read. When reading a symbol 2, the counter value remains the same and it is increased by 1 when a symbol 0 or 1 is read. Thus, their final counter values hit $ -t+1+n-j-(k-t) = (n-j+1)-k $.

-   If $ w[j] $ is 2, then the following configuration is created: $$-\frac{1}{2} {\langle p_3,-t \rangle} + \frac{1}{2} {\langle p_4,-t \rangle}.$$ In the remaining part of the computation, $ k-t-1 $ symbols 2 and $ n-j-(k-t-1) $ symbols 0 or 1 are read. Then, as explained in the previous item, their final counter values hit $ -t+n-j-(k-t-1) = (n-j+1)-k $.

It is clear that $ n-j+1 $ refers to $ i $ in the above equation, i.e. $ x[i] = x[n-j+1] = w[j] $, and so the correctness of this equation is verified. Moreover, we can follow that the counter value for these configurations is zero if and only if $ i = n-j+1 = k $, and, this refers to the input symbol $ x[|w|_2] = (w^r)[|w|_2] $.

Therefore, if we can determine the value of $ w^r[|w|_2] $ with zero error, then we can also determine whether the given input is in the language or not with zero error. For 