  We study the circuit complexity of boolean functions in a certain infinite
basis. The basis consists of all functions that take value $1$ on antichains
over the boolean cube. We prove that the circuit complexity of the parity
function and the majority function of $n$ variables in this basis is $\lfloor
\frac{n+1}{2} \rfloor$ and $\left\lfloor \frac{n}{2} \right \rfloor +1$
respectively. We show that the asymptotic of the maximum complexity of
$n$-variable boolean functions in this basis equals $n.$
