In making up the spreadsheet to analyze this, I added the situation whereby you do all of the investing within an RRSP.  So once a year you get to claim not only the interest payments on the investment (as a deduction), but you also get to claim the principal of the investments you make as an RRSP contribution, yielding a large tax return that can be applied to the principal of the mortgage.  This results in cutting your mortgage term by about 25-30%.

At that point, your "loan" balance is about 75% of your original mortgage, and your RRSP balance is about 125% of your original mortgage... But consider that you'll be taxed at your marginal rate if you withdraw enough to pay off that loan overnight.  Here's how the numbers (roughly) work for a $100K mortgage at 6%:

With all interest rates being equal (mortgage, loan, and investment), if the investment is done within an RRSP, the mortgage is done in about 7 years, with a loan balance around $75K, and an RRSP balance around $120K.  If the RRSP was cleaned out to pay the loan, it would leave around $10K in the RRSP.

If the investing is done outside the RRSP, the mortgage is done in about 9 years, with a "loan" equal to the same mortgage principal you started with, but with an investment portfolio worth about $175K.  Note that you'll pay capital gains tax on this portfolio if you remove anything from it, of course.

And finally, if you can turn over a better return rate than your mortgage, you'll be even further ahead, and vice-versa.