Table 2 The relations of variables \(h^i_\mathrm{ref}\), \(h^j_\mathrm{ref}\), \(h^k_\mathrm{ref}\) and \(h^\mathrm{grp}_\mathrm{ref}\) in Fig. 3

a-(1)

\(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j \le 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k \le 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i \le 1\)

a-(2)

\(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j > 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k \le 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i \le 1\)

a-(3)

\(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j \le 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k > 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i \le 1\)

a-(4)

\(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j \le 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k \le 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i > 1\)

a-(5)

\(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j > 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k > 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i \le 1\)

a-(6)

\(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j > 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k \le 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i > 1\)

a-(7)

\(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j \le 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k > 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i > 1\)

a-(8)

\(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^j > 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^k > 1, \, h_{\mathrm{ref}}^k + h_{\mathrm{ref}}^i > 1\)

b-(1)

\(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^{\mathrm{grp}} < 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^{\mathrm{grp}} < 1\)

b-(2)

\(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^{\mathrm{grp}} \ge 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^{\mathrm{grp}} < 1\)

b-(3)

\(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^{\mathrm{grp}} < 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^{\mathrm{grp}} \ge 1\)

b-(4)

\(h_{\mathrm{ref}}^i + h_{\mathrm{ref}}^{\mathrm{grp}} \ge 1, \,h_{\mathrm{ref}}^j + h_{\mathrm{ref}}^{\mathrm{grp}} \ge 1\)