I translated only the part with the statement of the results. Instead of the proof part, I appended a later (1979, unpublished) proof sketch of a slightly tighter version. The improvement is based on the results of Meyer and Winklmann [8] and Sipser [12]. Meyer and Winklmann extended earlier versions to machines with a separate input and working tape, thus allowing complexities smaller than the input length (down to its log). Sipser showed the space-bounded Halting Problem to require only additive constant overhead. The proof in the appendix below employs both advances to extend the original proofs to machines with a fixed alphabet and a separate input and working space. The extension has no (even logarithmic) restrictions on complexity and no overhead (beyond an additive constant). The sketch is very brief and a more detailed exposition is expected later [11].