  By developing various techniques of mould theory, we introduce
$\mathsf{GARI}(\mathscr{F})_{\mathsf{as}+\mathsf{bal}}$, a mould theoretic
formulation of Drinfeld's associator set. We give a mould-theoretical
generalization of the result that associator relations imply double shuffle
relations, namely, we explain that
$\mathsf{GARI}(\mathscr{F})_{\mathsf{as}+\mathsf{bal}}$ is embedded to Ecalle's
set $\mathsf{GARI}(\mathscr{F})_{\mathsf{as}\ast\mathsf{is}}$ which is a mould
theoretic version of Racinet's double shuffle set.
