Break a Purported Halting Decider

Recall that an instance of the halting problem is a string of the form M; y and the goal is to decide if the S-Java program M (encoded as a string) halts on input y. If M halts on y, then M; y is a yes instance. Otherwise, M; y is a no instance. Let us say that an S-Java program D fails to solve the halting problem for instance M; y if it never terminates or if it produces the wrong answer, i. e., it rejects in case that M; y is a yes instance or it accepts in case that M; y is a no instance. Because the halting problem is undecidable, we know that for every S-Java program D there exists an instance M; y of the halting problem such that D fails to solve M; y. Describe an algorithm to find such an instance. The input to your algorithm is a description of a S-Java program D. For every such input, your algorithm should run for a finite number of steps and output a halting problem instance M; y such that D fails to solve M; y