 $(\mathrm{a})$ There exists a decidable group presentation for which the word problem is solvable while the bounded and precise word problems are not solvable.  $(\mathrm{b})$ If the bounded word problem is solvable for , then the precise word problem is also solvable.  $(\mathrm{c})$ For every finite group presentation , the bounded word problem is in ${\textsf{NP}}$, i.e., it can be solved in nondeterministic polynomial time, and the precise word problem is in , i.e., it can be solved in polynomial space.  $(\mathrm{d})$ There exists a finite group presentation for which the bounded and precise word problems are solvable while the word problem is not solvable.  $(\mathrm{e})$ There exists a finitely presented group for which the bounded word problem is -complete and the precise word problem is -hard.  