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Annihilation dynamics plays a fundamental role in the baryon−antibaryon interaction (B−B¯¯¯¯) at low-energy and its strength and range are crucial in the assessment of possible baryon bound states. Experimental data on annihilation cross sections are available for the p−p¯¯¯ system but not in the low relative momentum region. Data regarding the BB¯¯¯¯ interaction with strange degrees of freedom are extremely scarce or absent, hence the modeling of the annihilation contributions is mainly based on nucleon−antinucleon (N−N¯¯¯¯) results, when available. In this letter we present a measurement of the p−p¯¯¯, p−Λ¯¯¯¯⊕p¯¯¯−Λ and Λ−Λ¯¯¯¯ interaction using correlation functions in the relative momentum space in high-multiplicity triggered pp collisions at s√=13 TeV recorded by ALICE at the LHC. In the p−p¯¯¯ system the couplings to the mesonic channels in different partial waves are extracted by adopting a coupled-channel approach with recent χEFT potentials. The inclusion of these inelastic channels provides good agreement with the data, showing a significant presence of the annihilation term down to zero momentum. Predictions obtained using the Lednický−Lyuboshits formula and scattering parameters obtained from heavy-ion collisions, hence mainly sensitive to elastic processes, are compared with the experimental p−Λ¯¯¯¯⊕p¯¯¯−Λ and Λ−Λ¯¯¯¯ correlations. The model describes the Λ−Λ¯¯¯¯ data and underestimates the p−Λ¯¯¯¯⊕p¯¯¯−Λ data in the region of momenta below 200 MeV/c. The observed deviation indicates a different contribution of annihilation channels to the two systems containing strange hadrons.