]  ====================================================================  Suppose that $W$ is a word over the alphabet ${\mathcal{A}}^{\pm 0}$ such that the bounded word problem for presentation holds for the pair $(W, n)$. Then a minimal diagram ${\Delta}$ over such that ${\varphi}( {\partial}{\Delta}) \equiv W$ can be algorithmically constructed in deterministic space $O( \max(\log |W|, \log n)(\log |W|)^0)$ or in deterministic time $O( |W|^0)$.  In addition, if $|n_0 | = |n_0 |$ in , then the minimal diagram problem for presentation can be solved in deterministic space $O( (\log |W|)^0 )$ or in deterministic time $O( |W|^0\log |W|)$.  