MAYBE

Problem:
 app(f(),app(app(cons(),nil()),y)) -> y
 app(f(),app(app(cons(),app(f(),app(app(cons(),nil()),y))),z)) -> app(app(app(copy(),n()),y),z)
 app(app(app(copy(),0()),y),z) -> app(f(),z)
 app(app(app(copy(),app(s(),x)),y),z) -> app(app(app(copy(),x),y),app(app(cons(),app(f(),y)),z))
 app(app(map(),fun),nil()) -> nil()
 app(app(map(),fun),app(app(cons(),x),xs)) -> app(app(cons(),app(fun,x)),app(app(map(),fun),xs))
 app(app(filter(),fun),nil()) -> nil()
 app(app(filter(),fun),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(fun,x)),fun),x),xs)
 app(app(app(app(filter2(),true()),fun),x),xs) -> app(app(cons(),x),app(app(filter(),fun),xs))
 app(app(app(app(filter2(),false()),fun),x),xs) -> app(app(filter(),fun),xs)

Proof:
 DP Processor:
  DPs:
   app#(f(),app(app(cons(),app(f(),app(app(cons(),nil()),y))),z)) -> app#(copy(),n())
   app#(f(),app(app(cons(),app(f(),app(app(cons(),nil()),y))),z)) -> app#(app(copy(),n()),y)
   app#(f(),app(app(cons(),app(f(),app(app(cons(),nil()),y))),z)) -> app#(app(app(copy(),n()),y),z)
   app#(app(app(copy(),0()),y),z) -> app#(f(),z)
   app#(app(app(copy(),app(s(),x)),y),z) -> app#(f(),y)
   app#(app(app(copy(),app(s(),x)),y),z) -> app#(cons(),app(f(),y))
   app#(app(app(copy(),app(s(),x)),y),z) -> app#(app(cons(),app(f(),y)),z)
   app#(app(app(copy(),app(s(),x)),y),z) -> app#(copy(),x)
   app#(app(app(copy(),app(s(),x)),y),z) -> app#(app(copy(),x),y)
   app#(app(app(copy(),app(s(),x)),y),z) ->
   app#(app(app(copy(),x),y),app(app(cons(),app(f(),y)),z))
   app#(app(map(),fun),app(app(cons(),x),xs)) -> app#(app(map(),fun),xs)
   app#(app(map(),fun),app(app(cons(),x),xs)) -> app#(fun,x)
   app#(app(map(),fun),app(app(cons(),x),xs)) -> app#(cons(),app(fun,x))
   app#(app(map(),fun),app(app(cons(),x),xs)) ->
   app#(app(cons(),app(fun,x)),app(app(map(),fun),xs))
   app#(app(filter(),fun),app(app(cons(),x),xs)) -> app#(fun,x)
   app#(app(filter(),fun),app(app(cons(),x),xs)) -> app#(filter2(),app(fun,x))
   app#(app(filter(),fun),app(app(cons(),x),xs)) -> app#(app(filter2(),app(fun,x)),fun)
   app#(app(filter(),fun),app(app(cons(),x),xs)) -> app#(app(app(filter2(),app(fun,x)),fun),x)
   app#(app(filter(),fun),app(app(cons(),x),xs)) ->
   app#(app(app(app(filter2(),app(fun,x)),fun),x),xs)
   app#(app(app(app(filter2(),true()),fun),x),xs) -> app#(filter(),fun)
   app#(app(app(app(filter2(),true()),fun),x),xs) -> app#(app(filter(),fun),xs)
   app#(app(app(app(filter2(),true()),fun),x),xs) -> app#(cons(),x)
   app#(app(app(app(filter2(),true()),fun),x),xs) -> app#(app(cons(),x),app(app(filter(),fun),xs))
   app#(app(app(app(filter2(),false()),fun),x),xs) -> app#(filter(),fun)
   app#(app(app(app(filter2(),false()),fun),x),xs) -> app#(app(filter(),fun),xs)
  TRS:
   app(f(),app(app(cons(),nil()),y)) -> y
   app(f(),app(app(cons(),app(f(),app(app(cons(),nil()),y))),z)) -> app(app(app(copy(),n()),y),z)
   app(app(app(copy(),0()),y),z) -> app(f(),z)
   app(app(app(copy(),app(s(),x)),y),z) -> app(app(app(copy(),x),y),app(app(cons(),app(f(),y)),z))
   app(app(map(),fun),nil()) -> nil()
   app(app(map(),fun),app(app(cons(),x),xs)) -> app(app(cons(),app(fun,x)),app(app(map(),fun),xs))
   app(app(filter(),fun),nil()) -> nil()
   app(app(filter(),fun),app(app(cons(),x),xs)) ->
   app(app(app(app(filter2(),app(fun,x)),fun),x),xs)
   app(app(app(app(filter2(),true()),fun),x),xs) -> app(app(cons(),x),app(app(filter(),fun),xs))
   app(app(app(app(filter2(),false()),fun),x),xs) -> app(app(filter(),fun),xs)
  Open