MAYBE

Problem:
 app(rev(),nil()) -> nil()
 app(rev(),app(app(cons(),x),l)) -> app(app(cons(),app(app(rev1(),x),l)),app(app(rev2(),x),l))
 app(app(rev1(),0()),nil()) -> 0()
 app(app(rev1(),app(s(),x)),nil()) -> app(s(),x)
 app(app(rev1(),x),app(app(cons(),y),l)) -> app(app(rev1(),y),l)
 app(app(rev2(),x),nil()) -> nil()
 app(app(rev2(),x),app(app(cons(),y),l)) -> app(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
 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#(rev(),app(app(cons(),x),l)) -> app#(rev2(),x)
   app#(rev(),app(app(cons(),x),l)) -> app#(app(rev2(),x),l)
   app#(rev(),app(app(cons(),x),l)) -> app#(rev1(),x)
   app#(rev(),app(app(cons(),x),l)) -> app#(app(rev1(),x),l)
   app#(rev(),app(app(cons(),x),l)) -> app#(cons(),app(app(rev1(),x),l))
   app#(rev(),app(app(cons(),x),l)) -> app#(app(cons(),app(app(rev1(),x),l)),app(app(rev2(),x),l))
   app#(app(rev1(),x),app(app(cons(),y),l)) -> app#(rev1(),y)
   app#(app(rev1(),x),app(app(cons(),y),l)) -> app#(app(rev1(),y),l)
   app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev2(),y)
   app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(rev2(),y),l)
   app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(cons(),x)
   app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(cons(),x),app(app(rev2(),y),l))
   app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
   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(rev(),nil()) -> nil()
   app(rev(),app(app(cons(),x),l)) -> app(app(cons(),app(app(rev1(),x),l)),app(app(rev2(),x),l))
   app(app(rev1(),0()),nil()) -> 0()
   app(app(rev1(),app(s(),x)),nil()) -> app(s(),x)
   app(app(rev1(),x),app(app(cons(),y),l)) -> app(app(rev1(),y),l)
   app(app(rev2(),x),nil()) -> nil()
   app(app(rev2(),x),app(app(cons(),y),l)) -> app(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
   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#(rev(),app(app(cons(),x),l)) -> app#(rev2(),x)
    app#(rev(),app(app(cons(),x),l)) -> app#(app(rev2(),x),l)
    app#(rev(),app(app(cons(),x),l)) -> app#(rev1(),x)
    app#(rev(),app(app(cons(),x),l)) -> app#(app(rev1(),x),l)
    app#(rev(),app(app(cons(),x),l)) -> app#(cons(),app(app(rev1(),x),l))
    app#(rev(),app(app(cons(),x),l)) -> app#(app(cons(),app(app(rev1(),x),l)),app(app(rev2(),x),l))
    app#(app(rev1(),x),app(app(cons(),y),l)) -> app#(rev1(),y)
    app#(app(rev1(),x),app(app(cons(),y),l)) -> app#(app(rev1(),y),l)
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev2(),y)
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(rev2(),y),l)
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(cons(),x)
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(cons(),x),app(app(rev2(),y),l))
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
    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(rev(),nil()) -> nil()
    app(rev(),app(app(cons(),x),l)) -> app(app(cons(),app(app(rev1(),x),l)),app(app(rev2(),x),l))
    app(app(rev1(),0()),nil()) -> 0()
    app(app(rev1(),app(s(),x)),nil()) -> app(s(),x)
    app(app(rev1(),x),app(app(cons(),y),l)) -> app(app(rev1(),y),l)
    app(app(rev2(),x),nil()) -> nil()
    app(app(rev2(),x),app(app(cons(),y),l)) -> app(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
    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#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(rev(),app(app(cons(),x),l)) -> app#(rev2(),x)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(rev(),app(app(cons(),x),l)) -> app#(app(rev2(),x),l)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(rev(),app(app(cons(),x),l)) -> app#(rev1(),x)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(rev(),app(app(cons(),x),l)) -> app#(app(rev1(),x),l)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(rev(),app(app(cons(),x),l)) -> app#(cons(),app(app(rev1(),x),l))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(rev(),app(app(cons(),x),l)) -> app#(app(cons(),app(app(rev1(),x),l)),app(app(rev2(),x),l))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(rev1(),x),app(app(cons(),y),l)) -> app#(rev1(),y)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(rev1(),x),app(app(cons(),y),l)) -> app#(app(rev1(),y),l)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev2(),y)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(rev2(),y),l)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(cons(),x)
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(cons(),x),app(app(rev2(),y),l))
    app#(app(filter(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
    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#(rev(),app(app(cons(),x),l)) -> app#(rev2(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(rev(),app(app(cons(),x),l)) -> app#(app(rev2(),x),l)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(rev(),app(app(cons(),x),l)) -> app#(rev1(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(rev(),app(app(cons(),x),l)) -> app#(app(rev1(),x),l)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(rev(),app(app(cons(),x),l)) -> app#(cons(),app(app(rev1(),x),l))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(rev(),app(app(cons(),x),l)) -> app#(app(cons(),app(app(rev1(),x),l)),app(app(rev2(),x),l))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(rev1(),x),app(app(cons(),y),l)) -> app#(rev1(),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(rev1(),x),app(app(cons(),y),l)) -> app#(app(rev1(),y),l)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev2(),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(rev2(),y),l)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(cons(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(cons(),x),app(app(rev2(),y),l))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
    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(rev2(),x),app(app(cons(),y),l)) -> app#(app(rev2(),y),l) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev2(),y)
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(rev2(),y),l) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(rev2(),y),l)
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(rev2(),y),l) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(cons(),x)
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(rev2(),y),l) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(cons(),x),app(app(rev2(),y),l))
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(rev2(),y),l) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
    ->
    app#(rev(),app(app(cons(),x),l)) -> app#(rev2(),x)
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
    ->
    app#(rev(),app(app(cons(),x),l)) -> app#(app(rev2(),x),l)
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
    ->
    app#(rev(),app(app(cons(),x),l)) -> app#(rev1(),x)
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
    ->
    app#(rev(),app(app(cons(),x),l)) -> app#(app(rev1(),x),l)
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
    ->
    app#(rev(),app(app(cons(),x),l)) -> app#(cons(),app(app(rev1(),x),l))
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
    ->
    app#(rev(),app(app(cons(),x),l)) -> app#(app(cons(),app(app(rev1(),x),l)),app(app(rev2(),x),l))
    app#(app(rev1(),x),app(app(cons(),y),l)) -> app#(app(rev1(),y),l) ->
    app#(app(rev1(),x),app(app(cons(),y),l)) -> app#(rev1(),y)
    app#(app(rev1(),x),app(app(cons(),y),l)) -> app#(app(rev1(),y),l) ->
    app#(app(rev1(),x),app(app(cons(),y),l)) -> app#(app(rev1(),y),l)
    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)
    app#(rev(),app(app(cons(),x),l)) -> app#(app(rev2(),x),l) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev2(),y)
    app#(rev(),app(app(cons(),x),l)) -> app#(app(rev2(),x),l) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(rev2(),y),l)
    app#(rev(),app(app(cons(),x),l)) -> app#(app(rev2(),x),l) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(cons(),x)
    app#(rev(),app(app(cons(),x),l)) -> app#(app(rev2(),x),l) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(cons(),x),app(app(rev2(),y),l))
    app#(rev(),app(app(cons(),x),l)) -> app#(app(rev2(),x),l) ->
    app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
    app#(rev(),app(app(cons(),x),l)) -> app#(app(rev1(),x),l) ->
    app#(app(rev1(),x),app(app(cons(),y),l)) -> app#(rev1(),y)
    app#(rev(),app(app(cons(),x),l)) -> app#(app(rev1(),x),l) ->
    app#(app(rev1(),x),app(app(cons(),y),l)) -> app#(app(rev1(),y),l)
   SCC Processor:
    #sccs: 3
    #rules: 9
    #arcs: 90/784
    DPs:
     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(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(rev(),nil()) -> nil()
     app(rev(),app(app(cons(),x),l)) -> app(app(cons(),app(app(rev1(),x),l)),app(app(rev2(),x),l))
     app(app(rev1(),0()),nil()) -> 0()
     app(app(rev1(),app(s(),x)),nil()) -> app(s(),x)
     app(app(rev1(),x),app(app(cons(),y),l)) -> app(app(rev1(),y),l)
     app(app(rev2(),x),nil()) -> nil()
     app(app(rev2(),x),app(app(cons(),y),l)) -> app(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
     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(rev2(),x),app(app(cons(),y),l)) ->
     app#(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
     app#(rev(),app(app(cons(),x),l)) -> app#(app(rev2(),x),l)
     app#(app(rev2(),x),app(app(cons(),y),l)) -> app#(app(rev2(),y),l)
    TRS:
     app(rev(),nil()) -> nil()
     app(rev(),app(app(cons(),x),l)) -> app(app(cons(),app(app(rev1(),x),l)),app(app(rev2(),x),l))
     app(app(rev1(),0()),nil()) -> 0()
     app(app(rev1(),app(s(),x)),nil()) -> app(s(),x)
     app(app(rev1(),x),app(app(cons(),y),l)) -> app(app(rev1(),y),l)
     app(app(rev2(),x),nil()) -> nil()
     app(app(rev2(),x),app(app(cons(),y),l)) -> app(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
     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(rev1(),x),app(app(cons(),y),l)) -> app#(app(rev1(),y),l)
    TRS:
     app(rev(),nil()) -> nil()
     app(rev(),app(app(cons(),x),l)) -> app(app(cons(),app(app(rev1(),x),l)),app(app(rev2(),x),l))
     app(app(rev1(),0()),nil()) -> 0()
     app(app(rev1(),app(s(),x)),nil()) -> app(s(),x)
     app(app(rev1(),x),app(app(cons(),y),l)) -> app(app(rev1(),y),l)
     app(app(rev2(),x),nil()) -> nil()
     app(app(rev2(),x),app(app(cons(),y),l)) -> app(rev(),app(app(cons(),x),app(app(rev2(),y),l)))
     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