\[t'=\frac{t_0}{\sqrt{1-\frac{v^{2}}{c^{2}}}}=\frac{t}{2}\sqrt{1-\frac{v^{2}}{c^{2}}}=t_1\sqrt{\frac{1-\frac{v}{c}}{1+\frac{v}{c}}}=t_2\sqrt{\frac{1+\frac{v}{c}}{1-\frac{v}{c}}}=\sqrt{t_1\cdot t_2}=\sqrt{\frac{t\cdot t_0}{2}}=\frac{l_0}{\sqrt{c^{2}-v^{2}}}\]