Then choose r'/r < 1/2 by a sufficient amount. For example: let (P; r; t) be ($100,000; 8%; 30 years). The payment is around $740/mo. Now take (P; r; t) equal to ($100,000; 3%; 15 years). The payment is around $700/mo.

You can adjust for the fact that some months of repayment already occurred so the term reduction is to a new term greater than half the remaining periods on the existing loan and the present value (i.e. new principle) is smaller and bump r' up accordingly to achieve the same result.

Either way it's hardly "impossible" and actually quite easy to do if there's a significant difference between the original loan conditions and the refinance/consolidation.