Resistive Plate Chambers (RPCs), used for the Muon Spectrometer of the ALICE experiment at CERN LHC, are currently operated in maxi-avalanche mode with a low threshold value and without amplification in the front-end electronics. RPC detectors have shown a good operation stability with the current gas mixture during the entire Run 1 (2010$-$2013) and the ongoing Run 2 (2015$-$2018) at the LHC. The gas mixture is made up of $C_{2}H_{2}F_{4}$, $SF_{6}$ and $iC_{4}H_{10}$. Since the first two gases have high Global Warming Potentials (GWPs), there is the risk that they will be phased out of production in the next years, due to the recent restrictions and regulations of the European Union. Therefore, finding a new eco-friendly gas mixture has become extremely important in order to reduce the emissions of greenhouse gases. In addition, the present $iC_{4}H_{10}$ contribution makes the current gas mixture flammable. Non-flammable components, or at least in non-flammable concentrations, would be advisable to make the operation of detectors simpler and safer. In order to identify a gas mixture suited to cope with the requirements of the ALICE Muon Identifier in the forthcoming High-Luminosity runs, a dedicated experimental set-up has been used to carry out R&D studies on promising gas mixtures with small-size RPCs. Hydrofluoroolefins ($HFOs$) are appropriate candidates to replace the $C_{2}H_{2}F_{4}$ thanks to their very low GWPs, especially $HFO1234ze$ which is not flammable at room temperature. Several tests on $HFO$-based mixtures with addition of various gases are ongoing and encouraging results have already been obtained. Furthermore, the use of $CO_{2}$ as a quencher has been studied as it might represent a valid solution to avoid flammability of the mixture. Finally, medium-term stability of detectors exposed to the cosmic-ray flux will be shown in this paper.
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