MAYBE
Time: 0.536653
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(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
          app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), 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(),
                 app(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y)),
                  app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y)),
                         app(not(), app(not(), x)) -> x}
 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(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y),
            app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z),
            app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
            app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)),
            app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y),
            app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z),
            app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
            app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x),
            app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)),
         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)),
                   app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)),
                   app#(not(), app(app(and(), x), y)) -> app#(not(), x),
                   app#(not(), app(app(and(), x), y)) -> app#(not(), y),
                   app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)),
                    app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)),
                    app#(not(), app(app(or(), x), y)) -> app#(not(), x),
                    app#(not(), app(app(or(), x), y)) -> app#(not(), y),
                    app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), 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(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
           app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), 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(),
                  app(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y)),
                   app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y)),
                          app(not(), app(not(), x)) -> x}
  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(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
            app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), 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(),
                   app(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y)),
                    app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y)),
                           app(not(), app(not(), x)) -> x,
                                             a(w, v) -> w,
                                             a(w, v) -> v}
   EDG:
    {
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (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#(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#(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(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#(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(), 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#(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#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (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(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(), 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#(cons(), x))
     (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#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (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#(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#(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(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#(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#(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#(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#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (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(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(), 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#(cons(), x))
     (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#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (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#(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#(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(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#(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#(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#(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#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (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(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(), 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#(cons(), x))
     (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#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), 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#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (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(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(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(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#(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(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#(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#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), 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#(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(), 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#(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#(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(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)), 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#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (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#(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#(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(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#(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(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#(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#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (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(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(), 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#(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#(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#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), 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#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (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(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(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(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#(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#(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#(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#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (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(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(), 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#(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#(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(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (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#(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#(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(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#(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(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(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#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (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(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(), 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#(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#(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#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), 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#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (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(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#(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(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#(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(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#(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#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (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(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(), 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#(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#(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(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), 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(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(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#(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#(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(), 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(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (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(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(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#(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(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(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(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(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#(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#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), 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(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(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#(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#(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(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (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(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(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#(cons(), 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(), 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#(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(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#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), 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(cons(), x), 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(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#(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#(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(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (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(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#(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#(cons(), 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#(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#(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(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#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), 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(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(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#(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#(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(), 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(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (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(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(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#(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(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#(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(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(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#(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#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (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#(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#(cons(), x))
     (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(), 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#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (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(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(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#(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#(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#(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(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#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     (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(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#(cons(), x))
     (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(), 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#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (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(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(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#(cons(), 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#(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#(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(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#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), 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#(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(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
     (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(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
    }
    EDG:
     {
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
      (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#(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#(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(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#(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#(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#(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#(f, x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
      (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(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(), 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#(cons(), x))
      (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#(app(cons(), x), app(app(filter(), f), xs)))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
      (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
      (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
      (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
      (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
      (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
      (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
      (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
      (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
      (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
      (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(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(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(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#(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(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(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#(f, x))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
      (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
      (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), 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(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(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#(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#(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(), false()), f), x), xs) -> app#(filter(), 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#(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#(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(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#(filter2(), app(f, x)))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
      (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
      (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
      (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#(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#(cons(), x))
      (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(), 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#(filter(), f))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
      (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(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(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#(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#(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#(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(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#(filter2(), app(f, x)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
     }
     EDG:
      {
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
       (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#(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#(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(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#(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#(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#(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#(f, x))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
       (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
       (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(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(), 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#(cons(), x))
       (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#(app(cons(), x), app(app(filter(), f), xs)))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
       (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
       (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
       (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
       (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
       (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
       (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
       (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
       (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
       (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
       (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(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(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(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#(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(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(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#(f, x))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
       (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
       (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), 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(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(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#(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#(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(), false()), f), x), xs) -> app#(filter(), 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#(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#(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(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#(filter2(), app(f, x)))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
       (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
       (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
       (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#(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#(cons(), x))
       (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(), 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#(filter(), f))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
       (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(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(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#(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#(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#(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(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#(filter2(), app(f, x)))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
       (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
      }
      EDG:
       {
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
        (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#(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#(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(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#(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#(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#(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#(f, x))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
        (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
        (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(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(), 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#(cons(), x))
        (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#(app(cons(), x), app(app(filter(), f), xs)))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
        (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
        (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
        (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
        (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
        (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
        (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
        (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
        (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
        (app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
        (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(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(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(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#(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(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(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#(f, x))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
        (app#(not(), app(app(and(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
        (app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), y), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), 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(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(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#(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#(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(), false()), f), x), xs) -> app#(filter(), 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#(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#(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(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#(filter2(), app(f, x)))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
        (app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
        (app#(not(), app(app(or(), x), y)) -> app#(not(), x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
        (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#(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#(cons(), x))
        (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(), 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#(filter(), f))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), x), app(app(or(), y), z)) -> app#(or(), app(app(and(), x), y)))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(app(or(), app(app(and(), x), y)), app(app(and(), x), z)))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(and(), x))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(and(), app(app(or(), y), z)), x) -> app#(or(), app(app(and(), x), y)))
        (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(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(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#(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#(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#(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(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#(filter2(), app(f, x)))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(app(or(), app(not(), x)), app(not(), y)))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), x))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(not(), y))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(and(), x), y)) -> app#(or(), app(not(), x)))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(app(and(), app(not(), x)), app(not(), y)))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), x))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(not(), y))
        (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(not(), app(app(or(), x), y)) -> app#(and(), app(not(), x)))
       }
       STATUS:
        arrows: 0.842773
        SCCS (3):
         Scc:
          { 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(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(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)}
         Scc:
          {app#(not(), app(app(and(), x), y)) -> app#(not(), x),
           app#(not(), app(app(and(), x), y)) -> app#(not(), y),
            app#(not(), app(app(or(), x), y)) -> app#(not(), x),
            app#(not(), app(app(or(), x), y)) -> app#(not(), y)}
         Scc:
          {app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y),
           app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z),
           app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y),
           app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z)}
         
         SCC (6):
          Strict:
           { 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(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(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)}
          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(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
                   app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), 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(),
                          app(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y)),
                           app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y)),
                                  app(not(), app(not(), x)) -> x}
          POLY:
           Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
           Interpretation:
            [app](x0, x1) = x0 + x1,
            
            [not] = 1,
            
            [and] = 0,
            
            [or] = 1,
            
            [nil] = 0,
            
            [map] = 0,
            
            [cons] = 1,
            
            [filter] = 0,
            
            [filter2] = 0,
            
            [true] = 0,
            
            [false] = 0,
            
            [app#](x0, x1) = x0
           Strict:
            app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs)
            1 + 1x + 0f + 1xs >= 0 + 0x + 0f + 1xs
            app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)
            1 + 1x + 0f + 1xs >= 0 + 1x + 0f
            app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)
            1 + 1x + 0f + 1xs >= 0 + 0f + 1xs
            app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x)
            1 + 1x + 0f + 1xs >= 0 + 1x + 0f
            app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs)
            0 + 0x + 0f + 1xs >= 0 + 0f + 1xs
            app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs)
            0 + 0x + 0f + 1xs >= 0 + 0f + 1xs
           Weak:
            app(not(), app(not(), x)) -> x
            2 + 1x >= 1x
            app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y))
            2 + 1x + 1y >= 2 + 1x + 1y
            app(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y))
            1 + 1x + 1y >= 3 + 1x + 1y
            app(app(filter(), f), nil()) -> nil()
            0 + 1f >= 0
            app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs)
            1 + 1x + 1f + 1xs >= 0 + 2x + 2f + 1xs
            app(app(map(), f), nil()) -> nil()
            0 + 1f >= 0
            app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs))
            1 + 1x + 1f + 1xs >= 1 + 1x + 2f + 1xs
            app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z))
            1 + 1x + 1y + 1z >= 1 + 2x + 1y + 1z
            app(app(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z))
            1 + 1x + 1y + 1z >= 1 + 2x + 1y + 1z
            app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs)
            0 + 1x + 1f + 1xs >= 0 + 1f + 1xs
            app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs))
            0 + 1x + 1f + 1xs >= 1 + 1x + 1f + 1xs
          SCCS (0):
           
           
           
        SCC (4):
         Strict:
          {app#(not(), app(app(and(), x), y)) -> app#(not(), x),
           app#(not(), app(app(and(), x), y)) -> app#(not(), y),
            app#(not(), app(app(or(), x), y)) -> app#(not(), x),
            app#(not(), app(app(or(), x), y)) -> app#(not(), y)}
         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(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
                  app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), 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(),
                         app(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y)),
                          app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y)),
                                 app(not(), app(not(), x)) -> x}
         POLY:
          Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
          Interpretation:
           [app](x0, x1) = x0 + x1,
           
           [not] = 1,
           
           [and] = 0,
           
           [or] = 1,
           
           [nil] = 0,
           
           [map] = 0,
           
           [cons] = 0,
           
           [filter] = 0,
           
           [filter2] = 0,
           
           [true] = 0,
           
           [false] = 0,
           
           [app#](x0, x1) = x0 + 1
          Strict:
           app#(not(), app(app(or(), x), y)) -> app#(not(), y)
           2 + 1x + 1y >= 1 + 1y
           app#(not(), app(app(or(), x), y)) -> app#(not(), x)
           2 + 1x + 1y >= 1 + 1x
           app#(not(), app(app(and(), x), y)) -> app#(not(), y)
           1 + 1x + 1y >= 1 + 1y
           app#(not(), app(app(and(), x), y)) -> app#(not(), x)
           1 + 1x + 1y >= 1 + 1x
          Weak:
           app(not(), app(not(), x)) -> x
           2 + 1x >= 1x
           app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y))
           2 + 1x + 1y >= 2 + 1x + 1y
           app(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y))
           1 + 1x + 1y >= 3 + 1x + 1y
           app(app(filter(), f), nil()) -> nil()
           0 + 1f >= 0
           app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs)
           0 + 1x + 1f + 1xs >= 0 + 2x + 2f + 1xs
           app(app(map(), f), nil()) -> nil()
           0 + 1f >= 0
           app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs))
           0 + 1x + 1f + 1xs >= 0 + 1x + 2f + 1xs
           app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z))
           1 + 1x + 1y + 1z >= 1 + 2x + 1y + 1z
           app(app(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z))
           1 + 1x + 1y + 1z >= 1 + 2x + 1y + 1z
           app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs)
           0 + 1x + 1f + 1xs >= 0 + 1f + 1xs
           app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs))
           0 + 1x + 1f + 1xs >= 0 + 1x + 1f + 1xs
         SCCS (1):
          Scc:
           {app#(not(), app(app(and(), x), y)) -> app#(not(), x),
            app#(not(), app(app(and(), x), y)) -> app#(not(), y)}
          
          SCC (2):
           Strict:
            {app#(not(), app(app(and(), x), y)) -> app#(not(), x),
             app#(not(), app(app(and(), x), y)) -> app#(not(), y)}
           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(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
                    app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), 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(),
                           app(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y)),
                            app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y)),
                                   app(not(), app(not(), x)) -> x}
           POLY:
            Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
            Interpretation:
             [app](x0, x1) = x0 + x1,
             
             [not] = 0,
             
             [and] = 1,
             
             [or] = 0,
             
             [nil] = 0,
             
             [map] = 0,
             
             [cons] = 0,
             
             [filter] = 0,
             
             [filter2] = 0,
             
             [true] = 0,
             
             [false] = 0,
             
             [app#](x0, x1) = x0 + 1
            Strict:
             app#(not(), app(app(and(), x), y)) -> app#(not(), y)
             2 + 1x + 1y >= 1 + 1y
             app#(not(), app(app(and(), x), y)) -> app#(not(), x)
             2 + 1x + 1y >= 1 + 1x
            Weak:
             app(not(), app(not(), x)) -> x
             0 + 1x >= 1x
             app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y))
             0 + 1x + 1y >= 1 + 1x + 1y
             app(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y))
             1 + 1x + 1y >= 0 + 1x + 1y
             app(app(filter(), f), nil()) -> nil()
             0 + 1f >= 0
             app(app(filter(), f), app(app(cons(), x), xs)) -> app(app(app(app(filter2(), app(f, x)), f), x), xs)
             0 + 1x + 1f + 1xs >= 0 + 2x + 2f + 1xs
             app(app(map(), f), nil()) -> nil()
             0 + 1f >= 0
             app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs))
             0 + 1x + 1f + 1xs >= 0 + 1x + 2f + 1xs
             app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z))
             1 + 1x + 1y + 1z >= 2 + 2x + 1y + 1z
             app(app(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z))
             1 + 1x + 1y + 1z >= 2 + 2x + 1y + 1z
             app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs)
             0 + 1x + 1f + 1xs >= 0 + 1f + 1xs
             app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs))
             0 + 1x + 1f + 1xs >= 0 + 1x + 1f + 1xs
           Qed
       
       
       
       
       
       
       SCC (4):
        Strict:
         {app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), y),
          app#(app(and(), x), app(app(or(), y), z)) -> app#(app(and(), x), z),
          app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), y),
          app#(app(and(), app(app(or(), y), z)), x) -> app#(app(and(), x), z)}
        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(and(), x), app(app(or(), y), z)) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), z)),
                 app(app(and(), app(app(or(), y), z)), x) -> app(app(or(), app(app(and(), x), y)), app(app(and(), x), 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(),
                        app(not(), app(app(and(), x), y)) -> app(app(or(), app(not(), x)), app(not(), y)),
                         app(not(), app(app(or(), x), y)) -> app(app(and(), app(not(), x)), app(not(), y)),
                                app(not(), app(not(), x)) -> x}
        Fail