# Is there any decidable problem that is NOT NP-HARD?

Is there a proof that there exists a decidable problem that is NOT NP-HARD??

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Since you need one $x \in A$, and one $x \not \in A$ for a polynomial time reduction, $A = \emptyset$ cannot be a hard language for NP.
and under $P=NP$ only $\emptyset$ and $A^{\ast}$ are not NP-hard under polynomial time reductions. –  sdcvvc Dec 3 '11 at 17:27