Multioperand pipelined adder
x is delayed by 1 cycle and the delayed signal is called \$x^{-1}\$ (is one older than x). The computation seems to last 4 cycles because the result is named \$x^{-4} + x^{-5}\$ (it's \$x + x^{-1}\$ but from 4 cycles before).

This schema is repeated in stage 2 but with a 2 cycle delay on operand 1. The result of stage 2 was computed of x from 8,9,10 and 11 cycles ago (says the image).

The final sum accumulates all inputs. I think it's no sliding window because it always increments.

The resulting sum is called s, but there is a fault.
(a) The is always a sum independet of the delay, so the index -12 is irrelevant.   OR
(b) The index should donated the first result unequal to zero. Then the index must be -15, because stage 3 also uses an adder with 4 cycles of delay.

I think the correct name must be \$s^{-15}\$.