Recent studies suggest that applying the Buscher rules to the dimensional reduction of ten-dimensional, one-loop effective actions generate \\\\\\\"purely stringy\\\\\\\" couplings in nine dimensions that cannot be lifted to a local, covariant form in ten dimensions. We investigate this phenomenon at order $\\\\\\\\alpha\\\\\\\'^3$ in type IIA string theory. By computing the circular reduction of the one-loop Chern-Simons term and pure-gravity couplings in type IIA theory and applying the T-duality transformation to the resulting couplings, we derive their counterparts in the type IIB effective action. We demonstrate that the resulting nine-dimensional type IIB couplings are invariant under S-duality without requiring contributions from the tree-level effective action or non-perturbative effects. As a consistency check, we show that the nine-dimensional type IIB couplings, when reduced on a K3 surface, reproduce the known heterotic string couplings on \\\\\\\\( T^5 \\\\\\\\) at order \\\\\\\\( \\\\\\\\alpha\\\\\\\' \\\\\\\\), via the duality between the two theories.

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