Given a finitely presented group $<x_1,x_2,...,x_nR_1,R_2,...,R_n>$, one specifies an automorphism $\phi$ by its action on the generators, i.e. $\phi(x_i)=w_i$ for some (reduced) words $w_i$ in the group. What are the known algorithms for finding such a presentation for $\phi^{1}$?
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