This is largely symantics. A bug is a problem that is observable erroneous behavior - if the correct output is always generated, there is no bug in the system.

So you only have one bug, in one component: your algorithm has a bug. If you've implemented it outside the specification (faulty implementation), even by accident, what you have isn't a bug but a workaround for the bug in the algorithm.

Your overall system, then, has no bugs. However, there is a vast difference between not buggy and provably correct. The hypothetical system here is not buggy, but neither is it provably correct. Which matters more largely depends on whether you're labor or management. ;-)