a<V1alengthV0Aa<=c0V1Aa<=V2alengthV0Aa<=V3V2Aa<=c0V3Aa<a-V2V3a-V2V1Aa<=c0a-V2V1La+V1c1INa<=V2V1Ia<=V2alengthV0Aa<=V1V2Aa<=c0V1F
VC for sum
ia=asumV0V1V2a+aV0V1asumV0a+V1c1V2a=asumV0V1V2c0a<=V2V1Ia<=V2alengthV0Aa<=V1V2Aa<=c0V1F
a<=c0ai
a<aiaj
a<=ajalengthaa
a<c0ax
a<axaj
a<=axc0
a=asumaaa-ajaxaja+asumaaa-ajaxa-ajc1aaaa-ajc1
base case (asserted formula)
a=asumaaa-ajV3aja+asumaaa-ajV3a-ajc1aaaa-ajc1Ia<V3ajIa<c0V3Ia<V3axF
a=asumaaa-aja-axc1aja+asumaaa-aja-axc1a-ajc1aaaa-ajc1Ia<a-axc1ajIa<c0a-axc1Ia<a-axc1ax
recursive case (asserted formula)
asserted formula
a=asumaaa-ajV3aja+asumaaa-ajV3a-ajc1aaaa-ajc1Ia<V3ajAa<c0V3F
a=asumaaa-aja-ajaiaja+asumaaa-aja-ajaia-ajc1aaaa-ajc1Ia<a-ajaiajAa<c0a-ajai
a=asumaaaiaja+asumaaaia-ajc1aaaa-ajc1
empty_shape
a=asumV3V4V5a+asumV3V4a-V5c1aV3a-V5c1Ia<=V5alengthV3Aa<V4V5Aa<=c0V4F
a=c0asumV0V1V1Ia<=V1a+V3c1La-V2c1Ia<=V2alengthV0Aa<=V1V2Aa<=c0V1F
loop invariant init
a<V5alengthV0Aa<=c0V5Ia=V4asumV0V1V5Aa<=V5V3Aa<=V1V5FFIa<=V1a+V3c1La-V2c1Ia<=V2alengthV0Aa<=V1V2Aa<=c0V1F
index in array bounds
a=V6asumV0V1a+V5c1Ia=V6a+V4aV0V5FIa=V4asumV0V1V5Aa<=V5V3Aa<=V1V5FFIa<=V1a+V3c1La-V2c1Ia<=V2alengthV0Aa<=V1V2Aa<=c0V1F
loop invariant preservation
a=V4asumV0V1V2Ia=V4asumV0V1a+V3c1FIa<=V1a+V3c1La-V2c1Ia<=V2alengthV0Aa<=V1V2Aa<=c0V1F
postcondition
a=c0asumV0V1V2Ia>V1a+V3c1La-V2c1Ia<=V2alengthV0Aa<=V1V2Aa<=c0V1F
a=c0asumV0V1V2Ia>V1a+V3c1Aa=V4asumV0V1V2Ia=V4asumV0V1a+V3c1Aa=V6asumV0V1a+V5c1Ia=V6a+V4aV0V5FAa<V5alengthV0Aa<=c0V5Ia=V4asumV0V1V5Aa<=V5V3Aa<=V1V5FFAa=c0asumV0V1V1Ia<=V1a+V3c1La-V2c1Ia<=V2alengthV0Aa<=V1V2Aa<=c0V1F
VC for query
a<=aiaj
a<=ajak
a<=akalengthaa
a<=akc0
a=asumaaaiaka+asumaaaiajasumaaajak
base case
a<c0ak
a=asumaaaiV0a+asumaaaiajasumaaajV0Ia<=V0alengthaaIa<=ajV0Ia<=aiajIa<=c0aiIa<V0akF
a=asumaaaiaka+asumaaaiajasumaaajakIa<=akalengthaaIa<=ajakIa<=aiajIa<=c0aiIa<akak
recursive case
a=asumV0V1V3a+asumV0V1V2asumV0V2V3Ia<=V3alengthV0Aa<=V2V3Aa<=V1V2Aa<=c0V1F
a<=ajalengthaa1
a<=ajalengthaa2
a=aaa1V4aaa2V4Ia<V4ajAa<=aiV4F
a<=c0ax
a<=axa-ajai
a=asumaa1a-ajaxajasumaa2a-ajaxaj
a=asumaa1a-ajV5ajasumaa2a-ajV5ajIa<=V5a-ajaiIa<=c0V5Ia<V5axF
a=asumaa1a-aja-axc1ajasumaa2a-aja-axc1ajIa<=a-axc1a-ajaiIa<=c0a-axc1Ia<a-axc1ax
a=asumaa1a-ajV5ajasumaa2a-ajV5ajIa<=V5a-ajaiAa<=c0V5F
a=asumaa1a-aja-ajaiajasumaa2a-aja-ajaiajIa<=a-ajaia-ajaiAa<=c0a-ajai
a=asumaa1aiajasumaa2aiaj
a=asumV4V6V7asumV5V6V7Ia=aV4V8aV5V8Ia<V8V7Aa<=V6V8FIa<=V7alengthV5Ia<=V7alengthV4Ia<=V6V7Aa<=c0V6F
a<=c0al
a<=alai
a<aiah
a<=ahalengthaa
a<=aha+aic1
a=asumaaaaiavalaha+a+asumaaalahava-a@aeltsaaai
a=asumaaaaiavalaha-a+asumaaalahavaaaai
a<a+aic1ah
a=asumaaaaiavalV9a-a+asumaaalV9avaaaaiIa<=V9alengthaaIa<aiV9Ia<=alaiIa<=c0alIa<V9ahF
a=asumaV9V10V11V12V13a-a+asumV9V12V13V11aV9V10Ia<=V13alengthV9Aa<V10V13Aa<=V12V10Aa<=c0V12F
ais_cumulative_array_forV3V0Ia>c1a+V1c1Aais_cumulative_array_forV4V0Ia=aV4V5asumV0c0V5Ia<V5a+V1c1Aa<=c0V5FAa=aV10V11asumV0c0V11Ia<V11a+V6c1Aa<=c0V11FIa=V10aV4V6V9Aa=aeltsV10asetaeltsV4V6V9Ia=alengthV10alengthV4FAa<V6alengthV4Aa<=c0V6La+aV4V8aV0V7Aa<V8alengthV4Aa<=c0V8La-V6c1Aa<V7alengthV0Aa<=c0V7La-V6c1Ia=aV4V12asumV0c0V12Ia<V12V6Aa<=c0V12FAa<=V6V1Aa<=c1V6FIa=alengthV4alengthV3FAa=aV3V13asumV0c0V13Ia<V13c1Aa<=c0V13FIa<=c1a+V1c1Ia=alengthV3V2Aa=aV3V14c0Ia<V14V2Aa<=c0V14FFAa>=V2c0La+V1c1LalengthV0F
VC for create
a=a-aV0V2aV0V1asumV3V1V2Aa<V2alengthV0Aa<=c0V2Aa<V1alengthV0Aa<=c0V1Ia<V2alengthV0Aa<=V1V2Aa<=c0V1Aais_cumulative_array_forV0V3F
a=aV6V9aV3V9INa=V9V1Aa<V9alengthV6Aa<=c0V9FAa=aV6V1V2Aais_cumulative_array_forV0V6Ia>V8a+V7c1Aa=aV6V11aV3V11INa=V11V1Aa<V11alengthV6Aa<=c0V11FAa=aV6V1V2Aais_cumulative_array_forV10V6Ia=aV10V12asumV6c0V12Ia<V12a+V7c1Aa<=c0V12FAa=aV10V13a-asumV6c0V13V5Ia<V13alengthV10Aa<=a+V7c1V13FAa=aV16V17asumV6c0V17Ia<V17a+V14c1Aa<=c0V17FAa=aV16V18a-asumV6c0V18V5Ia<V18alengthV16Aa<=a+V14c1V18FIa=V16aV10V14V15Aa=aeltsV16asetaeltsV10V14V15Ia=alengthV16alengthV10FAa<V14alengthV10Aa<=c0V14La+aV10V14V5Aa<V14alengthV10Aa<=c0V14Ia=aV10V19asumV6c0V19Ia<V19V14Aa<=c0V19FAa=aV10V20a-asumV6c0V20V5Ia<V20alengthV10Aa<=V14V20FAa<=V14V7Aa<=V8V14FIa=alengthV10alengthV0FAa=aV0V21asumV6c0V21Ia<V21V8Aa<=c0V21FAa=aV0V22a-asumV6c0V22V5Ia<V22alengthV0Aa<=V8V22FIa<=V8a+V7c1La+V1c1La-alengthV0c1Ia=V6aV3V1V2Aa=aeltsV6asetaeltsV3V1V2Ia=alengthV6alengthV3FAa<V1alengthV3Aa<=c0V1La+a-V2aV0V4aV0V1Aa<V4alengthV0Aa<=c0V4La+V1c1Aa<V1alengthV0Aa<=c0V1Ia<V1alengthV3Aa<=c0V1Aais_cumulative_array_forV0V3F
VC for update
a<V1alengthV0Aa<=c0V1Ia=a+V1c1V2Ia<=V2alengthV0Aa<V1V2Aa<=c0V1F
Na=c2c0INa=a+V1c1V2Ia<=V2alengthV0Aa<V1V2Aa<=c0V1F
precondition
a<V3V2Aa<V1V3Ladiva+V1V2c2INa=a+V1c1V2Ia<=V2alengthV0Aa<V1V2Aa<=c0V1F
assertion
a<a-V3V1a-V2V1Aa<=c0a-V2V1Ia<V3V2Aa<V1V3Ladiva+V1V2c2INa=a+V1c1V2Ia<=V2alengthV0Aa<V1V2Aa<=c0V1F
variant decrease
a<=V3alengthV0Aa<V1V3Aa<=c0V1Ia<V3V2Aa<V1V3Ladiva+V1V2c2INa=a+V1c1V2Ia<=V2alengthV0Aa<V1V2Aa<=c0V1F
a<a-V2V3a-V2V1Aa<=c0a-V2V1Iais_tree_forV4V0V1V3FIa<V3V2Aa<V1V3Ladiva+V1V2c2INa=a+V1c1V2Ia<=V2alengthV0Aa<V1V2Aa<=c0V1F
a<=V2alengthV0Aa<V3V2Aa<=c0V3Iais_tree_forV4V0V1V3FIa<V3V2Aa<V1V3Ladiva+V1V2c2INa=a+V1c1V2Ia<=V2alengthV0Aa<V1V2Aa<=c0V1F
Na=a+aic1aj
a<amajAa<aiam
a=alaNodeaxax1ax2
ais_tree_foralaaaiam
a=araNodeax3ax4ax5
ais_tree_foraraaamaj
a=a+aisumaindexesalaisumaindexesarasumaaaiaj
a=araLeafax3
a=alaLeafax
a=araNodeab2ab3ax1
a=araLeafab1
a=a+aisumaindexesV4aisumaindexesV5asumV0V1V2Iais_tree_forV5V0V3V2FIais_tree_forV4V0V1V3FIa<V3V2Aa<V1V3Ladiva+V1V2c2INa=a+V1c1V2Ia<=V2alengthV0Aa<V1V2Aa<=c0V1F
ais_tree_forV3V0V1V2Ia=V3aLeafaindexes'mkV1V2aV0V1Aa=a+V1c1V2FIa<=V2alengthV0Aa<V1V2Aa<=c0V1F
Ca=V2a+V1c1Aais_indexes_forV4V0V1V2aLeafVais_tree_forV7V0V8V2Aais_tree_forV6V0V1V8Aa=V8adiva+V1V2c2Aa<V8V2Aa<V1V8Aa=V8alowaindexesV7LahighaindexesV6Aa=V2ahighaindexesV7Aa=V1alowaindexesV6Aais_indexes_forV5V0V1V2aNodeVVVV3Ia=V3aNodeaindexes'mkV1V2V12V10V11Aa=V12asumV0V1V2La+aisumaindexesV10aisumaindexesV11ACa=V2a+V9c1Aais_indexes_forV13V0V9V2aLeafVais_tree_forV16V0V17V2Aais_tree_forV15V0V9V17Aa=V17adiva+V9V2c2Aa<V17V2Aa<V9V17Aa=V17alowaindexesV16LahighaindexesV15Aa=V2ahighaindexesV16Aa=V9alowaindexesV15Aais_indexes_forV14V0V9V2aNodeVVVV11EACa=V9a+V1c1Aais_indexes_forV18V0V1V9aLeafVais_tree_forV21V0V22V9Aais_tree_forV20V0V1V22Aa=V22adiva+V1V9c2Aa<V22V9Aa<V1V22Aa=V22alowaindexesV21LahighaindexesV20Aa=V9ahighaindexesV21Aa=V1alowaindexesV20Aais_indexes_forV19V0V1V9aNodeVVVV10EAa<V9V2Aa<V1V9Ladiva+V1V2c2ANa=a+V1c1V2FIa<=V2alengthV0Aa<V1V2Aa<=c0V1F
VC for tree_of_array
ais_tree_forV3V0V1V2Ia=V3aNodeaindexes'mkV1V2V7V5V6Aa=V7asumV0V1V2La+aisumaindexesV5aisumaindexesV6Aais_tree_forV6V0V4V2EAais_tree_forV5V0V1V4EAa<V4V2Aa<V1V4Ladiva+V1V2c2ANa=a+V1c1V2FIa<=V2alengthV0Aa<V1V2Aa<=c0V1F
ais_tree_forV3V0V1V2Iia=V3aNodeaindexes'mkV1V2V7V5V6Aa=V7asumV0V1V2La+aisumaindexesV5aisumaindexesV6Aais_tree_forV6V0V4V2EAais_tree_forV5V0V1V4EAa<V4V2Aa<V1V4Ladiva+V1V2c2a=V3aLeafaindexes'mkV1V2aV0V1a=a+V1c1V2FIa<=V2alengthV0Aa<V1V2Aa<=c0V1F
ais_tree_forV3V0V1V2Iia=V3aNodeaindexes'mkV1V2V7V5V6Aa=V7asumV0V1V2La+aisumaindexesV5aisumaindexesV6Aais_tree_forV6V0V4V2EAais_tree_forV5V0V1V4EAa<V4V2Aa<V1V4Ladiva+V1V2c2a=V3aLeafaindexes'mkV1V2aV0V1a=a+V1c1V2FAia=a+aisumaindexesV9aisumaindexesV10asumV0V1V2Iais_tree_forV10V0V8V2FAa<=V2alengthV0Aa<V8V2Aa<=c0V8Aa<a-V2V8a-V2V1Aa<=c0a-V2V1Iais_tree_forV9V0V1V8FAa<=V8alengthV0Aa<V1V8Aa<=c0V1Aa<a-V8V1a-V2V1Aa<=c0a-V2V1Ia<V8V2Aa<V1V8Aa<V8V2Aa<V1V8Ladiva+V1V2c2ANa=c2c0a<V1alengthV0Aa<=c0V1a=a+V1c1V2Ia<=V2alengthV0Aa<V1V2Aa<=c0V1F
ais_tree_forV2V0c0alengthV0Iais_tree_forV2V0c0V1FAa<=V1alengthV0Aa<c0V1Aa<=c0c0LalengthV0Ia>=alengthV0c1F
a=V4asumV1V2V3ICa=V4aisumV5aLeafViiia=V4a+asumV1V2V9asumV1V9V3a=V4asumV1V2V3a>=V2V9a=V4asumV1V2V3a<=V3V9LahighaindexesV7a=V4aisumV6a=V3ahighV6Aa=V2alowV6aNodeVVVV0FACtaLeafViia<=ahighaindexesV12alengthV1Aa<=V14ahighaindexesV12Aa<V2V14Aa<=alowaindexesV12V2Aa<=c0alowaindexesV12Aais_tree_forV12V1alowaindexesV12ahighaindexesV12ACfaLeafwa=V16V12Oa=V15V12aNodewVVV0Aa<=ahighaindexesV13alengthV1Aa<=V3ahighaindexesV13Aa<V14V3Aa<=alowaindexesV13V14Aa<=c0alowaindexesV13Aais_tree_forV13V1alowaindexesV13ahighaindexesV13ACfaLeafwa=V18V13Oa=V17V13aNodewVVV0a<=ahighaindexesV13alengthV1Aa<=V3ahighaindexesV13Aa<V2V3Aa<=alowaindexesV13V2Aa<=c0alowaindexesV13Aais_tree_forV13V1alowaindexesV13ahighaindexesV13ACfaLeafwa=V20V13Oa=V19V13aNodewVVV0a>=V2V14a<=ahighaindexesV12alengthV1Aa<=V3ahighaindexesV12Aa<V2V3Aa<=alowaindexesV12V2Aa<=c0alowaindexesV12Aais_tree_forV12V1alowaindexesV12ahighaindexesV12ACfaLeafwa=V22V12Oa=V21V12aNodewVVV0a<=V3V14LahighaindexesV12INa=V3ahighV11Aa=V2alowV11aNodeVVVV0Ia<=ahighaindexesV0alengthV1Aa<=V3ahigh
VC for query_aux
a=ataNodeaxax1ax2
ais_tree_forataac0alengthaa
a=V0asumaaaiajIia=V0asumaaaiaja=V0c0a=aiajFAa<=ahighaindexesatalengthaaAa<=ajahighaindexesatAa<aiajAa<=alowaindexesataiAa<=c0alowaindexesatAais_tree_forataaalowaindexesatahighaindexesatINa=aiaj
a=ataLeafax
a=V4asumV1V2V3Iia=V4asumV1V2V3a=V4c0a=V2V3FAa<=ahighaindexesV0alengthV1Aa<=V3ahighaindexesV0Aa<V2V3Aa<=alowaindexesV0V2Aa<=c0alowaindexesV0Aais_tree_forV0V1alowaindexesV0ahighaindexesV0INa=V2V3Iais_tree_forV0V1c0alengthV1Aa<=V3alengthV1Aa<=V2V3Aa<=c0V2F
Cais_tree_forV0aV2V3V4V5V6Iais_tree_forV0V2V5V6Ia>=V3V6Oa<V3V5Ia<V3alengthV2Aa<=c0V3FaLeafVais_tree_forV0aV10V11V12V13V14Iais_tree_forV0V10V13V14Ia>=V11V14Oa<V11V13Ia<V11alengthV10Aa<=c0V11FIais_tree_forV8aV15V16V17V18V19Iais_tree_forV8V15V18V19Ia>=V16V19Oa<V16V18Ia<V16alengthV15Aa<=c0V16FIais_tree_forV9aV20V21V22V23V24Iais_tree_forV9V20V23V24Ia>=V21V24Oa<V21V23Ia<V21alengthV20Aa<=c0V21FaNodeVVVV0F
ais_tree_forV0aV1V2V3V4V5Iais_tree_forV0V1V4V5Ia>=V2V5Oa<V2V4Ia<V2alengthV1Aa<=c0V2F
a=V7alowV10Ia=V6aLeafV10FIa<V7ahighaindexesV6Aa<=alowaindexesV6V7Aais_tree_forV6V8alowaindexesV6ahighaindexesV6F
CfaLeafwa=V15V11Oa=V14V11aNodewVVV6Ia<V7V13LahighaindexesV11Ia=V6aNodeV10V11V12FIa<V7ahighaindexesV6Aa<=alowaindexesV6V7Aais_tree_forV6V8alowaindexesV6ahighaindexesV6F
ais_tree_forV11V8alowaindexesV11ahighaindexesV11Ia<V7V13LahighaindexesV11Ia=V6aNodeV10V11V12FIa<V7ahighaindexesV6Aa<=alowaindexesV6V7Aais_tree_forV6V8alowaindexesV6ahighaindexesV6F
a<V7ahighaindexesV11Aa<=alowaindexesV11V7Iais_tree_forV11V8alowaindexesV11ahighaindexesV11Ia<V7V13LahighaindexesV11Ia=V6aNodeV10V11V12FIa<V7ahighaindexesV6Aa<=alowaindexesV6V7Aais_tree_forV6V8alowaindexesV6ahighaindexesV6F
ais_tree_forV14aV8V7V9alowaindexesV6V13Iais_tree_forV14aV8V7V9alowaindexesV14ahighaindexesV14Aa=ahighaindexesV14ahighaindexesV11Aa=alowaindexesV14alowaindexesV11Aa=V15a-V9aV8V7FIa<V7V13LahighaindexesV11Ia=V6aNodeV10V11V12FIa<V7ahighaindexesV6Aa<=alowaindexesV6V7Aais_tree_forV6V8alowaindexesV6ahighaindexesV6F
ais_tree_forV12aV8V7V9V13ahighaindexesV6Iais_tree_forV14aV8V7V9alowaindexesV6V13Iais_tree_forV14aV8V7V9alowaindexesV14ahighaindexesV14Aa=ahighaindexesV14ahighaindexesV11Aa=alowaindexesV14alowaindexesV11Aa=V15a-V9aV8V7FIa<V7V13LahighaindexesV11Ia=V6aNodeV10V11V12FIa<V7ahighaindexesV6Aa<=alowaindexesV6V7Aais_tree_forV6V8alowaindexesV6ahighaindexesV6F
CfaLeafwa=V15V12Oa=V14V12aNodewVVV6INa<V7V13LahighaindexesV11Ia=V6aNodeV10V11V12FIa<V7ahighaindexesV6Aa<=alowaindexesV6V7Aais_tree_forV6V8alowaindexesV6ahighaindexesV6F
ais_tree_forV12V8alowaindexesV12ahighaindexesV12INa<V7V13LahighaindexesV11Ia=V6aNodeV10V11V12FIa<V7ahighaindexesV6Aa<=alowaindexesV6V7Aais_tree_forV6V8alowaindexesV6ahighaindexesV6F
a<V7ahighaindexesV12Aa<=alowaindexesV12V7Iais_tree_forV12V8alowaindexesV12ahighaindexesV12INa<V7V13LahighaindexesV11Ia=V6aNodeV10V11V12FIa<V7ahighaindexesV6Aa<=alowaindexesV6V7Aais_tree_forV6V8alowaindexesV6ahighaindexesV6F
ais_tree_forV11aV8V7V9alowaindexesV6V13Iais_tree_forV14aV8V7V9alowaindexesV14ahighaindexesV14Aa=ahighaindexesV14ahighaindexesV12Aa=alowaindexesV14alowaindexesV12Aa=V15a-V9aV8V7FINa<V7V13LahighaindexesV11Ia=V6aNodeV10V11V12FIa<V7ahighaindexesV6Aa<=alowaindexesV6V7Aais_tree_forV6V8alowaindexesV6ahighaindexesV6F
ais_tree_forV14aV8V7V9V13ahighaindexesV6Iais_tree_forV11aV8V7V9alowaindexesV6V13Iais_tree_forV14aV8V7V9alowaindexesV14ahighaindexesV14Aa=ahighaindexesV14ahighaindexesV12Aa=alowaindexesV14alowaindexesV12Aa=V15a-V9aV8V7FINa<V7V13LahighaindexesV11Ia=V6aNodeV10V11V12FIa<V7ahighaindexesV6Aa<=alowaindexesV6V7Aais_tree_forV6V8alowaindexesV6ahighaindexesV6F
ais_tree_forV10aV8V7V9alowaindexesV10ahighaindexesV10Aa=ahighaindexesV10ahighaindexesV6Aa=alowaindexesV10alowaindexesV6Aa=V11a-V9aV8V7ICa=V11a-V9aisumV12Aa=V10aLeafaindexes'mkalowV12ahighV12V9Aa=V7alowV12aLeafVia=V11V18Aa=V10aNodeaindexes'mkalowV13ahighV13a+aisumV13V18V14V17Aais_tree_forV17aV8V7V9V16ahighaindexesV6Aais_tree_forV14aV8V7V9alowaindexesV6V16Aais_tree_forV17aV8V7V9alowaindexesV17ahighaindexesV17Aa=ahighaindexesV17ahighaindexesV15Aa=alowaindexesV17alowaindexesV15Aa=V18a-V9aV8V7Ea=V11V20Aa=V10aNodeaindexes'mkalowV13ahighV13a+aisumV13V20V19V15Aais_tree_forV15aV8V7V9V16ahighaindexesV6Aais_tree_forV19aV8V7V9alowaindexesV6V16Aais_tree_forV19aV8V7V9alowaindexesV19ahighaindexesV19Aa=ahighaindexesV19ahighaindexesV14Aa=alowaindexesV19alowaindexesV14Aa=V20a-V9aV8V7Ea<V7V16LahighaindexesV14aNodeVVVV6FIa<V7ahighaindexesV6Aa<=alowaindexesV6V7Aais_tree_forV6V8alowaindexesV6ahighaindexesV6F
ais_tree_forV10aV8V7V9alowaindexesV10ahighaindexesV10Aa=ahighaindexesV10ahighaindexesV6Aa=alowaindexesV10alowaindexesV6Aa=V11a-V9aV8V7ICa=V11a-V9aisumV12Aa=V10aLeafaindexes'mkalowV12ahighV12V9Aa=V7alowV12aLeafVia=V11V18Aa=V10aNodeaindexes'mkalowV13ahighV13a+aisumV13V18V14V17Aais_tree_forV17aV8V7V9V16ahighaindexesV6Aais_tree_forV14aV8V7V9alowaindexesV6V16Aais_tree_forV17aV8V7V9alowaindexesV17ahighaindexesV17Aa=ahighaindexesV17ahighaindexesV15Aa=alowaindexesV17alowaindexesV15Aa=V18a-V9aV8V7Ea=V11V20Aa=V10aNodeaindexes'mkalowV13ahighV13a+aisumV13V20V19V15Aais_tree_forV15aV8V7V9V16ahighaindexesV6Aais_tree_forV19aV8V7V9alowaindexesV6V16Aais_tree_forV19aV8V7V9alowaindexesV19ahighaindexesV19Aa=ahighaindexesV19ahighaindexesV14Aa=alowaindexesV19alowaindexesV14Aa=V20a-V9aV8V7Ea<V7V16LahighaindexesV14aNodeVVVV6FACa=V7alowV21aLeafViais_tree_forV26aV8V7V9V25ahighaindexesV6Iais_tree_forV23aV8V7V9alowaindexesV6V25Aais_tree_forV23aV8V7V9alowaindexesV6V25Iais_tree_forV26aV8V7V9alowaindexesV26ahighaindexesV26Aa=ahighaindexesV26
VC for update_aux
a<aialengthaa
ais_tree_forV6V8c0alengthV8Aa=aV8V9aaaV9INa=V9aiAa<V9alengthV8Aa<=c0V9FAa=aV8aiavIa=V8aaaaiavAa=aeltsV8asetaeltsaaaiavIa=alengthV8alengthaaFAa<aialengthaaAa<=c0aiAais_tree_forV6aaaaiavc0alengthaaIais_tree_forV6aaaaiavalowaindexesV6ahighaindexesV6Aa=ahighaindexesV6ahighaindexesatAa=alowaindexesV6alowaindexesatAa=V7a-avaaaaiFAa<aiahighaindexesatAa<=alowaindexesataiAais_tree_forataaalowaindexesatahighaindexesat
ais_tree_forV10V12c0alengthV12Aa=aV12V13aV7V13INa=V13V8Aa<V13alengthV12Aa<=c0V13FAa=aV12V8V9Ia=V12aV7V8V9Aa=aeltsV12asetaeltsV7V8V9Ia=alengthV12alengthV7FAa<V8alengthV7Aa<=c0V8Aais_tree_forV10aV7V8V9c0alengthV7Iais_tree_forV10aV7V8V9alowaindexesV10ahighaindexesV10Aa=ahighaindexesV10ahighaindexesV6Aa=alowaindexesV10alowaindexesV6Aa=V11a-V9aV7V8FAa<V8ahighaindexesV6Aa<=alowaindexesV6V8Aais_tree_forV6V7alowaindexesV6ahighaindexesV6Iais_tree_forV6V7c0alengthV7Aa<V8alengthV7Aa<=c0V8F
Ca>=adepthV6c1aLeafVa>=adepthV6c1Ia>=adepthV9c1Ia>=adepthV10c1aNodeVVVV6F
a>=adepthV6c1F
a<=adepthV7a+V9c1ICtaLeafwa<=adepthV11a+a-V9c1c1Aa<=adepthV10a+a-V9c1c1aNodewVVV7ACtaLeafwa<=a-ahighaindexesV13alowaindexesV13apow2V15Aais_tree_forV13V8alowaindexesV13ahighaindexesV13Aa>=V15c0ACfaLeafwa=V17V13Oa=V16V13aNodewVVV7La-V9c1Ia<=adepthV12a+V14c1Aa<=a-ahighaindexesV12alowaindexesV12apow2V14Aais_tree_forV12V8alowaindexesV12ahighaindexesV12Aa>=V14c0ACfaLeafwa=V19V12Oa=V18V12aNodewVVV7La-V9c1aNodewVVV7Ia<=a-ahighaindexesV7alowaindexesV7apow2V9Aais_tree_forV7V8alowaindexesV7ahighaindexesV7Aa>=V9c0F
VC for depth_is_log
a<=adepthV7a+V9c1Ia<=a-ahighaindexesV7alowaindexesV7apow2V9Iais_tree_forV7V8alowaindexesV7ahighaindexesV7Ia>=V9c0F
a=V11alowV16Ia=V10aLeafV16FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
a<=a-V15V14adepthV10Ia=V11alowV16Ia=V10aLeafV16FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
ais_tree_forV17aV12V11V13alowaindexesV17ahighaindexesV17Aa=ahighaindexesV17ahighaindexesV10Aa=alowaindexesV17alowaindexesV10Aa=a-V13aisumV16a-V13aV12V11LaLeafaindexes'mkalowV16ahighV16V13Ia<=a-V15V14adepthV10Ia=V11alowV16Ia=V10aLeafV16FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
CfaLeafwa=V21V17Oa=V20V17aNodewVVV10Ia<V11V19LahighaindexesV17Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
ais_tree_forV17V12alowaindexesV17ahighaindexesV17Ia<V11V19LahighaindexesV17Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
a<V11ahighaindexesV17Aa<=alowaindexesV17V11Iais_tree_forV17V12alowaindexesV17ahighaindexesV17Ia<V11V19LahighaindexesV17Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
ais_tree_forV21aV12V11V13alowaindexesV10V19Iais_tree_forV21aV12V11V13alowaindexesV21ahighaindexesV21Aa=ahighaindexesV21ahighaindexesV17Aa=alowaindexesV21alowaindexesV17Aa=V22a-V13aV12V11Aa<=a-V20V15adepthV17FFIa<V11V19LahighaindexesV17Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
ais_tree_forV18aV12V11V13V19ahighaindexesV10Iais_tree_forV21aV12V11V13alowaindexesV10V19Iais_tree_forV21aV12V11V13alowaindexesV21ahighaindexesV21Aa=ahighaindexesV21ahighaindexesV17Aa=alowaindexesV21alowaindexesV17Aa=V22a-V13aV12V11Aa<=a-V20V15adepthV17FFIa<V11V19LahighaindexesV17Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
a<=a-V20V14adepthV10Ia=V24V22Aa=V23aNodeaindexes'mkalowV16ahighV16a+aisumV16V22V21V18Aais_tree_forV18aV12V11V13V19ahighaindexesV10Aais_tree_forV21aV12V11V13alowaindexesV10V19FIais_tree_forV21aV12V11V13alowaindexesV21ahighaindexesV21Aa=ahighaindexesV21ahighaindexesV17Aa=alowaindexesV21alowaindexesV17Aa=V22a-V13aV12V11Aa<=a-V20V15adepthV17FFIa<V11V19LahighaindexesV17Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
ais_tree_forV23aV12V11V13alowaindexesV23ahighaindexesV23Aa=ahighaindexesV23ahighaindexesV10Aa=alowaindexesV23alowaindexesV10Aa=V24a-V13aV12V11Ia<=a-V20V14adepthV10Ia=V24V22Aa=V23aNodeaindexes'mkalowV16ahighV16a+aisumV16V22V21V18Aais_tree_forV18aV12V11V13V19ahighaindexesV10Aais_tree_forV21aV12V11V13alowaindexesV10V19FIais_tree_forV21aV12V11V13alowaindexesV21ahighaindexesV21Aa=ahighaindexesV21ahighaindexesV17Aa=alowaindexesV21alowaindexesV17Aa=V22a-V13aV12V11Aa<=a-V20V15adepthV17FFIa<V11V19LahighaindexesV17Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
CfaLeafwa=V21V18Oa=V20V18aNodewVVV10INa<V11V19LahighaindexesV17Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
ais_tree_forV18V12alowaindexesV18ahighaindexesV18INa<V11V19LahighaindexesV17Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
a<V11ahighaindexesV18Aa<=alowaindexesV18V11Iais_tree_forV18V12alowaindexesV18ahighaindexesV18INa<V11V19LahighaindexesV17Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
ais_tree_forV17aV12V11V13alowaindexesV10V19Iais_tree_forV21aV12V11V13alowaindexesV21ahighaindexesV21Aa=ahighaindexesV21ahighaindexesV18Aa=alowaindexesV21alowaindexesV18Aa=V22a-V13aV12V11Aa<=a-V20V15adepthV18FFINa<V11V19LahighaindexesV17Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
ais_tree_forV21aV12V11V13V19ahighaindexesV10Iais_tree_forV17aV12V11V13alowaindexesV10V19Iais_tree_forV21aV12V11V13alowaindexesV21ahighaindexesV21Aa=ahighaindexesV21ahighaindexesV18Aa=alowaindexesV21alowaindexesV18Aa=V22a-V13aV12V11Aa<=a-V20V15adepthV18FFINa<V11V19LahighaindexesV17Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
a<=a-V20V14adepthV10Ia=V24V22Aa=V23aNodeaindexes'mkalowV16ahighV16a+aisumV16V22V17V21Aais_tree_forV21aV12V11V13V19ahighaindexesV10Aais_tree_forV17aV12V11V13alowaindexesV10V19FIais_tree_forV21aV12V11V13alowaindexesV21ahighaindexesV21Aa=ahighaindexesV21ahighaindexesV18Aa=alowaindexesV21alowaindexesV18Aa=V22a-V13aV12V11Aa<=a-V20V15adepthV18FFINa<V11V19LahighaindexesV17Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
ais_tree_forV23aV12V11V13alowaindexesV23ahighaindexesV23Aa=ahighaindexesV23ahighaindexesV10Aa=alowaindexesV23alowaindexesV10Aa=V24a-V13aV12V11Ia<=a-V20V14adepthV10Ia=V24V22Aa=V23aNodeaindexes'mkalowV16ahighV16a+aisumV16V22V17V21Aais_tree_forV21aV12V11V13V19ahighaindexesV10Aais_tree_forV17aV12V11V13alowaindexesV10V19FIais_tree_forV21aV12V11V13alowaindexesV21ahighaindexesV21Aa=ahighaindexesV21ahighaindexesV18Aa=alowaindexesV21alowaindexesV18Aa=V22a-V13aV12V11Aa<=a-V20V15adepthV18FFINa<V11V19LahighaindexesV17Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<V11ahighaindexesV10Aa<=alowaindexesV10V11Aais_tree_forV10V12alowaindexesV10ahighaindexesV10F
Cais_tree_forV17aV12V11V13alowaindexesV17ahighaindexesV17Aa=ahighaindexesV17ahighaindexesV10Aa=alowaindexesV17alowaindexesV10Aa=a-V13aisumV16a-V13aV12V11LaLeafaindexes'mkalowV16ahighV16V13Aa<=a-V15V14adepthV10Aa=V11alowV16aLeafViais_tree_forV25aV12V11V13alowaindexesV25ahighaindexesV25Aa=ahighaindexesV25ahighaindexesV10Aa=alowaindexesV25alowaindexesV10Aa=V26a-V13aV12V11Aa<=a-V22V14adepthV10Ia=V26V24Aa=V25aNodeaindexes'mkalowV18ahighV18a+aisumV18V24V19V23Aais_tree_forV23aV12V11V13V21ahighaindexesV10Aais_tree_forV19aV12V11V13alowaindexesV10V21FAais_tree_forV23aV12V11V13V21ahighaindexesV10Iais_tree_forV19aV12V11V13alowaindexesV10V21Aais_tree_forV19aV12V11V13alowaindexesV10V21Iais_tree_forV23aV12V11V13alowaindexesV23ahighaindexesV23Aa=ahighaindexesV23ahighaindexesV20Aa=alowaindexesV23alowaindexesV20Aa=V24a-V13aV12V11Aa<=a-V22V15adepthV20FFAa<V11ahighaindexesV20Aa<=alowaindexesV20V11Aais_tree_forV20V12alowaindexesV20ahighaindexesV20ACfaLeafwa=V28V20Oa=V27V20aNodewVVV10ais_tree_forV32aV12V11V13alowaindexesV32ahighaindexes
VC for update_aux_complexity
a<=a-V15V14iia*c4adepthV10a*c2adepthV10a=V13ahighaindexesV10Oa=V12alowaindexesV10c1a=V13ahighaindexesV10Aa=V12alowaindexesV10Ia=V10aLeafV16FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
a=aisumV16asumV11V12V13Ia<=a-V15V14iia*c4adepthV10a*c2adepthV10a=V13ahighaindexesV10Oa=V12alowaindexesV10c1a=V13ahighaindexesV10Aa=V12alowaindexesV10Ia=V10aLeafV16FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
a<=a-V15V14iia*c4adepthV10a*c2adepthV10a=V13ahighaindexesV10Oa=V12alowaindexesV10c1a=V13ahighaindexesV10Aa=V12alowaindexesV10Ia=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
a=aisumV16asumV11V12V13Ia<=a-V15V14iia*c4adepthV10a*c2adepthV10a=V13ahighaindexesV10Oa=V12alowaindexesV10c1a=V13ahighaindexesV10Aa=V12alowaindexesV10Ia=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
CfaLeafwa=V21V17Oa=V20V17aNodewVVV10Ia<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
ais_tree_forV17V11alowaindexesV17ahighaindexesV17Ia<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
a<=ahighaindexesV17alengthV11Aa<=V13ahighaindexesV17Aa<V12V13Aa<=alowaindexesV17V12Aa<=c0alowaindexesV17Iais_tree_forV17V11alowaindexesV17ahighaindexesV17Ia<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
a<=a-V20V14iia*c4adepthV10a*c2adepthV10a=V13ahighaindexesV10Oa=V12alowaindexesV10c1a=V13ahighaindexesV10Aa=V12alowaindexesV10Ia=V21asumV11V12V13Aa<=a-V20V15iia*c4adepthV17a*c2adepthV17a=V13ahighaindexesV17Oa=V12alowaindexesV17c1a=V13ahighaindexesV17Aa=V12alowaindexesV17FFIa<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
a=V21asumV11V12V13Ia<=a-V20V14iia*c4adepthV10a*c2adepthV10a=V13ahighaindexesV10Oa=V12alowaindexesV10c1a=V13ahighaindexesV10Aa=V12alowaindexesV10Ia=V21asumV11V12V13Aa<=a-V20V15iia*c4adepthV17a*c2adepthV17a=V13ahighaindexesV17Oa=V12alowaindexesV17c1a=V13ahighaindexesV17Aa=V12alowaindexesV17FFIa<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
CfaLeafwa=V21V18Oa=V20V18aNodewVVV10Ia>=V12V19INa<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
ais_tree_forV18V11alowaindexesV18ahighaindexesV18Ia>=V12V19INa<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
a<=ahighaindexesV18alengthV11Aa<=V13ahighaindexesV18Aa<V12V13Aa<=alowaindexesV18V12Aa<=c0alowaindexesV18Iais_tree_forV18V11alowaindexesV18ahighaindexesV18Ia>=V12V19INa<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
a<=a-V20V14iia*c4adepthV10a*c2adepthV10a=V13ahighaindexesV10Oa=V12alowaindexesV10c1a=V13ahighaindexesV10Aa=V12alowaindexesV10Ia=V21asumV11V12V13Aa<=a-V20V15iia*c4adepthV18a*c2adepthV18a=V13ahighaindexesV18Oa=V12alowaindexesV18c1a=V13ahighaindexesV18Aa=V12alowaindexesV18FFIa>=V12V19INa<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
a=V21asumV11V12V13Ia<=a-V20V14iia*c4adepthV10a*c2adepthV10a=V13ahighaindexesV10Oa=V12alowaindexesV10c1a=V13ahighaindexesV10Aa=V12alowaindexesV10Ia=V21asumV11V12V13Aa<=a-V20V15iia*c4adepthV18a*c2adepthV18a=V13ahighaindexesV18Oa=V12alowaindexesV18c1a=V13ahighaindexesV18Aa=V12alowaindexesV18FFIa>=V12V19INa<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
CfaLeafwa=V21V18Oa=V20V18aNodewVVV10INa>=V12V19INa<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
ais_tree_forV18V11alowaindexesV18ahighaindexesV18INa>=V12V19INa<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
a<=ahighaindexesV18alengthV11Aa<=V13ahighaindexesV18Aa<V19V13Aa<=alowaindexesV18V19Aa<=c0alowaindexesV18Iais_tree_forV18V11alowaindexesV18ahighaindexesV18INa>=V12V19INa<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
CfaLeafwa=V23V17Oa=V22V17aNodewVVV10Ia=V21asumV11V19V13Aa<=a-V20V15iia*c4adepthV18a*c2adepthV18a=V13ahighaindexesV18Oa=V19alowaindexesV18c1a=V13ahighaindexesV18Aa=V19alowaindexesV18FFINa>=V12V19INa<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
ais_tree_forV17V11alowaindexesV17ahighaindexesV17Ia=V21asumV11V19V13Aa<=a-V20V15iia*c4adepthV18a*c2adepthV18a=V13ahighaindexesV18Oa=V19alowaindexesV18c1a=V13ahighaindexesV18Aa=V19alowaindexesV18FFINa>=V12V19INa<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
a<=ahighaindexesV17alengthV11Aa<=V19ahighaindexesV17Aa<V12V19Aa<=alowaindexesV17V12Aa<=c0alowaindexesV17Iais_tree_forV17V11alowaindexesV17ahighaindexesV17Ia=V21asumV11V19V13Aa<=a-V20V15iia*c4adepthV18a*c2adepthV18a=V13ahighaindexesV18Oa=V19alowaindexesV18c1a=V13ahighaindexesV18Aa=V19alowaindexesV18FFINa>=V12V19INa<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
a<=a-V22V14iia*c4adepthV10a*c2adepthV10a=V13ahighaindexesV10Oa=V12alowaindexesV10c1a=V13ahighaindexesV10Aa=V12alowaindexesV10Ia=V23asumV11V12V19Aa<=a-V22V20iia*c4adepthV17a*c2adepthV17a=V19ahighaindexesV17Oa=V12alowaindexesV17c1a=V19ahighaindexesV17Aa=V12alowaindexesV17FFIa=V21asumV11V19V13Aa<=a-V20V15iia*c4adepthV18a*c2adepthV18a=V13ahighaindexesV18Oa=V19alowaindexesV18c1a=V13ahighaindexesV18Aa=V19alowaindexesV18FFINa>=V12V19INa<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
a=a+V23V21asumV11V12V13Ia<=a-V22V14iia*c4adepthV10a*c2adepthV10a=V13ahighaindexesV10Oa=V12alowaindexesV10c1a=V13ahighaindexesV10Aa=V12alowaindexesV10Ia=V23asumV11V12V19Aa<=a-V22V20iia*c4adepthV17a*c2adepthV17a=V19ahighaindexesV17Oa=V12alowaindexesV17c1a=V19ahighaindexesV17Aa=V12alowaindexesV17FFIa=V21asumV11V19V13Aa<=a-V20V15iia*c4adepthV18a*c2adepthV18a=V13ahighaindexesV18Oa=V19alowaindexesV18c1a=V13ahighaindexesV18Aa=V19alowaindexesV18FFINa>=V12V19INa<=V13V19LahighaindexesV17INa=V13ahighV16Aa=V12alowV16Ia=V10aNodeV16V17V18FIa=V15a+V14c1FIa<=ahighaindexesV10alengthV11Aa<=V13ahighaindexesV10Aa<V12V13Aa<=alowaindexesV10V12Aa<=c0alowaindexesV10Aais_tree_forV10V11alowaindexesV10ahighaindexesV10F
Ca=aisumV16asumV11V12V13Aa<=a-V15V14iia*c4adepthV10a*c2adepthV10a=V13ahighaindexesV10Oa=V12alowaindexesV10c1a=V13ahighaindexesV10Aa=V12alowaindexesV10aLeafViiia=a+V24V22asumV11V12V13Aa<=a-V23V14iia*c4adepthV10a*c2adepthV10a=V13ahighaindexesV10Oa=V12alowaindexesV10c1a=V13ahighaindexesV10Aa=V12alowaindexesV10Ia=V24asumV11V12V20Aa<=a-V23V21iia*c4adepthV18a*c2adepthV18a=V20ahighaindexesV18Oa=V12alowaindexesV18c1a=V20ahighaindexesV18Aa=V12alowaindexesV18FFAa<=ahighaindexesV18alengthV11Aa<=V20ahighaindexesV18Aa<V12V20Aa<=alowaindexesV18V12Aa<=c0alowaindexesV18Aais_tree_forV18V11alowaindexesV18ahighaindexesV18ACfaLeafwa=V26V18Oa=V25V18aNodewVVV10Ia=V22asumV11V20V13Aa<=a-V21V15iia*c4adepthV19a*c2adepthV19a=V13ahighaindexesV19Oa=V20alowaindexesV19c1a=V13ahighaindexesV19Aa=V20alowaindexesV19FFAa<=ahighaindexesV19alengthV11Aa<=V13ahighaindexesV19Aa<V20V13Aa<=alowaindexesV19V20Aa<=c0alowaindexesV19Aais_tree_forV19V11alowaindexesV19ahighaindexesV19ACfaLeafwa=V28V19Oa=V27V19aNodewVVV10a=V30asumV11V12V13Aa<=a-V29V14iia*c4adepth
VC for query_aux_complexity

444348393f1dc35734f4593cb24e09bd 1H0
1307d653be2f80f098c8d9551a342fda 18H19H2
e72c601840272291805e8442f07c3786 18H17H5H4H3H2
f5bea7ac6809a36b8bb480a29e9d96ad 14H15H5H4H3H2
5d9624c915a92509b5597ca0e51b6bd3 14H9H7H6H5H4H3H2
d21ffc6f81c1c524f5cc8d31c1ecbbc0 10H9H8H7H6H5H4H3H2
c73835c682d44c39f73e7b3a222f8db5 13H9H11H6H7H6H5H4H3H2
a7008d699cc8e20714ecdc8d5156ea1b 13H9H12H11H6H7H6H5H4H3H2
6b9f099bcef6d574de38df88796fbf34 18H17H15H5H4H3H2
6adb1f12fa584981140d10d84b60143e 18H17H16H15H5H4H3H2
fa91fad2dd4b0c93c8aa974430c013eb 30H29
08e78bd4d229a209058f0e3a66ba113b 21H20
53ee5e114fce2b331463b99a27ab6dd2 23H22
d829c572cc696c5594b03833c35ea0d8 25H24
3a7fce834c920d89da5018b72dc58125 27H26
441ca95f06a86031ccdbe0ae5ffec34b 27H28
5fd349cb02f18cc53d88a44e0a65dda6 18H41
ec536263efb66bd1b5cd6a88368e118e 18H35H33H32H31H3
9dead4e00ecb743dcbbbbd6f41cfc78e 36H35H34H33H32H31H3
f7364e5704bf80061c952e6edb9c7cbe 40H35H38H37H33H32H31H3
3f16e09dd63204f8c7a054c5e67d4ec0 40H35H39H38H37H33H32H31H3
c248e6ab3f9d05191d9dfc11582e4d18 18H53H41
5d101979dcb9c2945fa7bf86267f971e 18H52H44H43H42H31H3H41
394cf426b26d73a3bbc611ba729093e7 14H50H44H43H42H31H3H41
4ca0ee3001c814441cbdd01cb21a8093 14H47H46H45H44H43H42H31H3H41
e331cf91c14b3fa6433e98ac60becfe7 10H47H8H46H45H44H43H42H31H3H41
9c48cd47d08aede34581f9aef05f669e 13H47H48H6H46H45H44H43H42H31H3H41
3f39b482ad14fe3669d534e5c96a640f 13H47H49H48H6H46H45H44H43H42H31H3H41
0a1a530d435ea4f3d70d726f0e186c38 18H52H50H44H43H42H31H3H41
4d051b55f6f4c93db51d6e8a9159410b 18H52H51H50H44H43H42H31H3H41
1b142135ac93e599a23f33350668f586 18H63H53H41
2195ecddf99bbeb1879df4419c5f4ee3 18H60H57H56H55H54H53H41
8b34b2453b288da789a0af8ea7968a3c 36H60H58H57H56H55H54H53H41
da2ca836f9e7161e8136def0ab122a21 36H59H58H57H56H55H54H53H41
b79f584af0c6d661e1f17f2916d53fac 40H60H62H61H57H56H55H54H53H41
ae6e93873abcd8a07a566bc2837d5a8a 40H59H62H61H57H56H55H54H53H41
a04eecd45a8409c8666e411e4b29a6db 65H64
4650c92ee4dffa88931f5b34aa839e64 30H66
f6ccd7358b95c0a72f42c9d3537d1645 68H67
a4dd0974efe211e4d9e4e1b3c5941c6f 93H96
206874b069b595838446d3e5198021b9 23H69
be008f1c16b1a3e219183e8f7088725d 71H70
5601b39a86baf7dffb48ac702aef4808 73H72
cb534218139daa39ad798af8718e4e29 75H74
774d8c69b087c8bc3f6ca4b083b1d569 71H76
5e23ef058295ac16cd719e0d2a5150aa 75H77
a4f953fc487b47c03b69f8052d1b39e2 71H78
50ba5e9c099dcff23d84f43ca56ec737 73H90
9a647151d9bbc52db18bf383275bd6e4 73H85H84H82H80H79H5H4H3
e906bdc7e0c23fb1aba3c3420555bffb 73H85H84H82H81H80H79H5H4H3
463805e8d5d12c9d594a31115fdb2293 73H85H84H83H82H81H80H79H5H4H3
059d11393f0e09ca7e92cfc61e01f2cd 73H85H84H86H82H81H80H79H5H4H3
b88ef6c433ad87e5aec92fe61b03f9b6 73H85H84H82H87H80H79H5H4H3
393f3b0611abb177ab421540cc346738 73H85H84H88H82H87H80H79H5H4H3
52c44d9ef4ece5fc8d564e834d0e9db0 73H85H84H89H82H87H80H79H5H4H3
7e63428ce8528fc3d82ec524bfe7404c 27H95
5eab1abad8e2ed5baef986b314526b5e 27H91
a8857eb9d6e3446cbdfa37fd75a804ac 27H94
71a22050a5e9dcdf07c9b289eb3fbd99 93H92
2de13054a147f48bb06071d0e1463a2d 65H97
04559d1c524d61f0d1af2026fa49b1e6 99H98
52fa5eef1a8223fed97c0b737c307628 30H104
d0441a66814ed433d60ef9a2ceb19d6d 30H102H101H5H31H3
a7a943b41ec6116852b811953a9a3fda 30H102H101H5H31H3H100
817cfc6861d3209934b29349d8368cec 30H102H101H5H31H3H103
0f17a2805112eecb070987fcc933b10e 18H106
d0023196d11b12b0f7203eecc6212164 18H105
1f52bea5abf6c85d6014fb48dc4ccf59 120H119H106
58be31550b0ea0127e330224fa563367 73H107H106
fa5f50f17455ff11c3ee6fc5ee614176 75H108H106
8fd71e58417b368cc25430517220d8d0 71H109H106
fd6fa3648daf9a4324c7bf5f68c7504c 71H110H106
45af368a18777ce2931fc542762de749 73H111H106
c88407a7ec6da67a41c65a3d2d461cd9 73H112H106
60824cdb29ed029573c954786e627948 75H113H106
353361ef0575e3d4ab483a4395f95625 71H114H106
292f0d80ff60375809088a64e672b979 71H115H106
fb730f57211d3bb9724740a4bf037866 73H116H106
8de7e5ae91d15529845ca30c5d2691ee 73H117H106
19aa35fac135ae82eee4f1c145d3cc60 27H118H106
9fe0ed80e6af6892bbc114c74d3fd9cf 68H123H106
b2c1195cf4ec7872edf19b0eb70cb16d 68H122H101H121H3H106
e76f26f0a977a488b22452c77cbb96d1 68H122H101H121H3H100H106
5f642a7b9ae755533ca15313049cb814 68H122H101H121H3H103H106
3a144c357e1b3dcca8a920e4218fa01a 18H125H106
45ffefd3eb7595c02f173540a11a495e 18H124H106
17eef93dbb4847b10429a39267f9b51d 127H126H125H106
30d216d2da522212ade10e68e0fca2e8 147H146H128H125H106
895cf5e8c18e350ef14f2439a5547d9e 73H129H128H125H106
b6b4d4b802b2f5a276f31b86b945ba7f 27H130H128H125H106
9a3d0b6cab43a60d30aa8161268802fa 27H131H128H125H106
2f4313c38e590aa66e0e72dde5c8cec6 75H132H128H125H106
6f6f87323032a905cd72e61ced35f048 71H133H128H125H106
f43d843b7a4348dc9fabaae682d2e4cc 71H134H128H125H106
3bbdfd5c7a2ef37da7aa65e4ea2e7f3f 73H135H128H125H106
d7d927e37dfd7453e8b2d9b78935663f 73H136H128H125H106
c09945ce59798f88796bb053e0f7ab17 27H137H128H125H106
c01dda1979f3be5eefe312ef32826b63 27H138H128H125H106
8b248b45d1d7ba99ead67f3fa4e10974 75H139H128H125H106
44c1d038dae382c13ee764645314f42d 71H140H128H125H106
16a530cb9194986811166c1c02008d9c 71H141H128H125H106
b37e25efc18e3bc79644c25128221c20 73H142H128H125H106
1a6f86f80201cf74296ffe52ce91987b 73H143H128H125H106
27641efd3e3896842e17c1b5965fd31d 27H144H128H125H106
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