Termination proofs of rewrite systems using the Knuth-Bendix ordering, {\sckbo}, imply multiply-recursive bounds on the lengths of derivations. Hofbauer has studied two restrictions of {\sc kbo}. The first is a restriction to the use of positive weights, the second is a restriction on the signature which is only allowed to contain at most unary symbols. In both cases, Hofbauer proves the derivation lengths to be bounded exponentially. We prove that it correspond exactly to computations in {\sc Linspace}. Under some further considerations, we give a caracterisation of {\sc Etime} with the help of the second type of computations.