MAYBE
Time: 0.137532
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(f(), app(g(), x)) -> app(g(), app(g(), app(g(), x))),
                               app(f(), app(g(), x)) -> app(g(), 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#(f(), app(g(), x)) -> app#(g(), app(g(), x)),
                                 app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))),
                                 app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))),
                                 app#(f(), app(g(), x)) -> app#(g(), app(f(), x)),
                                 app#(f(), app(g(), x)) -> 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(f(), app(g(), x)) -> app(g(), app(g(), app(g(), x))),
                                app(f(), app(g(), x)) -> app(g(), app(g(), app(f(), x)))}
  UR:
   { 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(f(), app(g(), x)) -> app(g(), app(g(), app(g(), x))),
                                 app(f(), app(g(), x)) -> app(g(), app(g(), app(f(), x))),
                                               a(y, z) -> y,
                                               a(y, z) -> z}
   EDG:
    {
     (app#(f(), app(g(), x)) -> app#(f(), x), app#(f(), app(g(), x)) -> app#(f(), x))
     (app#(f(), app(g(), x)) -> app#(f(), x), app#(f(), app(g(), x)) -> app#(g(), app(f(), x)))
     (app#(f(), app(g(), x)) -> app#(f(), x), app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))))
     (app#(f(), app(g(), x)) -> app#(f(), x), app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))))
     (app#(f(), app(g(), x)) -> app#(f(), x), app#(f(), app(g(), x)) -> app#(g(), app(g(), x)))
     (app#(f(), app(g(), x)) -> app#(f(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(f(), app(g(), x)) -> app#(f(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(f(), 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#(f(), 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#(f(), app(g(), x)) -> app#(f(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(f(), app(g(), x)) -> app#(f(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(f(), 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#(f(), app(g(), x)) -> app#(f(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(f(), app(g(), x)) -> app#(f(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(f(), app(g(), x)) -> app#(f(), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(f(), app(g(), x)) -> app#(f(), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(f(), app(g(), x)) -> app#(f(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(f(), app(g(), x)) -> app#(f(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(f(), app(g(), x)) -> app#(f(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(f(), 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(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(f(), app(g(), x)) -> app#(f(), x))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(f(), app(g(), x)) -> app#(g(), app(f(), x)))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(f(), app(g(), x)) -> app#(g(), app(g(), x)))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(f(), app(g(), x)) -> app#(g(), 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#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(f(), app(g(), x)) -> app#(g(), 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(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(g(), x)) -> app#(f(), x))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(g(), x)) -> app#(g(), app(f(), x)))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))))
     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(g(), x)) -> app#(g(), app(g(), 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(), 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(), 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(), false()), fun), x), xs) -> 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(), 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(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), 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#(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(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#(fun, x))
     (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(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(app(app(app(filter2(), false()), fun), x), xs) -> 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#(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#(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#(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(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(f(), 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#(f(), app(g(), x)) -> app#(g(), app(f(), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(f(), app(g(), x)) -> app#(g(), app(g(), 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#(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#(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(app(app(filter2(), app(fun, x)), fun), x), xs), 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(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#(app(app(app(filter2(), app(fun, x)), fun), x), 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#(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#(app(app(app(filter2(), app(fun, x)), fun), x), xs), 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(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(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(app(filter2(), false()), 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(), false()), fun), x), xs) -> 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#(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#(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#(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#(f(), 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#(f(), app(g(), 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#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(f(), app(g(), x)) -> app#(g(), app(g(), 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))
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     (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#(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(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#(filter(), fun))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> 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(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(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#(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(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(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(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(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(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(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(filter(), fun), xs), app#(f(), app(g(), x)) -> app#(g(), app(g(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(g(), x)) -> app#(g(), app(f(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs), app#(f(), app(g(), x)) -> app#(f(), x))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(f(), app(g(), x)) -> app#(g(), app(g(), x)))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(f(), app(g(), x)) -> app#(g(), app(f(), x)))
     (app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))), app#(f(), app(g(), x)) -> 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#(f(), app(g(), x)) -> app#(g(), app(g(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(f(), app(g(), x)) -> app#(g(), app(f(), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(f(), app(g(), x)) -> 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#(f(), app(g(), x)) -> app#(g(), app(g(), x)),
                                     app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))),
                                     app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))),
                                     app#(f(), app(g(), x)) -> app#(g(), app(f(), x)),
                                     app#(f(), app(g(), x)) -> app#(f(), x)}
      
      SCC (20):
       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#(f(), app(g(), x)) -> app#(g(), app(g(), x)),
                                      app#(f(), app(g(), x)) -> app#(g(), app(g(), app(g(), x))),
                                      app#(f(), app(g(), x)) -> app#(g(), app(g(), app(f(), x))),
                                      app#(f(), app(g(), x)) -> app#(g(), app(f(), x)),
                                      app#(f(), app(g(), x)) -> 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(f(), app(g(), x)) -> app(g(), app(g(), app(g(), x))),
                                     app(f(), app(g(), x)) -> app(g(), app(g(), app(f(), x)))}
       Fail