Time relativity? Seeing back in time? My theory.?

So I have been thinking for awhile now about this thought that I had a couple of months ago. If I am right with this, then relatively travelling back into time is possible. And like any other relativity theories, this one also requires the speed of light travel. So, consider two spacecraft that are CAPABLE of travelling at the speed of light and they both set out to a journey to Proxima Centauri (3 light years - i am rounding it). and let's say that they both start at the same time today May 25, 2011 and spaceship one is travelling at 'c' but spaceship 2 is travelling only at 'c/2'. spaceship 1 is going to arrive at Centauri exactly 3 years from now so its time is going to read May 25 2014. But the second spaceship which will arrive 6 years later. However consider this: If the spaceship 2 will increase its speed up to the speed of light once spaceship 1 arrived at proxima centauri, then spaceship two will arrive at proxima centauri in 1.5 years. So, by this time a total of 4.5 years have been passed. So the date on spaceship 2 will read November 25 2015 (remember 4.5 years). but more than 1.5 years will have been passed on the spaceship 1 that is stationary at centauri (time dilation). So therefore by the time spaceship 2 will have arrived at Centauri, an observer on spaceship 1 will perceive spaceship 2 as from the past. Thus due to time dilation, an observer on spaceship 1 will perceive spaceship 2 from the past. Even though the time difference will be minute, it can still be considered because time on spaceship 2 is much slower than on spaceship 1, which is stationary after 3 years of travel. So relatively speaking travelling back into time is possible. Am I right? Please tell me. Even though I did not use any specific numbers, this is just a thought that I have.