White needs to kill the F8 group unconditionally. If at any time you wish to start reducing the liberties of the black group please start at S11 and then T12.
(;SZ[19]AB[bs]AB[br]AB[bq]AB[bp]AB[bo]AB[bn]AB[co]AB[bk]AB[cl]AB[el]AB[fj]AB[bh]AB[eh]AB[dg]AB[df]AB[dd]AB[ce]AB[be]AB[ae]AB[fl]AB[hn]AB[io]AB[im]AB[jq]AB[mq]AB[pp]AB[km]AB[eb]AB[hl]AB[or]AB[nq]AB[qo]AB[qn]AB[rm]AB[qm]AB[sn]AB[qh]AB[ph]AB[oh]AB[oi]AB[oi]AB[nj]AB[mj]AB[mk]AB[ml]AB[om]AB[on]AB[pn]AB[lq]AB[kr]AB[gm]AB[ej]AB[np]AB[no]AB[jm]AB[kk]AB[in]AB[ir]AB[mo]AB[hg]AB[kf]AB[od]AB[ld]AB[nc]AB[nb]AB[me]AB[kb]AB[fe]AB[lm]AB[oa]AB[pa]AB[na]AB[nd]AB[kc]AB[mb]AB[ra]AB[rb]AB[rc]AB[rd]AB[re]AB[rh]AB[se]AB[rg]AB[jg]AB[go]AB[dp]AB[gf]AB[la]AB[ec]AB[ke]AB[if]AB[da]AB[cb]AB[fd]AB[jc]AB[fh]AB[ff]AB[ig]AB[de]AB[dk]AB[cm]AB[lc]AB[gl]AB[oq]AB[dm]AB[fk]AB[dl]AB[ko]AB[kp]AB[jn]AB[mm]AB[lh]AB[nh]AB[mi]AB[kh]AB[ii]AB[lk]AB[hk]AW[af]AW[bf]AW[cf]AW[cg]AW[dh]AW[fi]AW[gi]AW[gj]AW[ci]AW[cj]AW[aj]AW[bj]AW[cn]AW[dn]AW[do]AW[cp]AW[cq]AW[cr]AW[cs]AW[fn]AW[dj]AW[ho]AW[hp]AW[gn]AW[fp]AW[jp]AW[iq]AW[ik]AW[fc]AW[jd]AW[pd]AW[pr]AW[qp]AW[ro]AW[rn]AW[rl]AW[qk]AW[pl]AW[pm]AW[ol]AW[ok]AW[nk]AW[oj]AW[pj]AW[pi]AW[qi]AW[nm]AW[mn]AW[lp]AW[mp]AW[rp]AW[jo]AW[mh]AW[ei]AW[gk]AW[ln]AW[jk]AW[kj]AW[ki]AW[lg]AW[oc]AW[ob]AW[of]AW[fb]AW[jb]AW[hb]AW[qb]AW[qc]AW[qa]AW[oe]AW[pb]AW[qd]AW[qf]AW[og]AW[ne]AW[qg]AW[qe]AW[pg]AW[rf]AW[sf]AW[eq]AW[gp]AW[jf]AW[hf]AW[gg]AW[ge]AW[ie]AW[ea]AW[fa]AW[ka]AW[ja]AW[ic]AW[gd]AW[ed]AW[mc]AW[kd]AW[gh]AW[he]AW[id]AW[bm]AW[il]AW[pq]AW[rr]AW[ck]AW[bl]AW[em]AW[kn]AW[ip]AW[nl]AW[nn]AW[ng]AW[mf]AW[mg]AW[li]AW[kl]AW[jl]AW[kg]AW[sk]C[Black hits the keypoint at 'a'. How does white unconditionally kill the triangled stones?]LB[ii:a]TR[cl]TR[cm]TR[dm]TR[dl]TR[dk]TR[el]TR[ej]TR[fj]TR[fk]TR[fl]TR[gl]TR[gm]TR[hl]TR[hk]FF[4]GM[1]AP[Jago:Version 4.18]GN[temp]
(;W[ij];B[ch]
(;W[di];B[am];W[ak];B[hj]
(;W[hi];B[ll];W[jj];B[jh])
(;W[jh];B[hi];W[je];B[ai]C[white dies])
(;W[hh];B[ll];W[jj];B[jh]
(;W[ih];B[je];W[hi];B[lj])
(;W[hi];B[lj]))
(;W[ih];B[ll];W[jj];B[jh]
(;W[hh];B[je];W[hi];B[lj])
(;W[je];B[ji])
(;W[hi];B[lj]))
(;W[je];B[ll];W[jj];B[jh])
(;W[jj];B[hi]C[black has K15 or K12])
(;W[ji];B[ll];W[jj];B[jh])
(;W[jh];B[hi];W[je];B[ai]C[white dies]))
(;W[hj];B[am];W[ak];B[di]C[white has no ko-threat - he loses the race if he trys A2 or A6 as a threat.]))
(;W[hj];B[ch]
(;W[di];B[am];W[ak]
(;B[jh]
(;W[je];B[ij]
(;W[jj];B[ji])
(;W[hh];B[ji]))
(;W[le];B[ij]
(;W[jj];B[ji])
(;W[hh];B[ji]))
(;W[ij];B[je]
(;W[le];B[lf]
(;W[hh];B[le]
(;W[ag];B[ah]
(;W[jj];B[an]
(;W[al];B[eo];W[en]C[White wins by one move thanks to A13, H12 and K10. RIGHT])
(;W[ri];B[al]C[white dies]))
(;W[al];B[jj];W[ji];B[ih];W[an];B[ao]C[black should get a seki from this ko])
(;W[ri];B[jj];W[ji];B[ih]C[seki]))
(;W[jj];B[ai]C[seki])
(;W[ri];B[jj];W[ji];B[ih]C[seki])
(;W[al];B[jj];W[ji];B[ih];W[an];B[ao]C[black should get a seki from this ko]))
(;W[ag];B[ah]
(;W[hh];B[le]
(;W[jj];B[an]
(;W[al];B[eo];W[en]C[White wins by one move thanks to A13, H12 and K10. RIGHT])
(;W[ri];B[al]C[white dies]))
(;W[al];B[jj];W[ji];B[ih];W[an];B[ao]C[black should get a seki from this ko])
(;W[ri];B[jj];W[ji];B[ih]C[seki]))
(;W[jj];B[hh]C[seki])
(;W[ri];B[hh]C[seki])
(;W[al];B[hh];W[an];B[ao]C[black should get a seki from this ko]))
(;W[jj];B[hh]C[seki])
(;W[al];B[hh];W[an];B[ao]C[black should get a seki from this ko])
(;W[ri];B[hh]C[seki]))
(;W[hh];B[le]
(;W[ag];B[ah]
(;W[jj];B[an];W[al];B[eo];W[en]C[White wins by one move thanks to A13, H12 and K10. RIGHT])
(;W[ri];B[jj];W[ji];B[ih]C[seki])
(;W[al];B[jj];W[ji];B[ih];W[an];B[ao]C[black should get s seki from this ko]))
(;W[jj];B[ai]C[seki])
(;W[ri];B[jj];W[ji];B[ih]C[seki])
(;W[al];B[jj];W[ji];B[ih];W[an];B[ao]C[black should get a seki from this ko]))
(;W[ag];B[ah]
(;W[le];B[lf]
(;W[hh];B[le]
(;W[jj];B[an];W[al];B[eo];W[en]C[White wins by one move thanks to A13, H12 and K10. RIGHT])
(;W[ri];B[jj];W[ji];B[ih]C[seki])
(;W[al];B[jj];W[ji];B[ih];W[an];B[ao]C[black should get a seki from this ko]))
(;W[jj];B[hh]C[seki])
(;W[ri];B[hh]C[seki])
(;W[al];B[hh];W[an];B[ao]C[black should get a seki from this ko]))
(;W[jj];B[hh]C[seki])
(;W[al];B[hh];W[an];B[ao]C[black should get a seki from this ko])
(;W[ri];B[hh]C[seki])
(;W[hh];B[le]
(;W[jj];B[an]
(;W[al];B[eo];W[en]C[White wins by one move thanks to A13, H12 and K10. RIGHT])
(;W[ri];B[al]C[white dies]))
(;W[al];B[jj];W[ji];B[ih];W[an];B[ao]C[black should get a seki from this ko])
(;W[ri];B[jj];W[ji];B[ih]C[seki])))
(;W[jj];B[hh]C[seki])
(;W[ri];B[hh]C[seki])
(;W[al];B[hh];W[an];B[ao]C[black should get a seki from this ko])
(;W[hi];B[ji];W[jj];B[hh]C[seki]))
(;W[jj];B[hh]
(;W[je];B[ij]
(;W[hi];B[lj])
(;W[ji];B[lj]))
(;W[ij];B[je]C[seki])
(;W[hi];B[je]
(;W[ji];B[ai]C[seki - the ko needs too many approach moves])
(;W[ij];B[ji]C[seki]))
(;W[ji];B[je]
(;W[hi];B[ai]C[seki - the ko needs too many approach moves])
(;W[ij];B[hi]C[seki]))
(;W[ag];B[ij])
(;W[ri];B[ij]
(;W[ji];B[lj])
(;W[hi];B[lj])))
(;W[hh];B[jj])
(;W[hi];B[jj])
(;W[ih];B[jj])
(;W[ji];B[lj];W[jj];B[ij])
(;W[ri];B[jj]))
(;B[ij];W[jj]
(;B[jh];W[hh]
(;B[ji];W[ih];B[je];W[hi];B[jf];W[le])
(;B[ih];W[je]))
(;B[ih];W[je];B[jh];W[hh])
(;B[je];W[ih]
(;B[jh];W[hh]
(;B[ji];W[hi];B[jf];W[le])
(;B[lj];W[hi]))
(;B[hh];W[jh];B[hi];W[ji];B[jf];W[le]))
(;B[hi];W[jh];B[je];W[hh];B[ih];W[ji];B[jf];W[le]))
(;B[jj];W[ij];B[ji];W[jh]
(;B[ih];W[je])
(;B[je];W[ih]))
(;B[je];W[ij];B[jh];W[hh];B[le];W[ag];B[ah];W[jj];B[an];W[al];B[eo];W[en])
(;B[ji];W[jh]
(;B[ij];W[jj]
(;B[je];W[ih])
(;B[ih];W[je]))
(;B[jj];W[ij]
(;B[ih];W[je])
(;B[je];W[ih]))
(;B[je];W[ih]
(;B[ij];W[jj])
(;B[jj];W[ij])
(;B[hh];W[kh];B[hi];W[ij]))
(;B[ih];W[je]))
(;B[hh];W[jh]
(;B[ij];W[jj];B[je];W[hi];B[ih];W[ji];B[jf];W[le])
(;B[jj];W[ij];B[ji];W[hi])
(;B[je];W[ij]))
(;B[ih];W[ij]
(;B[jh];W[je])
(;B[je];W[jh]))
(;B[hi];W[ij]
(;B[jh];W[je])
(;B[je];W[jh])))
(;W[fm];B[eo]))
(;W[jj];B[ch];W[di];B[am];W[ak];B[jh]
(;W[hj];B[hh]
(;W[ij];B[je]C[seki])
(;W[je];B[ij]
(;W[hi];B[lj])
(;W[ji];B[lj]))
(;W[hi];B[je]
(;W[ji];B[ai]C[seki - the ko needs too many approach moves])
(;W[ij];B[ji]C[seki]))
(;W[ji];B[je]
(;W[hi];B[ai]C[seki - the ko needs too many approach moves])
(;W[ij];B[hi]C[seki]))
(;W[ag];B[ij]))
(;W[hi];B[je]
(;W[ij];B[ji]
(;W[hj];B[hh]C[seki])
(;W[hh];B[le];W[hj];B[ai]C[seki]))
(;W[hh];B[le]
(;W[ij];B[ji];W[hj];B[ai]C[seki])
(;W[hj];B[ai]C[seki]))
(;W[hj];B[le];W[ij];B[ai]C[seki]))
(;W[ij];B[je]
(;W[hh];B[le];W[hj];B[ai]C[seki])
(;W[hj];B[hh]C[seki]))
(;W[hh];B[je]
(;W[ij];B[le];W[hj];B[ai]C[seki])
(;W[hj];B[le];W[ij];B[ai]C[seki])))
(;W[ji];B[ch];W[di];B[am];W[ak];B[ij];W[jj];B[ih]
(;W[hj];B[je]
(;W[le];B[lf]
(;W[jh];B[ai]C[white dies by one move])
(;W[ag];B[jh]))
(;W[jh];B[ai]C[white dies by one move])
(;W[ag];B[jh]))
(;W[je];B[jh])
(;W[jh];B[hj];W[je];B[ai]C[white dies]))
(;W[jh];B[ch]
(;W[di];B[am];W[ak];B[hj]
(;W[ij];B[hi];W[je];B[ai]C[white dies])
(;W[jj];B[hi];W[je];B[ai]C[white dies])
(;W[ih];B[jj])
(;W[hh];B[jj])
(;W[hi];B[jj])
(;W[ji];B[hi];W[je];B[ai]C[white dies]))
(;W[ih];B[am];W[ak];B[di]C[white has no ko-threat, try one]
(;W[ar];B[dh]
(;W[an];B[ao];W[aq];B[bi]C[white loses];W[ri])
(;W[aq];B[an]C[white loses]))
(;W[sc];B[dh]C[too small])
(;W[sb];B[dh]C[too small])
(;W[dc];B[dh]C[too small]
(;W[db];B[cc];W[ca])
(;W[cc];B[db]))
(;W[le];B[dh]C[ineffective threat];W[md];B[me];W[md])
(;W[an];B[dh]
(;W[ao];B[ap])
(;W[ar];B[ao];W[aq];B[bi]C[white loses];W[ri])))
(;W[ak];B[di]
(;W[am];B[hj]C[white needs to save K9 group, save G11 group and prevent a black connection to the top - this isn't possible.])
(;W[hj];B[am];W[dh];B[ij];W[jj];B[di]C[white has no effective ko-threats, black wins the race if white plays A2 or A6 as a threat, T17/T18/D17 are all too small, M15 is ineffective, black's group in the lower right is too strong.])
(;W[ih];B[am];W[dh];B[jj];W[ij];B[di]C[white has no effective ko-threats, black wins the race if white plays A2 or A6 as a threat, T17/T18/D17 are all too small, M15 is ineffective, black's group in the lower right is too strong.]))
(;W[hj];B[am];W[ak];B[di]C[white has no effective ko-threats, black wins the race if white plays A2 or A6 as a threat, T17/T18/D17 are all too small, M15 is ineffective, black's group in the lower right is too strong.]))
(;W[ih];B[ch];W[di];B[am];W[ak];B[jh]
(;W[ji];B[ij]
(;W[hj];B[ll])
(;W[jj];B[hh];W[hi];B[je];W[hj];B[le];W[ih];B[ii]C[seki])
(;W[hi];B[ll])
(;W[hh];B[jj]))
(;W[hh];B[ji]
(;W[ij];B[je]
(;W[jj];B[le];W[hj];B[ai]C[seki])
(;W[hj];B[jj]))
(;W[hj];B[jj])
(;W[hi];B[je]
(;W[ij];B[le];W[jj];B[jf];W[hj];B[ai]C[seki])
(;W[jj];B[le];W[ij];B[jf];W[hj];B[ai]C[seki])
(;W[hj];B[jj]))
(;W[jj];B[hj]))
(;W[ij];B[hh]
(;W[hi];B[lj];W[jj];B[hj])
(;W[ji];B[lj];W[jj];B[hj])
(;W[hj];B[ji];W[jj];B[je]C[seki])
(;W[jj];B[hj]
(;W[ji];B[lj])
(;W[hi];B[lj])))
(;W[hi];B[ji]
(;W[hh];B[je]
(;W[ij];B[le];W[hj];B[ai]C[seki])
(;W[jj];B[le]
(;W[ij];B[jf];W[hj];B[ai]C[seki])
(;W[hj];B[ai]C[seki]))
(;W[hj];B[jj]))
(;W[ij];B[je]
(;W[hh];B[le]
(;W[jj];B[jf];W[hj];B[ai]C[seki])
(;W[hj];B[ai]C[seki]))
(;W[jj];B[hh];W[hj];B[ai]C[seki])
(;W[hj];B[hh];W[jj];B[ai]C[seki]))
(;W[jj];B[je]
(;W[hh];B[le]
(;W[ij];B[jf];W[hj];B[ai]C[seki])
(;W[hj];B[ai]C[seki]))
(;W[ij];B[hh];W[hj];B[ai]C[seki])
(;W[hj];B[hh];W[ij];B[ai]C[seki]))
(;W[hj];B[jj]))
(;W[hj];B[jj])
(;W[jj];B[hh]
(;W[je];B[hj])
(;W[hj];B[ij]
(;W[hi];B[lj])
(;W[ji];B[lj]))
(;W[ij];B[hi];W[hj];B[je]C[seki])
(;W[hi];B[je]
(;W[ij];B[ji];W[hj];B[ai]C[seki])
(;W[hj];B[ji];W[ij];B[ai]C[seki])
(;W[ji];B[le]
(;W[ij];B[hj]C[seki since black is unlikely to fight the ko])
(;W[hj];B[ai]C[seki - there are too many approach moves to fight the ko])
(;W[ag];B[ah]
(;W[hj];B[jf]C[seki])
(;W[ij];B[hj]C[seki - black is unlikely to fight the ko]))))
(;W[ji];B[hi];W[hj];B[je];W[ij];B[ai]C[seki])))
(;W[hh];B[ch];W[di];B[am];W[ak];B[jj]
(;W[ij];B[ji];W[jh];B[hj])
(;W[ji];B[ij])
(;W[jh];B[ij]))
(;W[hi];B[ch];W[di];B[am];W[ak];B[jh]
(;W[je];B[jj])
(;W[ij];B[ji]
(;W[jj];B[je]
(;W[hj];B[hh]C[seki])
(;W[hh];B[le];W[hj];B[ai]C[seki]))
(;W[hh];B[je];W[jj];B[le];W[hj];B[ai]C[seki])
(;W[ih];B[je]
(;W[jj];B[hh];W[hj];B[ai]C[seki])
(;W[hh];B[le]
(;W[hj];B[ai]C[seki])
(;W[jj];B[jf];W[hj];B[ai]C[seki]))))
(;W[ji];B[lj];W[jj];B[ij])
(;W[jj];B[ji]
(;W[hj];B[je]
(;W[hh];B[le];W[ij];B[ai]C[seki])
(;W[ij];B[hh]C[seki]))
(;W[ij];B[je]
(;W[hh];B[le];W[hj];B[ai]C[seki])
(;W[hj];B[hh]C[seki]))
(;W[hh];B[je]
(;W[ij];B[le];W[hj];B[ai]C[seki])
(;W[hj];B[le];W[ij];B[ai]C[seki])))
(;W[hj];B[jj])
(;W[hh];B[jj]
(;W[ij];B[lj])
(;W[ih];B[ij])
(;W[hj];B[ji]))
(;W[ih];B[ji]
(;W[ij];B[je]
(;W[hh];B[le]
(;W[jj];B[jf];W[hj];B[ai]C[seki])
(;W[hj];B[ai]C[seki]))
(;W[jj];B[hh];W[hj];B[ai]C[seki])
(;W[hj];B[jj]))
(;W[jj];B[je]
(;W[ij];B[hh];W[hj];B[ai]C[seki])
(;W[hj];B[hh];W[ij];B[ai]C[seki])
(;W[hh];B[le]
(;W[ij];B[jf];W[hj];B[ai]C[seki])
(;W[hj];B[ai]C[seki])))
(;W[hh];B[je]
(;W[ij];B[le]
(;W[jj];B[jf];W[hj];B[ai]C[seki])
(;W[hj];B[ai]C[seki]))
(;W[jj];B[le]
(;W[ij];B[jf];W[hj];B[ai]C[seki])
(;W[hj];B[ai]C[seki])))))
(;W[ch];B[jj]
(;W[ji];B[ij])
(;W[jh];B[ij])
(;W[ij];B[ji]
(;W[jh];B[hj])
(;W[hj];B[lj])))
(;W[ri];B[jj]
(;W[ji];B[ij])
(;W[ij];B[ji]
(;W[jh];B[hj])
(;W[hj];B[lj])))
(;W[fm];B[eo])
(;W[je];B[jj]
(;W[ij];B[ji]
(;W[jh];B[hj])
(;W[hj];B[lj]))
(;W[ji];B[ij])))