Working memory capacity (WMC) and fluid intelligence (Gf) are highly correlated, but what accounts for this relationship remains elusive. Process-overlap theory (POT) proposes that the positive manifold is mainly caused by the overlap of domain-general executive processes which are involved in a battery of mental tests. Thus, executive processes are proposed to explain the relationship between WMC and Gf. The current study aims to (1) achieve a relatively purified representation of the core executive processes including shifting and inhibition by a novel approach combining experimental manipulations and fixed-links modeling, and (2) to explore whether these executive processes account for the overlap between WMC and Gf. To these ends, we reanalyzed data of 215 university students who completed measures of WMC, Gf, and executive processes. Results showed that the model with a common factor, as well as shifting and inhibition factors, provided the best fit to the data of the executive function (EF) task. These components explained around 88% of the variance shared by WMC and Gf. However, it was the common EF factor, rather than inhibition and shifting, that played a major part in explaining the common variance. These results do not support POT as underlying the relationship between WMC and Gf.