\begin{table}%t4 \caption{\label{t:4}Basic model properties along the AGB for a total metallicity of $Z=0.02$ and solar and $\alpha$-enhanced metal distributions.} %\centerline {\small \begin{tabular}{ccccccccccrrr} \noalign{\smallskip}\hline\hline\noalign{\smallskip} $M_{{\rm ZAMS}}^a$ & No & $M_{\rm c}$(1)$^c$ & $M_{\rm c}$(3du)$^d$ & No & C/O$_{{\rm f}}$$^f$ & $M$(f)$^g$ & $M_{\rm c}$(f)$^h$ & No & No & \multicolumn{3}{c}{TP-AGB lifetime (10$^{3}$~yrs)$^l$} \\ \cline{11-13} & TPs$^b$ & & & TP$_{{\rm 3du}}$(i)$^e$ & & & & TP$_{{\rm HBB}}$(i)$^i$ & TP$_{{\rm HBB}}$(f)$^k$ & $t_{{\rm mod}}$ & $\approx t_{{\rm e}}$ (TPs) & $t_{{\rm TP}}$ \\ \hline \multicolumn{13}{c}{$Z = 0.02$ / solar (mixture III)} \\ %\hline 1.0 & 2 & 0.501 & 0.508 & 1 & 0.547 & 0.547 & 0.508 & -- & -- & {327.675} & {36 (0)} &{364} \\ 1.2 & 5 & 0.509 & -- & -- & 0.361 & 0.608 & 0.524 & -- & -- & {537.625} & {25 (0)} & {563} \\ 1.5 & 8 & 0.511 & 0.526 & 5 & 0.724 & 0.637 & 0.539 & -- & -- & {911.274} & {15 (0)} & {926} \\ 1.6 & 9 & 0.508 & 0.522 & 5 & 0.753 & 0.888 & 0.538 & -- & -- & {1066.336} & {69 (0)} & {1135} \\ 1.8 & 8 & 0.496 & 0.503 & 2 & 1.252 & 1.031 & 0.524 & -- & -- & {1372.882} & {159 (1)} & {1532} \\ 2.0 & 15 & 0.478 & 0.484 & 2 & 1.204 & 0.543 & 0.543 & -- & -- & {2581.483} & -- & {2581} \\ 2.6 & 14 & 0.518 & 0.533 & 5 & 1.426 & 1.802 & 0.560 & -- & -- & {1560.967} & {311 (2)} & {1872} \\ 3.0 & 12 & 0.596 & 0.596 & 1 & 1.407 & 2.029 & 0.617 & -- & -- & {693.755} & {141 (2)} & {835} \\ 4.0 & 14 & 0.765 & 0.766 & 2 & 0.711 & 2.137 & 0.783 & -- & -- & {156.353} & {54 (3)} & {210} \\ 5.0 & 29 & 0.830 & 0.831 & 2 & 1.051 & 2.354 & 0.850 & -- & -- & {169.289} & {60 (7)} & {229} \\ 6.0 & 34 & 0.928 & 0.928 & 1 & 0.226 & 3.178 & 0.937 & 3 & 29 & {98.985} & {71 (23)} & {170} \\ \hline \multicolumn{13}{c}{$Z = 0.02$ / $\alpha$-enhanced (mixture IV)} \\ %\hline 1.0 & 2 & 0.502 & -- & -- & 0.164 & 0.551 & 0.505 & -- & -- & {319.945} & {43 (0)} & {363} \\ 1.2 & 5 & 0.508 & 0.518 & 4 & 0.384 & 0.561 & 0.521 & -- & -- & {529.722} & {12 (0)} & {542} \\ 1.5 & 8 & 0.514 & 0.530 & 5 & 1.834 & 0.542 & 0.540 & -- & -- & {929.208} & -- & {929} \\ 1.6 & 9 & 0.513 & 0.523 & 4 & 0.859 & 0.545 & 0.544 & -- & -- & {1018.272} & -- & {1 018} \\ 1.8 & 11 & 0.501 & 0.509 & 4 & 1.240 & 0.551 & 0.540 & -- & -- & {1412.476} & {2 (0)} & {1 414} \\ 2.0 & 14 & 0.488 & 0.494 & 2 & 1.248 & 0.629 & 0.537 & -- & -- & {2196.938} & {9 (0)} & {2 206} \\ 2.6 & 15 & 0.513 & 0.527 & 5 & 1.453 & 1.853 & 0.547 & -- & -- & {1821.007} & {412 (3)} & {2 233} \\ 3.0 & 14 & 0.585 & 0.588 & 2 & 1.332 & 1.922 & 0.612 & -- & -- & {907.181} & {207 (2)} & {1 114} \\ 4.0 & 13 & 0.766 & 0.766 & 1 & 0.681 & 1.958 & 0.774 & -- & -- & {158.834} & {37 (2)} & {196} \\ 5.0 & 21 & 0.846 & 0.846 & 2 & 0.541 & 3.215 & 0.860 & -- & -- & {117.461} & {94 (15)} & {211} \\ 6.0 & 37 & 0.946 & 0.946 & 1 & 0.252 & 3.260 & 0.954 & 1 & 32 & {91.610} & {58 (19)} & {150} \\ \hline \end{tabular}} \medskip $^a$~Initial mass on ZAMS; $^b$~number of thermal pulses; $^c$~core mass at first TP; $^d$~mass at onset of third dredge-up; $^e$~TP number of 3du onset; $^f$~final C/O ratio; $^g$~final mass; $^h$~final core mass; $^i$~first~TP with HBB; $^k$~last TP with HBB; $^l$~TP-AGB lifetimes (see text). Equivalent tables for all other mixtures are contained in the on-line material (Tables~\ref{ta:3}--\ref{ta:6}). \end{table}