YES

Problem:
 app(not(),app(not(),x)) -> x
 app(not(),app(app(or(),x),y)) -> app(app(and(),app(not(),x)),app(not(),y))
 app(not(),app(app(and(),x),y)) -> app(app(or(),app(not(),x)),app(not(),y))
 app(app(and(),x),app(app(or(),y),z)) -> app(app(or(),app(app(and(),x),y)),app(app(and(),x),z))
 app(app(and(),app(app(or(),y),z)),x) -> app(app(or(),app(app(and(),x),y)),app(app(and(),x),z))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
 app(app(filter(),f),nil()) -> nil()
 app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
 app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
 app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)

Proof:
 Uncurry Processor:
  not1(not1(x)) -> x
  not1(or2(x,y)) -> and2(not1(x),not1(y))
  not1(and2(x,y)) -> or2(not1(x),not1(y))
  and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
  and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
  map2(f,nil()) -> nil()
  map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
  filter2(f,nil()) -> nil()
  filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
  filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
  filter24(false(),f,x,xs) -> filter2(f,xs)
  app(not(),x8) -> not1(x8)
  app(or1(x7),x8) -> or2(x7,x8)
  app(or(),x8) -> or1(x8)
  app(and1(x7),x8) -> and2(x7,x8)
  app(and(),x8) -> and1(x8)
  app(map1(x7),x8) -> map2(x7,x8)
  app(map(),x8) -> map1(x8)
  app(cons1(x7),x8) -> cons2(x7,x8)
  app(cons(),x8) -> cons1(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:
    not{1,#}(or2(x,y)) -> not{1,#}(y)
    not{1,#}(or2(x,y)) -> not{1,#}(x)
    not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y))
    not{1,#}(and2(x,y)) -> not{1,#}(y)
    not{1,#}(and2(x,y)) -> not{1,#}(x)
    and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
    and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
    and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
    and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
    map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
    map{2,#}(f,cons2(x,xs)) -> app#(f,x)
    filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
    filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
    filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
    filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs)
    app#(not(),x8) -> not{1,#}(x8)
    app#(and1(x7),x8) -> and{2,#}(x7,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:
    not1(not1(x)) -> x
    not1(or2(x,y)) -> and2(not1(x),not1(y))
    not1(and2(x,y)) -> or2(not1(x),not1(y))
    and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
    and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
    map2(f,nil()) -> nil()
    map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
    filter2(f,nil()) -> nil()
    filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
    filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
    filter24(false(),f,x,xs) -> filter2(f,xs)
    app(not(),x8) -> not1(x8)
    app(or1(x7),x8) -> or2(x7,x8)
    app(or(),x8) -> or1(x8)
    app(and1(x7),x8) -> and2(x7,x8)
    app(and(),x8) -> and1(x8)
    app(map1(x7),x8) -> map2(x7,x8)
    app(map(),x8) -> map1(x8)
    app(cons1(x7),x8) -> cons2(x7,x8)
    app(cons(),x8) -> cons1(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:
     not{1,#}(or2(x,y)) -> not{1,#}(y)
     not{1,#}(or2(x,y)) -> not{1,#}(x)
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y))
     not{1,#}(and2(x,y)) -> not{1,#}(y)
     not{1,#}(and2(x,y)) -> not{1,#}(x)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
     filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs)
     app#(not(),x8) -> not{1,#}(x8)
     app#(and1(x7),x8) -> and{2,#}(x7,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:
     not1(not1(x)) -> x
     not1(or2(x,y)) -> and2(not1(x),not1(y))
     not1(and2(x,y)) -> or2(not1(x),not1(y))
     and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
     and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
     map2(f,nil()) -> nil()
     map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
     filter2(f,nil()) -> nil()
     filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
     filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
     filter24(false(),f,x,xs) -> filter2(f,xs)
     app(not(),x8) -> not1(x8)
     app(or1(x7),x8) -> or2(x7,x8)
     app(or(),x8) -> or1(x8)
     app(and1(x7),x8) -> and2(x7,x8)
     app(and(),x8) -> and1(x8)
     app(map1(x7),x8) -> map2(x7,x8)
     app(map(),x8) -> map1(x8)
     app(cons1(x7),x8) -> cons2(x7,x8)
     app(cons(),x8) -> cons1(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(),f,x,xs) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) ->
     filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs)
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs) ->
     filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(and1(x7),x8) -> and{2,#}(x7,x8)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(not(),x8) -> not{1,#}(x8)
     app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8) ->
     filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8) ->
     filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter1(x7),x8) -> filter{2,#}(x7,x8) ->
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     app#(filter1(x7),x8) -> filter{2,#}(x7,x8) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x7),x8) -> map{2,#}(x7,x8) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x7),x8) -> map{2,#}(x7,x8) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     app#(and1(x7),x8) -> and{2,#}(x7,x8) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     app#(and1(x7),x8) -> and{2,#}(x7,x8) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
     app#(and1(x7),x8) -> and{2,#}(x7,x8) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
     app#(and1(x7),x8) -> and{2,#}(x7,x8) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
     app#(not(),x8) -> not{1,#}(x8) ->
     not{1,#}(and2(x,y)) -> not{1,#}(x)
     app#(not(),x8) -> not{1,#}(x8) ->
     not{1,#}(and2(x,y)) -> not{1,#}(y)
     app#(not(),x8) -> not{1,#}(x8) ->
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y))
     app#(not(),x8) -> not{1,#}(x8) ->
     not{1,#}(or2(x,y)) -> not{1,#}(x)
     app#(not(),x8) -> not{1,#}(x8) ->
     not{1,#}(or2(x,y)) -> not{1,#}(y)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x7),x8) -> map{2,#}(x7,x8)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(and1(x7),x8) -> and{2,#}(x7,x8)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(not(),x8) -> not{1,#}(x8)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
     not{1,#}(and2(x,y)) -> not{1,#}(y) ->
     not{1,#}(and2(x,y)) -> not{1,#}(x)
     not{1,#}(and2(x,y)) -> not{1,#}(y) ->
     not{1,#}(and2(x,y)) -> not{1,#}(y)
     not{1,#}(and2(x,y)) -> not{1,#}(y) ->
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y))
     not{1,#}(and2(x,y)) -> not{1,#}(y) ->
     not{1,#}(or2(x,y)) -> not{1,#}(x)
     not{1,#}(and2(x,y)) -> not{1,#}(y) ->
     not{1,#}(or2(x,y)) -> not{1,#}(y)
     not{1,#}(and2(x,y)) -> not{1,#}(x) ->
     not{1,#}(and2(x,y)) -> not{1,#}(x)
     not{1,#}(and2(x,y)) -> not{1,#}(x) ->
     not{1,#}(and2(x,y)) -> not{1,#}(y)
     not{1,#}(and2(x,y)) -> not{1,#}(x) ->
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y))
     not{1,#}(and2(x,y)) -> not{1,#}(x) ->
     not{1,#}(or2(x,y)) -> not{1,#}(x)
     not{1,#}(and2(x,y)) -> not{1,#}(x) ->
     not{1,#}(or2(x,y)) -> not{1,#}(y)
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y)) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y)) ->
     and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y)) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y)) ->
     and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
     not{1,#}(or2(x,y)) -> not{1,#}(y) ->
     not{1,#}(and2(x,y)) -> not{1,#}(x)
     not{1,#}(or2(x,y)) -> not{1,#}(y) ->
     not{1,#}(and2(x,y)) -> not{1,#}(y)
     not{1,#}(or2(x,y)) -> not{1,#}(y) ->
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y))
     not{1,#}(or2(x,y)) -> not{1,#}(y) ->
     not{1,#}(or2(x,y)) -> not{1,#}(x)
     not{1,#}(or2(x,y)) -> not{1,#}(y) ->
     not{1,#}(or2(x,y)) -> not{1,#}(y)
     not{1,#}(or2(x,y)) -> not{1,#}(x) ->
     not{1,#}(and2(x,y)) -> not{1,#}(x)
     not{1,#}(or2(x,y)) -> not{1,#}(x) ->
     not{1,#}(and2(x,y)) -> not{1,#}(y)
     not{1,#}(or2(x,y)) -> not{1,#}(x) ->
     not{1,#}(or2(x,y)) -> and{2,#}(not1(x),not1(y))
     not{1,#}(or2(x,y)) -> not{1,#}(x) ->
     not{1,#}(or2(x,y)) -> not{1,#}(x)
     not{1,#}(or2(x,y)) -> not{1,#}(x) -> not{1,#}(or2(x,y)) -> not{1,#}(y)
    SCC Processor:
     #sccs: 3
     #rules: 17
     #arcs: 73/400
     DPs:
      filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs)
      filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(map1(x7),x8) -> map{2,#}(x7,x8)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
      filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
      filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
      app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
     TRS:
      not1(not1(x)) -> x
      not1(or2(x,y)) -> and2(not1(x),not1(y))
      not1(and2(x,y)) -> or2(not1(x),not1(y))
      and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
      and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      filter2(f,nil()) -> nil()
      filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
      filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
      filter24(false(),f,x,xs) -> filter2(f,xs)
      app(not(),x8) -> not1(x8)
      app(or1(x7),x8) -> or2(x7,x8)
      app(or(),x8) -> or1(x8)
      app(and1(x7),x8) -> and2(x7,x8)
      app(and(),x8) -> and1(x8)
      app(map1(x7),x8) -> map2(x7,x8)
      app(map(),x8) -> map1(x8)
      app(cons1(x7),x8) -> cons2(x7,x8)
      app(cons(),x8) -> cons1(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(),f,x,xs) -> filter{2,#}(f,xs)
        app#(map1(x7),x8) -> map{2,#}(x7,x8)
        app#(filter1(x7),x8) -> filter{2,#}(x7,x8)
        filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
        app#(filter23(x7,x6,x5),x8) -> filter2{4,#}(x7,x6,x5,x8)
       TRS:
        not1(not1(x)) -> x
        not1(or2(x,y)) -> and2(not1(x),not1(y))
        not1(and2(x,y)) -> or2(not1(x),not1(y))
        and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
        and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        filter2(f,nil()) -> nil()
        filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
        filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
        filter24(false(),f,x,xs) -> filter2(f,xs)
        app(not(),x8) -> not1(x8)
        app(or1(x7),x8) -> or2(x7,x8)
        app(or(),x8) -> or1(x8)
        app(and1(x7),x8) -> and2(x7,x8)
        app(and(),x8) -> and1(x8)
        app(map1(x7),x8) -> map2(x7,x8)
        app(map(),x8) -> map1(x8)
        app(cons1(x7),x8) -> cons2(x7,x8)
        app(cons(),x8) -> cons1(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:
      not{1,#}(or2(x,y)) -> not{1,#}(y)
      not{1,#}(or2(x,y)) -> not{1,#}(x)
      not{1,#}(and2(x,y)) -> not{1,#}(y)
      not{1,#}(and2(x,y)) -> not{1,#}(x)
     TRS:
      not1(not1(x)) -> x
      not1(or2(x,y)) -> and2(not1(x),not1(y))
      not1(and2(x,y)) -> or2(not1(x),not1(y))
      and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
      and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      filter2(f,nil()) -> nil()
      filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
      filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
      filter24(false(),f,x,xs) -> filter2(f,xs)
      app(not(),x8) -> not1(x8)
      app(or1(x7),x8) -> or2(x7,x8)
      app(or(),x8) -> or1(x8)
      app(and1(x7),x8) -> and2(x7,x8)
      app(and(),x8) -> and1(x8)
      app(map1(x7),x8) -> map2(x7,x8)
      app(map(),x8) -> map1(x8)
      app(cons1(x7),x8) -> cons2(x7,x8)
      app(cons(),x8) -> cons1(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(not{1,#}) = 0
      problem:
       DPs:
        
       TRS:
        not1(not1(x)) -> x
        not1(or2(x,y)) -> and2(not1(x),not1(y))
        not1(and2(x,y)) -> or2(not1(x),not1(y))
        and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
        and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
        map2(f,nil()) -> nil()
        map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
        filter2(f,nil()) -> nil()
        filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
        filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
        filter24(false(),f,x,xs) -> filter2(f,xs)
        app(not(),x8) -> not1(x8)
        app(or1(x7),x8) -> or2(x7,x8)
        app(or(),x8) -> or1(x8)
        app(and1(x7),x8) -> and2(x7,x8)
        app(and(),x8) -> and1(x8)
        app(map1(x7),x8) -> map2(x7,x8)
        app(map(),x8) -> map1(x8)
        app(cons1(x7),x8) -> cons2(x7,x8)
        app(cons(),x8) -> cons1(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
     
     DPs:
      and{2,#}(x,or2(y,z)) -> and{2,#}(x,z)
      and{2,#}(x,or2(y,z)) -> and{2,#}(x,y)
      and{2,#}(or2(y,z),x) -> and{2,#}(x,z)
      and{2,#}(or2(y,z),x) -> and{2,#}(x,y)
     TRS:
      not1(not1(x)) -> x
      not1(or2(x,y)) -> and2(not1(x),not1(y))
      not1(and2(x,y)) -> or2(not1(x),not1(y))
      and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
      and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
      map2(f,nil()) -> nil()
      map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
      filter2(f,nil()) -> nil()
      filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
      filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
      filter24(false(),f,x,xs) -> filter2(f,xs)
      app(not(),x8) -> not1(x8)
      app(or1(x7),x8) -> or2(x7,x8)
      app(or(),x8) -> or1(x8)
      app(and1(x7),x8) -> and2(x7,x8)
      app(and(),x8) -> and1(x8)
      app(map1(x7),x8) -> map2(x7,x8)
      app(map(),x8) -> map1(x8)
      app(cons1(x7),x8) -> cons2(x7,x8)
      app(cons(),x8) -> cons1(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)
     Size-Change Termination Processor:
      DPs:
       
      TRS:
       not1(not1(x)) -> x
       not1(or2(x,y)) -> and2(not1(x),not1(y))
       not1(and2(x,y)) -> or2(not1(x),not1(y))
       and2(x,or2(y,z)) -> or2(and2(x,y),and2(x,z))
       and2(or2(y,z),x) -> or2(and2(x,y),and2(x,z))
       map2(f,nil()) -> nil()
       map2(f,cons2(x,xs)) -> cons2(app(f,x),map2(f,xs))
       filter2(f,nil()) -> nil()
       filter2(f,cons2(x,xs)) -> filter24(app(f,x),f,x,xs)
       filter24(true(),f,x,xs) -> cons2(x,filter2(f,xs))
       filter24(false(),f,x,xs) -> filter2(f,xs)
       app(not(),x8) -> not1(x8)
       app(or1(x7),x8) -> or2(x7,x8)
       app(or(),x8) -> or1(x8)
       app(and1(x7),x8) -> and2(x7,x8)
       app(and(),x8) -> and1(x8)
       app(map1(x7),x8) -> map2(x7,x8)
       app(map(),x8) -> map1(x8)
       app(cons1(x7),x8) -> cons2(x7,x8)
       app(cons(),x8) -> cons1(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)
      The DP: and{2,#}(x,or2(y,z)) -> and{2,#}(x,z) has the edges:
        0 >=  0
        1 >   1
      The DP: and{2,#}(x,or2(y,z)) -> and{2,#}(x,y) has the edges:
        0 >=  0
        1 >   1
      The DP: and{2,#}(or2(y,z),x) -> and{2,#}(x,z) has the edges:
        0 >   1
        1 >=  0
      The DP: and{2,#}(or2(y,z),x) -> and{2,#}(x,y) has the edges:
        0 >   1
        1 >=  0
      Qed