Synthesis of reliable non-branching programs with conditional stop in a complete finite basis containing $x_1 \& x_2$

The problem of synthesis of nobranching programs with conditional stop-operator is considered in full finite basis, contained $x_1 \& x_2$. All functional operators are supposed to be prone output inverse failures. This problem is solved for two cases: 1) conditional stop-operator is absolutely reliable; 2) conditional stop-operator is unreliable.