MAYBE
Time: 0.204078
TRS:
 { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
  app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
     app(app(:(), z), app(app(+(), x), app(f, y))) -> app(app(:(), app(app(g(), z), y)), app(app(+(), x), a())),
             app(app(:(), app(app(:(), x), y)), z) -> app(app(:(), x), app(app(:(), y), z)),
             app(app(:(), app(app(+(), x), y)), z) -> app(app(+(), app(app(:(), x), z)), app(app(:(), y), z)),
       app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                         app(app(map(), f), nil()) -> nil(),
    app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                      app(app(filter(), f), nil()) -> nil()}
 DP:
  DP:
   { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f),
       app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())),
       app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()),
       app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y),
       app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)),
       app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z),
               app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)),
               app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z),
               app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y),
               app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z),
               app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z),
               app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)),
               app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x),
               app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y),
               app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f),
      app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))}
  TRS:
  { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
   app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
      app(app(:(), z), app(app(+(), x), app(f, y))) -> app(app(:(), app(app(g(), z), y)), app(app(+(), x), a())),
              app(app(:(), app(app(:(), x), y)), z) -> app(app(:(), x), app(app(:(), y), z)),
              app(app(:(), app(app(+(), x), y)), z) -> app(app(+(), app(app(:(), x), z)), app(app(:(), y), z)),
        app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                          app(app(map(), f), nil()) -> nil(),
     app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                       app(app(filter(), f), nil()) -> nil()}
  UR:
   { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
    app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
       app(app(:(), z), app(app(+(), x), app(f, y))) -> app(app(:(), app(app(g(), z), y)), app(app(+(), x), a())),
               app(app(:(), app(app(:(), x), y)), z) -> app(app(:(), x), app(app(:(), y), z)),
               app(app(:(), app(app(+(), x), y)), z) -> app(app(+(), app(app(:(), x), z)), app(app(:(), y), z)),
         app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                           app(app(map(), f), nil()) -> nil(),
      app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                        app(app(filter(), f), nil()) -> nil(),
                                             b(w, v) -> w,
                                             b(w, v) -> v}
   EDG:
    {
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
    }
    STATUS:
     arrows: 0.000000
     SCCS (1):
      Scc:
       { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)),
         app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
         app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x),
         app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f),
        app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
        app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f),
           app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())),
           app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()),
           app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y),
           app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)),
           app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z),
                   app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)),
                   app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z),
                   app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y),
                   app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z),
                   app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z),
                   app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)),
                   app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x),
                   app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y),
                   app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)),
             app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
             app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
             app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)),
             app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)),
          app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x),
          app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs),
          app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x),
          app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f),
          app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))}
      
      SCC (29):
       Strict:
        { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)),
          app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
          app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x),
          app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f),
         app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
         app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f),
            app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(:(), app(app(g(), z), y)), app(app(+(), x), a())),
            app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(+(), x), a()),
            app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(app(g(), z), y),
            app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(:(), app(app(g(), z), y)),
            app#(app(:(), z), app(app(+(), x), app(f, y))) -> app#(g(), z),
                    app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), x), app(app(:(), y), z)),
                    app#(app(:(), app(app(:(), x), y)), z) -> app#(app(:(), y), z),
                    app#(app(:(), app(app(:(), x), y)), z) -> app#(:(), y),
                    app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), x), z),
                    app#(app(:(), app(app(+(), x), y)), z) -> app#(app(:(), y), z),
                    app#(app(:(), app(app(+(), x), y)), z) -> app#(app(+(), app(app(:(), x), z)), app(app(:(), y), z)),
                    app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), x),
                    app#(app(:(), app(app(+(), x), y)), z) -> app#(:(), y),
                    app#(app(:(), app(app(+(), x), y)), z) -> app#(+(), app(app(:(), x), z)),
              app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
              app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
              app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)),
              app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)),
           app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x),
           app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs),
           app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x),
           app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f),
           app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x))}
       Weak:
       { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
        app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
           app(app(:(), z), app(app(+(), x), app(f, y))) -> app(app(:(), app(app(g(), z), y)), app(app(+(), x), a())),
                   app(app(:(), app(app(:(), x), y)), z) -> app(app(:(), x), app(app(:(), y), z)),
                   app(app(:(), app(app(+(), x), y)), z) -> app(app(+(), app(app(:(), x), z)), app(app(:(), y), z)),
             app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                               app(app(map(), f), nil()) -> nil(),
          app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs),
                            app(app(filter(), f), nil()) -> nil()}
       Fail