Boundary value analysis and decision table testing are the best choice of one black box technique and one white box technique for test case design2. A black box technique is a technique that uses the external behaviour or specification of a system as a test basis to derive test cases without referring to its internal structure or logic2. A white box technique is a technique that uses the internal structure or logic of a system as a test basis to derive test cases and measure test coverage2. In this question, the system has complex business rules and many branches in the structure of its code components. Therefore, we need to choose a black box technique that can handle complex business rules and a white box technique that can cover many branches.
* Boundary value analysis is a black box technique that tests the values at or near the boundaries of an equivalence partition2. Boundary value analysis can handle complex business rules by identifying the boundary conditions that may cause errors or exceptions in the system's behaviour2.
* Decision table testing is a white box technique that tests all possible combinations of conditions and actions in a decision logic2. Decision table testing can cover many branches by creating a table that shows how each condition affects each action and then deriving test cases from each row of the table2.
Therefore, boundary value analysis and decision table testing are the best choice of one black box technique and one white box technique for test case design.