Final answer:
The base case in loop invariant proofs corresponds to the Termination step, where it is shown that upon loop completion, the loop invariant and the condition for the loop's termination establish the algorithm's correctness.
Step-by-step explanation:
The base case for loop invariant proofs is associated with the c) Termination step. When working with loop invariant proofs, we aim to demonstrate that a loop behaves as expected. There are three steps involved in proving a loop invariant: the Initialization step, the Maintenance step, and the Termination step.
The Initialization step shows that the invariant holds before the first iteration of the loop. The Maintenance step demonstrates that if the invariant holds before an iteration of the loop, it holds afterward as well. Lastly, the Termination step involves showing that when the loop finishes (terminates), the invariant gives us a useful property that helps establish the loop's correctness.
The base case typically refers to the condition under which the loop will cease to execute. In the context of loop invariant proofs, we need to verify that the loop terminates in a state where the invariant, along with the termination condition, implies the correctness of the overall algorithm.