1 - Jacob Pfister
I'm afraid your definitions of a memoryless/memory system are incorrect. If a system is memoryless, that simply means that the output depends only on the input at the current moment in time (and not on any past inputs). Therefore, the two examples you used are actually both memoryless. The $ t $ terms are not considered to cause the system to have memory because at each $ t $, $ t $ is simply a constant and not part of the input $ x(t) $.
