A terminating algorithm decides, for any two elements of SL_2 over a non-archimedean local field, whether the subgroup they generate is discrete and free of rank two.
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Discrete and free two-generated subgroups of ${\rm SL_2}$ over non-archimedean local fields
A terminating algorithm decides, for any two elements of SL_2 over a non-archimedean local field, whether the subgroup they generate is discrete and free of rank two.