Stage 2 Product Constraints

For all time steps \(t \in \{ 0, 1\}^{\log T}\) we want the following:

\[\begin{align} \text{LeftInstructionInput}(t) \cdot \text{RightInstructionInput}(t) &= \text{Product}(t) \\[10pt] \text{IsRdNotZero}(t) \cdot \text{WriteLookupOutputToRDFlag}(t) &= \text{WriteLookupOutputToRD}(t) \\[10pt] \text{IsRdNotZero}(t) \cdot \text{JumpFlag}(t) &= \text{WritePCtoRD}(t) \\[10pt] \text{LookupOutput}(t) \cdot \text{BranchFlag}(t) &= \text{ShouldBranch}(t) \\[10pt] \text{JumpFlag}(t) \cdot (1 - \text{NextIsNoop}(t)) &= \text{ShouldJump}(t) \end{align}\]