Totalistic Rules known to explicitly not be turing complete

[Colonizor48]

Does a list of such rules exist? It is trivial that any totalistic rule without b0 b1 b2 or b3 is not strongly Turing complete(not turing complete unless you allow infinity large initial conditions). As no pattern can grow beyond it's initial bounding box and must return to its initial condition after at most 2^n generations where n is the area of the box. But I am talking about rules proven to not be strongly or weakly Turing complete.

[silversmith]

edited; misread post