minusx0xminussxsyminusxyquot0sy0quotsxsysquotminusxysyle0ytruelesx0falselesxsylexyappnilyyappaddnxyaddnappxylownnilnillownaddmxif_lowlemnnaddmxif_lowtruenaddmxaddmlownxif_lowfalsenaddmxlownxhighnnilnilhighnaddmxif_highlemnnaddmxif_hightruenaddmxhighnxif_highfalsenaddmxaddmhighnxquicksortnilnilquicksortaddnxappquicksortlownxaddnquicksorthighnx2.110minussxsyminusxyquotsxsyquotminusxysyquotsxsyminusxylesxsylexyappaddnxyappxylownaddmxif_lowlemnnaddmxlownaddmxlemnif_lowtruenaddmxlownxif_lowfalsenaddmxlownxhighnaddmxif_highlemnnaddmxhighnaddmxlemnif_hightruenaddmxhighnxif_highfalsenaddmxhighnxquicksortaddnxappquicksortlownxaddnquicksorthighnxquicksortaddnxquicksortlownxquicksortaddnxlownxquicksortaddnxquicksorthighnxquicksortaddnxhighnxtruequicksortaddnxquicksorthighnxquicksortaddnxquicksortlownxtruelownnilnillownaddmxif_lowlemnnaddmxif_lowfalsenaddmxlownxle0ytruelesx0falselesxsylexyif_lowtruenaddmxaddmlownxhighnnilnilhighnaddmxif_highlemnnaddmxif_hightruenaddmxhighnxif_highfalsenaddmxaddmhighnxle0x0lesx00lesx0sx1lowx0nillowx0addx1x2if_lowtruex0addx1x2if_lowfalsex0addx1x2highx0nilhighx0addx1x2if_hightruex0addx1x2if_highfalsex0addx1x2quicksort12add21low21nil00le21true03if_low31false04005s16quicksort11add212high22low22nil0if_high33le2true0if_low33false000s11highnnilnilhighnaddmxif_highlemnnaddmxif_hightruenaddmxhighnxlownnilnillownaddmxif_lowlemnnaddmxif_lowfalsenaddmxlownxif_lowtruenaddmxaddmlownxif_highfalsenaddmxaddmhighnxquicksortaddnxlownxfalsequicksortaddnxhighnxfalsequotsxsyquotminusxysytrueminusx0xminussxsyminusxyminusx00minussx0sx11s101quot21s11minus21lownaddmxif_lowlemnnaddmxif_lowtruenaddmxlownxif_lowfalsenaddmxlownxtruele0ytruelesx0falselesxsylexyle0x0lesx00lesx0sx1lownaddmxif_lowlemnnaddmx1false22false3if_lowtruenaddmxlownx2false13true2if_lowfalsenaddmxlownx2false13true2highnaddmxif_highlemnnaddmxif_hightruenaddmxhighnxif_highfalsenaddmxhighnxtruele0ytruelesx0falselesxsylexyle0x0lesx00lesx0sx1highnaddmxif_highlemnnaddmx1false22false3if_hightruenaddmxhighnx2false13true2if_highfalsenaddmxhighnx2false13true2quotsxsyminusxyfalselownaddmxlemnfalsehighnaddmxlemnfalsequicksortaddnxappquicksortlownxaddnquicksorthighnxfalseminussxsyminusxytrueminussxsyminusxy1true12true2lesxsylexytruelesxsylexy1true12true2appaddnxyappxytrueappaddnxyappxy1true12false2AProVEAProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Statistics for single proof: 100.00 % (26 real / 0 unknown / 0 assumptions / 26 total proof steps)http://aprove.informatik.rwth-aachen.deJohnDoe