YES

Problem:
 app(app(minus(),x),0()) -> x
 app(app(minus(),app(s(),x)),app(s(),y)) -> app(app(minus(),x),y)
 app(app(quot(),0()),app(s(),y)) -> 0()
 app(app(quot(),app(s(),x)),app(s(),y)) ->
 app(s(),app(app(quot(),app(app(minus(),x),y)),app(s(),y)))
 app(app(plus(),0()),y) -> y
 app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
 app(app(plus(),app(app(minus(),x),app(s(),0()))),app(app(minus(),y),app(s(),app(s(),z)))) ->
 app(app(plus(),app(app(minus(),y),app(s(),app(s(),z)))),app(app(minus(),x),app(s(),0())))
 app(app(plus(),app(app(plus(),x),app(s(),0()))),app(app(plus(),y),app(s(),app(s(),z)))) ->
 app(app(plus(),app(app(plus(),y),app(s(),app(s(),z)))),app(app(plus(),x),app(s(),0())))
 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:
  minus2(x,0()) -> x
  minus2(s1(x),s1(y)) -> minus2(x,y)
  quot2(0(),s1(y)) -> 0()
  quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y)))
  plus2(0(),y) -> y
  plus2(s1(x),y) -> s1(plus2(x,y))
  plus2(minus2(x,s1(0())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(0())))
  plus2(plus2(x,s1(0())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(0())))
  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(minus1(x7),x8) -> minus2(x7,x8)
  app(minus(),x8) -> minus1(x8)
  app(s(),x8) -> s1(x8)
  app(quot1(x7),x8) -> quot2(x7,x8)
  app(quot(),x8) -> quot1(x8)
  app(plus1(x7),x8) -> plus2(x7,x8)
  app(plus(),x8) -> plus1(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:
    minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
    quot{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
    quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y))
    plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
    plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
    plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0())))
    plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
    plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0())))
    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#(minus1(x7),x8) -> minus{2,#}(x7,x8)
    app#(quot1(x7),x8) -> quot{2,#}(x7,x8)
    app#(plus1(x7),x8) -> plus{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:
    minus2(x,0()) -> x
    minus2(s1(x),s1(y)) -> minus2(x,y)
    quot2(0(),s1(y)) -> 0()
    quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y)))
    plus2(0(),y) -> y
    plus2(s1(x),y) -> s1(plus2(x,y))
    plus2(minus2(x,s1(0())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(0())))
    plus2(plus2(x,s1(0())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(0())))
    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(minus1(x7),x8) -> minus2(x7,x8)
    app(minus(),x8) -> minus1(x8)
    app(s(),x8) -> s1(x8)
    app(quot1(x7),x8) -> quot2(x7,x8)
    app(quot(),x8) -> quot1(x8)
    app(plus1(x7),x8) -> plus2(x7,x8)
    app(plus(),x8) -> plus1(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:
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     quot{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y))
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
     plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0())))
     plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
     plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0())))
     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#(minus1(x7),x8) -> minus{2,#}(x7,x8)
     app#(quot1(x7),x8) -> quot{2,#}(x7,x8)
     app#(plus1(x7),x8) -> plus{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:
     minus2(x,0()) -> x
     minus2(s1(x),s1(y)) -> minus2(x,y)
     quot2(0(),s1(y)) -> 0()
     quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y)))
     plus2(0(),y) -> y
     plus2(s1(x),y) -> s1(plus2(x,y))
     plus2(minus2(x,s1(0())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(0())))
     plus2(plus2(x,s1(0())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(0())))
     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(minus1(x7),x8) -> minus2(x7,x8)
     app(minus(),x8) -> minus1(x8)
     app(s(),x8) -> s1(x8)
     app(quot1(x7),x8) -> quot2(x7,x8)
     app(quot(),x8) -> quot1(x8)
     app(plus1(x7),x8) -> plus2(x7,x8)
     app(plus(),x8) -> plus1(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#(plus1(x7),x8) -> plus{2,#}(x7,x8)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(quot1(x7),x8) -> quot{2,#}(x7,x8)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(minus1(x7),x8) -> minus{2,#}(x7,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#(plus1(x7),x8) -> plus{2,#}(x7,x8) ->
     plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
     plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0())))
     app#(plus1(x7),x8) -> plus{2,#}(x7,x8) ->
     plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
     plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0())))
     app#(plus1(x7),x8) -> plus{2,#}(x7,x8) ->
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     app#(quot1(x7),x8) -> quot{2,#}(x7,x8) ->
     quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y))
     app#(quot1(x7),x8) -> quot{2,#}(x7,x8) ->
     quot{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     app#(minus1(x7),x8) -> minus{2,#}(x7,x8) ->
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,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#(plus1(x7),x8) -> plus{2,#}(x7,x8)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(quot1(x7),x8) -> quot{2,#}(x7,x8)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(minus1(x7),x8) -> minus{2,#}(x7,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)
     plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
     plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0()))) ->
     plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
     plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0())))
     plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
     plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0()))) ->
     plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
     plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0())))
     plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
     plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0()))) ->
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y) ->
     plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
     plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0())))
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y) ->
     plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
     plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0())))
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y) ->
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
     plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0()))) ->
     plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
     plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0())))
     plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
     plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0()))) ->
     plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
     plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0())))
     plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
     plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0()))) ->
     plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
     quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y)) ->
     quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y))
     quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y)) ->
     quot{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     quot{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) ->
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) -> minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
    SCC Processor:
     #sccs: 4
     #rules: 14
     #arcs: 45/324
     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:
      minus2(x,0()) -> x
      minus2(s1(x),s1(y)) -> minus2(x,y)
      quot2(0(),s1(y)) -> 0()
      quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y)))
      plus2(0(),y) -> y
      plus2(s1(x),y) -> s1(plus2(x,y))
      plus2(minus2(x,s1(0())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(0())))
      plus2(plus2(x,s1(0())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(0())))
      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(minus1(x7),x8) -> minus2(x7,x8)
      app(minus(),x8) -> minus1(x8)
      app(s(),x8) -> s1(x8)
      app(quot1(x7),x8) -> quot2(x7,x8)
      app(quot(),x8) -> quot1(x8)
      app(plus1(x7),x8) -> plus2(x7,x8)
      app(plus(),x8) -> plus1(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:
        minus2(x,0()) -> x
        minus2(s1(x),s1(y)) -> minus2(x,y)
        quot2(0(),s1(y)) -> 0()
        quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y)))
        plus2(0(),y) -> y
        plus2(s1(x),y) -> s1(plus2(x,y))
        plus2(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
        plus2(minus2(y,s1(s1(z))),minus2(x,s1(0())))
        plus2(plus2(x,s1(0())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(0())))
        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(minus1(x7),x8) -> minus2(x7,x8)
        app(minus(),x8) -> minus1(x8)
        app(s(),x8) -> s1(x8)
        app(quot1(x7),x8) -> quot2(x7,x8)
        app(quot(),x8) -> quot1(x8)
        app(plus1(x7),x8) -> plus2(x7,x8)
        app(plus(),x8) -> plus1(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:
      plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
      plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
      plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0())))
      plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
      plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0())))
     TRS:
      minus2(x,0()) -> x
      minus2(s1(x),s1(y)) -> minus2(x,y)
      quot2(0(),s1(y)) -> 0()
      quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y)))
      plus2(0(),y) -> y
      plus2(s1(x),y) -> s1(plus2(x,y))
      plus2(minus2(x,s1(0())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(0())))
      plus2(plus2(x,s1(0())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(0())))
      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(minus1(x7),x8) -> minus2(x7,x8)
      app(minus(),x8) -> minus1(x8)
      app(s(),x8) -> s1(x8)
      app(quot1(x7),x8) -> quot2(x7,x8)
      app(quot(),x8) -> quot1(x8)
      app(plus1(x7),x8) -> plus2(x7,x8)
      app(plus(),x8) -> plus1(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)
     CDG Processor:
      DPs:
       plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
       plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
       plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0())))
       plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
       plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0())))
      TRS:
       minus2(x,0()) -> x
       minus2(s1(x),s1(y)) -> minus2(x,y)
       quot2(0(),s1(y)) -> 0()
       quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y)))
       plus2(0(),y) -> y
       plus2(s1(x),y) -> s1(plus2(x,y))
       plus2(minus2(x,s1(0())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(0())))
       plus2(plus2(x,s1(0())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(0())))
       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(minus1(x7),x8) -> minus2(x7,x8)
       app(minus(),x8) -> minus1(x8)
       app(s(),x8) -> s1(x8)
       app(quot1(x7),x8) -> quot2(x7,x8)
       app(quot(),x8) -> quot1(x8)
       app(plus1(x7),x8) -> plus2(x7,x8)
       app(plus(),x8) -> plus1(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:
       plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
       plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0()))) ->
       plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
       plus{2,#}(s1(x),y) -> plus{2,#}(x,y) ->
       plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
       plus{2,#}(s1(x),y) -> plus{2,#}(x,y) ->
       plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
       plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0())))
       plus{2,#}(s1(x),y) -> plus{2,#}(x,y) ->
       plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
       plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0())))
       plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
       plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0()))) ->
       plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
       plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
       plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0()))) ->
       plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
       plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0())))
       plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
       plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0()))) ->
       plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
       plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0())))
      Usable Rule Processor:
       DPs:
        plus{2,#}(s1(x),y) -> plus{2,#}(x,y)
        plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
        plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0())))
        plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
        plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0())))
       TRS:
        minus2(s1(x),s1(y)) -> minus2(x,y)
        minus2(x,0()) -> x
        plus2(0(),y) -> y
        plus2(s1(x),y) -> s1(plus2(x,y))
        plus2(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
        plus2(minus2(y,s1(s1(z))),minus2(x,s1(0())))
        plus2(plus2(x,s1(0())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(0())))
       Semantic Labeling Processor:
        dimension: 1
        usable rules:
         
        interpretation:
         [plus2](x0, x1) = x0 + x1,
         
         [s1](x0) = x0 + 1,
         
         [minus2](x0, x1) = x0,
         
         [0] = 0
         labeled:
          plus{2,#}
         usable (for model):
          plus{2,#}
          s1
          minus2
          0
          plus2
         argument filtering:
          pi(0) = []
          pi(minus2) = 1
          pi(s1) = []
          pi(plus2) = 1
          pi(plus{2,#}) = []
        precedence:
         plus{2,#} ~ plus2 ~ s1 ~ minus2 ~ 0
        problem:
         DPs:
          plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
          plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0())))
          plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
          plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0())))
         TRS:
          minus2(s1(x),s1(y)) -> minus2(x,y)
          minus2(x,0()) -> x
          plus2(0(),y) -> y
          plus2(s1(x),y) -> s1(plus2(x,y))
          plus2(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
          plus2(minus2(y,s1(s1(z))),minus2(x,s1(0())))
          plus2(plus2(x,s1(0())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(0())))
        Restore Modifier:
         DPs:
          plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
          plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0())))
          plus{2,#}(plus2(x,s1(0())),plus2(y,s1(s1(z)))) ->
          plus{2,#}(plus2(y,s1(s1(z))),plus2(x,s1(0())))
         TRS:
          minus2(x,0()) -> x
          minus2(s1(x),s1(y)) -> minus2(x,y)
          quot2(0(),s1(y)) -> 0()
          quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y)))
          plus2(0(),y) -> y
          plus2(s1(x),y) -> s1(plus2(x,y))
          plus2(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
          plus2(minus2(y,s1(s1(z))),minus2(x,s1(0())))
          plus2(plus2(x,s1(0())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(0())))
          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(minus1(x7),x8) -> minus2(x7,x8)
          app(minus(),x8) -> minus1(x8)
          app(s(),x8) -> s1(x8)
          app(quot1(x7),x8) -> quot2(x7,x8)
          app(quot(),x8) -> quot1(x8)
          app(plus1(x7),x8) -> plus2(x7,x8)
          app(plus(),x8) -> plus1(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: 1
          #rules: 1
          #arcs: 7/4
          DPs:
           plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
           plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0())))
          TRS:
           minus2(x,0()) -> x
           minus2(s1(x),s1(y)) -> minus2(x,y)
           quot2(0(),s1(y)) -> 0()
           quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y)))
           plus2(0(),y) -> y
           plus2(s1(x),y) -> s1(plus2(x,y))
           plus2(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
           plus2(minus2(y,s1(s1(z))),minus2(x,s1(0())))
           plus2(plus2(x,s1(0())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(0())))
           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(minus1(x7),x8) -> minus2(x7,x8)
           app(minus(),x8) -> minus1(x8)
           app(s(),x8) -> s1(x8)
           app(quot1(x7),x8) -> quot2(x7,x8)
           app(quot(),x8) -> quot1(x8)
           app(plus1(x7),x8) -> plus2(x7,x8)
           app(plus(),x8) -> plus1(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)
          Usable Rule Processor:
           DPs:
            plus{2,#}(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
            plus{2,#}(minus2(y,s1(s1(z))),minus2(x,s1(0())))
           TRS:
            minus2(s1(x),s1(y)) -> minus2(x,y)
            minus2(x,0()) -> x
           Semantic Labeling Processor:
            dimension: 2
            usable rules:
             
            interpretation:
                        [1 1]     [0]
             [s1](x0) = [0 0]x0 + [1],
             
                                [1 1]     [1 0]  
             [minus2](x0, x1) = [1 1]x0 + [0 0]x1,
             
                   [0]
             [0] = [0]
             labeled:
              plus{2,#}
              s1
             usable (for model):
              plus{2,#}
              minus2
              s1
              0
             argument filtering:
              pi(0) = []
              pi(minus2) = 1
              pi(s1) = []
              pi(plus{2,#}) = []
            precedence:
             plus{2,#} ~ s1 ~ minus2 ~ 0
            problem:
             DPs:
              
             TRS:
              minus2(s1(x),s1(y)) -> minus2(x,y)
              minus2(x,0()) -> x
            Qed
     
     DPs:
      quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y))
     TRS:
      minus2(x,0()) -> x
      minus2(s1(x),s1(y)) -> minus2(x,y)
      quot2(0(),s1(y)) -> 0()
      quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y)))
      plus2(0(),y) -> y
      plus2(s1(x),y) -> s1(plus2(x,y))
      plus2(minus2(x,s1(0())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(0())))
      plus2(plus2(x,s1(0())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(0())))
      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(minus1(x7),x8) -> minus2(x7,x8)
      app(minus(),x8) -> minus1(x8)
      app(s(),x8) -> s1(x8)
      app(quot1(x7),x8) -> quot2(x7,x8)
      app(quot(),x8) -> quot1(x8)
      app(plus1(x7),x8) -> plus2(x7,x8)
      app(plus(),x8) -> plus1(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)
     Usable Rule Processor:
      DPs:
       quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y))
      TRS:
       minus2(x,0()) -> x
       minus2(s1(x),s1(y)) -> minus2(x,y)
      Arctic Interpretation Processor:
       dimension: 1
       usable rules:
        minus2(x,0()) -> x
        minus2(s1(x),s1(y)) -> minus2(x,y)
       interpretation:
        [quot{2,#}](x0, x1) = 3x0 + -16,
        
        [s1](x0) = 1x0 + -3,
        
        [minus2](x0, x1) = x0 + -11,
        
        [0] = 8
       orientation:
        quot{2,#}(s1(x),s1(y)) = 4x + 0 >= 3x + -8 = quot{2,#}(minus2(x,y),s1(y))
        
        minus2(x,0()) = x + -11 >= x = x
        
        minus2(s1(x),s1(y)) = 1x + -3 >= x + -11 = minus2(x,y)
       problem:
        DPs:
         
        TRS:
         minus2(x,0()) -> x
         minus2(s1(x),s1(y)) -> minus2(x,y)
       Qed
     
     DPs:
      minus{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     TRS:
      minus2(x,0()) -> x
      minus2(s1(x),s1(y)) -> minus2(x,y)
      quot2(0(),s1(y)) -> 0()
      quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y)))
      plus2(0(),y) -> y
      plus2(s1(x),y) -> s1(plus2(x,y))
      plus2(minus2(x,s1(0())),minus2(y,s1(s1(z)))) -> plus2(minus2(y,s1(s1(z))),minus2(x,s1(0())))
      plus2(plus2(x,s1(0())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(0())))
      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(minus1(x7),x8) -> minus2(x7,x8)
      app(minus(),x8) -> minus1(x8)
      app(s(),x8) -> s1(x8)
      app(quot1(x7),x8) -> quot2(x7,x8)
      app(quot(),x8) -> quot1(x8)
      app(plus1(x7),x8) -> plus2(x7,x8)
      app(plus(),x8) -> plus1(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(minus{2,#}) = 1
      problem:
       DPs:
        
       TRS:
        minus2(x,0()) -> x
        minus2(s1(x),s1(y)) -> minus2(x,y)
        quot2(0(),s1(y)) -> 0()
        quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(y)))
        plus2(0(),y) -> y
        plus2(s1(x),y) -> s1(plus2(x,y))
        plus2(minus2(x,s1(0())),minus2(y,s1(s1(z)))) ->
        plus2(minus2(y,s1(s1(z))),minus2(x,s1(0())))
        plus2(plus2(x,s1(0())),plus2(y,s1(s1(z)))) -> plus2(plus2(y,s1(s1(z))),plus2(x,s1(0())))
        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(minus1(x7),x8) -> minus2(x7,x8)
        app(minus(),x8) -> minus1(x8)
        app(s(),x8) -> s1(x8)
        app(quot1(x7),x8) -> quot2(x7,x8)
        app(quot(),x8) -> quot1(x8)
        app(plus1(x7),x8) -> plus2(x7,x8)
        app(plus(),x8) -> plus1(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