a=aV7a-a-alengthV7c1V8aV2a-a-alengthV2c1V8Ia<V8alengthV2Aa<=c0V8FAa=aV7V9V0Ia<V9a-alengthV7alengthV2Aa<=c0V9FAa=alengthV7amaxV1alengthV2Ia=aV7V10aV2a-a+c0V10V6Ia<V10a+V6V5Aa<=V6V10FAa=aV7V11aV4V11Ia<V11alengthV7Aa<=a+V6V5V11Oa<V11V6Aa<=c0V11FIa=alengthV7alengthV4FAa<=a+V6V5alengthV4Aa<=c0V6Aa<=a+c0V5alengthV2Aa<=c0V5Aa<=c0c0La-V3alengthV2LalengthV2Ia=alengthV4V3Aa=aV4V12V0Ia<V12V3Aa<=c0V12FFAa>=V3c0LamaxV1alengthV2F
VC for leftpad
a=ato_fmapahaempty
a>=anc0
array creation size
a=aaresV0c0Ia<V0anAa<=c0V0F
a=alengtharesan
a<=c0a+a-anc1c1
a<=c0c0Aa<=c0c0
loop invariant init
amemaxato_fmapahqamem1axaac0
amemV1ato_fmapahqamem1V1aac0F
amem1axaresc0qamem1axaac0
amem1V2aresc0qamem1V2aac0F
a<=c0ai
a<aiaj
a<ajc0
Na=aaresaiaaresaj
a=alengthares1alengthares
a<=aia-anc1
a<=c0alen
a<=alenai
amemV1ato_fmapah1qamem1V1aaaiF
amem1V2ares1alenqamem1V2aaaiF
Na=aares1V3aares1V4Ia<V4alenAa<V3V4Aa<=c0V3F
a<aialengthaaAa<=c0ai
index in array bounds
Namemaaaaiato_fmapah1
a=ato_fmapah2aaddaaaaiaTuple0ato_fmapah1
a<alenalengthares1Aa<=c0alen
a=alengthares2alengthares1
a=aeltsares2asetaeltsares1alenaaaai
a=ares2aares1alenaaaai
a=alen1a+alenc1
a<=alen1a+aic1Aa<=c0alen1
loop invariant preservation
amemaxato_fmapah2qamem1axaaa+aic1
amemV5ato_fmapah2qamem1V5aaa+aic1F
amem1axares2alen1qamem1axaaa+aic1
amem1V6ares2alen1qamem1V6aaa+aic1F
a<=c0ai1
a<ai1aj
a<ajalen1
Na=aares2ai1aares2aj
NNamemaaaaiato_fmapah1
a<=alena+aic1Aa<=c0alen
amemaxato_fmapah1qamem1axaaa+aic1
amemV5ato_fmapah1qamem1V5aaa+aic1F
a=axaaaai
amem1axares1alenqamem1axaaa+aic1
true case (loop invariant preservation)
Na=axaaaai
amem1axaaaiqamem1axaaa+aic1
asserted formula
false case (loop invariant preservation)
amem1V6ares1alenqamem1V6aaa+aic1F
a<ajalen
Na=aares1ai1aares1aj
a<=alena+a-anc1c1
amemV1ato_fmapah1qamem1V1aaa+a-anc1c1F
amem1V2ares1alenqamem1V2aaa+a-anc1c1F
a<=a+c0alenalengthares1Aa<=c0alenAa<=c0c0
precondition
a=alengtharesultalen
a=aaresultV5aares1a+c0V5Ia<V5alenAa<=c0V5F
amem1axaaalengthaaqamem1axaresultalengtharesult
postcondition
amem1V6aaalengthaaqamem1V6aresultalengtharesultF
a<ajalengtharesult
Na=aaresultaiaaresultaj
a>c0a+a-anc1c1
Na=aV1V2aV1V3Ia<V3alengthV1Aa<V2V3Aa<=c0V2FAamemV4aaalengthaaqamemV4V1alengthV1FIa=aV1V5aaresa+c0V5Ia<V5c0Aa<=c0V5FAa=alengthV1c0FAa<=a+c0c0alengtharesAa<=c0c0Aa<=c0c0
out of loop bounds
Na=aV5V6aV5V7Ia<V7alengthV5Aa<V6V7Aa<=c0V6FAamemV8V0alengthV0qamemV8V5alengthV5FIa=aV5V9aV3a+c0V9Ia<V9c0Aa<=c0V9FAa=alengthV5c0FAa<=a+c0c0alengthV3Aa<=c0c0Aa<=c0c0Ia>c0a+V4c1ANa=aV13V14aV13V15Ia<V15alengthV13Aa<V14V15Aa<=c0V14FAamemV16V0alengthV0qamemV16V13alengthV13FIa=aV13V17aV11a+c0V17Ia<V17V10Aa<=c0V17FAa=alengthV13V10FAa<=a+c0V10alengthV11Aa<=c0V10Aa<=c0c0INa=aV11V18aV11V19Ia<V19V10Aa<V18V19Aa<=c0V18FAamemV20V11V10qamemV20V0a+V4c1FAamem1V21ato_fmapV12qamemV21V0a+V4c1FAa<=V10a+V4c1Aa<=c0V10AiNa=aV11V23aV11V24Ia<V24V10Aa<V23V24Aa<=c0V23FAamemV25V11V10qamemV25V0a+V22c1FAamem1V26ato_fmapV12qamemV26V0a+V22c1FAa<=V10a+V22c1Aa<=c0V10Na=aV29V31aV29V32Ia<V32V30Aa<V31V32Aa<=c0V31FAamemV33V29V30qamemV33V0a+V22c1FAamem1V34ato_fmapV27qamemV34V0a+V22c1FAa<=V30a+V22c1Aa<=c0V30Ia=V30a+V10c1FIa=V29aV11V10V28Aa=aeltsV29asetaeltsV11V10V28Ia=alengthV29alengthV11FAa<V10alengthV11Aa<=c0V10LaV0V22Aa<V22alengthV0Aa<=c0V22Ia=ato_fmapV27aaddaV0V22aTuple0ato_fmapV12FAa<V22alengthV0Aa<=c0V22Namem1aV0V22ato_fmapV12Aa<V22alengthV0Aa<=
VC for unique
a=c0asumaac0c0
a=arightasumaac0ai
a=aright1a+arightaaaai
a=aright1asumaac0a+aic1
a=arightasumaac0a+a-anc1c1
a=arightasumaac0an
a=aabsarightadiffaac0
a<=c0aj
a<=ajc0
a<=aabsarightadiffaaaj
a=aleftasumaac0ai
a=aright1asumaaaian
a<=c0abesti
a<=abestiai
a=abestdadiffaaabesti
a<=abestdadiffaaV0Ia<=V0aiAa<=c0V0F
a=aleft1a+aleftaaaai
a=aright2a-aright1aaaai
a<adabestd
a=abestd1ad
a=abesti1a+aic1
a=aleft1asumaac0a+aic1
a=aright2asumaaa+aic1an
a<=abesti1a+aic1Aa<=c0abesti1
a=abestd1adiffaaabesti1
a<=aja+aic1
a<=abestd1adiffaaaj
Na<adabestd
a<=abestia+aic1Aa<=c0abesti
a<=abestdadiffaaaj
a=aleftasumaac0a+a-anc1c1
a=aright1asumaaa+a-anc1c1an
a<=abestia+a-anc1c1
a<=abestdadiffaaV0Ia<=V0a+a-anc1c1Aa<=c0V0F
a<=abestialengthaaAa<=c0abesti
a<=aialengthaa
a<=adiffaaabestiadiffaaai
a<=adiffaac0adiffaaV0Ia<=V0alengthaaAa<=c0V0FAa<=c0alengthaaAa<=c0c0
a<=adiffaac0adiffaaV0Ia<=V0alengthaaAa<=c0V0FAa<=c0alengthaaAa<=c0c0Ia>c0a+a-anc1c1Aa<=adiffaaV2adiffaaV5Ia<=V5alengthaaAa<=c0V5FAa<=V2alengthaaAa<=c0V2Ia<=V1adiffaaV6Ia<=V6a+a-anc1c1Aa<=c0V6FAa=V1adiffaaV2Aa<=V2a+a-anc1c1Aa<=c0V2Aa=V4asumaaa+a-anc1c1anAa=V3asumaac0a+a-anc1c1Aia<=V1adiffaaV11Ia<=V11a+V7c1Aa<=c0V11FAa=V1adiffaaV2Aa<=V2a+V7c1Aa<=c0V2Aa=V9asumaaa+V7c1anAa=V8asumaac0a+V7c1a<=V12adiffaaV14Ia<=V14a+V7c1Aa<=c0V14FAa=V12adiffaaV13Aa<=V13a+V7c1Aa<=c0V13Aa=V9asumaaa+V7c1anAa=V8asumaac0a+V7c1Ia=V13a+V7c1FIa=V12V10Fa<V10V1Laabsa-V8V9Ia=V9a-V4aaaV7FAa<V7alengthaaAa<=c0V7Ia=V8a+V3aaaV7FAa<V7alengthaaAa<=c0V7Ia<=V1adiffaaV15Ia<=V15V7Aa<=c0V15FAa=V1adiffaaV2Aa<=V2V7Aa<=c0V2Aa=V4asumaaV7anAa=V3asumaac0V7Aa<=V7a-anc1Aa<=c0V7FFAa<=aabsc0adiffaaV16Ia<=V16c0Aa<=c0V16FAa=aabsc0adiffaac0Aa<=c0c0Aa<=c0c0Aa=c0asumaac0anAa=c0asumaac0c0Ia<=c0a+a-anc1c1
a<=adiffV0c0adiffV0V4Ia<=V4alengthV0Aa<=c0V4FAa<=c0alengthV0Aa<=c0c0Ia>c0a+V3c1Aa<=adiffV0V6adiffV0V9Ia<=V9alengthV0Aa<=c0V9FAa<=V6alengthV0Aa<=c0V6Ia<=V5adiffV0V10Ia<=V10a+V3c1Aa<=c0V10FAa=V5adiffV0V6Aa<=V6a+V3c1Aa<=c0V6Aa=V8asumV0a+V3c1V1Aa=V7asumV0c0a+V3c1Aia<=V5adiffV0V15Ia<=V15a+V11c1Aa<=c0V15FAa=V5adiffV0V6Aa<=V6a+V11c1Aa<=c0V6Aa=V13asumV0a+V11c1V1Aa=V12asumV0c0a+V11c1a<=V16adiffV0V18Ia<=V18a+V11c1Aa<=c0V18FAa=V16adiffV0V17Aa<=V17a+V11c1Aa<=c0V17Aa=V13asumV0a+V11c1V1Aa=V12asumV0c0a+V11c1Ia=V17a+V11c1FIa=V16V14Fa<V14V5Laabsa-V12V13Ia=V13a-V8aV0V11FAa<V11alengthV0Aa<=c0V11Ia=V12a+V7aV0V11FAa<V11alengthV0Aa<=c0V11Ia<=V5adiffV0V19Ia<=V19V11Aa<=c0V19FAa=V5adiffV0V6Aa<=V6V11Aa<=c0V6Aa=V8asumV0V11V1Aa=V7asumV0c0V11Aa<=V11V3Aa<=c0V11FFAa<=aabsc0adiffV0V20Ia<=V20c0Aa<=c0V20FAa=aabsc0adiffV0c0Aa<=c0c0Aa<=c0c0Aa=c0asumV0c0V1Aa=c0asumV0c0c0Ia<=c0a+V3c1La-V1c1Ia>c0a+V2c1Aa<=adiffV0c0adiffV0V23Ia<=V23alengthV0Aa<=c0V23FAa<=c0alengthV0Aa<=c0c0Ia>c0a+V22c1Aa<=adiffV0V25adiffV0V28Ia<=V28alengthV0Aa<=c0V28FAa<=V25alength
VC for fulcrum
a=c0a+a*c0amc0Aa<=c0a-amc1Aa<=c0c0Aa<=c0a-amc1Aa<=a-amc0
VC for big
a=avV0a+a*aint32'intaqV0amaint32'intarV0Aa<=aint32'intarV0a-amc1Aa<=c0aint32'intarV0Aa<=aint32'intaqV0a-amc1Aa<=a-amaint32'intaqV0FavV0arV0aqV0
tIa=avV1c0Aa=arV1c0Aa=aqV1c0Aa=V4aqV1Aa=V3arV1Aa=V2avV1FAa=c0a+a*c0amc0Aa<=c0a-amc1Aa<=c0c0Aa<=c0a-amc1Aa<=a-amc0
VC for big_zero
a=avabig_zeroV1c0Aa=arabig_zeroV1c0Aa=aqabig_zeroV1c0F
a=ab_qaqabAa=ab_rarabAa=ab_vavab
a<=amin_biga+avabaint32'intax
a<=a+avabaint32'intaxamax_big
a<aint32'intaxc0
ain_boundsa+aint32'intarabaint32'intax
integer overflow
a=aint32'intar'a+aint32'intarabaint32'intax
a<aint32'intar'c0
ain_boundsa-aint32'intaqabc1
a=aint32'intab_q1a-aint32'intaqabc1
ain_boundsa+aint32'intar'c1
a=aint32'intaoa+aint32'intar'c1
ain_boundsa+aint32'intaoaint32'intamax_int32
a=aint32'intab_r1a+aint32'intaoaint32'intamax_int32
a=a+avabaint32'intaxa+a*aint32'intab_q1amaint32'intab_r1Aa<=aint32'intab_r1a-amc1Aa<=c0aint32'intab_r1Aa<=aint32'intab_q1a-amc1Aa<=a-amaint32'intab_q1
type invariant
a=ab_q1aqab1Aa=ab_r1arab1Aa=a+avabaint32'intaxavab1
a=avab1a+avabaint32'intax
Na<aint32'intar'c0
a<=a-amaint32'intaqab
a<=aint32'intaqaba-amc1
a<=c0aint32'intar'
a<=aint32'intar'a-amc1
a=a+avabaint32'intaxa+a*aint32'intaqabamaint32'intar'
a=a+avabaint32'intaxa+a*aint32'intaqabamaint32'intar'Aa<=aint32'intar'a-amc1Aa<=c0aint32'intar'Aa<=aint32'intaqaba-amc1Aa<=a-amaint32'intaqab
a=aqabaqab1Aa=ar'arab1Aa=a+avabaint32'intaxavab1
Na<aint32'intaxc0
ain_boundsa+aint32'intamin_int32aint32'intax
a=aint32'intaoa+aint32'intamin_int32aint32'intax
ain_boundsa+aint32'intarabaint32'intao
a=aint32'intar'a+aint32'intarabaint32'intao
a=aint32'intao1a+aint32'intar'c1
ain_boundsa+aint32'intao1aint32'intamax_int32
a=aint32'intab_r1a+aint32'intao1aint32'intamax_int32
a=a+avabaint32'intaxa+a*aint32'intaqabamaint32'intab_r1Aa<=aint32'intab_r1a-amc1Aa<=c0aint32'intab_r1Aa<=aint32'intaqaba-amc1Aa<=a-amaint32'intaqab
a=aqabaqab1Aa=ab_r1arab1Aa=a+avabaint32'intaxavab1
ain_boundsa+aint32'intaqabc1
a=aint32'intab_q1a+aint32'intaqabc1
a=a+avabaint32'intaxa+a*aint32'intab_q1amaint32'intar'Aa<=aint32'intar'a-amc1Aa<=c0aint32'intar'Aa<=aint32'intab_q1a-amc1Aa<=a-amaint32'intab_q1
a=ab_q1aqab1Aa=ar'arab1Aa=a+avabaint32'intaxavab1
iia=avV19a+avV2aint32'intV6Ia=V22aqV19Aa=V21arV19Aa=V20avV19Aa=V20a+a*aint32'intV22amaint32'intV21Aa<=aint32'intV21a-amc1Aa<=c0aint32'intV21Aa<=aint32'intV22a-amc1Aa<=a-amaint32'intV22Ia=V20a+V16aint32'intV6Aa=V21V17Aa=V22V18FIa=V16V13Aa=V17V10Aa=V18V15FIa=V13avV2Aa=V14arV2Aa=V15V12FIa=aint32'intV12a+aint32'intV11c1FAain_boundsa+aint32'intV11c1LaqV2a=avV29a+avV2aint32'intV6Ia=V32aqV29Aa=V31arV29Aa=V30avV29Aa=V30a+a*aint32'intV32amaint32'intV31Aa<=aint32'intV31a-amc1Aa<=c0aint32'intV31Aa<=aint32'intV32a-amc1Aa<=a-amaint32'intV32Ia=V30a+V26aint32'intV6Aa=V31V27Aa=V32V28FIa=V26avV2Aa=V27V25Aa=V28aqV2FIa=aint32'intV25a+aint32'intV24aint32'intV23FAain_boundsa+aint32'intV24aint32'intV23Ia=aint32'intV24a+aint32'intV10c1FAain_boundsa+aint32'intV10c1Lamax_int32a<aint32'intV10c0Ia=aint32'intV10a+aint32'intV9aint32'intV8FAain_boundsa+aint32'intV9aint32'intV8LarV2Ia=aint32'intV8a+aint32'intV7aint32'intV6FAain_boundsa+aint32'intV7aint32'intV6Lamin_int32ia=avV38a+avV2aint32'intV6Ia=V41aqV38Aa=V40arV38Aa=V39avV38Aa=V39a+a*a
VC for add_big
ia=avV10a-avV2aint32'intV6ItAtIa=avV10a+avV2aint32'intV9Ia=V13aqV10Aa=V12arV10Aa=V11avV10FAa<=a+avV2aint32'intV9amax_bigAa<=amin_biga+avV2aint32'intV9ItAtIa=aint32'intV9a-aint32'intV6FAain_boundsa-aint32'intV6a=avV19a-avV2aint32'intV6Ia=V22aqV19Aa=V21arV19Aa=V20avV19Aa=V20a+a*aint32'intV22amaint32'intV21Aa<=aint32'intV21a-amc1Aa<=c0aint32'intV21Aa<=aint32'intV22a-amc1Aa<=a-amaint32'intV22Ia=V20a-V16aint32'intV6Aa=V21V17Aa=V22V18FIa=V16avV2Aa=V17arV2Aa=V18V15FIa=aint32'intV15a+aint32'intV14c1FAain_boundsa+aint32'intV14c1LaqV2a=V8aTrueIa=V6V7Ia=V8aTrueAa=V8aTrueIa=aint32'intV6aint32'intV7FLamin_int32Ia<=a-avV2aint32'intV6amax_bigAa<=amin_biga-avV2aint32'intV6Aa=V5aqV2Aa=V4arV2Aa=V3avV2F
VC for sub_big
a=ax_qaqaxAa=ax_raraxAa=ax_vavax
a=ay_qaqayAa=ay_rarayAa=ay_vavay
a<=amin_bigaabsa-avaxavay
a<=aabsa-avaxavayamax_big
ain_boundsa-aint32'intarayaint32'intarax
a=aint32'intar1a-aint32'intarayaint32'intarax
a<aint32'intaqayaint32'intaqax
a>aint32'intar1c0
ain_boundsa-aint32'intar1
a=aint32'intaresulta-aint32'intar1
ain_boundsa+aint32'intaresultc1
a=aint32'intaoa+aint32'intaresultc1
a=aint32'intao1a+aint32'intaoaint32'intamax_int32
ain_boundsa-aint32'intaqaxc1
a=aint32'intao2a-aint32'intaqaxc1
ain_boundsa-aint32'intao2aint32'intaqay
a=aint32'intao3a-aint32'intao2aint32'intaqay
a=av1a+a*aint32'intao3amaint32'intao1Aa<=aint32'intao1a-amc1Aa<=c0aint32'intao1Aa<=aint32'intao3a-amc1Aa<=a-amaint32'intao3
Na>aint32'intar1c0
ain_boundsa-aint32'intaqaxaint32'intaqay
a=aint32'intaoa-aint32'intaqaxaint32'intaqay
a=av1a+a*aint32'intaoamaint32'intaresultAa<=aint32'intaresulta-amc1Aa<=c0aint32'intaresultAa<=aint32'intaoa-amc1Aa<=a-amaint32'intao
Na<aint32'intaqayaint32'intaqax
a=aTrueaTrueIa=aint32'intaqayaint32'intaqax
a=aqayaqaxIa=aTrueaTrue
a<aint32'intar1c0
a=av1a+a*c0amaint32'intaresultAa<=aint32'intaresulta-amc1Aa<=c0aint32'intaresultAa<=c0a-amc1Aa<=a-amc0
Na<aint32'intar1c0
a=av1a+a*c0amaint32'intar1Aa<=aint32'intar1a-amc1Aa<=c0aint32'intar1Aa<=c0a-amc1Aa<=a-amc0
a=aoaTrueIa=aint32'intaqayaint32'intaqax
a=aqayaqaxIa=aoaTrue
Na=aoaTrue
ain_boundsa+aint32'intar1c1
a=aint32'intao1a+aint32'intar1c1
a=aint32'intao2a+aint32'intao1aint32'intamax_int32
ain_boundsa-aint32'intaqayc1
a=aint32'intao3a-aint32'intaqayc1
ain_boundsa-aint32'intao3aint32'intaqax
a=aint32'intao4a-aint32'intao3aint32'intaqax
a=av1a+a*aint32'intao4amaint32'intao2Aa<=aint32'intao2a-amc1Aa<=c0aint32'intao2Aa<=aint32'intao4a-amc1Aa<=a-amaint32'intao4
ain_boundsa-aint32'intaqayaint32'intaqax
a=aint32'intao1a-aint32'intaqayaint32'intaqax
a=av1a+a*aint32'intao1amaint32'intar1Aa<=aint32'intar1a-amc1Aa<=c0aint32'intar1Aa<=aint32'intao1a-amc1Aa<=a-amaint32'intao1
iiia=avaresultav1Aa=araresultar1Aa=aqaresultaoAa=aresult_qaqaresultAa=aresult_rararesultAa=aresult_vavaresultAa=aint32'intaoa-aint32'intaqayaint32'intaqaxa=avaresultav1Aa=araresultao1Aa=aqaresultao2Aa=aresult_qaqaresultAa=aresult_rararesultAa=aresult_vavaresultAa=aint32'intao2a-aint32'intao3aint32'intaqaxAa=aint32'intao3a-aint32'intaqayc1Aa=aint32'intao1a+aint32'intao4aint32'intamax_int32Aa=aint32'intao4a+aint32'intar1c1a<aint32'intar1c0ia=avaresultav1Aa=araresultar1Aa=aqaresultc0Aa=aresult_qaqaresultAa=aresult_rararesultAa=aresult_vavaresulta=avaresultav1Aa=araresultaresult1Aa=aqaresultc0Aa=aresult_qaqaresultAa=aresult_rararesultAa=aresult_vavaresultAa=aint32'intaresult1a-aint32'intar1a<aint32'intar1c0a=ao5aTrueAa=V3V2Ia=ao5aTrueAa=ao5aTrueIa=aint32'intV3aint32'intV2LaqayLaqaxia=avaresultav1Aa=araresultaresult2Aa=aqaresultao6Aa=aresult_qaqaresultAa=aresult_rararesultAa=aresult_vavaresultAa=aint32'intao6a-aint32'intaqaxaint32'intaqayAa=aint32'intaresult2a-aint32'intar1a=avaresultav1Aa=araresultao7Aa=aqaresult
a=avaresultaabsa-avaxavay
a=avV14aabsa-avV2avV6ItAtIiiia=avV14V13Aa=arV14V12Aa=aqV14V21Aa=V17aqV14Aa=V16arV14Aa=V15avV14Aa=aint32'intV21a-aint32'intaqV6aint32'intaqV2Ea=avV14V13Aa=arV14V23Aa=aqV14V25Aa=V17aqV14Aa=V16arV14Aa=V15avV14Aa=aint32'intV25a-aint32'intV24aint32'intaqV2EAa=aint32'intV24a-aint32'intaqV6c1EAa=aint32'intV23a+aint32'intV22aint32'intamax_int32EAa=aint32'intV22a+aint32'intV12c1Ea<aint32'intV12c0ia=avV14V13Aa=arV14V12Aa=aqV14c0Aa=V17aqV14Aa=V16arV14Aa=V15avV14a=avV14V13Aa=arV14V26Aa=aqV14c0Aa=V17aqV14Aa=V16arV14Aa=V15avV14Aa=aint32'intV26a-aint32'intV12Ea<aint32'intV12c0a=V20aTrueAa=V19V18Ia=V20aTrueAa=V20aTrueIa=aint32'intV19aint32'intV18ELaqV6LaqV2ia=avV14V13Aa=arV14V27Aa=aqV14V28Aa=V17aqV14Aa=V16arV14Aa=V15avV14Aa=aint32'intV28a-aint32'intaqV2aint32'intaqV6EAa=aint32'intV27a-aint32'intV12Ea=avV14V13Aa=arV14V31Aa=aqV14V33Aa=V17aqV14Aa=V16arV14Aa=V15avV14Aa=aint32'intV33a-aint32'intV32aint32'intaqV6EAa=aint32'intV32a-aint32'intaqV2c1EAa=aint32'intV31a+aint32'intV30aint32'intamax_int32EAa=aint32'intV30a+aint32'intV29c
VC for delta
a<avV2avV6qa=V10aTrueIia=V10iaFalseiaFalseaTruea<aint32'intarV2aint32'intarV6a=V13aTrueAa=V12V11Ia=V13aTrueAa=V13aTrueIa=aint32'intV12aint32'intV11ELaqV2LaqV6a=V10aTruea<aint32'intaqV2aint32'intaqV6FIa>=avV6c0Aa>=avV2c0Aa=V9aqV6Aa=V8arV6Aa=V7avV6Aa=V5aqV2Aa=V4arV2Aa=V3avV2F
VC for big_lt
a<=asumV2V3V4a*a-V4V3aint32'intamax_int32Aa<=a*a-V4V3aint32'intamin_int32asumV2V3V4Ia>V3a+V5c1Aa<=asumV2V3V4a*a-V4V3aint32'intamax_int32Aa<=a*a-V4V3aint32'intamin_int32asumV2V3V4Ia<=V6a*a-a+V5c1V3aint32'intamax_int32Aa<=a*a-a+V5c1V3aint32'intamin_int32V6Aa=V6asumV2V3a+V5c1Aa<=V8a*a-a+V7c1V3aint32'intamax_int32Aa<=a*a-a+V7c1V3aint32'intamin_int32V8Aa=V8asumV2V3a+V7c1Ia=V8a+V6aint32'inta@aeltsV2V7FIa<=V6a*a-V7V3aint32'intamax_int32Aa<=a*a-V7V3aint32'intamin_int32V6Aa=V6asumV2V3V7Aa<=V7V5Aa<=V3V7FFAa<=c0a*a-V3V3aint32'intamax_int32Aa<=a*a-V3V3aint32'intamin_int32c0Aa=c0asumV2V3V3Ia<=V3a+V5c1La-V4c1Ia<=V4aint32'intalengthV2Aa<=V3V4Aa<=c0V3F
VC for sum_bounds
a<=asumV2V3V4a*a-V4V3aint32'intamax_int32Aa<=a*a-V4V3aint32'intamin_int32asumV2V3V4Ia<=V4aint32'intalengthV2Aa<=V3V4Aa<=c0V3F
a<aint32'intalengthaaaint32'intamax_int32
ain_boundsa-aint32'intanc1
a=aint32'intaoa-aint32'intanc1
a<=c0a+aint32'intaoc1
abiginvaright
a=avarightasumaac0c0
a=aright_qaqarightAa=aright_rararightAa=aright_vavaright
a<=aiaint32'intao
a=avarightasumaac0ai
a<aint32'intai1aint32'intalengthaaAa<=c0aint32'intai1
a<=a+avarightaint32'intaaaaint32'intai1amax_bigAa<=amin_biga+avarightaint32'intaaaaint32'intai1
a=aright_q1aqaright1Aa=aright_r1araright1Aa=aright_v1avaright1
a=avaright1a+avarightaint32'intaaaaint32'intai1
abiginvaright1
a=avaright1asumaac0a+aic1
a=avarightasumaac0a+aint32'intaoc1
a<=aabsa-avaleftavarightamax_bigAa<=amin_bigaabsa-avaleftavaright
a=abestd_qaqabestdAa=abestd_rarabestdAa=abestd_vavabestd
a=avabestdaabsa-avaleftavaright
a=aint32'intao1a-aint32'intanc1
a<=c0a+aint32'intao1c1
abiginvabestdAabiginvaleftAabiginvaright
a=avaleftasumaac0c0
a=avarightasumaac0aint32'intan
a=avabestdadiffaac0
a<=avabestdadiffaaaj
a=aleft_qaqaleft1Aa=aleft_raraleft1Aa=aleft_vavaleft1
a=abestd_q1aqabestd1Aa=abestd_r1arabestd1Aa=abestd_v1avabestd1
a<=aiaint32'intao1
abiginvaleft1
abiginvabestd1
a=avaleft1asumaac0ai
a=avaright1asumaaaiaint32'intan
a<=c0aint32'intabesti
a<=aint32'intabestiai
a=avabestd1adiffaaaint32'intabesti
a<=avabestd1adiffaaV5Ia<=V5aiAa<=c0V5F
a<=a+avaleft1aint32'intaaaaint32'intai1amax_bigAa<=amin_biga+avaleft1aint32'intaaaaint32'intai1
a=aleft_q1aqaleft2Aa=aleft_r1araleft2Aa=aleft_v1avaleft2
a=avaleft2a+avaleft1aint32'intaaaaint32'intai1
a<=a-avaright1aint32'intaaaaint32'intai1amax_bigAa<=amin_biga-avaright1aint32'intaaaaint32'intai1
a=aright_q2aqaright2Aa=aright_r2araright2Aa=aright_v2avaright2
a=avaright2a-avaright1aint32'intaaaaint32'intai1
a<=aabsa-avaleft2avaright2amax_bigAa<=amin_bigaabsa-avaleft2avaright2
a=ad_qaqadAa=ad_raradAa=ad_vavad
a=avadaabsa-avaleft2avaright2
a>=avabestd1c0Aa>=avadc0
a<avadavabestd1
ain_boundsa+aint32'intai1c1
a=aint32'intabesti1a+aint32'intai1c1
a=avada+a*aint32'intaqadamaint32'intaradAa<=aint32'intarada-amc1Aa<=c0aint32'intaradAa<=aint32'intaqada-amc1Aa<=a-amaint32'intaqad
a=aqadaqabestd2Aa=aradarabestd2Aa=avadavabestd2
abiginvabestd2Aabiginvaleft2Aabiginvaright2
a=avaleft2asumaac0a+aic1
a=avaright2asumaaa+aic1aint32'intan
a<=aint32'intabesti1a+aic1Aa<=c0aint32'intabesti1
a=avabestd2adiffaaaint32'intabesti1
a<=avabestd2adiffaaaj
Na<avadavabestd1
abiginvabestd1Aabiginvaleft2Aabiginvaright2
a<=aint32'intabestia+aic1Aa<=c0aint32'intabesti
a<=avabestd1adiffaaaj
a=avaleft1asumaac0a+aint32'intao1c1
a=avaright1asumaaa+aint32'intao1c1aint32'intan
a<=aint32'intabestia+aint32'intao1c1
a<=avabestd1adiffaaV5Ia<=V5a+aint32'intao1c1Aa<=c0V5F
a<=aint32'intabestiaint32'intalengthaaAa<=c0aint32'intabesti
a<=aiaint32'intalengthaa
a<=adiffaaaint32'intabestiadiffaaai
a>c0a+aint32'intao1c1
a<=adiffaac0adiffaaV5Ia<=V5aint32'intalengthaaAa<=c0V5FAa<=c0aint32'intalengthaaAa<=c0c0
a>c0a+aint32'intaoc1
a<=adiffaac0adiffaaV10Ia<=V10aint32'intalengthaaAa<=c0V10FAa<=c0aint32'intalengthaaAa<=c0c0Ia>c0a+aint32'intV9c1Aa<=adiffaaaint32'intV15adiffaaV24Ia<=V24aint32'intalengthaaAa<=c0V24FAa<=aint32'intV15aint32'intalengthaaAa<=c0aint32'intV15Ia<=avV11adiffaaV25Ia<=V25a+aint32'intV9c1Aa<=c0V25FAa=avV11adiffaaaint32'intV15Aa<=aint32'intV15a+aint32'intV9c1Aa<=c0aint32'intV15Aa=avV20asumaaa+aint32'intV9c1aint32'intanAa=avV16asumaac0a+aint32'intV9c1AabiginvV11AabiginvV16AabiginvV20Aia<=avV11adiffaaV42Ia<=V42a+V27c1Aa<=c0V42FAa=avV11adiffaaaint32'intV15Aa<=aint32'intV15a+V27c1Aa<=c0aint32'intV15Aa=avV34asumaaa+V27c1aint32'intanAa=avV29asumaac0a+V27c1AabiginvV11AabiginvV29AabiginvV34ItAtItAtItAta<=avV49adiffaaV55Ia<=V55a+V27c1Aa<=c0V55FAa=avV49adiffaaaint32'intV54Aa<=aint32'intV54a+V27c1Aa<=c0aint32'intV54Aa=avV34asumaaa+V27c1aint32'intanAa=avV29asumaac0a+V27c1AabiginvV49AabiginvV29AabiginvV34Ia=V52aqV49Aa=V51arV49Aa=V50avV49Aa=V50a+a*aint32'intV52amaint32'intV51Aa<=aint32'intV51a-amc1Aa<=c0aint32'intV51Aa<=aint32'intV52
a<=adiffV5c0adiffV5V15Ia<=V15aint32'intalengthV5Aa<=c0V15FAa<=c0aint32'intalengthV5Aa<=c0c0Ia>c0a+aint32'intV14c1Aa<=adiffV5aint32'intV20adiffV5V29Ia<=V29aint32'intalengthV5Aa<=c0V29FAa<=aint32'intV20aint32'intalengthV5Aa<=c0aint32'intV20Ia<=avV16adiffV5V30Ia<=V30a+aint32'intV14c1Aa<=c0V30FAa=avV16adiffV5aint32'intV20Aa<=aint32'intV20a+aint32'intV14c1Aa<=c0aint32'intV20Aa=avV25asumV5a+aint32'intV14c1aint32'intV6Aa=avV21asumV5c0a+aint32'intV14c1AabiginvV16AabiginvV21AabiginvV25Aia<=avV16adiffV5V47Ia<=V47a+V32c1Aa<=c0V47FAa=avV16adiffV5aint32'intV20Aa<=aint32'intV20a+V32c1Aa<=c0aint32'intV20Aa=avV39asumV5a+V32c1aint32'intV6Aa=avV34asumV5c0a+V32c1AabiginvV16AabiginvV34AabiginvV39ItAtItAtItAta<=avV54adiffV5V60Ia<=V60a+V32c1Aa<=c0V60FAa=avV54adiffV5aint32'intV59Aa<=aint32'intV59a+V32c1Aa<=c0aint32'intV59Aa=avV39asumV5a+V32c1aint32'intV6Aa=avV34asumV5c0a+V32c1AabiginvV54AabiginvV34AabiginvV39Ia=V57aqV54Aa=V56arV54Aa=V55avV54Aa=V55a+a*aint32'intV57amaint32'intV56Aa<=aint32'intV56a-amc1Aa<=c0aint32'intV56Aa<=aint32'int

a1eab0b80006b803b8ab710ae443513c 1H0
7a4e22d26ed1205472d959ebe0172794 74H73
6cf44b8ab561be0f8c9a6823ec4437ff 4H3H2
50b8b28a94804302ca11252442cc7e44 9H8H7H6H5H2
dee909a97a7622c7fc5755618be9f4fc 9H10H8H7H6H5H2
9f8d459a9e04896e63edb9e7319542d5 9H12H11H8H7H6H5H2
30b464bff01da8808315dcc34648a549 9H17H16H15H14H13H11H8H7H6H5H2
16cfd40a86999c6bb0bf61021bf2b538 26H25H24H23H22H21H20H19H14H18H7H6H5H2
d7337610064bdc578c1bf16e62d39b55 26H25H27H24H23H22H21H20H19H14H18H7H6H5H2
8bcf7ae701ccefc8365b832fc0923208 26H25H28H27H24H23H22H21H20H19H14H18H7H6H5H2
edb3c77ba0719a912045fa774ac518b6 26H29H28H27H24H23H22H21H20H19H14H18H7H6H5H2
cd9fa63c5e7d9cf024f85eda5ce2545e 35H34H33H32H31H30H28H27H24H23H22H21H20H19H14H18H7H6H5H2
cfa18afeec6660af49b85b1e2a706455 35H36H34H33H32H31H30H28H27H24H23H22H21H20H19H14H18H7H6H5H2
990f4852596b6b79492d654d33fee915 35H38H37H34H33H32H31H30H28H27H24H23H22H21H20H19H14H18H7H6H5H2
f433edb2e93f90a19ac9d5ea6c9874ed 35H43H42H41H40H39H37H34H33H32H31H30H28H27H24H23H22H21H20H19H14H18H7H6H5H2
ea14d25f4667502681247ca519efc573 35H45H44H24H23H22H21H20H19H14H18H7H6H5H2
feaa32430cea46c2741b42da71ca1d31 35H46H45H44H24H23H22H21H20H19H14H18H7H6H5H2
8e7f1719ee233790ef618d4beded5260 35H49H47H45H44H24H23H22H21H20H19H14H18H7H6H5H2
4517d4eef61b4822002da2f95fe0b574 50H49H48H47H45H44H24H23H22H21H20H19H14H18H7H6H5H2
2baf86545f98877c779d005442d6cc12 54H49H51H47H45H44H24H23H22H21H20H19H14H18H7H6H5H2
e9cf74d305ee20b8e8b7fe663ded220a 53H52H51H47H45H44H24H23H22H21H20H19H14H18H7H6H5H2
3e9c6730f8a55522cef65d133eec9aaf 54H49H52H51H47H45H44H24H23H22H21H20H19H14H18H7H6H5H2
9e4b0ba550fa188a3c42e7a4ddefa25f 35H57H56H41H40H55H47H45H44H24H23H22H21H20H19H14H18H7H6H5H2
b32d091b705c7cd9364fdccd3ac0a20e 62H61H24H60H59H58H20H18H7H6H5H2
e63250be4d718ce7680008fd72b220c8 66H65H64H63H24H60H59H58H20H18H7H6H5H2
84f705162069540e65f20a8af5e4ea54 66H69H68H15H14H67H64H63H24H60H59H58H20H18H7H6H5H2
ed9df3f2db82a8b2c4f10e6ef28bb6f2 72H71H70H6H5H2
bddfd5deec2503b01268e415ee01b6b0 115H114
ade96b06431031b03a312191b7b633c8 9H75H7
c12c2528af7dd31a671f74115bd0f6ad 26H25H76H19H14H7
61ea32328fcfac5e34c460f4059189ee 35H78H77H76H19H14H7
efd1a5b776cf5f8a784d20eec4170fcc 9H75H7H79H7
3d5084bf0b232c04f4217cf1510fd68d 9H80H75H7H79H7
bc2cef4d2f7f7554881aa2cc4697ea9d 9H8H80H75H7H79H7
9da2c6d03546ccb45987d97d8cbb29ec 9H81H8H80H75H7H79H7
f34ea919203115bcf131c3e6b9dac565 9H84H83H82H81H8H80H75H7H79H7
ddde8a87296857457968f3178016eb6b 26H25H90H89H88H87H86H85H19H14H7H79H7
8bc27530e1451fa471d96aaaad2bd5f0 26H25H91H90H89H88H87H86H85H19H14H7H79H7
cdc526793d662bc6ab28cb1f93bbf0e8 35H96H95H94H93H92H91H90H89H88H87H86H85H19H14H7H79H7
a4fcc7a9aa6df1838c66e4e621307e47 35H97H96H95H94H93H92H91H90H89H88H87H86H85H19H14H7H79H7
643354195eba48bc87448f1f51ce272e 35H98H97H96H95H94H93H92H91H90H89H88H87H86H85H19H14H7H79H7
eee19204fcc74de493af2e106365a3cf 35H99H98H97H96H95H94H93H92H91H90H89H88H87H86H85H19H14H7H79H7
d4c7e1534cab5256929a056ff0a9758a 35H101H100H82H99H98H97H96H95H94H93H92H91H90H89H88H87H86H85H19H14H7H79H7
131fc3a9c00c02f704ffc8d46ac11e0d 35H96H102H92H91H90H89H88H87H86H85H19H14H7H79H7
0ac3fc6a8a3fedc98aba6a2f3e756ca9 35H97H96H102H92H91H90H89H88H87H86H85H19H14H7H79H7
d66426813cb3d5b5050ac9b8dc9319cd 35H103H97H96H102H92H91H90H89H88H87H86H85H19H14H7H79H7
1c048b7513a7164d21c637b32c77d0c7 35H89H103H97H96H102H92H91H90H89H88H87H86H85H19H14H7H79H7
e419d3bdd48ab3d561cbb9586040585e 35H104H100H82H89H103H97H96H102H92H91H90H89H88H87H86H85H19H14H7H79H7
70898b843b099cddbe17f42d38d87f6d 66H109H108H89H107H87H106H105H7H79H7
a8eea91c05381789589378ac650f0e09 66H111H110H14H109H108H89H107H87H106H105H7H79H7
8257ddc033185973076efbec3687b85e 72H112H70H79H7
c847dc7c2e27decf6a2dc636a720505f 72H113H70
a6094b3ea2d6f68b19f6cc1c0a5b8c11 117H116
4d826744fddc2a20d15fbb2dbb4b5c11 120H119H118
c8ea8d59e3038285ccc402aff39c3c46 163H162H121H118
dce69741b287c34822ac4eda1a05a8c0 127H126H125H124H123H122H121H118
45896270654b2ab3d69da3b30b9b1375 127H130H129H128H125H124H123H122H121H118
ad38ad8c1a17bef3b7aace3c1e67fb20 127H132H131H129H128H125H124H123H122H121H118
57aecf65da5d5fc4ac2611db29657b85 127H134H133H131H129H128H125H124H123H122H121H118
da7ad1c29e72cf7f4780f869b32df976 137H136H135H133H131H129H128H125H124H123H122H121H118
6e71a9da769907bf17af285f91269656 66H139H138H135H133H131H129H128H125H124H123H122H121H118
8a4f87974bf3244d273dfbc297e5ad14 137H146H140H128H125H124H123H122H121H118
81a185a5b609441e71828995ba68da46 137H141H140H128H125H124H123H121H118
cfb8fd0c5a416fdfe9c751da3146e01e 137H142H140H128H125H124H123H121H118
3b0fa981e022bd5f97aeea458d57df39 137H143H140H128H125H124H123H121H118
64eb97ad4be81347c5baf4137ae27a26 137H144H140H128H125H124H123H121H118
6b728d25862af709d9a75db61c89b89e 137H145H140H128H125H124H123H121H118
d0c6c505c492bdd1bbe321be660d8483 66H139H147H140H128H125H124H123H122H121H118
add258486ffcf09c92d7e0c39458a3b9 127H149H148H124H123H122H121H118
2a54b7c05c5e212c36978fe51b4bf1cf 127H151H150H148H124H123H122H121H118
2456deea199ef7c2178b3c23e1ed8afc 127H132H129H152H150H148H124H123H122H121H118
afe9ccfceb9e8b1e85138e3978a0e095 127H154H153H129H152H150H148H124H123H122H121H118
639948ad91953d10d3fb8c3956a7952e 137H156H155H153H129H152H150H148H124H123H122H121H118
2f08344cbb77230470e06c86f7ea8749 66H139H157H155H153H129H152H150H148H124H123H122H121H118
243e73ce43d606d5ad25bafc9604d3ad 127H158H140H152H150H148H124H123H122H121H118
8929b2367587888a7dbd56aa0ffc07bf 137H160H159H140H152H150H148H124H123H122H121H118
a08b3548366ed6aa9a57cc9ed14e63c1 66H139H161H159H140H152H150H148H124H123H122H121H118
c4b3c6f3eb7793ebe21d092ddb1e4995 165H164H121H118
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49e1aa99c645639c2e9cdfb88a153c40 35H272H271H277H276H263H262H260H259H257H256H254H253H252H251H250H249H248H247H231H246H14H245H244H229H238H237H236H235H233H222H224H221H220H218H217H121H118
c0e4cd36ec626d5a0c1dc62e263bc453 35H278H272H271H277H276H263H262H260H259H257H256H254H253H252H251H250H249H248H247H231H246H14H245H244H229H238H237H236H235H233H222H224H221H220H218H217H121H118
966ba95a4b362dd4e1ab2fde5fdf04f5 35H253H278H272H271H277H276H263H262H260H259H257H256H254H253H252H251H250H249H248H247H231H246H14H245H244H229H238H237H236H235H233H222H224H221H220H218H217H121H118
36b1701233af9c94b19d77d90a295c13 35H279H100H82H253H278H272H271H277H276H263H262H260H259H257H256H254H253H252H251H250H249H248H247H231H246H14H245H244H229H238H237H236H235H233H222H224H221H220H218H217H121H118
78021b197f1c184989c7bd3367f50da4 66H284H283H253H282H251H281H280H248H247H231H245H244H229H238H237H236H235H233H222H224H221H220H218H217H121H118
cddf3a5c5599ee3397c403731467a241 66H286H285H14H284H283H253H282H251H281H280H248H247H231H245H244H229H238H237H236H235H233H222H224H221H220H218H217H121H118
73e73b2a4002cc3103e90ea0af077a29 72H288H287H237H236H235H233H222H224H221H220H218H217H121H118
65b370e93093a3391fb28354b42fb661 72H290H289H220H218H217H121H118
