  The $\bar{\rm p} $ over p multiplicity ratio is measured in deep-inelastic
scattering for the first time using (anti-) protons carrying a large fraction
of the virtual-photon energy, $z>0.5$. The data were obtained by the COMPASS
Collaboration using a 160 GeV muon beam impinging on an isoscalar $^6$LiD
target. The regime of deep-inelastic scattering is ensured by requiring $Q^2$ >
1 (GeV/$c$)$^2$ for the photon virtuality and $W > 5$ GeV/$c^2$ for the
invariant mass of the produced hadronic system. The range in Bjorken-$x$ is
restricted to $0.01 < x < 0.40$. Protons and antiprotons are identified in the
momentum range $20 \div 60$ GeV/$c$. In the whole studied $z$-region, the
$\bar{\rm p}$ over p multiplicity ratio is found to be below the lower limit
expected from calculations based on leading-order perturbative Quantum
Chromodynamics (pQCD). Extending our earlier analysis of the K$^-$ over K$^+$
multiplicity ratio by including now events with larger virtual-photon energies,
this ratio becomes closer to the expectation of next-to-leading order pQCD. The
results of both analyses strengthen our earlier conclusion that the phase space
available for hadronisation should be taken into account in the pQCD formalism.
