MAYBE
Time: 1.031378
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(.(), x), app(i(), x)) -> 1(),
                             app(app(.(), x), 1()) -> x,
   app(app(.(), y), app(app(.(), app(i(), y)), z)) -> z,
             app(app(.(), app(app(.(), x), y)), z) -> app(app(.(), x), app(app(.(), y), z)),
                     app(app(.(), app(i(), x)), x) -> 1(),
   app(app(.(), app(i(), y)), app(app(.(), y), z)) -> z,
                             app(app(.(), 1()), x) -> 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), 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(i(), app(app(.(), x), y)) -> app(app(.(), app(i(), y)), app(i(), x)),
                             app(i(), app(i(), x)) -> x,
                                     app(i(), 1()) -> 1()}
 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(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)),
               app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z),
               app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y),
         app#(app(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#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)),
                       app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)),
                       app#(i(), app(app(.(), x), y)) -> app#(i(), x),
                       app#(i(), app(app(.(), x), y)) -> app#(i(), y)}
  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(.(), x), app(i(), x)) -> 1(),
                              app(app(.(), x), 1()) -> x,
    app(app(.(), y), app(app(.(), app(i(), y)), z)) -> z,
              app(app(.(), app(app(.(), x), y)), z) -> app(app(.(), x), app(app(.(), y), z)),
                      app(app(.(), app(i(), x)), x) -> 1(),
    app(app(.(), app(i(), y)), app(app(.(), y), z)) -> z,
                              app(app(.(), 1()), x) -> 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), 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(i(), app(app(.(), x), y)) -> app(app(.(), app(i(), y)), app(i(), x)),
                              app(i(), app(i(), x)) -> x,
                                      app(i(), 1()) -> 1()}
  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(.(), x), app(i(), x)) -> 1(),
                               app(app(.(), x), 1()) -> x,
     app(app(.(), y), app(app(.(), app(i(), y)), z)) -> z,
               app(app(.(), app(app(.(), x), y)), z) -> app(app(.(), x), app(app(.(), y), z)),
                       app(app(.(), app(i(), x)), x) -> 1(),
     app(app(.(), app(i(), y)), app(app(.(), y), z)) -> z,
                               app(app(.(), 1()), x) -> 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), 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(i(), app(app(.(), x), y)) -> app(app(.(), app(i(), y)), app(i(), x)),
                               app(i(), app(i(), x)) -> x,
                                       app(i(), 1()) -> 1(),
                                             a(w, v) -> w,
                                             a(w, v) -> v}
   EDG:
    {
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(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(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(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#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(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(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(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(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(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(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(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#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), 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(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(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(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#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(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#(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(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#(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(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#(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#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(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(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(), 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#(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#(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#(f, x), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), 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#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(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(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), 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#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (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(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(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#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
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     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
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     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
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     (app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
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     (app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
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     (app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
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     (app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
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     (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))
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     (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))
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     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
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     (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))
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     (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#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
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     (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(app(app(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(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), 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#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)), app#(i(), app(app(.(), x), y)) -> app#(i(), 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#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
     (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
    }
    EDG:
     {
      (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
      (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
      (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
      (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
      (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
      (app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
      (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
      (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
      (app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
      (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#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), 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#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(.(), app(app(.(), x), y)), z) -> app#(.(), y))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
      (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
      (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
      (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
      (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
      (app#(i(), app(app(.(), x), y)) -> app#(i(), y), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
      (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs), app#(app(app(app(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#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(i(), app(app(.(), x), y)) -> app#(app(.(), app(i(), y)), app(i(), x)))
      (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(i(), app(app(.(), x), y)) -> app#(.(), app(i(), y)))
      (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(i(), app(app(.(), x), y)) -> app#(i(), x))
      (app#(i(), app(app(.(), x), y)) -> app#(i(), x), app#(i(), app(app(.(), x), y)) -> app#(i(), y))
     }
     STATUS:
      arrows: 0.832645
      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#(i(), app(app(.(), x), y)) -> app#(i(), x),
         app#(i(), app(app(.(), x), y)) -> app#(i(), y)}
       Scc:
        {app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)),
         app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z)}
       
       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(.(), x), app(i(), x)) -> 1(),
                                    app(app(.(), x), 1()) -> x,
          app(app(.(), y), app(app(.(), app(i(), y)), z)) -> z,
                    app(app(.(), app(app(.(), x), y)), z) -> app(app(.(), x), app(app(.(), y), z)),
                            app(app(.(), app(i(), x)), x) -> 1(),
          app(app(.(), app(i(), y)), app(app(.(), y), z)) -> z,
                                    app(app(.(), 1()), x) -> 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), 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(i(), app(app(.(), x), y)) -> app(app(.(), app(i(), y)), app(i(), x)),
                                    app(i(), app(i(), x)) -> x,
                                            app(i(), 1()) -> 1()}
        Open
       
       
       
       SCC (2):
        Strict:
         {app#(i(), app(app(.(), x), y)) -> app#(i(), x),
          app#(i(), app(app(.(), x), y)) -> app#(i(), 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(.(), x), app(i(), x)) -> 1(),
                                    app(app(.(), x), 1()) -> x,
          app(app(.(), y), app(app(.(), app(i(), y)), z)) -> z,
                    app(app(.(), app(app(.(), x), y)), z) -> app(app(.(), x), app(app(.(), y), z)),
                            app(app(.(), app(i(), x)), x) -> 1(),
          app(app(.(), app(i(), y)), app(app(.(), y), z)) -> z,
                                    app(app(.(), 1()), x) -> 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), 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(i(), app(app(.(), x), y)) -> app(app(.(), app(i(), y)), app(i(), x)),
                                    app(i(), app(i(), x)) -> x,
                                            app(i(), 1()) -> 1()}
        Open
       
       
       
       
       
       
       
       SCC (2):
        Strict:
         {app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), x), app(app(.(), y), z)),
          app#(app(.(), app(app(.(), x), y)), z) -> app#(app(.(), y), z)}
        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(.(), x), app(i(), x)) -> 1(),
                                    app(app(.(), x), 1()) -> x,
          app(app(.(), y), app(app(.(), app(i(), y)), z)) -> z,
                    app(app(.(), app(app(.(), x), y)), z) -> app(app(.(), x), app(app(.(), y), z)),
                            app(app(.(), app(i(), x)), x) -> 1(),
          app(app(.(), app(i(), y)), app(app(.(), y), z)) -> z,
                                    app(app(.(), 1()), x) -> 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), 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(i(), app(app(.(), x), y)) -> app(app(.(), app(i(), y)), app(i(), x)),
                                    app(i(), app(i(), x)) -> x,
                                            app(i(), 1()) -> 1()}
        Open