Probability estimation in a recursive recursive tree algorithm (Java)

Question

What is the best way to theoretically determine (i.e., without executing it) the circumstances under which a particular recursive tree traversal algorithm will lead to a stack overflow in Java?

To clarify my question, consider the following example. Given a simple binary tree implemented in Java:

public class Node {
    private int value;
    private Node left;
    private Node right;
    ...

    //in-order traversal
    public void inOrder() {
        if (left != null) {
            left.inOrder();
        }
        System.out.println(value);
        if (right != null) {
            right.inOrder();
        }
    }
}

In this algorithm, the maximum number of nested recursive calls is linear with respect to the depth of the tree. So, how can I determine what is the maximum depth of the tree that will allow the roundabout algorithm (or similar) to complete without throwing an error?

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UPDATE:

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Answer 1

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