to a Runge-Kutta-Method
$$ y^{j+1}= y^j +\tau \sum_{i=1}^s b_ik_i, k_i=f(t_j+c_i\tau,y^j+\tau \sum_{l=1}^{s} a_{i,l}k_l)$$ the adjoint Method is given by $$ y^j = y^{j+1}- \tau \sum_{l=1}^s \tilde{b_i} \tilde{k_i}, \tilde{k_i}= f(t_j+ \tau -c_i \tau, y^{j+1}- \tau \sum_{l=1}^s \tilde{a_{i,l}} \tilde{k_l})$$
to show is that in case of ascending knots $c_1 \leq ...\leq c_s$ , $ \tilde{c_1} \leq ...\leq \tilde{c_s} $ the parameters of the adjoint Runge-Kutta Method are given by $$ \tilde{c_i}= 1-c_{s-i+1}, \tilde{b_i}= 1-b_{s-i+1}, \tilde{a_{i,l}}= b_{s-l+1}-a_{s-i} , 1\leq i,l \leq s$$
so if I put $\tilde{c_i}$ in the second case, it follows that: $\tilde{k_i}= f(t_j+ \tau -(1-c_{s-i+1}) \tau, y^{j+1}- \tau \sum_{l=1}^s \tilde{a_{i,l}} \tilde{k_l})$ $ \leftrightarrow \tilde{k_i}= f(t_j-c_{s-i+1} \tau, y^{j+1}- \tau \sum_{l=1}^s \tilde{a_{i,l}} \tilde{k_l})$
how can i change those idices so i get the parameters right?
First of all: The claimed equation $ \tilde{b}_i = 1 - b_{s-i+1} $ seems wrong to me. For example, if you try to apply it to the Forward Euler method ($ c_1=0, a_{1,1}=0, b_1=1 $), its adjoint method would be $ y^{j+1} = y^j $, following $ \tilde{b}_1 = 1-b_1 = 0 $. Obviously, this cannot be true.
I guess, you better try to show $ \tilde{b}_i = b_{s-i+1} $ here.
Consider to define $$ \tilde{k}_i := k_{s-i+1} $$ and make use of the identity $$ \sum_{i=1}^s{b_i k_i} = \sum_{i=1}^s{b_{s-i+1} k_{s-i+1}}. $$ This should get you pretty easily to the claimed equations.
With so many indices and signs in the game, mistakes occur more frequently. Especially, think about the sign of $ c_{s-i+1} \tau $ in your last claimed equivalence.