MAYBE
Time: 1.050419
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(f(), 0()), app(s(), 0())), x) -> app(app(app(f(), x), app(app(plus(), x), x)), x),
                    app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                            app(app(plus(), x), 0()) -> x,
                                 app(app(g(), x), y) -> x,
                                 app(app(g(), x), y) -> 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()}
 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(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x),
             app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x),
             app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)),
             app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x),
             app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x),
                      app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y),
                      app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)),
         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))}
  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(f(), 0()), app(s(), 0())), x) -> app(app(app(f(), x), app(app(plus(), x), x)), x),
                     app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                             app(app(plus(), x), 0()) -> x,
                                  app(app(g(), x), y) -> x,
                                  app(app(g(), x), y) -> 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()}
  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(app(f(), 0()), app(s(), 0())), x) -> app(app(app(f(), x), app(app(plus(), x), x)), x),
                      app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                              app(app(plus(), x), 0()) -> x,
                                   app(app(g(), x), y) -> x,
                                   app(app(g(), x), y) -> 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()}
   EDG:
    {
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), 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#(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(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), 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(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), 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#(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(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), 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#(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#(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(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(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#(fun, x))
     (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(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(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#(fun, x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
     (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(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(), true()), fun), x), xs) -> app#(filter(), fun))
     (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#(app(filter(), fun), xs))
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     (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#(filter2(), app(fun, x)))
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     (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#(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#(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(), 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(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(app(f(), 0()), app(s(), 0())), 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#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (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(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#(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#(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(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(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(filter2(), app(fun, x)), fun), x))
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     (app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (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(app(app(filter2(), false()), 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(), 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#(filter(), fun), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), 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#(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#(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#(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#(filter(), 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(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(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#(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#(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(), 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(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (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(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#(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#(cons(), 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(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#(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(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#(filter2(), app(fun, x)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
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     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
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     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
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     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
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     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(filter2(), app(fun, x)))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), 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(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(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#(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#(filter(), fun))
     (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#(cons(), 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#(cons(), app(fun, x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
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     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (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(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), 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#(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#(cons(), 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#(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#(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#(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#(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(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(cons(), x))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(app(filter(), fun), xs))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(app(filter2(), false()), fun), x), xs) -> app#(filter(), fun))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(map(), fun), xs))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(app(cons(), app(fun, x)), app(app(map(), fun), xs)))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(cons(), app(fun, x)))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(fun, x)), fun), x), xs))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(fun, x)), fun), x))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(app(filter2(), app(fun, x)), fun))
     (app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)), 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#(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(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
     (app#(app(app(app(filter2(), true()), fun), x), xs) -> app#(app(cons(), x), app(app(filter(), fun), xs)), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     (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)))
    }
    EDG:
     {
      (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
      (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
      (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#(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(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(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#(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#(cons(), 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#(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#(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(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#(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(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#(fun, x))
      (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(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(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#(fun, x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
      (app#(app(map(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
      (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(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(), 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#(cons(), x))
      (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#(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#(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#(cons(), x))
      (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(), 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#(filter(), fun))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
      (app#(app(filter(), fun), app(app(cons(), x), xs)) -> app#(fun, x), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
      (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(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#(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#(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#(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#(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(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#(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(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(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#(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#(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(), false()), fun), x), xs) -> app#(filter(), 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#(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#(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(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#(filter2(), app(fun, x)))
      (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x))
      (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(plus(), x), x))
      (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(f(), x), app(app(plus(), x), x)))
      (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(plus(), x))
      (app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x), app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(f(), x))
      (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y))
      (app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y), app#(app(plus(), x), app(s(), y)) -> app#(s(), app(app(plus(), x), y)))
     }
     STATUS:
      arrows: 0.849174
      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(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), x)}
       Scc:
        {app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), y)}
       
       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(f(), 0()), app(s(), 0())), x) -> app(app(app(f(), x), app(app(plus(), x), x)), x),
                           app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                                   app(app(plus(), x), 0()) -> x,
                                        app(app(g(), x), y) -> x,
                                        app(app(g(), x), y) -> 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()}
        Open
       
       
       
       
       SCC (1):
        Strict:
         {app#(app(app(f(), 0()), app(s(), 0())), x) -> app#(app(app(f(), x), app(app(plus(), x), x)), 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(f(), 0()), app(s(), 0())), x) -> app(app(app(f(), x), app(app(plus(), x), x)), x),
                           app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                                   app(app(plus(), x), 0()) -> x,
                                        app(app(g(), x), y) -> x,
                                        app(app(g(), x), y) -> 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()}
        Open
       
       
       
       
       SCC (1):
        Strict:
         {app#(app(plus(), x), app(s(), y)) -> app#(app(plus(), x), 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(f(), 0()), app(s(), 0())), x) -> app(app(app(f(), x), app(app(plus(), x), x)), x),
                           app(app(plus(), x), app(s(), y)) -> app(s(), app(app(plus(), x), y)),
                                   app(app(plus(), x), 0()) -> x,
                                        app(app(g(), x), y) -> x,
                                        app(app(g(), x), y) -> 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()}
        Open