le0ytruelesx0falselesxsylexyappnilyyappaddnxyaddnappxylownnilnillownaddmxif_lowlemnnaddmxif_lowtruenaddmxaddmlownxif_lowfalsenaddmxlownxhighnnilnilhighnaddmxif_highlemnnaddmxif_hightruenaddmxhighnxif_highfalsenaddmxaddmhighnxheadaddnxntailaddnxxisemptyniltrueisemptyaddnxfalsequicksortxif_qsisemptyxlowheadxtailxheadxhighheadxtailxif_qstruexnynilif_qsfalsexnyappquicksortxaddnquicksorty2.110lesxsylexyappaddnxyappxylownaddmxif_lowlemnnaddmxlownaddmxlemnif_lowtruenaddmxlownxif_lowfalsenaddmxlownxhighnaddmxif_highlemnnaddmxhighnaddmxlemnif_hightruenaddmxhighnxif_highfalsenaddmxhighnxquicksortxif_qsisemptyxlowheadxtailxheadxhighheadxtailxquicksortxisemptyxquicksortxlowheadxtailxquicksortxheadxquicksortxtailxquicksortxhighheadxtailxif_qsfalsexnyappquicksortxaddnquicksortyif_qsfalsexnyquicksortxif_qsfalsexnyquicksortytruequicksortxif_qsisemptyxlowheadxtailxheadxhighheadxtailxif_qsfalsexnyquicksortxif_qsfalsexnyquicksortytrueisemptyniltrueisemptyaddnxfalseheadaddnxntailaddnxxlownnilnillownaddmxif_lowlemnnaddmxif_lowfalsenaddmxlownxhighnnilnilhighnaddmxif_highlemnnaddmxif_hightruenaddmxhighnxle0ytruelesx0falselesxsylexyif_highfalsenaddmxaddmhighnxif_lowtruenaddmxaddmlownxle0x0lesx00lesx0sx1lowx0nillowx0addx1x2if_lowtruex0addx1x2if_lowfalsex0addx1x2highx0nilhighx0addx1x2if_hightruex0addx1x2if_highfalsex0addx1x2headaddx0x1tailaddx0x1isemptynilisemptyaddx0x1181quicksort101411if_qs401121412143414isempty101141low201011212head101121tail101141high201011112false014nil014true001add241211412if_low301011012213le201011012if_high3010110121130001s101011quicksortxif_qsisemptyxlowheadxtailxheadxhighheadxtailxisemptyniltrueisemptyaddnxfalseheadaddnxntailaddnxxlownnilnillownaddmxif_lowlemnnaddmxif_lowfalsenaddmxlownxhighnnilnilhighnaddmxif_highlemnnaddmxif_hightruenaddmxhighnxif_lowtruenaddmxaddmlownxif_highfalsenaddmxaddmhighnx1quicksort112if_qs401quicksort1if_qs4quicksortxlowheadxtailxfalsequicksortxhighheadxtailxfalselownaddmxif_lowlemnnaddmxif_lowtruenaddmxlownxif_lowfalsenaddmxlownxtruele0ytruelesx0falselesxsylexyle0x0lesx00lesx0sx1lownaddmxif_lowlemnnaddmx1false22false3if_lowtruenaddmxlownx2false13true2if_lowfalsenaddmxlownx2false13true2highnaddmxif_highlemnnaddmxif_hightruenaddmxhighnxif_highfalsenaddmxhighnxtruele0ytruelesx0falselesxsylexyle0x0lesx00lesx0sx1highnaddmxif_highlemnnaddmx1false22false3if_hightruenaddmxhighnx2false13true2if_highfalsenaddmxhighnx2false13true2lownaddmxlemnfalsehighnaddmxlemnfalseif_qsfalsexnyappquicksortxaddnquicksortyfalselesxsylexytruelesxsylexy1true12true2appaddnxyappxytrueappaddnxyappxy1true12false2quicksortxisemptyxfalsequicksortxheadxfalsequicksortxtailxfalseAProVEAProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Statistics for single proof: 100.00 % (20 real / 0 unknown / 0 assumptions / 20 total proof steps)http://aprove.informatik.rwth-aachen.deJohnDoe