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(app(if_gcd(), true()), app(s(), x)), app(s(), y)) ->
  app(app(gcd(), app(app(minus(), x), y)), app(s(), y)),
  app(app(app(if_gcd(), false()), app(s(), x)), app(s(), y)) ->
  app(app(gcd(), app(app(minus(), y), x)), app(s(), x)),
                    app(app(le(), app(s(), x)), app(s(), y)) ->
  app(app(le(), x), y),
                            app(app(le(), app(s(), x)), 0()) -> false(),
                                      app(app(le(), 0()), y) -> true(),
                           app(app(minus(), x), app(s(), y)) ->
  app(pred(), app(app(minus(), x), y)),
                                   app(app(minus(), x), 0()) -> x,
                   app(app(gcd(), app(s(), x)), app(s(), y)) ->
  app(app(app(if_gcd(), app(app(le(), y), x)), app(s(), x)), app(s(), y)),
                           app(app(gcd(), app(s(), x)), 0()) -> app(s(), x),
                                     app(app(gcd(), 0()), y) -> 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(),
                                    app(pred(), app(s(), x)) -> x
 }
 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(app(if_gcd(), true()), app(s(), x)), app(s(), y)) ->
    app(app(gcd(), app(app(minus(), x), y)), app(s(), y)),
    app(app(app(if_gcd(), false()), app(s(), x)), app(s(), y)) ->
    app(app(gcd(), app(app(minus(), y), x)), app(s(), x)),
                      app(app(le(), app(s(), x)), app(s(), y)) ->
    app(app(le(), x), y),
                              app(app(le(), app(s(), x)), 0()) -> false(),
                                        app(app(le(), 0()), y) -> true(),
                             app(app(minus(), x), app(s(), y)) ->
    app(pred(), app(app(minus(), x), y)),
                                     app(app(minus(), x), 0()) -> x,
                     app(app(gcd(), app(s(), x)), app(s(), y)) ->
    app(app(app(if_gcd(), app(app(le(), y), x)), app(s(), x)), app(s(), y)),
                             app(app(gcd(), app(s(), x)), 0()) -> app(s(), x),
                                       app(app(gcd(), 0()), y) -> 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(),
                                      app(pred(), app(s(), x)) -> x
   }
  Fail