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MILD oxyfuel combustion has been attracting increasing attention as a promising clean combustion technology. How to design a pathway to reach MILD oxyfuel combustion regime and what can provide a theoretical guide to design such a pathway are two critical questions that need to be answered. So far there has been no open literature on these issues. A type of combustion regime classification map proposed in our previous work, based on the so-called "Hot Diluted Diffusion Ignition" (HDDI) configuration, is adopted here as a simple but useful tool to solve these problems. Firstly, we analyze comprehensively the influences of various dilution atmosphere and fuel type on combustion regimes. The combustion regime classification maps are made out according to the analyses. In succession, we conduct a comparison between the map in air-firing condition and its oxyfuel counterpart. With the aid of the second thermodynamic-law analysis on the maps, it is easy to identify the major contributors to entropy generation in various combustion regimes in advance, which is crucial for combustion system optimization. Moreover, we find that, for the first time, a combustion regime classification map also may be used as a safety indicator. With the aid of these maps, some conclusions in previous publications can be explained more straightforwardly.