Abstract: Pixton relations in $R^{*}(\overline{\mathcal{M}}_{g,n})$ are extensions of Faber-Zagier relations in $R^{*}(\mathcal{M}_{g})$. We propose an algorithm to derive tautological relations from Pixton relations. We carry out this algorithm to derive some results in genus 0,1,2,3 from Pixton relations and analyze the possibility to generalize in higher genera. As an application, some results about reconstruction of Gromov-Witten invariants can be derived.