Complete fault detection tests of the length two for logic networks under stuck-at faults of gates

We consider a problem of synthesis of logic networks implementing Boolean functions on $n$ variables and allowing short complete fault detection tests regarding arbitrary stuck-at faults on outputs of gates. It is proved that there exists a basis consisting of two Boolean functions not more than on four variables, in which one can implement any Boolean function by a network allowing such a test with a length not exceeding $2$.