x8) -> map{2,#}(x7,x8)
      map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
      map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
      app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
      filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
      filter2{4,#}(true(),fun,x,xs) -> filter{2,#}(fun,xs)
      app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
     TRS:
      f1(cons2(nil(),y)) -> y
      f1(cons2(f1(cons2(nil(),y)),z)) -> copy3(n(),y,z)
      copy3(0(),y,z) -> f1(z)
      copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
      map2(fun,nil()) -> nil()
      map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
      filter2(fun,nil()) -> nil()
      filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
      filter24(true(),fun,x,xs) -> cons2(x,filter2(fun,xs))
      filter24(false(),fun,x,xs) -> filter2(fun,xs)
      app(f(),x8) -> f1(x8)
      app(cons1(x7),x8) -> cons2(x7,x8)
      app(cons(),x8) -> cons1(x8)
      app(copy2(x7,x6),x8) -> copy3(x7,x6,x8)
      app(copy1(x7),x8) -> copy2(x7,x8)
      app(copy(),x8) -> copy1(x8)
      app(s(),x8) -> s1(x8)
      app(map1(x7),x8) -> map2(x7,x8)
      app(map(),x8) -> map1(x8)
      app(filter1(x7),x8) -> filter2(x7,x8)
      app(filter(),x8) -> filter1(x8)
      app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
      app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
      app(filter21(x7),x8) -> filter22(x7,x8)
      app(filter2(),x8) -> filter21(x8)
     Subterm Criterion Processor:
      simple projection:
       pi(map{2,#}) = 1
       pi(app#) = 1
       pi(filter{2,#}) = 1
       pi(filter2{4,#}) = 3
      problem:
       DPs:
        filter2{4,#}(false(),fun,x,xs) -> filter{2,#}(fun,xs)
        app#(map1(x7),x8) -> map{2,#}(x7,x8)
        app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
        filter2{4,#}(true(),fun,x,xs) -> filter{2,#}(fun,xs)
        app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
       TRS:
        f1(cons2(nil(),y)) -> y
        f1(cons2(f1(cons2(nil(),y)),z)) -> copy3(n(),y,z)
        copy3(0(),y,z) -> f1(z)
        copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
        map2(fun,nil()) -> nil()
        map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
        filter2(fun,nil()) -> nil()
        filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
        filter24(true(),fun,x,xs) -> cons2(x,filter2(fun,xs))
        filter24(false(),fun,x,xs) -> filter2(fun,xs)
        app(f(),x8) -> f1(x8)
        app(cons1(x7),x8) -> cons2(x7,x8)
        app(cons(),x8) -> cons1(x8)
        app(copy2(x7,x6),x8) -> copy3(x7,x6,x8)
        app(copy1(x7),x8) -> copy2(x7,x8)
        app(copy(),x8) -> copy1(x8)
        app(s(),x8) -> s1(x8)
        app(map1(x7),x8) -> map2(x7,x8)
        app(map(),x8) -> map1(x8)
        app(filter1(x7),x8) -> filter2(x7,x8)
        app(filter(),x8) -> filter1(x8)
        app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
        app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
        app(filter21(x7),x8) -> filter22(x7,x8)
        app(filter2(),x8) -> filter21(x8)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 20/25
       
     
     DPs:
      f{1,#}(cons2(f1(cons2(nil(),y)),z)) -> copy{3,#}(n(),y,z)
      copy{3,#}(0(),y,z) -> f{1,#}(z)
      copy{3,#}(s1(x),y,z) -> f{1,#}(y)
      copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
     TRS:
      f1(cons2(nil(),y)) -> y
      f1(cons2(f1(cons2(nil(),y)),z)) -> copy3(n(),y,z)
      copy3(0(),y,z) -> f1(z)
      copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
      map2(fun,nil()) -> nil()
      map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
      filter2(fun,nil()) -> nil()
      filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
      filter24(true(),fun,x,xs) -> cons2(x,filter2(fun,xs))
      filter24(false(),fun,x,xs) -> filter2(fun,xs)
      app(f(),x8) -> f1(x8)
      app(cons1(x7),x8) -> cons2(x7,x8)
      app(cons(),x8) -> cons1(x8)
      app(copy2(x7,x6),x8) -> copy3(x7,x6,x8)
      app(copy1(x7),x8) -> copy2(x7,x8)
      app(copy(),x8) -> copy1(x8)
      app(s(),x8) -> s1(x8)
      app(map1(x7),x8) -> map2(x7,x8)
      app(map(),x8) -> map1(x8)
      app(filter1(x7),x8) -> filter2(x7,x8)
      app(filter(),x8) -> filter1(x8)
      app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
      app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
      app(filter21(x7),x8) -> filter22(x7,x8)
      app(filter2(),x8) -> filter21(x8)
     EDG Processor:
      DPs:
       f{1,#}(cons2(f1(cons2(nil(),y)),z)) -> copy{3,#}(n(),y,z)
       copy{3,#}(0(),y,z) -> f{1,#}(z)
       copy{3,#}(s1(x),y,z) -> f{1,#}(y)
       copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
      TRS:
       f1(cons2(nil(),y)) -> y
       f1(cons2(f1(cons2(nil(),y)),z)) -> copy3(n(),y,z)
       copy3(0(),y,z) -> f1(z)
       copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
       map2(fun,nil()) -> nil()
       map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
       filter2(fun,nil()) -> nil()
       filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
       filter24(true(),fun,x,xs) -> cons2(x,filter2(fun,xs))
       filter24(false(),fun,x,xs) -> filter2(fun,xs)
       app(f(),x8) -> f1(x8)
       app(cons1(x7),x8) -> cons2(x7,x8)
       app(cons(),x8) -> cons1(x8)
       app(copy2(x7,x6),x8) -> copy3(x7,x6,x8)
       app(copy1(x7),x8) -> copy2(x7,x8)
       app(copy(),x8) -> copy1(x8)
       app(s(),x8) -> s1(x8)
       app(map1(x7),x8) -> map2(x7,x8)
       app(map(),x8) -> map1(x8)
       app(filter1(x7),x8) -> filter2(x7,x8)
       app(filter(),x8) -> filter1(x8)
       app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
       app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
       app(filter21(x7),x8) -> filter22(x7,x8)
       app(filter2(),x8) -> filter21(x8)
      graph:
       copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z)) ->
       copy{3,#}(0(),y,z) -> f{1,#}(z)
       copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z)) ->
       copy{3,#}(s1(x),y,z) -> f{1,#}(y)
       copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z)) ->
       copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
       copy{3,#}(s1(x),y,z) -> f{1,#}(y) ->
       f{1,#}(cons2(f1(cons2(nil(),y)),z)) -> copy{3,#}(n(),y,z)
       copy{3,#}(0(),y,z) -> f{1,#}(z) -> f{1,#}(cons2(f1(cons2(nil(),y)),z)) -> copy{3,#}(n(),y,z)
      SCC Processor:
       #sccs: 1
       #rules: 1
       #arcs: 5/16
       DPs:
        copy{3,#}(s1(x),y,z) -> copy{3,#}(x,y,cons2(f1(y),z))
       TRS:
        f1(cons2(nil(),y)) -> y
        f1(cons2(f1(cons2(nil(),y)),z)) -> copy3(n(),y,z)
        copy3(0(),y,z) -> f1(z)
        copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
        map2(fun,nil()) -> nil()
        map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
        filter2(fun,nil()) -> nil()
        filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
        filter24(true(),fun,x,xs) -> cons2(x,filter2(fun,xs))
        filter24(false(),fun,x,xs) -> filter2(fun,xs)
        app(f(),x8) -> f1(x8)
        app(cons1(x7),x8) -> cons2(x7,x8)
        app(cons(),x8) -> cons1(x8)
        app(copy2(x7,x6),x8) -> copy3(x7,x6,x8)
        app(copy1(x7),x8) -> copy2(x7,x8)
        app(copy(),x8) -> copy1(x8)
        app(s(),x8) -> s1(x8)
        app(map1(x7),x8) -> map2(x7,x8)
        app(map(),x8) -> map1(x8)
        app(filter1(x7),x8) -> filter2(x7,x8)
        app(filter(),x8) -> filter1(x8)
        app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
        app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
        app(filter21(x7),x8) -> filter22(x7,x8)
        app(filter2(),x8) -> filter21(x8)
       Subterm Criterion Processor:
        simple projection:
         pi(copy{3,#}) = 0
        problem:
         DPs:
          
         TRS:
          f1(cons2(nil(),y)) -> y
          f1(cons2(f1(cons2(nil(),y)),z)) -> copy3(n(),y,z)
          copy3(0(),y,z) -> f1(z)
          copy3(s1(x),y,z) -> copy3(x,y,cons2(f1(y),z))
          map2(fun,nil()) -> nil()
          map2(fun,cons2(x,xs)) -> cons2(app(fun,x),map2(fun,xs))
          filter2(fun,nil()) -> nil()
          filter2(fun,cons2(x,xs)) -> filter24(app(fun,x),fun,x,xs)
          filter24(true(),fun,x,xs) -> cons2(x,filter2(fun,xs))
          filter24(false(),fun,x,xs) -> filter2(fun,xs)
          app(f(),x8) -> f1(x8)
          app(cons1(x7),x8) -> cons2(x7,x8)
          app(cons(),x8) -> cons1(x8)
          app(copy2(x7,x6),x8) -> copy3(x7,x6,x8)
          app(copy1(x7),x8) -> copy2(x7,x8)
          app(copy(),x8) -> copy1(x8)
          app(s(),x8) -> s1(x8)
          app(map1(x7),x8) -> map2(x7,x8)
          app(map(),x8) -> map1(x8)
          app(filter1(x7),x8) -> filter2(x7,x8)
          app(filter(),x8) -> filter1(x8)
          app(filter23(x7,x6,x5),x8) -> filter24(x7,x6,x5,x8)
          app(filter22(x7,x6),x8) -> filter23(x7,x6,x8)
          app(filter21(x7),x8) -> filter22(x7,x8)
          app(filter2(),x8) -> filter21(x8)
        Qed