YES

Problem:
 app(p(),app(s(),x)) -> x
 app(fact(),0()) -> app(s(),0())
 app(fact(),app(s(),x)) -> app(app(*(),app(s(),x)),app(fact(),app(p(),app(s(),x))))
 app(app(*(),0()),y) -> 0()
 app(app(*(),app(s(),x)),y) -> app(app(+(),app(app(*(),x),y)),y)
 app(app(+(),x),0()) -> x
 app(app(+(),x),app(s(),y)) -> app(s(),app(app(+(),x),y))
 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:
  p1(s1(x)) -> x
  fact1(0()) -> s1(0())
  fact1(s1(x)) -> *2(s1(x),fact1(p1(s1(x))))
  *2(0(),y) -> 0()
  *2(s1(x),y) -> +2(*2(x,y),y)
  +2(x,0()) -> x
  +2(x,s1(y)) -> s1(+2(x,y))
  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(p(),x7) -> p1(x7)
  app(s(),x7) -> s1(x7)
  app(fact(),x7) -> fact1(x7)
  app(*1(x6),x7) -> *2(x6,x7)
  app(*(),x7) -> *1(x7)
  app(+1(x6),x7) -> +2(x6,x7)
  app(+(),x7) -> +1(x7)
  app(map1(x6),x7) -> map2(x6,x7)
  app(map(),x7) -> map1(x7)
  app(cons1(x6),x7) -> cons2(x6,x7)
  app(cons(),x7) -> cons1(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:
    fact{1,#}(s1(x)) -> p{1,#}(s1(x))
    fact{1,#}(s1(x)) -> fact{1,#}(p1(s1(x)))
    fact{1,#}(s1(x)) -> *{2,#}(s1(x),fact1(p1(s1(x))))
    *{2,#}(s1(x),y) -> *{2,#}(x,y)
    *{2,#}(s1(x),y) -> +{2,#}(*2(x,y),y)
    +{2,#}(x,s1(y)) -> +{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#(p(),x7) -> p{1,#}(x7)
    app#(fact(),x7) -> fact{1,#}(x7)
    app#(*1(x6),x7) -> *{2,#}(x6,x7)
    app#(+1(x6),x7) -> +{2,#}(x6,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:
    p1(s1(x)) -> x
    fact1(0()) -> s1(0())
    fact1(s1(x)) -> *2(s1(x),fact1(p1(s1(x))))
    *2(0(),y) -> 0()
    *2(s1(x),y) -> +2(*2(x,y),y)
    +2(x,0()) -> x
    +2(x,s1(y)) -> s1(+2(x,y))
    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(p(),x7) -> p1(x7)
    app(s(),x7) -> s1(x7)
    app(fact(),x7) -> fact1(x7)
    app(*1(x6),x7) -> *2(x6,x7)
    app(*(),x7) -> *1(x7)
    app(+1(x6),x7) -> +2(x6,x7)
    app(+(),x7) -> +1(x7)
    app(map1(x6),x7) -> map2(x6,x7)
    app(map(),x7) -> map1(x7)
    app(cons1(x6),x7) -> cons2(x6,x7)
    app(cons(),x7) -> cons1(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:
     fact{1,#}(s1(x)) -> p{1,#}(s1(x))
     fact{1,#}(s1(x)) -> fact{1,#}(p1(s1(x)))
     fact{1,#}(s1(x)) -> *{2,#}(s1(x),fact1(p1(s1(x))))
     *{2,#}(s1(x),y) -> *{2,#}(x,y)
     *{2,#}(s1(x),y) -> +{2,#}(*2(x,y),y)
     +{2,#}(x,s1(y)) -> +{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#(p(),x7) -> p{1,#}(x7)
     app#(fact(),x7) -> fact{1,#}(x7)
     app#(*1(x6),x7) -> *{2,#}(x6,x7)
     app#(+1(x6),x7) -> +{2,#}(x6,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:
     p1(s1(x)) -> x
     fact1(0()) -> s1(0())
     fact1(s1(x)) -> *2(s1(x),fact1(p1(s1(x))))
     *2(0(),y) -> 0()
     *2(s1(x),y) -> +2(*2(x,y),y)
     +2(x,0()) -> x
     +2(x,s1(y)) -> s1(+2(x,y))
     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(p(),x7) -> p1(x7)
     app(s(),x7) -> s1(x7)
     app(fact(),x7) -> fact1(x7)
     app(*1(x6),x7) -> *2(x6,x7)
     app(*(),x7) -> *1(x7)
     app(+1(x6),x7) -> +2(x6,x7)
     app(+(),x7) -> +1(x7)
     app(map1(x6),x7) -> map2(x6,x7)
     app(map(),x7) -> map1(x7)
     app(cons1(x6),x7) -> cons2(x6,x7)
     app(cons(),x7) -> cons1(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(),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(x6,x5,x4),x7) -> filter2{4,#}(x6,x5,x4,x7)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x6),x7) -> filter{2,#}(x6,x7)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x6),x7) -> map{2,#}(x6,x7)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(+1(x6),x7) -> +{2,#}(x6,x7)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(*1(x6),x7) -> *{2,#}(x6,x7)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(fact(),x7) -> fact{1,#}(x7)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(p(),x7) -> p{1,#}(x7)
     app#(filter23(x6,x5,x4),x7) -> filter2{4,#}(x6,x5,x4,x7) ->
     filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter23(x6,x5,x4),x7) -> filter2{4,#}(x6,x5,x4,x7) ->
     filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
     app#(filter1(x6),x7) -> filter{2,#}(x6,x7) ->
     filter{2,#}(f,cons2(x,xs)) -> filter2{4,#}(app(f,x),f,x,xs)
     app#(filter1(x6),x7) -> filter{2,#}(x6,x7) ->
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x6),x7) -> map{2,#}(x6,x7) ->
     map{2,#}(f,cons2(x,xs)) -> app#(f,x)
     app#(map1(x6),x7) -> map{2,#}(x6,x7) ->
     map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
     app#(+1(x6),x7) -> +{2,#}(x6,x7) ->
     +{2,#}(x,s1(y)) -> +{2,#}(x,y)
     app#(*1(x6),x7) -> *{2,#}(x6,x7) ->
     *{2,#}(s1(x),y) -> +{2,#}(*2(x,y),y)
     app#(*1(x6),x7) -> *{2,#}(x6,x7) ->
     *{2,#}(s1(x),y) -> *{2,#}(x,y)
     app#(fact(),x7) -> fact{1,#}(x7) ->
     fact{1,#}(s1(x)) -> *{2,#}(s1(x),fact1(p1(s1(x))))
     app#(fact(),x7) -> fact{1,#}(x7) ->
     fact{1,#}(s1(x)) -> fact{1,#}(p1(s1(x)))
     app#(fact(),x7) -> fact{1,#}(x7) ->
     fact{1,#}(s1(x)) -> p{1,#}(s1(x))
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter23(x6,x5,x4),x7) -> filter2{4,#}(x6,x5,x4,x7)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(filter1(x6),x7) -> filter{2,#}(x6,x7)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(map1(x6),x7) -> map{2,#}(x6,x7)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(+1(x6),x7) -> +{2,#}(x6,x7)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(*1(x6),x7) -> *{2,#}(x6,x7)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(fact(),x7) -> fact{1,#}(x7)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(p(),x7) -> p{1,#}(x7)
     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)
     +{2,#}(x,s1(y)) -> +{2,#}(x,y) ->
     +{2,#}(x,s1(y)) -> +{2,#}(x,y)
     *{2,#}(s1(x),y) -> +{2,#}(*2(x,y),y) ->
     +{2,#}(x,s1(y)) -> +{2,#}(x,y)
     *{2,#}(s1(x),y) -> *{2,#}(x,y) ->
     *{2,#}(s1(x),y) -> +{2,#}(*2(x,y),y)
     *{2,#}(s1(x),y) -> *{2,#}(x,y) ->
     *{2,#}(s1(x),y) -> *{2,#}(x,y)
     fact{1,#}(s1(x)) -> *{2,#}(s1(x),fact1(p1(s1(x)))) ->
     *{2,#}(s1(x),y) -> +{2,#}(*2(x,y),y)
     fact{1,#}(s1(x)) -> *{2,#}(s1(x),fact1(p1(s1(x)))) ->
     *{2,#}(s1(x),y) -> *{2,#}(x,y)
     fact{1,#}(s1(x)) -> fact{1,#}(p1(s1(x))) ->
     fact{1,#}(s1(x)) -> *{2,#}(s1(x),fact1(p1(s1(x))))
     fact{1,#}(s1(x)) -> fact{1,#}(p1(s1(x))) ->
     fact{1,#}(s1(x)) -> fact{1,#}(p1(s1(x)))
     fact{1,#}(s1(x)) -> fact{1,#}(p1(s1(x))) -> fact{1,#}(s1(x)) -> p{1,#}(s1(x))
    SCC Processor:
     #sccs: 4
     #rules: 12
     #arcs: 43/361
     DPs:
      filter2{4,#}(false(),f,x,xs) -> filter{2,#}(f,xs)
      filter{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(map1(x6),x7) -> map{2,#}(x6,x7)
      map{2,#}(f,cons2(x,xs)) -> map{2,#}(f,xs)
      map{2,#}(f,cons2(x,xs)) -> app#(f,x)
      app#(filter1(x6),x7) -> filter{2,#}(x6,x7)
      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(x6,x5,x4),x7) -> filter2{4,#}(x6,x5,x4,x7)
     TRS:
      p1(s1(x)) -> x
      fact1(0()) -> s1(0())
      fact1(s1(x)) -> *2(s1(x),fact1(p1(s1(x))))
      *2(0(),y) -> 0()
      *2(s1(x),y) -> +2(*2(x,y),y)
      +2(x,0()) -> x
      +2(x,s1(y)) -> s1(+2(x,y))
      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(p(),x7) -> p1(x7)
      app(s(),x7) -> s1(x7)
      app(fact(),x7) -> fact1(x7)
      app(*1(x6),x7) -> *2(x6,x7)
      app(*(),x7) -> *1(x7)
      app(+1(x6),x7) -> +2(x6,x7)
      app(+(),x7) -> +1(x7)
      app(map1(x6),x7) -> map2(x6,x7)
      app(map(),x7) -> map1(x7)
      app(cons1(x6),x7) -> cons2(x6,x7)
      app(cons(),x7) -> cons1(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(),f,x,xs) -> filter{2,#}(f,xs)
        app#(map1(x6),x7) -> map{2,#}(x6,x7)
        app#(filter1(x6),x7) -> filter{2,#}(x6,x7)
        filter2{4,#}(true(),f,x,xs) -> filter{2,#}(f,xs)
        app#(filter23(x6,x5,x4),x7) -> filter2{4,#}(x6,x5,x4,x7)
       TRS:
        p1(s1(x)) -> x
        fact1(0()) -> s1(0())
        fact1(s1(x)) -> *2(s1(x),fact1(p1(s1(x))))
        *2(0(),y) -> 0()
        *2(s1(x),y) -> +2(*2(x,y),y)
        +2(x,0()) -> x
        +2(x,s1(y)) -> s1(+2(x,y))
        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(p(),x7) -> p1(x7)
        app(s(),x7) -> s1(x7)
        app(fact(),x7) -> fact1(x7)
        app(*1(x6),x7) -> *2(x6,x7)
        app(*(),x7) -> *1(x7)
        app(+1(x6),x7) -> +2(x6,x7)
        app(+(),x7) -> +1(x7)
        app(map1(x6),x7) -> map2(x6,x7)
        app(map(),x7) -> map1(x7)
        app(cons1(x6),x7) -> cons2(x6,x7)
        app(cons(),x7) -> cons1(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:
      fact{1,#}(s1(x)) -> fact{1,#}(p1(s1(x)))
     TRS:
      p1(s1(x)) -> x
      fact1(0()) -> s1(0())
      fact1(s1(x)) -> *2(s1(x),fact1(p1(s1(x))))
      *2(0(),y) -> 0()
      *2(s1(x),y) -> +2(*2(x,y),y)
      +2(x,0()) -> x
      +2(x,s1(y)) -> s1(+2(x,y))
      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(p(),x7) -> p1(x7)
      app(s(),x7) -> s1(x7)
      app(fact(),x7) -> fact1(x7)
      app(*1(x6),x7) -> *2(x6,x7)
      app(*(),x7) -> *1(x7)
      app(+1(x6),x7) -> +2(x6,x7)
      app(+(),x7) -> +1(x7)
      app(map1(x6),x7) -> map2(x6,x7)
      app(map(),x7) -> map1(x7)
      app(cons1(x6),x7) -> cons2(x6,x7)
      app(cons(),x7) -> cons1(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)
     Usable Rule Processor:
      DPs:
       fact{1,#}(s1(x)) -> fact{1,#}(p1(s1(x)))
      TRS:
       p1(s1(x)) -> x
      Semantic Labeling Processor:
       dimension: 2
       usable rules:
        
       interpretation:
                   [1 1]     [0]
        [s1](x0) = [1 1]x0 + [1],
        
                   [1 0]  
        [p1](x0) = [1 0]x0
        labeled:
         fact{1,#}
        usable (for model):
         fact{1,#}
         s1
         p1
        argument filtering:
         pi(p1) = 0
         pi(s1) = 0
         pi(fact{1,#}) = []
       precedence:
        fact{1,#} ~ s1 ~ p1
       problem:
        DPs:
         
        TRS:
         p1(s1(x)) -> x
       Qed
     
     DPs:
      *{2,#}(s1(x),y) -> *{2,#}(x,y)
     TRS:
      p1(s1(x)) -> x
      fact1(0()) -> s1(0())
      fact1(s1(x)) -> *2(s1(x),fact1(p1(s1(x))))
      *2(0(),y) -> 0()
      *2(s1(x),y) -> +2(*2(x,y),y)
      +2(x,0()) -> x
      +2(x,s1(y)) -> s1(+2(x,y))
      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(p(),x7) -> p1(x7)
      app(s(),x7) -> s1(x7)
      app(fact(),x7) -> fact1(x7)
      app(*1(x6),x7) -> *2(x6,x7)
      app(*(),x7) -> *1(x7)
      app(+1(x6),x7) -> +2(x6,x7)
      app(+(),x7) -> +1(x7)
      app(map1(x6),x7) -> map2(x6,x7)
      app(map(),x7) -> map1(x7)
      app(cons1(x6),x7) -> cons2(x6,x7)
      app(cons(),x7) -> cons1(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(*{2,#}) = 0
      problem:
       DPs:
        
       TRS:
        p1(s1(x)) -> x
        fact1(0()) -> s1(0())
        fact1(s1(x)) -> *2(s1(x),fact1(p1(s1(x))))
        *2(0(),y) -> 0()
        *2(s1(x),y) -> +2(*2(x,y),y)
        +2(x,0()) -> x
        +2(x,s1(y)) -> s1(+2(x,y))
        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(p(),x7) -> p1(x7)
        app(s(),x7) -> s1(x7)
        app(fact(),x7) -> fact1(x7)
        app(*1(x6),x7) -> *2(x6,x7)
        app(*(),x7) -> *1(x7)
        app(+1(x6),x7) -> +2(x6,x7)
        app(+(),x7) -> +1(x7)
        app(map1(x6),x7) -> map2(x6,x7)
        app(map(),x7) -> map1(x7)
        app(cons1(x6),x7) -> cons2(x6,x7)
        app(cons(),x7) -> cons1(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:
      +{2,#}(x,s1(y)) -> +{2,#}(x,y)
     TRS:
      p1(s1(x)) -> x
      fact1(0()) -> s1(0())
      fact1(s1(x)) -> *2(s1(x),fact1(p1(s1(x))))
      *2(0(),y) -> 0()
      *2(s1(x),y) -> +2(*2(x,y),y)
      +2(x,0()) -> x
      +2(x,s1(y)) -> s1(+2(x,y))
      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(p(),x7) -> p1(x7)
      app(s(),x7) -> s1(x7)
      app(fact(),x7) -> fact1(x7)
      app(*1(x6),x7) -> *2(x6,x7)
      app(*(),x7) -> *1(x7)
      app(+1(x6),x7) -> +2(x6,x7)
      app(+(),x7) -> +1(x7)
      app(map1(x6),x7) -> map2(x6,x7)
      app(map(),x7) -> map1(x7)
      app(cons1(x6),x7) -> cons2(x6,x7)
      app(cons(),x7) -> cons1(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(+{2,#}) = 1
      problem:
       DPs:
        
       TRS:
        p1(s1(x)) -> x
        fact1(0()) -> s1(0())
        fact1(s1(x)) -> *2(s1(x),fact1(p1(s1(x))))
        *2(0(),y) -> 0()
        *2(s1(x),y) -> +2(*2(x,y),y)
        +2(x,0()) -> x
        +2(x,s1(y)) -> s1(+2(x,y))
        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(p(),x7) -> p1(x7)
        app(s(),x7) -> s1(x7)
        app(fact(),x7) -> fact1(x7)
        app(*1(x6),x7) -> *2(x6,x7)
        app(*(),x7) -> *1(x7)
        app(+1(x6),x7) -> +2(x6,x7)
        app(+(),x7) -> +1(x7)
        app(map1(x6),x7) -> map2(x6,x7)
        app(map(),x7) -> map1(x7)
        app(cons1(x6),x7) -> cons2(x6,x7)
        app(cons(),x7) -> cons1(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