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Access to justice as a constitutional guarantee faces the problematic delay in the processing cases. In this sense, the present work studies the reasonable duration of the process through Amartya Sen's idea of justice, if the cognition of the just is achieved. In this view, access to justice when faced with an impact on the democratic structure of access to the judiciary enables a new way of operating, efficiently and in search of reforms that speed up the guarantee of rights. Finally, the methodology of bibliographic research with revision technique is adopted, to print critical cognition to the analyzed sources. [ABSTRACT FROM AUTHOR]