# Reducing a P-complete search problem to an NP-complete decision problem

Let us say that a search problem $$R$$ has an A-reduction if there is a polynomial algorithm $$A$$ that solves $$R$$ using an oracle to the decision problem $$S_R$$, so that for each input $$x$$, the number of oracle calls that $$A$$ makes is at most $$100log|x|$$.

Assume that $$P ne NP$$. Prove or disprove:
There is a search problem $$R in FNP$$ so that $$S_R$$ is $$NPC$$ and $$R$$ has an A-reduction.

I am a bit confused about what “at most $$100log|x|$$” means. I also don’t know how to find a search problem $$R$$ that satisfies the requirement.