YES

Problem:
 app(f(),app(g(),x)) -> app(g(),app(f(),app(f(),x)))
 app(f(),app(h(),x)) -> app(h(),app(g(),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(g1(x)) -> g1(f1(f1(x)))
  f1(h1(x)) -> h1(g1(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(h(),x6) -> h1(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,#}(g1(x)) -> f{1,#}(x)
    f{1,#}(g1(x)) -> f{1,#}(f1(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#(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(g1(x)) -> g1(f1(f1(x)))
    f1(h1(x)) -> h1(g1(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(h(),x6) -> h1(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,#}(g1(x)) -> f{1,#}(x)
     f{1,#}(g1(x)) -> f{1,#}(f1(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#(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(g1(x)) -> g1(f1(f1(x)))
     f1(h1(x)) -> h1(g1(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(h(),x6) -> h1(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#(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#(f(),x6) -> f{1,#}(x6) -> f{1,#}(g1(x)) -> f{1,#}(f1(x))
     app#(f(),x6) -> f{1,#}(x6) ->
     f{1,#}(g1(x)) -> f{1,#}(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#(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)
     f{1,#}(g1(x)) -> f{1,#}(f1(x)) -> f{1,#}(g1(x)) -> f{1,#}(f1(x))
     f{1,#}(g1(x)) -> f{1,#}(f1(x)) -> f{1,#}(g1(x)) -> f{1,#}(x)
     f{1,#}(g1(x)) -> f{1,#}(x) -> f{1,#}(g1(x)) -> f{1,#}(f1(x))
     f{1,#}(g1(x)) -> f{1,#}(x) -> f{1,#}(g1(x)) -> f{1,#}(x)
    SCC Processor:
     #sccs: 2
     #rules: 11
     #arcs: 28/144
     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(g1(x)) -> g1(f1(f1(x)))
      f1(h1(x)) -> h1(g1(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(h(),x6) -> h1(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(g1(x)) -> g1(f1(f1(x)))
        f1(h1(x)) -> h1(g1(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(h(),x6) -> h1(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,#}(g1(x)) -> f{1,#}(x)
      f{1,#}(g1(x)) -> f{1,#}(f1(x))
     TRS:
      f1(g1(x)) -> g1(f1(f1(x)))
      f1(h1(x)) -> h1(g1(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(h(),x6) -> h1(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)
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [f{1,#}](x0) = x0,
       
       [filter21](x0) = x0,
       
       [filter22](x0, x1) = x0 + 1x1,
       
       [filter24](x0, x1, x2, x3) = x1 + x3 + 0,
       
       [filter23](x0, x1, x2) = x0 + x1 + x2 + 0,
       
       [filter2](x0, x1) = x0 + x1 + 0,
       
       [filter1](x0) = 1x0,
       
       [cons2](x0, x1) = x1 + 0,
       
       [cons1](x0) = x0 + 0,
       
       [map2](x0, x1) = x1 + 0,
       
       [map1](x0) = x0 + 1,
       
       [h1](x0) = 1,
       
       [g1](x0) = 2x0,
       
       [f1](x0) = x0,
       
       [false] = 6,
       
       [true] = 1,
       
       [filter2] = 4,
       
       [filter] = 0,
       
       [cons] = 0,
       
       [nil] = 0,
       
       [map] = 6,
       
       [h] = 1,
       
       [app](x0, x1) = x0 + 2x1 + 0,
       
       [g] = 0,
       
       [f] = 7
      orientation:
       f{1,#}(g1(x)) = 2x >= x = f{1,#}(x)
       
       f{1,#}(g1(x)) = 2x >= x = f{1,#}(f1(x))
       
       f1(g1(x)) = 2x >= 2x = g1(f1(f1(x)))
       
       f1(h1(x)) = 1 >= 1 = h1(g1(x))
       
       map2(fun,nil()) = 0 >= 0 = nil()
       
       map2(fun,cons2(x,xs)) = xs + 0 >= xs + 0 = cons2(app(fun,x),map2(fun,xs))
       
       filter2(fun,nil()) = fun + 0 >= 0 = nil()
       
       filter2(fun,cons2(x,xs)) = fun + xs + 0 >= fun + xs + 0 = filter24(app(fun,x),fun,x,xs)
       
       filter24(true(),fun,x,xs) = fun + xs + 0 >= fun + xs + 0 = cons2(x,filter2(fun,xs))
       
       filter24(false(),fun,x,xs) = fun + xs + 0 >= fun + xs + 0 = filter2(fun,xs)
       
       app(f(),x6) = 2x6 + 7 >= x6 = f1(x6)
       
       app(g(),x6) = 2x6 + 0 >= 2x6 = g1(x6)
       
       app(h(),x6) = 2x6 + 1 >= 1 = h1(x6)
       
       app(map1(x5),x6) = x5 + 2x6 + 1 >= x6 + 0 = map2(x5,x6)
       
       app(map(),x6) = 2x6 + 6 >= x6 + 1 = map1(x6)
       
       app(cons1(x5),x6) = x5 + 2x6 + 0 >= x6 + 0 = cons2(x5,x6)
       
       app(cons(),x6) = 2x6 + 0 >= x6 + 0 = cons1(x6)
       
       app(filter1(x5),x6) = 1x5 + 2x6 + 0 >= x5 + x6 + 0 = filter2(x5,x6)
       
       app(filter(),x6) = 2x6 + 0 >= 1x6 = filter1(x6)
       
       app(filter23(x5,x4,x3),x6) = x3 + x4 + x5 + 2x6 + 0 >= x4 + x6 + 0 = filter24(x5,x4,x3,x6)
       
       app(filter22(x5,x4),x6) = 1x4 + x5 + 2x6 + 0 >= x4 + x5 + x6 + 0 = filter23(x5,x4,x6)
       
       app(filter21(x5),x6) = x5 + 2x6 + 0 >= x5 + 1x6 = filter22(x5,x6)
       
       app(filter2(),x6) = 2x6 + 4 >= x6 = filter21(x6)
      problem:
       DPs:
        
       TRS:
        f1(g1(x)) -> g1(f1(f1(x)))
        f1(h1(x)) -> h1(g1(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(h(),x6) -> h1(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)
      Qed