YES

Problem:
 app(app(le(),0()),y) -> true()
 app(app(le(),app(s(),x)),0()) -> false()
 app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y)
 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(gcd(),0()),y) -> y
 app(app(gcd(),app(s(),x)),0()) -> app(s(),x)
 app(app(gcd(),app(s(),x)),app(s(),y)) ->
 app(app(app(if_gcd(),app(app(le(),y),x)),app(s(),x)),app(s(),y))
 app(app(app(if_gcd(),true()),app(s(),x)),app(s(),y)) ->
 app(app(gcd(),app(app(minus(),x),y)),app(s(),y))
 app(app(app(if_gcd(),false()),app(s(),x)),app(s(),y)) ->
 app(app(gcd(),app(app(minus(),y),x)),app(s(),x))
 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:
  le2(0(),y) -> true()
  le2(s1(x),0()) -> false()
  le2(s1(x),s1(y)) -> le2(x,y)
  pred1(s1(x)) -> x
  minus2(x,0()) -> x
  minus2(x,s1(y)) -> pred1(minus2(x,y))
  gcd2(0(),y) -> y
  gcd2(s1(x),0()) -> s1(x)
  gcd2(s1(x),s1(y)) -> if_gcd3(le2(y,x),s1(x),s1(y))
  if_gcd3(true(),s1(x),s1(y)) -> gcd2(minus2(x,y),s1(y))
  if_gcd3(false(),s1(x),s1(y)) -> gcd2(minus2(y,x),s1(x))
  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(le1(x6),x7) -> le2(x6,x7)
  app(le(),x7) -> le1(x7)
  app(s(),x7) -> s1(x7)
  app(pred(),x7) -> pred1(x7)
  app(minus1(x6),x7) -> minus2(x6,x7)
  app(minus(),x7) -> minus1(x7)
  app(gcd1(x6),x7) -> gcd2(x6,x7)
  app(gcd(),x7) -> gcd1(x7)
  app(if_gcd2(x6,x5),x7) -> if_gcd3(x6,x5,x7)
  app(if_gcd1(x6),x7) -> if_gcd2(x6,x7)
  app(if_gcd(),x7) -> if_gcd1(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:
    le{2,#}(s1(x),s1(y)) -> le{2,#}(x,y)
    minus{2,#}(x,s1(y)) -> minus{2,#}(x,y)
    minus{2,#}(x,s1(y)) -> pred{1,#}(minus2(x,y))
    gcd{2,#}(s1(x),s1(y)) -> le{2,#}(y,x)
    gcd{2,#}(s1(x),s1(y)) -> if_gcd{3,#}(le2(y,x),s1(x),s1(y))
    if_gcd{3,#}(true(),s1(x),s1(y)) -> minus{2,#}(x,y)
    if_gcd{3,#}(true(),s1(x),s1(y)) -> gcd{2,#}(minus2(x,y),s1(y))
    if_gcd{3,#}(false(),s1(x),s1(y)) -> minus{2,#}(y,x)
    if_gcd{3,#}(false(),s1(x),s1(y)) -> gcd{2,#}(minus2(y,x),s1(x))
    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#(le1(x6),x7) -> le{2,#}(x6,x7)
    app#(pred(),x7) -> pred{1,#}(x7)
    app#(minus1(x6),x7) -> minus{2,#}(x6,x7)
    app#(gcd1(x6),x7) -> gcd{2,#}(x6,x7)
    app#(if_gcd2(x6,x5),x7) -> if_gcd{3,#}(x6,x5,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:
    le2(0(),y) -> true()
    le2(s1(x),0()) -> false()
    le2(s1(x),s1(y)) -> le2(x,y)
    pred1(s1(x)) -> x
    minus2(x,0()) -> x
    minus2(x,s1(y)) -> pred1(minus2(x,y))
    gcd2(0(),y) -> y
    gcd2(s1(x),0()) -> s1(x)
    gcd2(s1(x),s1(y)) -> if_gcd3(le2(y,x),s1(x),s1(y))
    if_gcd3(true(),s1(x),s1(y)) -> gcd2(minus2(x,y),s1(y))
    if_gcd3(false(),s1(x),s1(y)) -> gcd2(minus2(y,x),s1(x))
    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(le1(x6),x7) -> le2(x6,x7)
    app(le(),x7) -> le1(x7)
    app(s(),x7) -> s1(x7)
    app(pred(),x7) -> pred1(x7)
    app(minus1(x6),x7) -> minus2(x6,x7)
    app(minus(),x7) -> minus1(x7)
    app(gcd1(x6),x7) -> gcd2(x6,x7)
    app(gcd(),x7) -> gcd1(x7)
    app(if_gcd2(x6,x5),x7) -> if_gcd3(x6,x5,x7)
    app(if_gcd1(x6),x7) -> if_gcd2(x6,x7)
    app(if_gcd(),x7) -> if_gcd1(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:
     le{2,#}(s1(x),s1(y)) -> le{2,#}(x,y)
     minus{2,#}(x,s1(y)) -> minus{2,#}(x,y)
     minus{2,#}(x,s1(y)) -> pred{1,#}(minus2(x,y))
     gcd{2,#}(s1(x),s1(y)) -> le{2,#}(y,x)
     gcd{2,#}(s1(x),s1(y)) -> if_gcd{3,#}(le2(y,x),s1(x),s1(y))
     if_gcd{3,#}(true(),s1(x),s1(y)) -> minus{2,#}(x,y)
     if_gcd{3,#}(true(),s1(x),s1(y)) -> gcd{2,#}(minus2(x,y),s1(y))
     if_gcd{3,#}(false(),s1(x),s1(y)) -> minus{2,#}(y,x)
     if_gcd{3,#}(false(),s1(x),s1(y)) -> gcd{2,#}(minus2(y,x),s1(x))
     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#(le1(x6),x7) -> le{2,#}(x6,x7)
     app#(pred(),x7) -> pred{1,#}(x7)
     app#(minus1(x6),x7) -> minus{2,#}(x6,x7)
     app#(gcd1(x6),x7) -> gcd{2,#}(x6,x7)
     app#(if_gcd2(x6,x5),x7) -> if_gcd{3,#}(x6,x5,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:
     le2(0(),y) -> true()
     le2(s1(x),0()) -> false()
     le2(s1(x),s1(y)) -> le2(x,y)
     pred1(s1(x)) -> x
     minus2(x,0()) -> x
     minus2(x,s1(y)) -> pred1(minus2(x,y))
     gcd2(0(),y) -> y
     gcd2(s1(x),0()) -> s1(x)
     gcd2(s1(x),s1(y)) -> if_gcd3(le2(y,x),s1(x),s1(y))
     if_gcd3(true(),s1(x),s1(y)) -> gcd2(minus2(x,y),s1(y))
     if_gcd3(false(),s1(x),s1(y)) -> gcd2(minus2(y,x),s1(x))
     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(le1(x6),x7) -> le2(x6,x7)
     app(le(),x7) -> le1(x7)
     app(s(),x7) -> s1(x7)
     app(pred(),x7) -> pred1(x7)
     app(minus1(x6),x7) -> minus2(x6,x7)
     app(minus(),x7) -> minus1(x7)
     app(gcd1(x6),x7) -> gcd2(x6,x7)
     app(gcd(),x7) -> gcd1(x7)
     app(if_gcd2(x6,x5),x7) -> if_gcd3(x6,x5,x7)
     app(if_gcd1(x6),x7) -> if_gcd2(x6,x7)
     app(if_gcd(),x7) -> if_gcd1(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#(if_gcd2(x6,x5),x7) -> if_gcd{3,#}(x6,x5,x7)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(gcd1(x6),x7) -> gcd{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)
     filter{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(le1(x6),x7) -> le{2,#}(x6,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#(if_gcd2(x6,x5),x7) -> if_gcd{3,#}(x6,x5,x7) ->
     if_gcd{3,#}(false(),s1(x),s1(y)) -> gcd{2,#}(minus2(y,x),s1(x))
     app#(if_gcd2(x6,x5),x7) -> if_gcd{3,#}(x6,x5,x7) ->
     if_gcd{3,#}(false(),s1(x),s1(y)) -> minus{2,#}(y,x)
     app#(if_gcd2(x6,x5),x7) -> if_gcd{3,#}(x6,x5,x7) ->
     if_gcd{3,#}(true(),s1(x),s1(y)) -> gcd{2,#}(minus2(x,y),s1(y))
     app#(if_gcd2(x6,x5),x7) -> if_gcd{3,#}(x6,x5,x7) ->
     if_gcd{3,#}(true(),s1(x),s1(y)) -> minus{2,#}(x,y)
     app#(gcd1(x6),x7) -> gcd{2,#}(x6,x7) ->
     gcd{2,#}(s1(x),s1(y)) -> if_gcd{3,#}(le2(y,x),s1(x),s1(y))
     app#(gcd1(x6),x7) -> gcd{2,#}(x6,x7) ->
     gcd{2,#}(s1(x),s1(y)) -> le{2,#}(y,x)
     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)
     app#(le1(x6),x7) -> le{2,#}(x6,x7) ->
     le{2,#}(s1(x),s1(y)) -> le{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#(if_gcd2(x6,x5),x7) -> if_gcd{3,#}(x6,x5,x7)
     map{2,#}(f,cons2(x,xs)) -> app#(f,x) ->
     app#(gcd1(x6),x7) -> gcd{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)) -> app#(f,x) ->
     app#(le1(x6),x7) -> le{2,#}(x6,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)
     if_gcd{3,#}(false(),s1(x),s1(y)) -> gcd{2,#}(minus2(y,x),s1(x)) ->
     gcd{2,#}(s1(x),s1(y)) -> if_gcd{3,#}(le2(y,x),s1(x),s1(y))
     if_gcd{3,#}(false(),s1(x),s1(y)) -> gcd{2,#}(minus2(y,x),s1(x)) ->
     gcd{2,#}(s1(x),s1(y)) -> le{2,#}(y,x)
     if_gcd{3,#}(false(),s1(x),s1(y)) -> minus{2,#}(y,x) ->
     minus{2,#}(x,s1(y)) -> pred{1,#}(minus2(x,y))
     if_gcd{3,#}(false(),s1(x),s1(y)) -> minus{2,#}(y,x) ->
     minus{2,#}(x,s1(y)) -> minus{2,#}(x,y)
     if_gcd{3,#}(true(),s1(x),s1(y)) -> gcd{2,#}(minus2(x,y),s1(y)) ->
     gcd{2,#}(s1(x),s1(y)) -> if_gcd{3,#}(le2(y,x),s1(x),s1(y))
     if_gcd{3,#}(true(),s1(x),s1(y)) -> gcd{2,#}(minus2(x,y),s1(y)) ->
     gcd{2,#}(s1(x),s1(y)) -> le{2,#}(y,x)
     if_gcd{3,#}(true(),s1(x),s1(y)) -> minus{2,#}(x,y) ->
     minus{2,#}(x,s1(y)) -> pred{1,#}(minus2(x,y))
     if_gcd{3,#}(true(),s1(x),s1(y)) -> minus{2,#}(x,y) ->
     minus{2,#}(x,s1(y)) -> minus{2,#}(x,y)
     gcd{2,#}(s1(x),s1(y)) -> if_gcd{3,#}(le2(y,x),s1(x),s1(y)) ->
     if_gcd{3,#}(false(),s1(x),s1(y)) -> gcd{2,#}(minus2(y,x),s1(x))
     gcd{2,#}(s1(x),s1(y)) -> if_gcd{3,#}(le2(y,x),s1(x),s1(y)) ->
     if_gcd{3,#}(false(),s1(x),s1(y)) -> minus{2,#}(y,x)
     gcd{2,#}(s1(x),s1(y)) -> if_gcd{3,#}(le2(y,x),s1(x),s1(y)) ->
     if_gcd{3,#}(true(),s1(x),s1(y)) -> gcd{2,#}(minus2(x,y),s1(y))
     gcd{2,#}(s1(x),s1(y)) -> if_gcd{3,#}(le2(y,x),s1(x),s1(y)) ->
     if_gcd{3,#}(true(),s1(x),s1(y)) -> minus{2,#}(x,y)
     gcd{2,#}(s1(x),s1(y)) -> le{2,#}(y,x) ->
     le{2,#}(s1(x),s1(y)) -> le{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)
     le{2,#}(s1(x),s1(y)) -> le{2,#}(x,y) -> le{2,#}(s1(x),s1(y)) -> le{2,#}(x,y)
    SCC Processor:
     #sccs: 4
     #rules: 14
     #arcs: 55/529
     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:
      le2(0(),y) -> true()
      le2(s1(x),0()) -> false()
      le2(s1(x),s1(y)) -> le2(x,y)
      pred1(s1(x)) -> x
      minus2(x,0()) -> x
      minus2(x,s1(y)) -> pred1(minus2(x,y))
      gcd2(0(),y) -> y
      gcd2(s1(x),0()) -> s1(x)
      gcd2(s1(x),s1(y)) -> if_gcd3(le2(y,x),s1(x),s1(y))
      if_gcd3(true(),s1(x),s1(y)) -> gcd2(minus2(x,y),s1(y))
      if_gcd3(false(),s1(x),s1(y)) -> gcd2(minus2(y,x),s1(x))
      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(le1(x6),x7) -> le2(x6,x7)
      app(le(),x7) -> le1(x7)
      app(s(),x7) -> s1(x7)
      app(pred(),x7) -> pred1(x7)
      app(minus1(x6),x7) -> minus2(x6,x7)
      app(minus(),x7) -> minus1(x7)
      app(gcd1(x6),x7) -> gcd2(x6,x7)
      app(gcd(),x7) -> gcd1(x7)
      app(if_gcd2(x6,x5),x7) -> if_gcd3(x6,x5,x7)
      app(if_gcd1(x6),x7) -> if_gcd2(x6,x7)
      app(if_gcd(),x7) -> if_gcd1(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:
        le2(0(),y) -> true()
        le2(s1(x),0()) -> false()
        le2(s1(x),s1(y)) -> le2(x,y)
        pred1(s1(x)) -> x
        minus2(x,0()) -> x
        minus2(x,s1(y)) -> pred1(minus2(x,y))
        gcd2(0(),y) -> y
        gcd2(s1(x),0()) -> s1(x)
        gcd2(s1(x),s1(y)) -> if_gcd3(le2(y,x),s1(x),s1(y))
        if_gcd3(true(),s1(x),s1(y)) -> gcd2(minus2(x,y),s1(y))
        if_gcd3(false(),s1(x),s1(y)) -> gcd2(minus2(y,x),s1(x))
        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(le1(x6),x7) -> le2(x6,x7)
        app(le(),x7) -> le1(x7)
        app(s(),x7) -> s1(x7)
        app(pred(),x7) -> pred1(x7)
        app(minus1(x6),x7) -> minus2(x6,x7)
        app(minus(),x7) -> minus1(x7)
        app(gcd1(x6),x7) -> gcd2(x6,x7)
        app(gcd(),x7) -> gcd1(x7)
        app(if_gcd2(x6,x5),x7) -> if_gcd3(x6,x5,x7)
        app(if_gcd1(x6),x7) -> if_gcd2(x6,x7)
        app(if_gcd(),x7) -> if_gcd1(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:
      gcd{2,#}(s1(x),s1(y)) -> if_gcd{3,#}(le2(y,x),s1(x),s1(y))
      if_gcd{3,#}(true(),s1(x),s1(y)) -> gcd{2,#}(minus2(x,y),s1(y))
      if_gcd{3,#}(false(),s1(x),s1(y)) -> gcd{2,#}(minus2(y,x),s1(x))
     TRS:
      le2(0(),y) -> true()
      le2(s1(x),0()) -> false()
      le2(s1(x),s1(y)) -> le2(x,y)
      pred1(s1(x)) -> x
      minus2(x,0()) -> x
      minus2(x,s1(y)) -> pred1(minus2(x,y))
      gcd2(0(),y) -> y
      gcd2(s1(x),0()) -> s1(x)
      gcd2(s1(x),s1(y)) -> if_gcd3(le2(y,x),s1(x),s1(y))
      if_gcd3(true(),s1(x),s1(y)) -> gcd2(minus2(x,y),s1(y))
      if_gcd3(false(),s1(x),s1(y)) -> gcd2(minus2(y,x),s1(x))
      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(le1(x6),x7) -> le2(x6,x7)
      app(le(),x7) -> le1(x7)
      app(s(),x7) -> s1(x7)
      app(pred(),x7) -> pred1(x7)
      app(minus1(x6),x7) -> minus2(x6,x7)
      app(minus(),x7) -> minus1(x7)
      app(gcd1(x6),x7) -> gcd2(x6,x7)
      app(gcd(),x7) -> gcd1(x7)
      app(if_gcd2(x6,x5),x7) -> if_gcd3(x6,x5,x7)
      app(if_gcd1(x6),x7) -> if_gcd2(x6,x7)
      app(if_gcd(),x7) -> if_gcd1(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)
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [if_gcd{3,#}](x0, x1, x2) = 1/2x0 + x1 + 1/2x2 + 2,
       
       [gcd{2,#}](x0, x1) = x0 + 1/2x1 + 7/2,
       
       [filter21](x0) = 0,
       
       [filter22](x0, x1) = 1,
       
       [filter24](x0, x1, x2, x3) = 0,
       
       [filter23](x0, x1, x2) = 1,
       
       [filter2](x0, x1) = 0,
       
       [filter1](x0) = 2x0 + 1,
       
       [cons2](x0, x1) = 0,
       
       [cons1](x0) = 0,
       
       [map2](x0, x1) = 2x1 + 1,
       
       [map1](x0) = 2x0 + 1,
       
       [if_gcd1](x0) = 2x0,
       
       [if_gcd3](x0, x1, x2) = x1 + x2 + 1/2,
       
       [if_gcd2](x0, x1) = 2x1 + 1,
       
       [gcd2](x0, x1) = x0 + x1 + 2,
       
       [gcd1](x0) = 2x0 + 2,
       
       [minus2](x0, x1) = x0 + 1/2,
       
       [minus1](x0) = 2x0,
       
       [pred1](x0) = x0,
       
       [s1](x0) = 2x0 + 2,
       
       [le2](x0, x1) = 1,
       
       [le1](x0) = 0,
       
       [filter2] = 0,
       
       [filter] = 3,
       
       [cons] = 0,
       
       [nil] = 0,
       
       [map] = 2,
       
       [if_gcd] = 2,
       
       [gcd] = 2,
       
       [minus] = 0,
       
       [pred] = 0,
       
       [false] = 1,
       
       [s] = 3,
       
       [true] = 0,
       
       [app](x0, x1) = 1/2x0 + 2x1 + 1,
       
       [0] = 0,
       
       [le] = 0
      orientation:
       gcd{2,#}(s1(x),s1(y)) = 2x + y + 13/2 >= 2x + y + 11/2 = if_gcd{3,#}(le2(y,x),s1(x),s1(y))
       
       if_gcd{3,#}(true(),s1(x),s1(y)) = 2x + y + 5 >= x + y + 5 = gcd{2,#}(minus2(x,y),s1(y))
       
       if_gcd{3,#}(false(),s1(x),s1(y)) = 2x + y + 11/2 >= x + y + 5 = gcd{2,#}(minus2(y,x),s1(x))
       
       le2(0(),y) = 1 >= 0 = true()
       
       le2(s1(x),0()) = 1 >= 1 = false()
       
       le2(s1(x),s1(y)) = 1 >= 1 = le2(x,y)
       
       pred1(s1(x)) = 2x + 2 >= x = x
       
       minus2(x,0()) = x + 1/2 >= x = x
       
       minus2(x,s1(y)) = x + 1/2 >= x + 1/2 = pred1(minus2(x,y))
       
       gcd2(0(),y) = y + 2 >= y = y
       
       gcd2(s1(x),0()) = 2x + 4 >= 2x + 2 = s1(x)
       
       gcd2(s1(x),s1(y)) = 2x + 2y + 6 >= 2x + 2y + 9/2 = if_gcd3(le2(y,x),s1(x),s1(y))
       
       if_gcd3(true(),s1(x),s1(y)) = 2x + 2y + 9/2 >= x + 2y + 9/2 = gcd2(minus2(x,y),s1(y))
       
       if_gcd3(false(),s1(x),s1(y)) = 2x + 2y + 9/2 >= 2x + y + 9/2 = gcd2(minus2(y,x),s1(x))
       
       map2(f,nil()) = 1 >= 0 = nil()
       
       map2(f,cons2(x,xs)) = 1 >= 0 = cons2(app(f,x),map2(f,xs))
       
       filter2(f,nil()) = 0 >= 0 = nil()
       
       filter2(f,cons2(x,xs)) = 0 >= 0 = filter24(app(f,x),f,x,xs)
       
       filter24(true(),f,x,xs) = 0 >= 0 = cons2(x,filter2(f,xs))
       
       filter24(false(),f,x,xs) = 0 >= 0 = filter2(f,xs)
       
       app(le1(x6),x7) = 2x7 + 1 >= 1 = le2(x6,x7)
       
       app(le(),x7) = 2x7 + 1 >= 0 = le1(x7)
       
       app(s(),x7) = 2x7 + 5/2 >= 2x7 + 2 = s1(x7)
       
       app(pred(),x7) = 2x7 + 1 >= x7 = pred1(x7)
       
       app(minus1(x6),x7) = x6 + 2x7 + 1 >= x6 + 1/2 = minus2(x6,x7)
       
       app(minus(),x7) = 2x7 + 1 >= 2x7 = minus1(x7)
       
       app(gcd1(x6),x7) = x6 + 2x7 + 2 >= x6 + x7 + 2 = gcd2(x6,x7)
       
       app(gcd(),x7) = 2x7 + 2 >= 2x7 + 2 = gcd1(x7)
       
       app(if_gcd2(x6,x5),x7) = x5 + 2x7 + 3/2 >= x5 + x7 + 1/2 = if_gcd3(x6,x5,x7)
       
       app(if_gcd1(x6),x7) = x6 + 2x7 + 1 >= 2x7 + 1 = if_gcd2(x6,x7)
       
       app(if_gcd(),x7) = 2x7 + 2 >= 2x7 = if_gcd1(x7)
       
       app(map1(x6),x7) = x6 + 2x7 + 3/2 >= 2x7 + 1 = map2(x6,x7)
       
       app(map(),x7) = 2x7 + 2 >= 2x7 + 1 = map1(x7)
       
       app(cons1(x6),x7) = 2x7 + 1 >= 0 = cons2(x6,x7)
       
       app(cons(),x7) = 2x7 + 1 >= 0 = cons1(x7)
       
       app(filter1(x6),x7) = x6 + 2x7 + 3/2 >= 0 = filter2(x6,x7)
       
       app(filter(),x7) = 2x7 + 5/2 >= 2x7 + 1 = filter1(x7)
       
       app(filter23(x6,x5,x4),x7) = 2x7 + 3/2 >= 0 = filter24(x6,x5,x4,x7)
       
       app(filter22(x6,x5),x7) = 2x7 + 3/2 >= 1 = filter23(x6,x5,x7)
       
       app(filter21(x6),x7) = 2x7 + 1 >= 1 = filter22(x6,x7)
       
       app(filter2(),x7) = 2x7 + 1 >= 0 = filter21(x7)
      problem:
       DPs:
        if_gcd{3,#}(true(),s1(x),s1(y)) -> gcd{2,#}(minus2(x,y),s1(y))
       TRS:
        le2(0(),y) -> true()
        le2(s1(x),0()) -> false()
        le2(s1(x),s1(y)) -> le2(x,y)
        pred1(s1(x)) -> x
        minus2(x,0()) -> x
        minus2(x,s1(y)) -> pred1(minus2(x,y))
        gcd2(0(),y) -> y
        gcd2(s1(x),0()) -> s1(x)
        gcd2(s1(x),s1(y)) -> if_gcd3(le2(y,x),s1(x),s1(y))
        if_gcd3(true(),s1(x),s1(y)) -> gcd2(minus2(x,y),s1(y))
        if_gcd3(false(),s1(x),s1(y)) -> gcd2(minus2(y,x),s1(x))
        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(le1(x6),x7) -> le2(x6,x7)
        app(le(),x7) -> le1(x7)
        app(s(),x7) -> s1(x7)
        app(pred(),x7) -> pred1(x7)
        app(minus1(x6),x7) -> minus2(x6,x7)
        app(minus(),x7) -> minus1(x7)
        app(gcd1(x6),x7) -> gcd2(x6,x7)
        app(gcd(),x7) -> gcd1(x7)
        app(if_gcd2(x6,x5),x7) -> if_gcd3(x6,x5,x7)
        app(if_gcd1(x6),x7) -> if_gcd2(x6,x7)
        app(if_gcd(),x7) -> if_gcd1(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: 4/1
       
     
     DPs:
      minus{2,#}(x,s1(y)) -> minus{2,#}(x,y)
     TRS:
      le2(0(),y) -> true()
      le2(s1(x),0()) -> false()
      le2(s1(x),s1(y)) -> le2(x,y)
      pred1(s1(x)) -> x
      minus2(x,0()) -> x
      minus2(x,s1(y)) -> pred1(minus2(x,y))
      gcd2(0(),y) -> y
      gcd2(s1(x),0()) -> s1(x)
      gcd2(s1(x),s1(y)) -> if_gcd3(le2(y,x),s1(x),s1(y))
      if_gcd3(true(),s1(x),s1(y)) -> gcd2(minus2(x,y),s1(y))
      if_gcd3(false(),s1(x),s1(y)) -> gcd2(minus2(y,x),s1(x))
      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(le1(x6),x7) -> le2(x6,x7)
      app(le(),x7) -> le1(x7)
      app(s(),x7) -> s1(x7)
      app(pred(),x7) -> pred1(x7)
      app(minus1(x6),x7) -> minus2(x6,x7)
      app(minus(),x7) -> minus1(x7)
      app(gcd1(x6),x7) -> gcd2(x6,x7)
      app(gcd(),x7) -> gcd1(x7)
      app(if_gcd2(x6,x5),x7) -> if_gcd3(x6,x5,x7)
      app(if_gcd1(x6),x7) -> if_gcd2(x6,x7)
      app(if_gcd(),x7) -> if_gcd1(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:
        le2(0(),y) -> true()
        le2(s1(x),0()) -> false()
        le2(s1(x),s1(y)) -> le2(x,y)
        pred1(s1(x)) -> x
        minus2(x,0()) -> x
        minus2(x,s1(y)) -> pred1(minus2(x,y))
        gcd2(0(),y) -> y
        gcd2(s1(x),0()) -> s1(x)
        gcd2(s1(x),s1(y)) -> if_gcd3(le2(y,x),s1(x),s1(y))
        if_gcd3(true(),s1(x),s1(y)) -> gcd2(minus2(x,y),s1(y))
        if_gcd3(false(),s1(x),s1(y)) -> gcd2(minus2(y,x),s1(x))
        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(le1(x6),x7) -> le2(x6,x7)
        app(le(),x7) -> le1(x7)
        app(s(),x7) -> s1(x7)
        app(pred(),x7) -> pred1(x7)
        app(minus1(x6),x7) -> minus2(x6,x7)
        app(minus(),x7) -> minus1(x7)
        app(gcd1(x6),x7) -> gcd2(x6,x7)
        app(gcd(),x7) -> gcd1(x7)
        app(if_gcd2(x6,x5),x7) -> if_gcd3(x6,x5,x7)
        app(if_gcd1(x6),x7) -> if_gcd2(x6,x7)
        app(if_gcd(),x7) -> if_gcd1(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:
      le{2,#}(s1(x),s1(y)) -> le{2,#}(x,y)
     TRS:
      le2(0(),y) -> true()
      le2(s1(x),0()) -> false()
      le2(s1(x),s1(y)) -> le2(x,y)
      pred1(s1(x)) -> x
      minus2(x,0()) -> x
      minus2(x,s1(y)) -> pred1(minus2(x,y))
      gcd2(0(),y) -> y
      gcd2(s1(x),0()) -> s1(x)
      gcd2(s1(x),s1(y)) -> if_gcd3(le2(y,x),s1(x),s1(y))
      if_gcd3(true(),s1(x),s1(y)) -> gcd2(minus2(x,y),s1(y))
      if_gcd3(false(),s1(x),s1(y)) -> gcd2(minus2(y,x),s1(x))
      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(le1(x6),x7) -> le2(x6,x7)
      app(le(),x7) -> le1(x7)
      app(s(),x7) -> s1(x7)
      app(pred(),x7) -> pred1(x7)
      app(minus1(x6),x7) -> minus2(x6,x7)
      app(minus(),x7) -> minus1(x7)
      app(gcd1(x6),x7) -> gcd2(x6,x7)
      app(gcd(),x7) -> gcd1(x7)
      app(if_gcd2(x6,x5),x7) -> if_gcd3(x6,x5,x7)
      app(if_gcd1(x6),x7) -> if_gcd2(x6,x7)
      app(if_gcd(),x7) -> if_gcd1(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(le{2,#}) = 1
      problem:
       DPs:
        
       TRS:
        le2(0(),y) -> true()
        le2(s1(x),0()) -> false()
        le2(s1(x),s1(y)) -> le2(x,y)
        pred1(s1(x)) -> x
        minus2(x,0()) -> x
        minus2(x,s1(y)) -> pred1(minus2(x,y))
        gcd2(0(),y) -> y
        gcd2(s1(x),0()) -> s1(x)
        gcd2(s1(x),s1(y)) -> if_gcd3(le2(y,x),s1(x),s1(y))
        if_gcd3(true(),s1(x),s1(y)) -> gcd2(minus2(x,y),s1(y))
        if_gcd3(false(),s1(x),s1(y)) -> gcd2(minus2(y,x),s1(x))
        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(le1(x6),x7) -> le2(x6,x7)
        app(le(),x7) -> le1(x7)
        app(s(),x7) -> s1(x7)
        app(pred(),x7) -> pred1(x7)
        app(minus1(x6),x7) -> minus2(x6,x7)
        app(minus(),x7) -> minus1(x7)
        app(gcd1(x6),x7) -> gcd2(x6,x7)
        app(gcd(),x7) -> gcd1(x7)
        app(if_gcd2(x6,x5),x7) -> if_gcd3(x6,x5,x7)
        app(if_gcd1(x6),x7) -> if_gcd2(x6,x7)
        app(if_gcd(),x7) -> if_gcd1(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