YES

Problem:
 app(f(),app(s(),x)) -> app(f(),x)
 app(g(),app(app(cons(),0()),y)) -> app(g(),y)
 app(g(),app(app(cons(),app(s(),x)),y)) -> app(s(),x)
 app(h(),app(app(cons(),x),y)) -> app(h(),app(g(),app(app(cons(),x),y)))
 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(s1(x)) -> f1(x)
  g1(cons2(0(),y)) -> g1(y)
  g1(cons2(s1(x),y)) -> s1(x)
  h1(cons2(x,y)) -> h1(g1(cons2(x,y)))
  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(),x7) -> f1(x7)
  app(s(),x7) -> s1(x7)
  app(g(),x7) -> g1(x7)
  app(cons1(x6),x7) -> cons2(x6,x7)
  app(cons(),x7) -> cons1(x7)
  app(h(),x7) -> h1(x7)
  app(map1(x6),x7) -> map2(x6,x7)
  app(map(),x7) -> map1(x7)
  app(filter1(x6),x7) -> filter2(x6,x7)
  app(filter(),x7) -> filter1(x7)
  app(filter23(x6,x5,x4),x7) -> filter24(x6,x5,x4,x7)
  app(filter22(x6,x5),x7) -> filter23(x6,x5,x7)
  app(filter21(x6),x7) -> filter22(x6,x7)
  app(filter2(),x7) -> filter21(x7)
  DP Processor:
   DPs:
    f{1,#}(s1(x)) -> f{1,#}(x)
    g{1,#}(cons2(0(),y)) -> g{1,#}(y)
    h{1,#}(cons2(x,y)) -> g{1,#}(cons2(x,y))
    h{1,#}(cons2(x,y)) -> h{1,#}(g1(cons2(x,y)))
    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(),x7) -> f{1,#}(x7)
    app#(g(),x7) -> g{1,#}(x7)
    app#(h(),x7) -> h{1,#}(x7)
    app#(map1(x6),x7) -> map{2,#}(x6,x7)
    app#(filter1(x6),x7) -> filter{2,#}(x6,x7)
    app#(filter23(x6,x5,x4),x7) -> filter2{4,#}(x6,x5,x4,x7)
   TRS:
    f1(s1(x)) -> f1(x)
    g1(cons2(0(),y)) -> g1(y)
    g1(cons2(s1(x),y)) -> s1(x)
    h1(cons2(x,y)) -> h1(g1(cons2(x,y)))
    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(),x7) -> f1(x7)
    app(s(),x7) -> s1(x7)
    app(g(),x7) -> g1(x7)
    app(cons1(x6),x7) -> cons2(x6,x7)
    app(cons(),x7) -> cons1(x7)
    app(h(),x7) -> h1(x7)
    app(map1(x6),x7) -> map2(x6,x7)
    app(map(),x7) -> map1(x7)
    app(filter1(x6),x7) -> filter2(x6,x7)
    app(filter(),x7) -> filter1(x7)
    app(filter23(x6,x5,x4),x7) -> filter24(x6,x5,x4,x7)
    app(filter22(x6,x5),x7) -> filter23(x6,x5,x7)
    app(filter21(x6),x7) -> filter22(x6,x7)
    app(filter2(),x7) -> filter21(x7)
   TDG Processor:
    DPs:
     f{1,#}(s1(x)) -> f{1,#}(x)
     g{1,#}(cons2(0(),y)) -> g{1,#}(y)
     h{1,#}(cons2(x,y)) -> g{1,#}(cons2(x,y))
     h{1,#}(cons2(x,y)) -> h{1,#}(g1(cons2(x,y)))
     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(),x7) -> f{1,#}(x7)
     app#(g(),x7) -> g{1,#}(x7)
     app#(h(),x7) -> h{1,#}(x7)
     app#(map1(x6),x7) -> map{2,#}(x6,x7)
     app#(filter1(x6),x7) -> filter{2,#}(x6,x7)
     app#(filter23(x6,x5,x4),x7) -> filter2{4,#}(x6,x5,x4,x7)
    TRS:
     f1(s1(x)) -> f1(x)
     g1(cons2(0(),y)) -> g1(y)
     g1(cons2(s1(x),y)) -> s1(x)
     h1(cons2(x,y)) -> h1(g1(cons2(x,y)))
     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(),x7) -> f1(x7)
     app(s(),x7) -> s1(x7)
     app(g(),x7) -> g1(x7)
     app(cons1(x6),x7) -> cons2(x6,x7)
     app(cons(),x7) -> cons1(x7)
     app(h(),x7) -> h1(x7)
     app(map1(x6),x7) -> map2(x6,x7)
     app(map(),x7) -> map1(x7)
     app(filter1(x6),x7) -> filter2(x6,x7)
     app(filter(),x7) -> filter1(x7)
     app(filter23(x6,x5,x4),x7) -> filter24(x6,x5,x4,x7)
     app(filter22(x6,x5),x7) -> filter23(x6,x5,x7)
     app(filter21(x6),x7) -> filter22(x6,x7)
     app(filter2(),x7) -> filter21(x7)
    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(x6,x5,x4),x7) -> filter2{4,#}(x6,x5,x4,x7)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter1(x6),x7) -> filter{2,#}(x6,x7)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(map1(x6),x7) -> map{2,#}(x6,x7)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(h(),x7) -> h{1,#}(x7)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(g(),x7) -> g{1,#}(x7)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(f(),x7) -> f{1,#}(x7)
     app#(filter23(x6,x5,x4),x7) -> filter2{4,#}(x6,x5,x4,x7) ->
     filter2{4,#}(false(),fun,x,xs) -> filter{2,#}(fun,xs)
     app#(filter23(x6,x5,x4),x7) -> filter2{4,#}(x6,x5,x4,x7) ->
     filter2{4,#}(true(),fun,x,xs) -> filter{2,#}(fun,xs)
     app#(filter1(x6),x7) -> filter{2,#}(x6,x7) ->
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
     app#(filter1(x6),x7) -> filter{2,#}(x6,x7) ->
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     app#(map1(x6),x7) -> map{2,#}(x6,x7) ->
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     app#(map1(x6),x7) -> map{2,#}(x6,x7) ->
     map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
     app#(h(),x7) -> h{1,#}(x7) ->
     h{1,#}(cons2(x,y)) -> h{1,#}(g1(cons2(x,y)))
     app#(h(),x7) -> h{1,#}(x7) ->
     h{1,#}(cons2(x,y)) -> g{1,#}(cons2(x,y))
     app#(g(),x7) -> g{1,#}(x7) -> g{1,#}(cons2(0(),y)) -> g{1,#}(y)
     app#(f(),x7) -> f{1,#}(x7) ->
     f{1,#}(s1(x)) -> f{1,#}(x)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter23(x6,x5,x4),x7) -> filter2{4,#}(x6,x5,x4,x7)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter1(x6),x7) -> filter{2,#}(x6,x7)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(map1(x6),x7) -> map{2,#}(x6,x7)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(h(),x7) -> h{1,#}(x7)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(g(),x7) -> g{1,#}(x7)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(f(),x7) -> f{1,#}(x7)
     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)
     h{1,#}(cons2(x,y)) -> h{1,#}(g1(cons2(x,y))) ->
     h{1,#}(cons2(x,y)) -> h{1,#}(g1(cons2(x,y)))
     h{1,#}(cons2(x,y)) -> h{1,#}(g1(cons2(x,y))) ->
     h{1,#}(cons2(x,y)) -> g{1,#}(cons2(x,y))
     h{1,#}(cons2(x,y)) -> g{1,#}(cons2(x,y)) ->
     g{1,#}(cons2(0(),y)) -> g{1,#}(y)
     g{1,#}(cons2(0(),y)) -> g{1,#}(y) ->
     g{1,#}(cons2(0(),y)) -> g{1,#}(y)
     f{1,#}(s1(x)) -> f{1,#}(x) -> f{1,#}(s1(x)) -> f{1,#}(x)
    SCC Processor:
     #sccs: 4
     #rules: 12
     #arcs: 35/256
     DPs:
      filter2{4,#}(false(),fun,x,xs) -> filter{2,#}(fun,xs)
      filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
      app#(map1(x6),x7) -> map{2,#}(x6,x7)
      map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
      map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
      app#(filter1(x6),x7) -> filter{2,#}(x6,x7)
      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(x6,x5,x4),x7) -> filter2{4,#}(x6,x5,x4,x7)
     TRS:
      f1(s1(x)) -> f1(x)
      g1(cons2(0(),y)) -> g1(y)
      g1(cons2(s1(x),y)) -> s1(x)
      h1(cons2(x,y)) -> h1(g1(cons2(x,y)))
      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(),x7) -> f1(x7)
      app(s(),x7) -> s1(x7)
      app(g(),x7) -> g1(x7)
      app(cons1(x6),x7) -> cons2(x6,x7)
      app(cons(),x7) -> cons1(x7)
      app(h(),x7) -> h1(x7)
      app(map1(x6),x7) -> map2(x6,x7)
      app(map(),x7) -> map1(x7)
      app(filter1(x6),x7) -> filter2(x6,x7)
      app(filter(),x7) -> filter1(x7)
      app(filter23(x6,x5,x4),x7) -> filter24(x6,x5,x4,x7)
      app(filter22(x6,x5),x7) -> filter23(x6,x5,x7)
      app(filter21(x6),x7) -> filter22(x6,x7)
      app(filter2(),x7) -> filter21(x7)
     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(x6),x7) -> map{2,#}(x6,x7)
        app#(filter1(x6),x7) -> filter{2,#}(x6,x7)
        filter2{4,#}(true(),fun,x,xs) -> filter{2,#}(fun,xs)
        app#(filter23(x6,x5,x4),x7) -> filter2{4,#}(x6,x5,x4,x7)
       TRS:
        f1(s1(x)) -> f1(x)
        g1(cons2(0(),y)) -> g1(y)
        g1(cons2(s1(x),y)) -> s1(x)
        h1(cons2(x,y)) -> h1(g1(cons2(x,y)))
        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(),x7) -> f1(x7)
        app(s(),x7) -> s1(x7)
        app(g(),x7) -> g1(x7)
        app(cons1(x6),x7) -> cons2(x6,x7)
        app(cons(),x7) -> cons1(x7)
        app(h(),x7) -> h1(x7)
        app(map1(x6),x7) -> map2(x6,x7)
        app(map(),x7) -> map1(x7)
        app(filter1(x6),x7) -> filter2(x6,x7)
        app(filter(),x7) -> filter1(x7)
        app(filter23(x6,x5,x4),x7) -> filter24(x6,x5,x4,x7)
        app(filter22(x6,x5),x7) -> filter23(x6,x5,x7)
        app(filter21(x6),x7) -> filter22(x6,x7)
        app(filter2(),x7) -> filter21(x7)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 20/25
       
     
     DPs:
      h{1,#}(cons2(x,y)) -> h{1,#}(g1(cons2(x,y)))
     TRS:
      f1(s1(x)) -> f1(x)
      g1(cons2(0(),y)) -> g1(y)
      g1(cons2(s1(x),y)) -> s1(x)
      h1(cons2(x,y)) -> h1(g1(cons2(x,y)))
      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(),x7) -> f1(x7)
      app(s(),x7) -> s1(x7)
      app(g(),x7) -> g1(x7)
      app(cons1(x6),x7) -> cons2(x6,x7)
      app(cons(),x7) -> cons1(x7)
      app(h(),x7) -> h1(x7)
      app(map1(x6),x7) -> map2(x6,x7)
      app(map(),x7) -> map1(x7)
      app(filter1(x6),x7) -> filter2(x6,x7)
      app(filter(),x7) -> filter1(x7)
      app(filter23(x6,x5,x4),x7) -> filter24(x6,x5,x4,x7)
      app(filter22(x6,x5),x7) -> filter23(x6,x5,x7)
      app(filter21(x6),x7) -> filter22(x6,x7)
      app(filter2(),x7) -> filter21(x7)
     CDG Processor:
      DPs:
       h{1,#}(cons2(x,y)) -> h{1,#}(g1(cons2(x,y)))
      TRS:
       f1(s1(x)) -> f1(x)
       g1(cons2(0(),y)) -> g1(y)
       g1(cons2(s1(x),y)) -> s1(x)
       h1(cons2(x,y)) -> h1(g1(cons2(x,y)))
       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(),x7) -> f1(x7)
       app(s(),x7) -> s1(x7)
       app(g(),x7) -> g1(x7)
       app(cons1(x6),x7) -> cons2(x6,x7)
       app(cons(),x7) -> cons1(x7)
       app(h(),x7) -> h1(x7)
       app(map1(x6),x7) -> map2(x6,x7)
       app(map(),x7) -> map1(x7)
       app(filter1(x6),x7) -> filter2(x6,x7)
       app(filter(),x7) -> filter1(x7)
       app(filter23(x6,x5,x4),x7) -> filter24(x6,x5,x4,x7)
       app(filter22(x6,x5),x7) -> filter23(x6,x5,x7)
       app(filter21(x6),x7) -> filter22(x6,x7)
       app(filter2(),x7) -> filter21(x7)
      graph:
       
      Qed
     
     DPs:
      g{1,#}(cons2(0(),y)) -> g{1,#}(y)
     TRS:
      f1(s1(x)) -> f1(x)
      g1(cons2(0(),y)) -> g1(y)
      g1(cons2(s1(x),y)) -> s1(x)
      h1(cons2(x,y)) -> h1(g1(cons2(x,y)))
      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(),x7) -> f1(x7)
      app(s(),x7) -> s1(x7)
      app(g(),x7) -> g1(x7)
      app(cons1(x6),x7) -> cons2(x6,x7)
      app(cons(),x7) -> cons1(x7)
      app(h(),x7) -> h1(x7)
      app(map1(x6),x7) -> map2(x6,x7)
      app(map(),x7) -> map1(x7)
      app(filter1(x6),x7) -> filter2(x6,x7)
      app(filter(),x7) -> filter1(x7)
      app(filter23(x6,x5,x4),x7) -> filter24(x6,x5,x4,x7)
      app(filter22(x6,x5),x7) -> filter23(x6,x5,x7)
      app(filter21(x6),x7) -> filter22(x6,x7)
      app(filter2(),x7) -> filter21(x7)
     Subterm Criterion Processor:
      simple projection:
       pi(g{1,#}) = 0
      problem:
       DPs:
        
       TRS:
        f1(s1(x)) -> f1(x)
        g1(cons2(0(),y)) -> g1(y)
        g1(cons2(s1(x),y)) -> s1(x)
        h1(cons2(x,y)) -> h1(g1(cons2(x,y)))
        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(),x7) -> f1(x7)
        app(s(),x7) -> s1(x7)
        app(g(),x7) -> g1(x7)
        app(cons1(x6),x7) -> cons2(x6,x7)
        app(cons(),x7) -> cons1(x7)
        app(h(),x7) -> h1(x7)
        app(map1(x6),x7) -> map2(x6,x7)
        app(map(),x7) -> map1(x7)
        app(filter1(x6),x7) -> filter2(x6,x7)
        app(filter(),x7) -> filter1(x7)
        app(filter23(x6,x5,x4),x7) -> filter24(x6,x5,x4,x7)
        app(filter22(x6,x5),x7) -> filter23(x6,x5,x7)
        app(filter21(x6),x7) -> filter22(x6,x7)
        app(filter2(),x7) -> filter21(x7)
      Qed
     
     DPs:
      f{1,#}(s1(x)) -> f{1,#}(x)
     TRS:
      f1(s1(x)) -> f1(x)
      g1(cons2(0(),y)) -> g1(y)
      g1(cons2(s1(x),y)) -> s1(x)
      h1(cons2(x,y)) -> h1(g1(cons2(x,y)))
      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(),x7) -> f1(x7)
      app(s(),x7) -> s1(x7)
      app(g(),x7) -> g1(x7)
      app(cons1(x6),x7) -> cons2(x6,x7)
      app(cons(),x7) -> cons1(x7)
      app(h(),x7) -> h1(x7)
      app(map1(x6),x7) -> map2(x6,x7)
      app(map(),x7) -> map1(x7)
      app(filter1(x6),x7) -> filter2(x6,x7)
      app(filter(),x7) -> filter1(x7)
      app(filter23(x6,x5,x4),x7) -> filter24(x6,x5,x4,x7)
      app(filter22(x6,x5),x7) -> filter23(x6,x5,x7)
      app(filter21(x6),x7) -> filter22(x6,x7)
      app(filter2(),x7) -> filter21(x7)
     Subterm Criterion Processor:
      simple projection:
       pi(f{1,#}) = 0
      problem:
       DPs:
        
       TRS:
        f1(s1(x)) -> f1(x)
        g1(cons2(0(),y)) -> g1(y)
        g1(cons2(s1(x),y)) -> s1(x)
        h1(cons2(x,y)) -> h1(g1(cons2(x,y)))
        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(),x7) -> f1(x7)
        app(s(),x7) -> s1(x7)
        app(g(),x7) -> g1(x7)
        app(cons1(x6),x7) -> cons2(x6,x7)
        app(cons(),x7) -> cons1(x7)
        app(h(),x7) -> h1(x7)
        app(map1(x6),x7) -> map2(x6,x7)
        app(map(),x7) -> map1(x7)
        app(filter1(x6),x7) -> filter2(x6,x7)
        app(filter(),x7) -> filter1(x7)
        app(filter23(x6,x5,x4),x7) -> filter24(x6,x5,x4,x7)
        app(filter22(x6,x5),x7) -> filter23(x6,x5,x7)
        app(filter21(x6),x7) -> filter22(x6,x7)
        app(filter2(),x7) -> filter21(x7)
      Qed