Its my understanding that relativistic length contraction l = l0√ 1-v2 also applies to the space itself in the moving S' system. For example a rocket traveling at .6 c. A distance that is 1000 meters in S frame is contracted to 800 meters in rockets frame. (1000/γ) Therefore the elapsed time / proper time in rocket S' frame ( 800m/.6c) is less than as calculated as seen from stationary S frame ( 1000m/.6c.) Hence time dilation equated to length/distance contraction. And allowing the proper"time between ticks" of both clocks, S and S' being equal.