MAYBE

Problem:
 app(intlist(),nil()) -> nil()
 app(intlist(),app(app(cons(),x),y)) -> app(app(cons(),app(s(),x)),app(intlist(),y))
 app(app(int(),0()),0()) -> app(app(cons(),0()),nil())
 app(app(int(),0()),app(s(),y)) -> app(app(cons(),0()),app(app(int(),app(s(),0())),app(s(),y)))
 app(app(int(),app(s(),x)),0()) -> nil()
 app(app(int(),app(s(),x)),app(s(),y)) -> app(intlist(),app(app(int(),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#(intlist(),app(app(cons(),x),y)) -> app#(intlist(),y)
   app#(intlist(),app(app(cons(),x),y)) -> app#(s(),x)
   app#(intlist(),app(app(cons(),x),y)) -> app#(cons(),app(s(),x))
   app#(intlist(),app(app(cons(),x),y)) -> app#(app(cons(),app(s(),x)),app(intlist(),y))
   app#(app(int(),0()),0()) -> app#(cons(),0())
   app#(app(int(),0()),0()) -> app#(app(cons(),0()),nil())
   app#(app(int(),0()),app(s(),y)) -> app#(s(),0())
   app#(app(int(),0()),app(s(),y)) -> app#(int(),app(s(),0()))
   app#(app(int(),0()),app(s(),y)) -> app#(app(int(),app(s(),0())),app(s(),y))
   app#(app(int(),0()),app(s(),y)) -> app#(cons(),0())
   app#(app(int(),0()),app(s(),y)) -> app#(app(cons(),0()),app(app(int(),app(s(),0())),app(s(),y)))
   app#(app(int(),app(s(),x)),app(s(),y)) -> app#(int(),x)
   app#(app(int(),app(s(),x)),app(s(),y)) -> app#(app(int(),x),y)
   app#(app(int(),app(s(),x)),app(s(),y)) -> app#(intlist(),app(app(int(),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(intlist(),nil()) -> nil()
   app(intlist(),app(app(cons(),x),y)) -> app(app(cons(),app(s(),x)),app(intlist(),y))
   app(app(int(),0()),0()) -> app(app(cons(),0()),nil())
   app(app(int(),0()),app(s(),y)) -> app(app(cons(),0()),app(app(int(),app(s(),0())),app(s(),y)))
   app(app(int(),app(s(),x)),0()) -> nil()
   app(app(int(),app(s(),x)),app(s(),y)) -> app(intlist(),app(app(int(),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)
  SCC Processor:
   #sccs: 1
   #rules: 29
   #arcs: 841/841
   DPs:
    app#(intlist(),app(app(cons(),x),y)) -> app#(intlist(),y)
    app#(intlist(),app(app(cons(),x),y)) -> app#(s(),x)
    app#(intlist(),app(app(cons(),x),y)) -> app#(cons(),app(s(),x))
    app#(intlist(),app(app(cons(),x),y)) -> app#(app(cons(),app(s(),x)),app(intlist(),y))
    app#(app(int(),0()),0()) -> app#(cons(),0())
    app#(app(int(),0()),0()) -> app#(app(cons(),0()),nil())
    app#(app(int(),0()),app(s(),y)) -> app#(s(),0())
    app#(app(int(),0()),app(s(),y)) -> app#(int(),app(s(),0()))
    app#(app(int(),0()),app(s(),y)) -> app#(app(int(),app(s(),0())),app(s(),y))
    app#(app(int(),0()),app(s(),y)) -> app#(cons(),0())
    app#(app(int(),0()),app(s(),y)) ->
    app#(app(cons(),0()),app(app(int(),app(s(),0())),app(s(),y)))
    app#(app(int(),app(s(),x)),app(s(),y)) -> app#(int(),x)
    app#(app(int(),app(s(),x)),app(s(),y)) -> app#(app(int(),x),y)
    app#(app(int(),app(s(),x)),app(s(),y)) -> app#(intlist(),app(app(int(),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(intlist(),nil()) -> nil()
    app(intlist(),app(app(cons(),x),y)) -> app(app(cons(),app(s(),x)),app(intlist(),y))
    app(app(int(),0()),0()) -> app(app(cons(),0()),nil())
    app(app(int(),0()),app(s(),y)) -> app(app(cons(),0()),app(app(int(),app(s(),0())),app(s(),y)))
    app(app(int(),app(s(),x)),0()) -> nil()
    app(app(int(),app(s(),x)),app(s(),y)) -> app(intlist(),app(app(int(),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