MAYBE
Time: 0.057427
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(app(if(), true()), x), y) -> x,
                  app(app(app(if(), false()), x), y) -> y,
                       app(app(g(), x), app(c(), y)) -> app(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)),
             app(app(g(), app(s(), x)), app(s(), y)) -> app(app(app(if(), app(f(), x)), app(s(), x)), app(s(), y)),
       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(s(), x)) -> app(f(), x),
                                       app(f(), 0()) -> true(),
                                       app(f(), 1()) -> false()}
 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(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)),
                         app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), app(c(), y))), y),
                         app#(app(g(), x), app(c(), y)) -> app#(s(), app(c(), y)),
                         app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), app(c(), y))),
               app#(app(g(), app(s(), x)), app(s(), y)) -> app#(app(app(if(), app(f(), x)), app(s(), x)), app(s(), y)),
               app#(app(g(), app(s(), x)), app(s(), y)) -> app#(app(if(), app(f(), x)), app(s(), x)),
               app#(app(g(), app(s(), x)), app(s(), y)) -> app#(f(), x),
               app#(app(g(), app(s(), x)), app(s(), y)) -> app#(if(), app(f(), 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#(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(s(), 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(app(if(), true()), x), y) -> x,
                   app(app(app(if(), false()), x), y) -> y,
                        app(app(g(), x), app(c(), y)) -> app(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)),
              app(app(g(), app(s(), x)), app(s(), y)) -> app(app(app(if(), app(f(), x)), app(s(), x)), app(s(), y)),
        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(s(), x)) -> app(f(), x),
                                        app(f(), 0()) -> true(),
                                        app(f(), 1()) -> false()}
  EDG:
   {
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(f(), app(s(), 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(g(), app(s(), x)), app(s(), y)) -> app#(if(), app(f(), x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), app(s(), x)), app(s(), y)) -> app#(f(), x))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), app(s(), x)), app(s(), y)) -> app#(app(if(), app(f(), x)), app(s(), x)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), app(s(), x)), app(s(), y)) -> app#(app(app(if(), app(f(), x)), app(s(), x)), app(s(), y)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), app(c(), y))))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(s(), app(c(), y)))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), app(c(), y))), y))
    (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)))
    (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(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(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(g(), x), app(c(), y)) -> app#(app(g(), app(s(), app(c(), y))), y), app#(app(g(), app(s(), x)), app(s(), y)) -> app#(if(), app(f(), x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), app(c(), y))), y), app#(app(g(), app(s(), x)), app(s(), y)) -> app#(f(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), app(c(), y))), y), app#(app(g(), app(s(), x)), app(s(), y)) -> app#(app(if(), app(f(), x)), app(s(), x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), app(c(), y))), y), app#(app(g(), app(s(), x)), app(s(), y)) -> app#(app(app(if(), app(f(), x)), app(s(), x)), app(s(), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), app(c(), y))), y), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), app(c(), y))))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), app(c(), y))), y), app#(app(g(), x), app(c(), y)) -> app#(s(), app(c(), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), app(c(), y))), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), app(c(), y))), y))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), app(c(), y))), y), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)))
    (app#(app(g(), app(s(), x)), app(s(), y)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(f(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)), app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), app(c(), y))), y))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)), app#(app(g(), x), app(c(), y)) -> app#(s(), app(c(), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), app(c(), y))))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)), app#(app(g(), app(s(), x)), app(s(), y)) -> app#(app(app(if(), app(f(), x)), app(s(), x)), app(s(), y)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)), app#(app(g(), app(s(), x)), app(s(), y)) -> app#(app(if(), app(f(), x)), app(s(), x)))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)), app#(app(g(), app(s(), x)), app(s(), y)) -> app#(f(), x))
    (app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)), app#(app(g(), app(s(), x)), app(s(), y)) -> app#(if(), app(f(), x)))
    (app#(f(), app(s(), x)) -> app#(f(), x), app#(f(), app(s(), x)) -> app#(f(), 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(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(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#(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(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(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), app(c(), y))), y))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(s(), app(c(), y)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), x), app(c(), y)) -> app#(g(), app(s(), app(c(), y))))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), app(s(), x)), app(s(), y)) -> app#(app(app(if(), app(f(), x)), app(s(), x)), app(s(), y)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), app(s(), x)), app(s(), y)) -> app#(app(if(), app(f(), x)), app(s(), x)))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), app(s(), x)), app(s(), y)) -> app#(f(), x))
    (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(g(), app(s(), x)), app(s(), y)) -> app#(if(), app(f(), 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#(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#(f(), app(s(), x)) -> app#(f(), x))
   }
   STATUS:
    arrows: 0.850694
    SCCS (3):
     Scc:
      { 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(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(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)}
     Scc:
      {app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)),
       app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), app(c(), y))), y)}
     Scc:
      {app#(f(), app(s(), x)) -> app#(f(), x)}
     
     SCC (6):
      Strict:
       { 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(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(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)}
      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(app(if(), true()), x), y) -> x,
                       app(app(app(if(), false()), x), y) -> y,
                            app(app(g(), x), app(c(), y)) -> app(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)),
                  app(app(g(), app(s(), x)), app(s(), y)) -> app(app(app(if(), app(f(), x)), app(s(), x)), app(s(), y)),
            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(s(), x)) -> app(f(), x),
                                            app(f(), 0()) -> true(),
                                            app(f(), 1()) -> false()}
      Open
     
     
     SCC (2):
      Strict:
       {app#(app(g(), x), app(c(), y)) -> app#(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)),
        app#(app(g(), x), app(c(), y)) -> app#(app(g(), app(s(), app(c(), y))), y)}
      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(app(if(), true()), x), y) -> x,
                       app(app(app(if(), false()), x), y) -> y,
                            app(app(g(), x), app(c(), y)) -> app(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)),
                  app(app(g(), app(s(), x)), app(s(), y)) -> app(app(app(if(), app(f(), x)), app(s(), x)), app(s(), y)),
            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(s(), x)) -> app(f(), x),
                                            app(f(), 0()) -> true(),
                                            app(f(), 1()) -> false()}
      Open
     
     
     SCC (1):
      Strict:
       {app#(f(), app(s(), 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(app(if(), true()), x), y) -> x,
                       app(app(app(if(), false()), x), y) -> y,
                            app(app(g(), x), app(c(), y)) -> app(app(g(), x), app(app(g(), app(s(), app(c(), y))), y)),
                  app(app(g(), app(s(), x)), app(s(), y)) -> app(app(app(if(), app(f(), x)), app(s(), x)), app(s(), y)),
            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(s(), x)) -> app(f(), x),
                                            app(f(), 0()) -> true(),
                                            app(f(), 1()) -> false()}
      Open