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On pp. 43 and 57 in
http://www.courses.fas.harvard.edu/~phys16/handouts/textbook/ch10.pdf
a modified twin paradox is analysed. The conclusion is that, even
in the absence of accelerations, the moving clock is slower.
In fact, the trip involves an obscure episode. Clarifying it
leads to the opposite conclusion:
The obscure episode in this story is when "C sets his clock to
read the same as B's". It is not clear how this could happen
without wasting time.
So let us simplify the problem by assuming that, as B meets C, it
just sets C's clock (which has read zero so far) in motion.
With this simplification, let C's clock read t_C as C meets A.
The time t_C characterizes the movement of C between B and A. The
respective time on A's clock is T_A / 2. Since no frame is more
fundamental than the other, the conclusion is
t_C = T_A / 2
I don't see how time dilation could be introduced without declaring
either A or C as more fundamental.