Most DBAs would tell you that this is a very critical situation that you will want to fix as soon as possible. But it is not so critical that your system has probably crashed. Yet. The problem with non-SYS or SYSTEM objects in the SYSTEM tablespace is that you can potentially interfere with the data dictionary. If non-SYS and SYSTEM objects use up all of the space, then there will be no room for the data dictionary to grow. If this is the case, then certain critical operations can't complete and your instance can crash. So it is important to move these objects as soon as possible.
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