The paper proves that the iterated join $ J^{+}(S) $ is equal to the join $ J(S) $ for any set $ S $ in a control flow graph (CFG). This is shown by proving that $ J(S \cup J(S)) = J(S) $, which implies that iterating the join operation does not add any new nodes. The join $ J(a, b) $ is defined as the set of nodes $ c $ such that there are paths from $ a $ and $ b $ to predecessors of $ c $, with no common nodes on the paths. The iterated join $ J^{+}(S) $ is defined as the limit of the increasing sequence of nodes generated by repeatedly applying the join operation. The paper shows that for any $ S $, $ J^{+}(S) = J(S) $, which has implications for the correctness of advanced analysis algorithms like Static Single Assignment (SSA). Although the join set is used in theoretical proofs, there are no practical algorithms that directly use it due to its computational complexity. The work is supported by various grants and is of interest to researchers who use these methods.The paper proves that the iterated join $ J^{+}(S) $ is equal to the join $ J(S) $ for any set $ S $ in a control flow graph (CFG). This is shown by proving that $ J(S \cup J(S)) = J(S) $, which implies that iterating the join operation does not add any new nodes. The join $ J(a, b) $ is defined as the set of nodes $ c $ such that there are paths from $ a $ and $ b $ to predecessors of $ c $, with no common nodes on the paths. The iterated join $ J^{+}(S) $ is defined as the limit of the increasing sequence of nodes generated by repeatedly applying the join operation. The paper shows that for any $ S $, $ J^{+}(S) = J(S) $, which has implications for the correctness of advanced analysis algorithms like Static Single Assignment (SSA). Although the join set is used in theoretical proofs, there are no practical algorithms that directly use it due to its computational complexity. The work is supported by various grants and is of interest to researchers who use these methods.