MAYBE
MAYBE
TRS:
 {
   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),
                               app(app(\(), x), x) -> e(),
             app(app(\(), x), app(app(.(), x), y)) -> y,
                             app(app(\(), e()), x) -> x,
             app(app(\(), app(app(/(), x), y)), x) -> y,
                             app(app(.(), x), e()) -> x,
             app(app(.(), x), app(app(\(), x), y)) -> y,
                             app(app(.(), e()), x) -> x,
             app(app(.(), app(app(/(), y), x)), x) -> y,
                               app(app(/(), x), x) -> e(),
                             app(app(/(), x), e()) -> x,
             app(app(/(), x), app(app(\(), y), x)) -> y,
             app(app(/(), app(app(.(), y), x)), x) -> y,
       app(app(map(), f), app(app(cons(), x), xs)) ->
  app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                         app(app(map(), 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(filter(), f), nil()) -> nil()
 }
 DUP: We consider a duplicating system.
  Trs:
   {
     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),
                                 app(app(\(), x), x) -> e(),
               app(app(\(), x), app(app(.(), x), y)) -> y,
                               app(app(\(), e()), x) -> x,
               app(app(\(), app(app(/(), x), y)), x) -> y,
                               app(app(.(), x), e()) -> x,
               app(app(.(), x), app(app(\(), x), y)) -> y,
                               app(app(.(), e()), x) -> x,
               app(app(.(), app(app(/(), y), x)), x) -> y,
                                 app(app(/(), x), x) -> e(),
                               app(app(/(), x), e()) -> x,
               app(app(/(), x), app(app(\(), y), x)) -> y,
               app(app(/(), app(app(.(), y), x)), x) -> y,
         app(app(map(), f), app(app(cons(), x), xs)) ->
    app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                           app(app(map(), 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(filter(), f), nil()) -> nil()
   }
  Fail