YES

Problem:
 app(pred(),app(s(),x)) -> x
 app(app(minus(),x),0()) -> x
 app(app(minus(),x),app(s(),y)) -> app(pred(),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(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:
  pred1(s1(x)) -> x
  minus2(x,0()) -> x
  minus2(x,s1(y)) -> pred1(minus2(x,y))
  quot2(0(),s1(y)) -> 0()
  quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(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(pred(),x7) -> pred1(x7)
  app(s(),x7) -> s1(x7)
  app(minus1(x6),x7) -> minus2(x6,x7)
  app(minus(),x7) -> minus1(x7)
  app(quot1(x6),x7) -> quot2(x6,x7)
  app(quot(),x7) -> quot1(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:
    minus{2,#}(x,s1(y)) -> minus{2,#}(x,y)
    minus{2,#}(x,s1(y)) -> pred{1,#}(minus2(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))
    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#(pred(),x7) -> pred{1,#}(x7)
    app#(minus1(x6),x7) -> minus{2,#}(x6,x7)
    app#(quot1(x6),x7) -> quot{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:
    pred1(s1(x)) -> x
    minus2(x,0()) -> x
    minus2(x,s1(y)) -> pred1(minus2(x,y))
    quot2(0(),s1(y)) -> 0()
    quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(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(pred(),x7) -> pred1(x7)
    app(s(),x7) -> s1(x7)
    app(minus1(x6),x7) -> minus2(x6,x7)
    app(minus(),x7) -> minus1(x7)
    app(quot1(x6),x7) -> quot2(x6,x7)
    app(quot(),x7) -> quot1(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:
     minus{2,#}(x,s1(y)) -> minus{2,#}(x,y)
     minus{2,#}(x,s1(y)) -> pred{1,#}(minus2(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))
     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#(pred(),x7) -> pred{1,#}(x7)
     app#(minus1(x6),x7) -> minus{2,#}(x6,x7)
     app#(quot1(x6),x7) -> quot{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:
     pred1(s1(x)) -> x
     minus2(x,0()) -> x
     minus2(x,s1(y)) -> pred1(minus2(x,y))
     quot2(0(),s1(y)) -> 0()
     quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(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(pred(),x7) -> pred1(x7)
     app(s(),x7) -> s1(x7)
     app(minus1(x6),x7) -> minus2(x6,x7)
     app(minus(),x7) -> minus1(x7)
     app(quot1(x6),x7) -> quot2(x6,x7)
     app(quot(),x7) -> quot1(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#(quot1(x6),x7) -> quot{2,#}(x6,x7)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(minus1(x6),x7) -> minus{2,#}(x6,x7)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(pred(),x7) -> pred{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#(quot1(x6),x7) -> quot{2,#}(x6,x7) ->
     quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y))
     app#(quot1(x6),x7) -> quot{2,#}(x6,x7) ->
     quot{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y)
     app#(minus1(x6),x7) -> minus{2,#}(x6,x7) ->
     minus{2,#}(x,s1(y)) -> pred{1,#}(minus2(x,y))
     app#(minus1(x6),x7) -> minus{2,#}(x6,x7) ->
     minus{2,#}(x,s1(y)) -> minus{2,#}(x,y)
     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#(quot1(x6),x7) -> quot{2,#}(x6,x7)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(minus1(x6),x7) -> minus{2,#}(x6,x7)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(pred(),x7) -> pred{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)
     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,#}(x,s1(y)) -> pred{1,#}(minus2(x,y))
     quot{2,#}(s1(x),s1(y)) -> minus{2,#}(x,y) ->
     minus{2,#}(x,s1(y)) -> minus{2,#}(x,y)
     minus{2,#}(x,s1(y)) -> minus{2,#}(x,y) ->
     minus{2,#}(x,s1(y)) -> pred{1,#}(minus2(x,y))
     minus{2,#}(x,s1(y)) -> minus{2,#}(x,y) -> minus{2,#}(x,s1(y)) -> minus{2,#}(x,y)
    SCC Processor:
     #sccs: 3
     #rules: 11
     #arcs: 36/256
     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:
      pred1(s1(x)) -> x
      minus2(x,0()) -> x
      minus2(x,s1(y)) -> pred1(minus2(x,y))
      quot2(0(),s1(y)) -> 0()
      quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(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(pred(),x7) -> pred1(x7)
      app(s(),x7) -> s1(x7)
      app(minus1(x6),x7) -> minus2(x6,x7)
      app(minus(),x7) -> minus1(x7)
      app(quot1(x6),x7) -> quot2(x6,x7)
      app(quot(),x7) -> quot1(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:
        pred1(s1(x)) -> x
        minus2(x,0()) -> x
        minus2(x,s1(y)) -> pred1(minus2(x,y))
        quot2(0(),s1(y)) -> 0()
        quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(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(pred(),x7) -> pred1(x7)
        app(s(),x7) -> s1(x7)
        app(minus1(x6),x7) -> minus2(x6,x7)
        app(minus(),x7) -> minus1(x7)
        app(quot1(x6),x7) -> quot2(x6,x7)
        app(quot(),x7) -> quot1(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:
      quot{2,#}(s1(x),s1(y)) -> quot{2,#}(minus2(x,y),s1(y))
     TRS:
      pred1(s1(x)) -> x
      minus2(x,0()) -> x
      minus2(x,s1(y)) -> pred1(minus2(x,y))
      quot2(0(),s1(y)) -> 0()
      quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(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(pred(),x7) -> pred1(x7)
      app(s(),x7) -> s1(x7)
      app(minus1(x6),x7) -> minus2(x6,x7)
      app(minus(),x7) -> minus1(x7)
      app(quot1(x6),x7) -> quot2(x6,x7)
      app(quot(),x7) -> quot1(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)
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [quot{2,#}](x0, x1) = x0,
       
       [filter21](x0) = x0 + 6,
       
       [filter22](x0, x1) = x0 + 2x1 + 6,
       
       [filter24](x0, x1, x2, x3) = x3 + 5,
       
       [filter23](x0, x1, x2) = x1,
       
       [filter2](x0, x1) = x1 + 5,
       
       [filter1](x0) = 1x0 + 1,
       
       [cons2](x0, x1) = x1 + 0,
       
       [cons1](x0) = 0,
       
       [map2](x0, x1) = 5,
       
       [map1](x0) = x0 + 7,
       
       [quot2](x0, x1) = x0,
       
       [quot1](x0) = 2x0 + 5,
       
       [minus2](x0, x1) = x0,
       
       [minus1](x0) = x0,
       
       [s1](x0) = 1x0,
       
       [pred1](x0) = x0,
       
       [false] = 2,
       
       [true] = 4,
       
       [filter2] = 6,
       
       [filter] = 2,
       
       [cons] = 5,
       
       [nil] = 4,
       
       [map] = 7,
       
       [quot] = 2,
       
       [0] = 0,
       
       [minus] = 5,
       
       [app](x0, x1) = x0 + 2x1 + 5,
       
       [s] = 0,
       
       [pred] = 5
      orientation:
       quot{2,#}(s1(x),s1(y)) = 1x >= x = quot{2,#}(minus2(x,y),s1(y))
       
       pred1(s1(x)) = 1x >= x = x
       
       minus2(x,0()) = x >= x = x
       
       minus2(x,s1(y)) = x >= x = pred1(minus2(x,y))
       
       quot2(0(),s1(y)) = 0 >= 0 = 0()
       
       quot2(s1(x),s1(y)) = 1x >= 1x = s1(quot2(minus2(x,y),s1(y)))
       
       map2(f,nil()) = 5 >= 4 = nil()
       
       map2(f,cons2(x,xs)) = 5 >= 5 = cons2(app(f,x),map2(f,xs))
       
       filter2(f,nil()) = 5 >= 4 = nil()
       
       filter2(f,cons2(x,xs)) = xs + 5 >= xs + 5 = filter24(app(f,x),f,x,xs)
       
       filter24(true(),f,x,xs) = xs + 5 >= xs + 5 = cons2(x,filter2(f,xs))
       
       filter24(false(),f,x,xs) = xs + 5 >= xs + 5 = filter2(f,xs)
       
       app(pred(),x7) = 2x7 + 5 >= x7 = pred1(x7)
       
       app(s(),x7) = 2x7 + 5 >= 1x7 = s1(x7)
       
       app(minus1(x6),x7) = x6 + 2x7 + 5 >= x6 = minus2(x6,x7)
       
       app(minus(),x7) = 2x7 + 5 >= x7 = minus1(x7)
       
       app(quot1(x6),x7) = 2x6 + 2x7 + 5 >= x6 = quot2(x6,x7)
       
       app(quot(),x7) = 2x7 + 5 >= 2x7 + 5 = quot1(x7)
       
       app(map1(x6),x7) = x6 + 2x7 + 7 >= 5 = map2(x6,x7)
       
       app(map(),x7) = 2x7 + 7 >= x7 + 7 = map1(x7)
       
       app(cons1(x6),x7) = 2x7 + 5 >= x7 + 0 = cons2(x6,x7)
       
       app(cons(),x7) = 2x7 + 5 >= 0 = cons1(x7)
       
       app(filter1(x6),x7) = 1x6 + 2x7 + 5 >= x7 + 5 = filter2(x6,x7)
       
       app(filter(),x7) = 2x7 + 5 >= 1x7 + 1 = filter1(x7)
       
       app(filter23(x6,x5,x4),x7) = x5 + 2x7 + 5 >= x7 + 5 = filter24(x6,x5,x4,x7)
       
       app(filter22(x6,x5),x7) = 2x5 + x6 + 2x7 + 6 >= x5 = filter23(x6,x5,x7)
       
       app(filter21(x6),x7) = x6 + 2x7 + 6 >= x6 + 2x7 + 6 = filter22(x6,x7)
       
       app(filter2(),x7) = 2x7 + 6 >= x7 + 6 = filter21(x7)
      problem:
       DPs:
        
       TRS:
        pred1(s1(x)) -> x
        minus2(x,0()) -> x
        minus2(x,s1(y)) -> pred1(minus2(x,y))
        quot2(0(),s1(y)) -> 0()
        quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(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(pred(),x7) -> pred1(x7)
        app(s(),x7) -> s1(x7)
        app(minus1(x6),x7) -> minus2(x6,x7)
        app(minus(),x7) -> minus1(x7)
        app(quot1(x6),x7) -> quot2(x6,x7)
        app(quot(),x7) -> quot1(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:
      minus{2,#}(x,s1(y)) -> minus{2,#}(x,y)
     TRS:
      pred1(s1(x)) -> x
      minus2(x,0()) -> x
      minus2(x,s1(y)) -> pred1(minus2(x,y))
      quot2(0(),s1(y)) -> 0()
      quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(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(pred(),x7) -> pred1(x7)
      app(s(),x7) -> s1(x7)
      app(minus1(x6),x7) -> minus2(x6,x7)
      app(minus(),x7) -> minus1(x7)
      app(quot1(x6),x7) -> quot2(x6,x7)
      app(quot(),x7) -> quot1(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(minus{2,#}) = 1
      problem:
       DPs:
        
       TRS:
        pred1(s1(x)) -> x
        minus2(x,0()) -> x
        minus2(x,s1(y)) -> pred1(minus2(x,y))
        quot2(0(),s1(y)) -> 0()
        quot2(s1(x),s1(y)) -> s1(quot2(minus2(x,y),s1(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(pred(),x7) -> pred1(x7)
        app(s(),x7) -> s1(x7)
        app(minus1(x6),x7) -> minus2(x6,x7)
        app(minus(),x7) -> minus1(x7)
        app(quot1(x6),x7) -> quot2(x6,x7)
        app(quot(),x7) -> quot1(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