MAYBE
Time: 0.117954
TRS:
 { 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),
       app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                         app(app(map(), 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(filter(), fun), nil()) -> nil(),
                               app(g(), app(g(), x)) -> app(f(), x),
                               app(f(), app(f(), x)) -> app(g(), app(f(), x))}
 DP:
  DP:
   { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)),
     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#(filter(), fun),
    app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
    app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
         app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs),
      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(filter2(), app(fun, x)), fun),
      app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)),
                                 app#(g(), app(g(), x)) -> app#(f(), x),
                                 app#(f(), app(f(), x)) -> app#(g(), app(f(), x))}
  TRS:
  { 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),
        app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                          app(app(map(), 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(filter(), fun), nil()) -> nil(),
                                app(g(), app(g(), x)) -> app(f(), x),
                                app(f(), app(f(), x)) -> app(g(), app(f(), x))}
  EDG:
   {
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(f(), app(f(), x)) -> app#(g(), app(f(), x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(g(), app(g(), x)) -> app#(f(), x))
    (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#(filter2(), app(fun, x)))
    (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(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(filter2(), app(fun, x)), fun), x))
    (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(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#(fun, x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), 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#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(f(), app(f(), x)) -> app#(g(), app(f(), x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(g(), app(g(), x)) -> app#(f(), 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#(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(filter2(), app(fun, x)), fun))
    (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(filter2(), app(fun, x)), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (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#(fun, x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), 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#(app(filter2(), app(fun, x)), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(f(), x)) -> app#(g(), app(f(), x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(g(), x)) -> app#(f(), x))
    (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#(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#(fun, x), 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#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(filter(), 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(filter(), fun), app(app(cons(), x), xs)) -> 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(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(f(), app(f(), x)) -> app#(g(), app(f(), x)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(g(), app(g(), x)) -> app#(f(), 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#(filter2(), 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#(app(filter2(), app(fun, x)), fun))
    (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#(app(app(filter2(), app(fun, x)), 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#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (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(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), 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(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), 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#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(f(), app(f(), x)) -> app#(g(), app(f(), x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(g(), app(g(), x)) -> app#(f(), 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#(filter2(), 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#(filter2(), app(fun, x)), 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#(filter2(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), 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(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), 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#(filter2(), app(fun, x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(map(), 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(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(f(), app(f(), x)) -> app#(g(), app(f(), x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(g(), app(g(), x)) -> app#(f(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), 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(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
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    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(g(), app(g(), x)) -> app#(f(), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(f(), app(f(), x)) -> app#(g(), app(f(), x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), 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(), true()), fun), x), xs) -> app#(filter(), fun))
    (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))
    (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(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), 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(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(g(), app(g(), x)) -> app#(f(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(f(), app(f(), x)) -> app#(g(), app(f(), x)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), 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#(app(cons(), app(fun, x)), 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#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(map(), 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(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(g(), app(g(), x)) -> app#(f(), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(f(), x)) -> app#(g(), app(f(), x)))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(g(), app(g(), x)) -> app#(f(), x))
    (app#(g(), app(g(), x)) -> app#(f(), x), app#(f(), app(f(), x)) -> app#(g(), app(f(), x)))
    (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(), true()), fun), x), xs) -> app#(cons(), x), 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#(cons(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), false()), 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(), false()), fun), x), xs) -> app#(filter(), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), 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#(cons(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(g(), app(g(), x)) -> app#(f(), x))
    (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(f(), app(f(), x)) -> app#(g(), app(f(), x)))
   }
   STATUS:
    arrows: 0.000000
    SCCS (1):
     Scc:
      { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)),
        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#(filter(), fun),
       app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
       app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun),
            app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
            app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
            app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
            app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)),
         app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
         app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs),
         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(filter2(), app(fun, x)), fun),
         app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)),
                                    app#(g(), app(g(), x)) -> app#(f(), x),
                                    app#(f(), app(f(), x)) -> app#(g(), app(f(), x))}
     
     SCC (17):
      Strict:
       { app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)),
         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#(filter(), fun),
        app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs),
        app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun),
             app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
             app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs),
             app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
             app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)),
          app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x),
          app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs),
          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(filter2(), app(fun, x)), fun),
          app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)),
                                     app#(g(), app(g(), x)) -> app#(f(), x),
                                     app#(f(), app(f(), x)) -> app#(g(), app(f(), x))}
      Weak:
      { 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),
            app(app(map(), fun), app(app(cons(), x), xs)) -> app(app(cons(), app(fun, x)), app(app(map(), fun), xs)),
                              app(app(map(), 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(filter(), fun), nil()) -> nil(),
                                    app(g(), app(g(), x)) -> app(f(), x),
                                    app(f(), app(f(), x)) -> app(g(), app(f(), x))}
      Fail