Planning is a very important AI problem, and it is also a very time-consuming AI problem. To get an idea of how complex different planning problems are, it is useful to describe the computational complexity of different general planning problems. This complexity has been described for problems in which planning is based on the (complete or partial) information about the current state of the system. In real-life planning, in addition to this information, we often also use the knowledge about the system's past behavior. To describe such more realistic planning situations, a special language L was developed in 1997 by C. Baral, M. Gelfond and A. Provetti. In this paper, we expand the known results about computational complexity of planning (including our own previous results about complexity of planning in the planning language A) to this more general class of planning problems.