MAYBE

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:
 DP Processor:
  DPs:
   app#(fact(),0()) -> app#(s(),0())
   app#(fact(),app(s(),x)) -> app#(p(),app(s(),x))
   app#(fact(),app(s(),x)) -> app#(fact(),app(p(),app(s(),x)))
   app#(fact(),app(s(),x)) -> app#(*(),app(s(),x))
   app#(fact(),app(s(),x)) -> app#(app(*(),app(s(),x)),app(fact(),app(p(),app(s(),x))))
   app#(app(*(),app(s(),x)),y) -> app#(*(),x)
   app#(app(*(),app(s(),x)),y) -> app#(app(*(),x),y)
   app#(app(*(),app(s(),x)),y) -> app#(+(),app(app(*(),x),y))
   app#(app(*(),app(s(),x)),y) -> app#(app(+(),app(app(*(),x),y)),y)
   app#(app(+(),x),app(s(),y)) -> app#(app(+(),x),y)
   app#(app(+(),x),app(s(),y)) -> app#(s(),app(app(+(),x),y))
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x)
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(filter2(),app(f,x))
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f)
   app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x)
   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#(filter(),f)
   app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs)
   app#(app(app(app(filter2(),true()),f),x),xs) -> app#(cons(),x)
   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#(filter(),f)
   app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs)
  TRS:
   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)
  EDG Processor:
   DPs:
    app#(fact(),0()) -> app#(s(),0())
    app#(fact(),app(s(),x)) -> app#(p(),app(s(),x))
    app#(fact(),app(s(),x)) -> app#(fact(),app(p(),app(s(),x)))
    app#(fact(),app(s(),x)) -> app#(*(),app(s(),x))
    app#(fact(),app(s(),x)) -> app#(app(*(),app(s(),x)),app(fact(),app(p(),app(s(),x))))
    app#(app(*(),app(s(),x)),y) -> app#(*(),x)
    app#(app(*(),app(s(),x)),y) -> app#(app(*(),x),y)
    app#(app(*(),app(s(),x)),y) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),app(s(),x)),y) -> app#(app(+(),app(app(*(),x),y)),y)
    app#(app(+(),x),app(s(),y)) -> app#(app(+(),x),y)
    app#(app(+(),x),app(s(),y)) -> app#(s(),app(app(+(),x),y))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(filter2(),app(f,x))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x)
    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#(filter(),f)
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs)
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(cons(),x)
    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#(filter(),f)
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs)
   TRS:
    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)
   graph:
    app#(fact(),app(s(),x)) -> app#(fact(),app(p(),app(s(),x))) ->
    app#(fact(),0()) -> app#(s(),0())
    app#(fact(),app(s(),x)) -> app#(fact(),app(p(),app(s(),x))) ->
    app#(fact(),app(s(),x)) -> app#(p(),app(s(),x))
    app#(fact(),app(s(),x)) -> app#(fact(),app(p(),app(s(),x))) ->
    app#(fact(),app(s(),x)) -> app#(fact(),app(p(),app(s(),x)))
    app#(fact(),app(s(),x)) -> app#(fact(),app(p(),app(s(),x))) ->
    app#(fact(),app(s(),x)) -> app#(*(),app(s(),x))
    app#(fact(),app(s(),x)) -> app#(fact(),app(p(),app(s(),x))) ->
    app#(fact(),app(s(),x)) -> app#(app(*(),app(s(),x)),app(fact(),app(p(),app(s(),x))))
    app#(fact(),app(s(),x)) -> app#(app(*(),app(s(),x)),app(fact(),app(p(),app(s(),x)))) ->
    app#(app(*(),app(s(),x)),y) -> app#(*(),x)
    app#(fact(),app(s(),x)) -> app#(app(*(),app(s(),x)),app(fact(),app(p(),app(s(),x)))) ->
    app#(app(*(),app(s(),x)),y) -> app#(app(*(),x),y)
    app#(fact(),app(s(),x)) -> app#(app(*(),app(s(),x)),app(fact(),app(p(),app(s(),x)))) ->
    app#(app(*(),app(s(),x)),y) -> app#(+(),app(app(*(),x),y))
    app#(fact(),app(s(),x)) -> app#(app(*(),app(s(),x)),app(fact(),app(p(),app(s(),x)))) ->
    app#(app(*(),app(s(),x)),y) -> app#(app(+(),app(app(*(),x),y)),y)
    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#(filter(),f)
    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(filter(),f),xs)
    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#(cons(),x)
    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(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(app(filter2(),app(f,x)),f),x),xs)
    ->
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(filter(),f)
    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(),false()),f),x),xs) -> app#(app(filter(),f),xs)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(fact(),0()) -> app#(s(),0())
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(fact(),app(s(),x)) -> app#(p(),app(s(),x))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(fact(),app(s(),x)) -> app#(fact(),app(p(),app(s(),x)))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(fact(),app(s(),x)) -> app#(*(),app(s(),x))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(fact(),app(s(),x)) -> app#(app(*(),app(s(),x)),app(fact(),app(p(),app(s(),x))))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(s(),x)),y) -> app#(*(),x)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(s(),x)),y) -> app#(app(*(),x),y)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(s(),x)),y) -> app#(+(),app(app(*(),x),y))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(s(),x)),y) -> app#(app(+(),app(app(*(),x),y)),y)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(+(),x),app(s(),y)) -> app#(app(+(),x),y)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(+(),x),app(s(),y)) -> app#(s(),app(app(+(),x),y))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(filter2(),app(f,x))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(app(filter2(),app(f,x)),f),x),xs)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(filter(),f)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(cons(),x)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(cons(),x),app(app(filter(),f),xs))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(filter(),f)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(fact(),0()) -> app#(s(),0())
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(fact(),app(s(),x)) -> app#(p(),app(s(),x))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(fact(),app(s(),x)) -> app#(fact(),app(p(),app(s(),x)))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(fact(),app(s(),x)) -> app#(*(),app(s(),x))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(fact(),app(s(),x)) -> app#(app(*(),app(s(),x)),app(fact(),app(p(),app(s(),x))))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(s(),x)),y) -> app#(*(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(s(),x)),y) -> app#(app(*(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(s(),x)),y) -> app#(+(),app(app(*(),x),y))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(*(),app(s(),x)),y) -> app#(app(+(),app(app(*(),x),y)),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(+(),x),app(s(),y)) -> app#(app(+(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(+(),x),app(s(),y)) -> app#(s(),app(app(+(),x),y))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(filter2(),app(f,x))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(app(filter2(),app(f,x)),f),x),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(filter(),f)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(cons(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(cons(),x),app(app(filter(),f),xs))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(filter(),f)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs)
    app#(app(+(),x),app(s(),y)) -> app#(app(+(),x),y) ->
    app#(app(+(),x),app(s(),y)) -> app#(app(+(),x),y)
    app#(app(+(),x),app(s(),y)) -> app#(app(+(),x),y) ->
    app#(app(+(),x),app(s(),y)) -> app#(s(),app(app(+(),x),y))
    app#(app(*(),app(s(),x)),y) -> app#(app(+(),app(app(*(),x),y)),y) ->
    app#(app(+(),x),app(s(),y)) -> app#(app(+(),x),y)
    app#(app(*(),app(s(),x)),y) -> app#(app(+(),app(app(*(),x),y)),y) ->
    app#(app(+(),x),app(s(),y)) -> app#(s(),app(app(+(),x),y))
    app#(app(*(),app(s(),x)),y) -> app#(app(*(),x),y) ->
    app#(app(*(),app(s(),x)),y) -> app#(*(),x)
    app#(app(*(),app(s(),x)),y) -> app#(app(*(),x),y) ->
    app#(app(*(),app(s(),x)),y) -> app#(app(*(),x),y)
    app#(app(*(),app(s(),x)),y) -> app#(app(*(),x),y) ->
    app#(app(*(),app(s(),x)),y) -> app#(+(),app(app(*(),x),y))
    app#(app(*(),app(s(),x)),y) -> app#(app(*(),x),y) ->
    app#(app(*(),app(s(),x)),y) -> app#(app(+(),app(app(*(),x),y)),y)
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(filter2(),app(f,x))
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f)
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x)
    app#(app(app(app(filter2(),false()),f),x),xs) -> app#(app(filter(),f),xs) ->
    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(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(filter2(),app(f,x))
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(filter2(),app(f,x)),f)
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(f,x)),f),x)
    app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs) ->
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(app(app(app(filter2(),app(f,x)),f),x),xs)
   SCC Processor:
    #sccs: 4
    #rules: 9
    #arcs: 89/676
    DPs:
     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(),false()),f),x),xs) -> app#(app(filter(),f),xs)
     app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x)
     app#(app(app(app(filter2(),true()),f),x),xs) -> app#(app(filter(),f),xs)
     app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
     app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    TRS:
     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)
    Open
    
    DPs:
     app#(fact(),app(s(),x)) -> app#(fact(),app(p(),app(s(),x)))
    TRS:
     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)
    Open
    
    DPs:
     app#(app(*(),app(s(),x)),y) -> app#(app(*(),x),y)
    TRS:
     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)
    Open
    
    DPs:
     app#(app(+(),x),app(s(),y)) -> app#(app(+(),x),y)
    TRS:
     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)
    Open