YES

Problem:
 app(f(),app(f(),x)) -> app(g(),app(f(),x))
 app(g(),app(g(),x)) -> app(f(),x)
 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(f1(x)) -> g1(f1(x))
  g1(g1(x)) -> f1(x)
  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(),x6) -> f1(x6)
  app(g(),x6) -> g1(x6)
  app(map1(x5),x6) -> map2(x5,x6)
  app(map(),x6) -> map1(x6)
  app(cons1(x5),x6) -> cons2(x5,x6)
  app(cons(),x6) -> cons1(x6)
  app(filter1(x5),x6) -> filter2(x5,x6)
  app(filter(),x6) -> filter1(x6)
  app(filter23(x5,x4,x3),x6) -> filter24(x5,x4,x3,x6)
  app(filter22(x5,x4),x6) -> filter23(x5,x4,x6)
  app(filter21(x5),x6) -> filter22(x5,x6)
  app(filter2(),x6) -> filter21(x6)
  DP Processor:
   DPs:
    f{1,#}(f1(x)) -> g{1,#}(f1(x))
    g{1,#}(g1(x)) -> f{1,#}(x)
    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(),x6) -> f{1,#}(x6)
    app#(g(),x6) -> g{1,#}(x6)
    app#(map1(x5),x6) -> map{2,#}(x5,x6)
    app#(filter1(x5),x6) -> filter{2,#}(x5,x6)
    app#(filter23(x5,x4,x3),x6) -> filter2{4,#}(x5,x4,x3,x6)
   TRS:
    f1(f1(x)) -> g1(f1(x))
    g1(g1(x)) -> f1(x)
    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(),x6) -> f1(x6)
    app(g(),x6) -> g1(x6)
    app(map1(x5),x6) -> map2(x5,x6)
    app(map(),x6) -> map1(x6)
    app(cons1(x5),x6) -> cons2(x5,x6)
    app(cons(),x6) -> cons1(x6)
    app(filter1(x5),x6) -> filter2(x5,x6)
    app(filter(),x6) -> filter1(x6)
    app(filter23(x5,x4,x3),x6) -> filter24(x5,x4,x3,x6)
    app(filter22(x5,x4),x6) -> filter23(x5,x4,x6)
    app(filter21(x5),x6) -> filter22(x5,x6)
    app(filter2(),x6) -> filter21(x6)
   TDG Processor:
    DPs:
     f{1,#}(f1(x)) -> g{1,#}(f1(x))
     g{1,#}(g1(x)) -> f{1,#}(x)
     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(),x6) -> f{1,#}(x6)
     app#(g(),x6) -> g{1,#}(x6)
     app#(map1(x5),x6) -> map{2,#}(x5,x6)
     app#(filter1(x5),x6) -> filter{2,#}(x5,x6)
     app#(filter23(x5,x4,x3),x6) -> filter2{4,#}(x5,x4,x3,x6)
    TRS:
     f1(f1(x)) -> g1(f1(x))
     g1(g1(x)) -> f1(x)
     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(),x6) -> f1(x6)
     app(g(),x6) -> g1(x6)
     app(map1(x5),x6) -> map2(x5,x6)
     app(map(),x6) -> map1(x6)
     app(cons1(x5),x6) -> cons2(x5,x6)
     app(cons(),x6) -> cons1(x6)
     app(filter1(x5),x6) -> filter2(x5,x6)
     app(filter(),x6) -> filter1(x6)
     app(filter23(x5,x4,x3),x6) -> filter24(x5,x4,x3,x6)
     app(filter22(x5,x4),x6) -> filter23(x5,x4,x6)
     app(filter21(x5),x6) -> filter22(x5,x6)
     app(filter2(),x6) -> filter21(x6)
    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(x5,x4,x3),x6) -> filter2{4,#}(x5,x4,x3,x6)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter1(x5),x6) -> filter{2,#}(x5,x6)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(map1(x5),x6) -> map{2,#}(x5,x6)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(g(),x6) -> g{1,#}(x6)
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(f(),x6) -> f{1,#}(x6)
     app#(filter23(x5,x4,x3),x6) -> filter2{4,#}(x5,x4,x3,x6) ->
     filter2{4,#}(false(),fun,x,xs) -> filter{2,#}(fun,xs)
     app#(filter23(x5,x4,x3),x6) -> filter2{4,#}(x5,x4,x3,x6) ->
     filter2{4,#}(true(),fun,x,xs) -> filter{2,#}(fun,xs)
     app#(filter1(x5),x6) -> filter{2,#}(x5,x6) ->
     filter{2,#}(fun,cons2(x,xs)) -> filter2{4,#}(app(fun,x),fun,x,xs)
     app#(filter1(x5),x6) -> filter{2,#}(x5,x6) ->
     filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     app#(map1(x5),x6) -> map{2,#}(x5,x6) ->
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
     app#(map1(x5),x6) -> map{2,#}(x5,x6) ->
     map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
     app#(g(),x6) -> g{1,#}(x6) -> g{1,#}(g1(x)) -> f{1,#}(x)
     app#(f(),x6) -> f{1,#}(x6) ->
     f{1,#}(f1(x)) -> g{1,#}(f1(x))
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter23(x5,x4,x3),x6) -> filter2{4,#}(x5,x4,x3,x6)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(filter1(x5),x6) -> filter{2,#}(x5,x6)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(map1(x5),x6) -> map{2,#}(x5,x6)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(g(),x6) -> g{1,#}(x6)
     map{2,#}(fun,cons2(x,xs)) -> app#(fun,x) ->
     app#(f(),x6) -> f{1,#}(x6)
     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)
     g{1,#}(g1(x)) -> f{1,#}(x) -> f{1,#}(f1(x)) -> g{1,#}(f1(x))
     f{1,#}(f1(x)) -> g{1,#}(f1(x)) -> g{1,#}(g1(x)) -> f{1,#}(x)
    SCC Processor:
     #sccs: 2
     #rules: 11
     #arcs: 28/169
     DPs:
      filter2{4,#}(false(),fun,x,xs) -> filter{2,#}(fun,xs)
      filter{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
      app#(map1(x5),x6) -> map{2,#}(x5,x6)
      map{2,#}(fun,cons2(x,xs)) -> map{2,#}(fun,xs)
      map{2,#}(fun,cons2(x,xs)) -> app#(fun,x)
      app#(filter1(x5),x6) -> filter{2,#}(x5,x6)
      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(x5,x4,x3),x6) -> filter2{4,#}(x5,x4,x3,x6)
     TRS:
      f1(f1(x)) -> g1(f1(x))
      g1(g1(x)) -> f1(x)
      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(),x6) -> f1(x6)
      app(g(),x6) -> g1(x6)
      app(map1(x5),x6) -> map2(x5,x6)
      app(map(),x6) -> map1(x6)
      app(cons1(x5),x6) -> cons2(x5,x6)
      app(cons(),x6) -> cons1(x6)
      app(filter1(x5),x6) -> filter2(x5,x6)
      app(filter(),x6) -> filter1(x6)
      app(filter23(x5,x4,x3),x6) -> filter24(x5,x4,x3,x6)
      app(filter22(x5,x4),x6) -> filter23(x5,x4,x6)
      app(filter21(x5),x6) -> filter22(x5,x6)
      app(filter2(),x6) -> filter21(x6)
     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(x5),x6) -> map{2,#}(x5,x6)
        app#(filter1(x5),x6) -> filter{2,#}(x5,x6)
        filter2{4,#}(true(),fun,x,xs) -> filter{2,#}(fun,xs)
        app#(filter23(x5,x4,x3),x6) -> filter2{4,#}(x5,x4,x3,x6)
       TRS:
        f1(f1(x)) -> g1(f1(x))
        g1(g1(x)) -> f1(x)
        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(),x6) -> f1(x6)
        app(g(),x6) -> g1(x6)
        app(map1(x5),x6) -> map2(x5,x6)
        app(map(),x6) -> map1(x6)
        app(cons1(x5),x6) -> cons2(x5,x6)
        app(cons(),x6) -> cons1(x6)
        app(filter1(x5),x6) -> filter2(x5,x6)
        app(filter(),x6) -> filter1(x6)
        app(filter23(x5,x4,x3),x6) -> filter24(x5,x4,x3,x6)
        app(filter22(x5,x4),x6) -> filter23(x5,x4,x6)
        app(filter21(x5),x6) -> filter22(x5,x6)
        app(filter2(),x6) -> filter21(x6)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 20/25
       
     
     DPs:
      f{1,#}(f1(x)) -> g{1,#}(f1(x))
      g{1,#}(g1(x)) -> f{1,#}(x)
     TRS:
      f1(f1(x)) -> g1(f1(x))
      g1(g1(x)) -> f1(x)
      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(),x6) -> f1(x6)
      app(g(),x6) -> g1(x6)
      app(map1(x5),x6) -> map2(x5,x6)
      app(map(),x6) -> map1(x6)
      app(cons1(x5),x6) -> cons2(x5,x6)
      app(cons(),x6) -> cons1(x6)
      app(filter1(x5),x6) -> filter2(x5,x6)
      app(filter(),x6) -> filter1(x6)
      app(filter23(x5,x4,x3),x6) -> filter24(x5,x4,x3,x6)
      app(filter22(x5,x4),x6) -> filter23(x5,x4,x6)
      app(filter21(x5),x6) -> filter22(x5,x6)
      app(filter2(),x6) -> filter21(x6)
     Subterm Criterion Processor:
      simple projection:
       pi(f{1,#}) = 0
       pi(g{1,#}) = 0
      problem:
       DPs:
        f{1,#}(f1(x)) -> g{1,#}(f1(x))
       TRS:
        f1(f1(x)) -> g1(f1(x))
        g1(g1(x)) -> f1(x)
        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(),x6) -> f1(x6)
        app(g(),x6) -> g1(x6)
        app(map1(x5),x6) -> map2(x5,x6)
        app(map(),x6) -> map1(x6)
        app(cons1(x5),x6) -> cons2(x5,x6)
        app(cons(),x6) -> cons1(x6)
        app(filter1(x5),x6) -> filter2(x5,x6)
        app(filter(),x6) -> filter1(x6)
        app(filter23(x5,x4,x3),x6) -> filter24(x5,x4,x3,x6)
        app(filter22(x5,x4),x6) -> filter23(x5,x4,x6)
        app(filter21(x5),x6) -> filter22(x5,x6)
        app(filter2(),x6) -> filter21(x6)
      SCC Processor:
       #sccs: 0
       #rules: 0
       #arcs: 2/1