The Higgs boson production can be affected by several anomalous couplings, e.g. $c_t$ and $c_g$ anomalous couplings. Precise measurement of $gg\to h$ production yields two degenerate parameter spaces of $c_t$ and $c_g$; one parameter space exhibits the SM limit while the other does not. Such a degeneracy could be resolved by Higgs boson pair production. In this work we adapt the strategy suggested by the ATLAS collaboration to explore the potential of distinguishing the degeneracy at the 14 TeV LHC. If the $c_t$ anomalous coupling is induced only by the operator $H^���H \bar Q_L \tilde{H} t_R$, then the non-SM-like band could be excluded with an integrated luminosity of $\sim 235~{\rm fb}^{-1}$. Making use of the fact that the Higgs boson pair is mainly produced through an $s$-wave scattering, we propose an analytical function to describe the fraction of signal events surviving a series of experimental cuts for a given invariant mass of Higgs boson pair. The function is model independent and can be applied to estimate the discovery potential of various NP models.