YES
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(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(D(), app(app(+(), x), y)) -> app(app(+(), app(D(), x)), app(D(), y)),
                     app(D(), app(app(*(), x), y)) -> app(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))),
                     app(D(), app(app(-(), x), y)) -> app(app(-(), app(D(), x)), app(D(), y)),
                                     app(D(), t()) -> 1(),
                              app(D(), constant()) -> 0()}
 DP:
  Strict:
   { app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(cons(), x), app(app(filter(), f), xs)),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(cons(), x),
     app#(app(app(app(filter2(), true()), f), x), xs) -> app#(filter(), f),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs),
    app#(app(app(app(filter2(), false()), f), x), xs) -> app#(filter(), f),
         app#(app(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#(D(), app(app(+(), x), y)) -> app#(app(+(), app(D(), x)), app(D(), y)),
                       app#(D(), app(app(+(), x), y)) -> app#(D(), x),
                       app#(D(), app(app(+(), x), y)) -> app#(D(), y),
                       app#(D(), app(app(+(), x), y)) -> app#(+(), app(D(), x)),
                       app#(D(), app(app(*(), x), y)) -> app#(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))),
                       app#(D(), app(app(*(), x), y)) -> app#(app(*(), x), app(D(), y)),
                       app#(D(), app(app(*(), x), y)) -> app#(app(*(), y), app(D(), x)),
                       app#(D(), app(app(*(), x), y)) -> app#(D(), x),
                       app#(D(), app(app(*(), x), y)) -> app#(D(), y),
                       app#(D(), app(app(*(), x), y)) -> app#(+(), app(app(*(), y), app(D(), x))),
                       app#(D(), app(app(*(), x), y)) -> app#(*(), y),
                       app#(D(), app(app(-(), x), y)) -> app#(app(-(), app(D(), x)), app(D(), y)),
                       app#(D(), app(app(-(), x), y)) -> app#(D(), x),
                       app#(D(), app(app(-(), x), y)) -> app#(D(), y),
                       app#(D(), app(app(-(), x), y)) -> app#(-(), app(D(), x))}
  Weak:
  { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
   app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
        app(app(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(D(), app(app(+(), x), y)) -> app(app(+(), app(D(), x)), app(D(), y)),
                      app(D(), app(app(*(), x), y)) -> app(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))),
                      app(D(), app(app(-(), x), y)) -> app(app(-(), app(D(), x)), app(D(), y)),
                                      app(D(), t()) -> 1(),
                               app(D(), constant()) -> 0()}
  EDG:
   {
    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(-(), app(D(), x)))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(app(-(), app(D(), x)), app(D(), y)))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(*(), y))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(+(), app(app(*(), y), app(D(), x))))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(app(*(), y), app(D(), x)))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(app(*(), x), app(D(), y)))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(+(), app(D(), x)))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(app(+(), app(D(), x)), app(D(), y)))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(-(), app(D(), x)))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(app(-(), app(D(), x)), app(D(), y)))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(*(), y))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(+(), app(app(*(), y), app(D(), x))))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(app(*(), y), app(D(), x)))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(app(*(), x), app(D(), y)))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(+(), app(D(), x)))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(app(+(), app(D(), x)), app(D(), y)))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(-(), app(D(), x)))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(app(-(), app(D(), x)), app(D(), y)))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(*(), y))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(+(), app(app(*(), y), app(D(), x))))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(app(*(), y), app(D(), x)))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(app(*(), x), app(D(), y)))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(+(), app(D(), x)))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(app(+(), app(D(), x)), app(D(), y)))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(-(), app(D(), x)))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(app(-(), app(D(), x)), app(D(), y)))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(*(), y))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(+(), app(app(*(), y), app(D(), x))))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(app(*(), y), app(D(), x)))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(app(*(), x), app(D(), y)))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(+(), app(D(), x)))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(app(+(), app(D(), x)), app(D(), y)))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
    (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(-(), x), y)) -> app#(-(), app(D(), x)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(-(), x), y)) -> app#(app(-(), app(D(), x)), app(D(), y)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(*(), x), y)) -> app#(*(), y))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(*(), x), y)) -> app#(+(), app(app(*(), y), app(D(), x))))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(*(), x), y)) -> app#(D(), x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(*(), x), y)) -> app#(app(*(), y), app(D(), x)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(*(), x), y)) -> app#(app(*(), x), app(D(), y)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(*(), x), y)) -> app#(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(+(), x), y)) -> app#(+(), app(D(), x)))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(+(), x), y)) -> app#(D(), y))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
    (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(+(), x), y)) -> app#(app(+(), app(D(), x)), app(D(), y)))
    (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(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(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#(D(), app(app(+(), x), y)) -> app#(app(+(), app(D(), x)), app(D(), y)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(+(), x), y)) -> app#(D(), y))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(+(), x), y)) -> app#(+(), app(D(), x)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(*(), x), y)) -> app#(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(*(), x), y)) -> app#(app(*(), x), app(D(), y)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(*(), x), y)) -> app#(app(*(), y), app(D(), x)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(*(), x), y)) -> app#(D(), x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(*(), x), y)) -> app#(+(), app(app(*(), y), app(D(), x))))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(*(), x), y)) -> app#(*(), y))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(-(), x), y)) -> app#(app(-(), app(D(), x)), app(D(), y)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(D(), app(app(-(), x), y)) -> app#(-(), app(D(), 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(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
    (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
    (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x))
    (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(app(filter2(), app(f, x)), f), x), xs))
    (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(app(filter2(), app(f, x)), f), x))
    (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(app(filter2(), app(f, x)), f))
    (app#(app(app(app(filter2(), true()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(filter2(), app(f, x)))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(app(+(), app(D(), x)), app(D(), y)))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(+(), app(D(), x)))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(app(*(), x), app(D(), y)))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(app(*(), y), app(D(), x)))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(+(), app(app(*(), y), app(D(), x))))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(*(), y))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(app(-(), app(D(), x)), app(D(), y)))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(-(), app(D(), x)))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(app(+(), app(D(), x)), app(D(), y)))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(+(), app(D(), x)))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(app(*(), x), app(D(), y)))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(app(*(), y), app(D(), x)))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(+(), app(app(*(), y), app(D(), x))))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(*(), y))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(app(-(), app(D(), x)), app(D(), y)))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
    (app#(D(), app(app(+(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(-(), app(D(), x)))
   }
   SCCS:
    Scc:
     {app#(D(), app(app(+(), x), y)) -> app#(D(), x),
      app#(D(), app(app(+(), x), y)) -> app#(D(), y),
      app#(D(), app(app(*(), x), y)) -> app#(D(), x),
      app#(D(), app(app(*(), x), y)) -> app#(D(), y),
      app#(D(), app(app(-(), x), y)) -> app#(D(), x),
      app#(D(), app(app(-(), x), y)) -> app#(D(), y)}
    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)}
    SCC:
     Strict:
      {app#(D(), app(app(+(), x), y)) -> app#(D(), x),
       app#(D(), app(app(+(), x), y)) -> app#(D(), y),
       app#(D(), app(app(*(), x), y)) -> app#(D(), x),
       app#(D(), app(app(*(), x), y)) -> app#(D(), y),
       app#(D(), app(app(-(), x), y)) -> app#(D(), x),
       app#(D(), app(app(-(), x), y)) -> app#(D(), 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(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(D(), app(app(+(), x), y)) -> app(app(+(), app(D(), x)), app(D(), y)),
                         app(D(), app(app(*(), x), y)) -> app(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))),
                         app(D(), app(app(-(), x), y)) -> app(app(-(), app(D(), x)), app(D(), y)),
                                         app(D(), t()) -> 1(),
                                  app(D(), constant()) -> 0()}
     SPSC:
      Simple Projection:
       pi(app#) = 1
      Strict:
       {app#(D(), app(app(+(), x), y)) -> app#(D(), x),
        app#(D(), app(app(*(), x), y)) -> app#(D(), x),
        app#(D(), app(app(*(), x), y)) -> app#(D(), y),
        app#(D(), app(app(-(), x), y)) -> app#(D(), x),
        app#(D(), app(app(-(), x), y)) -> app#(D(), y)}
      EDG:
       {(app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
        (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
        (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
        (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), x))
        (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
        (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
        (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
        (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
        (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(D(), x))
        (app#(D(), app(app(*(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
        (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
        (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(D(), x))
        (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
        (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
        (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
        (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
        (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(D(), x))
        (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
        (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
        (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
        (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
        (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), x))
        (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
        (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
        (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), y))}
       SCCS:
        Scc:
         {app#(D(), app(app(+(), x), y)) -> app#(D(), x),
          app#(D(), app(app(*(), x), y)) -> app#(D(), x),
          app#(D(), app(app(*(), x), y)) -> app#(D(), y),
          app#(D(), app(app(-(), x), y)) -> app#(D(), x),
          app#(D(), app(app(-(), x), y)) -> app#(D(), y)}
        SCC:
         Strict:
          {app#(D(), app(app(+(), x), y)) -> app#(D(), x),
           app#(D(), app(app(*(), x), y)) -> app#(D(), x),
           app#(D(), app(app(*(), x), y)) -> app#(D(), y),
           app#(D(), app(app(-(), x), y)) -> app#(D(), x),
           app#(D(), app(app(-(), x), y)) -> app#(D(), 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(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(D(), app(app(+(), x), y)) -> app(app(+(), app(D(), x)), app(D(), y)),
                             app(D(), app(app(*(), x), y)) -> app(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))),
                             app(D(), app(app(-(), x), y)) -> app(app(-(), app(D(), x)), app(D(), y)),
                                             app(D(), t()) -> 1(),
                                      app(D(), constant()) -> 0()}
         SPSC:
          Simple Projection:
           pi(app#) = 1
          Strict:
           {app#(D(), app(app(+(), x), y)) -> app#(D(), x),
            app#(D(), app(app(*(), x), y)) -> app#(D(), y),
            app#(D(), app(app(-(), x), y)) -> app#(D(), x),
            app#(D(), app(app(-(), x), y)) -> app#(D(), y)}
          EDG:
           {(app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
            (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
            (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
            (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
            (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
            (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
            (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
            (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
            (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
            (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
            (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
            (app#(D(), app(app(+(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
            (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(+(), x), y)) -> app#(D(), x))
            (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
            (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
            (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), y))}
           SCCS:
            Scc:
             {app#(D(), app(app(+(), x), y)) -> app#(D(), x),
              app#(D(), app(app(*(), x), y)) -> app#(D(), y),
              app#(D(), app(app(-(), x), y)) -> app#(D(), x),
              app#(D(), app(app(-(), x), y)) -> app#(D(), y)}
            SCC:
             Strict:
              {app#(D(), app(app(+(), x), y)) -> app#(D(), x),
               app#(D(), app(app(*(), x), y)) -> app#(D(), y),
               app#(D(), app(app(-(), x), y)) -> app#(D(), x),
               app#(D(), app(app(-(), x), y)) -> app#(D(), 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(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(D(), app(app(+(), x), y)) -> app(app(+(), app(D(), x)), app(D(), y)),
                                 app(D(), app(app(*(), x), y)) -> app(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))),
                                 app(D(), app(app(-(), x), y)) -> app(app(-(), app(D(), x)), app(D(), y)),
                                                 app(D(), t()) -> 1(),
                                          app(D(), constant()) -> 0()}
             SPSC:
              Simple Projection:
               pi(app#) = 1
              Strict:
               {app#(D(), app(app(*(), x), y)) -> app#(D(), y),
                app#(D(), app(app(-(), x), y)) -> app#(D(), x),
                app#(D(), app(app(-(), x), y)) -> app#(D(), y)}
              EDG:
               {(app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
                (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
                (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
                (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
                (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
                (app#(D(), app(app(-(), x), y)) -> app#(D(), x), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
                (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
                (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), x))
                (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), y))}
               SCCS:
                Scc:
                 {app#(D(), app(app(*(), x), y)) -> app#(D(), y),
                  app#(D(), app(app(-(), x), y)) -> app#(D(), x),
                  app#(D(), app(app(-(), x), y)) -> app#(D(), y)}
                SCC:
                 Strict:
                  {app#(D(), app(app(*(), x), y)) -> app#(D(), y),
                   app#(D(), app(app(-(), x), y)) -> app#(D(), x),
                   app#(D(), app(app(-(), x), y)) -> app#(D(), 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(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(D(), app(app(+(), x), y)) -> app(app(+(), app(D(), x)), app(D(), y)),
                                     app(D(), app(app(*(), x), y)) -> app(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))),
                                     app(D(), app(app(-(), x), y)) -> app(app(-(), app(D(), x)), app(D(), y)),
                                                     app(D(), t()) -> 1(),
                                              app(D(), constant()) -> 0()}
                 SPSC:
                  Simple Projection:
                   pi(app#) = 1
                  Strict:
                   {app#(D(), app(app(*(), x), y)) -> app#(D(), y),
                    app#(D(), app(app(-(), x), y)) -> app#(D(), y)}
                  EDG:
                   {(app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), y))
                    (app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
                    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(*(), x), y)) -> app#(D(), y))
                    (app#(D(), app(app(*(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), y))}
                   SCCS:
                    Scc:
                     {app#(D(), app(app(*(), x), y)) -> app#(D(), y),
                      app#(D(), app(app(-(), x), y)) -> app#(D(), y)}
                    SCC:
                     Strict:
                      {app#(D(), app(app(*(), x), y)) -> app#(D(), y),
                       app#(D(), app(app(-(), x), y)) -> app#(D(), 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(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(D(), app(app(+(), x), y)) -> app(app(+(), app(D(), x)), app(D(), y)),
                                         app(D(), app(app(*(), x), y)) -> app(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))),
                                         app(D(), app(app(-(), x), y)) -> app(app(-(), app(D(), x)), app(D(), y)),
                                                         app(D(), t()) -> 1(),
                                                  app(D(), constant()) -> 0()}
                     SPSC:
                      Simple Projection:
                       pi(app#) = 1
                      Strict:
                       {app#(D(), app(app(-(), x), y)) -> app#(D(), y)}
                      EDG:
                       {(app#(D(), app(app(-(), x), y)) -> app#(D(), y), app#(D(), app(app(-(), x), y)) -> app#(D(), y))}
                       SCCS:
                        Scc:
                         {app#(D(), app(app(-(), x), y)) -> app#(D(), y)}
                        SCC:
                         Strict:
                          {app#(D(), app(app(-(), x), y)) -> app#(D(), 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(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(D(), app(app(+(), x), y)) -> app(app(+(), app(D(), x)), app(D(), y)),
                                             app(D(), app(app(*(), x), y)) -> app(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))),
                                             app(D(), app(app(-(), x), y)) -> app(app(-(), app(D(), x)), app(D(), y)),
                                                             app(D(), t()) -> 1(),
                                                      app(D(), constant()) -> 0()}
                         SPSC:
                          Simple Projection:
                           pi(app#) = 1
                          Strict:
                           {}
                          Qed
    SCC:
     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)}
     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(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(D(), app(app(+(), x), y)) -> app(app(+(), app(D(), x)), app(D(), y)),
                         app(D(), app(app(*(), x), y)) -> app(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))),
                         app(D(), app(app(-(), x), y)) -> app(app(-(), app(D(), x)), app(D(), y)),
                                         app(D(), t()) -> 1(),
                                  app(D(), constant()) -> 0()}
     SPSC:
      Simple Projection:
       pi(app#) = 1
      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(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)}
      EDG:
       {(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#(f, x))
        (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#(app(filter(), f), xs))
        (app#(app(app(app(filter2(), false()), f), x), xs) -> app#(app(filter(), f), xs), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(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(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(), 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#(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))}
       SCCS:
        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(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)}
        SCC:
         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(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)}
         Weak:
         { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
          app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
               app(app(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(D(), app(app(+(), x), y)) -> app(app(+(), app(D(), x)), app(D(), y)),
                             app(D(), app(app(*(), x), y)) -> app(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))),
                             app(D(), app(app(-(), x), y)) -> app(app(-(), app(D(), x)), app(D(), y)),
                                             app(D(), t()) -> 1(),
                                      app(D(), constant()) -> 0()}
         SPSC:
          Simple Projection:
           pi(app#) = 1
          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(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)}
          EDG:
           {(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(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(), false()), f), x), xs) -> app#(app(filter(), f), xs))
            (app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(filter(), f), app(app(cons(), x), xs)) -> app#(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))}
           SCCS:
            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(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)}
            SCC:
             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(filter(), f), app(app(cons(), x), xs)) -> app#(f, x)}
             Weak:
             { app(app(app(app(filter2(), true()), f), x), xs) -> app(app(cons(), x), app(app(filter(), f), xs)),
              app(app(app(app(filter2(), false()), f), x), xs) -> app(app(filter(), f), xs),
                   app(app(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(D(), app(app(+(), x), y)) -> app(app(+(), app(D(), x)), app(D(), y)),
                                 app(D(), app(app(*(), x), y)) -> app(app(+(), app(app(*(), y), app(D(), x))), app(app(*(), x), app(D(), y))),
                                 app(D(), app(app(-(), x), y)) -> app(app(-(), app(D(), x)), app(D(), y)),
                                                 app(D(), t()) -> 1(),
                                          app(D(), constant()) -> 0()}
             SPSC:
              Simple Projection:
               pi(app#) = 1
              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)}
              EDG:
               {}
               SCCS:
                
                Qed