activenatsmarkcons0incrnatsactivepairsmarkcons0incroddsactiveoddsmarkincrpairsactiveincrconsXXSmarkconssXincrXSactiveheadconsXXSmarkXactivetailconsXXSmarkXSmarknatsactivenatsmarkconsX1X2activeconsmarkX1X2mark0active0markincrXactiveincrmarkXmarkpairsactivepairsmarkoddsactiveoddsmarksXactivesmarkXmarkheadXactiveheadmarkXmarktailXactivetailmarkXconsmarkX1X2consX1X2consX1markX2consX1X2consactiveX1X2consX1X2consX1activeX2consX1X2incrmarkXincrXincractiveXincrXsmarkXsXsactiveXsXheadmarkXheadXheadactiveXheadXtailmarkXtailXtailactiveXtailX2.11active111nats00mark111cons21112000incr121pairs00odds00s111head1111tail111activenatsmarkcons0incrnatsactivepairsmarkcons0incroddsactiveoddsmarkincrpairsactiveincrconsXXSmarkconssXincrXSactivetailconsXXSmarkXSmarknatsactivenatsmarkconsX1X2activeconsmarkX1X2mark0active0markincrXactiveincrmarkXmarkpairsactivepairsmarkoddsactiveoddsmarksXactivesmarkXmarkheadXactiveheadmarkXmarktailXactivetailmarkXconsmarkX1X2consX1X2consX1markX2consX1X2consactiveX1X2consX1X2consX1activeX2consX1X2incrmarkXincrXincractiveXincrXsmarkXsXsactiveXsXheadmarkXheadXheadactiveXheadXtailmarkXtailXtailactiveXtailX1active111nats00mark111cons21112000incr121pairs00odds00s111tail1121head121activenatsmarkcons0incrnatsactivepairsmarkcons0incroddsactiveoddsmarkincrpairsactiveincrconsXXSmarkconssXincrXSmarknatsactivenatsmarkconsX1X2activeconsmarkX1X2mark0active0markincrXactiveincrmarkXmarkpairsactivepairsmarkoddsactiveoddsmarksXactivesmarkXmarkheadXactiveheadmarkXmarktailXactivetailmarkXconsmarkX1X2consX1X2consX1markX2consX1X2consactiveX1X2consX1X2consX1activeX2consX1X2incrmarkXincrXincractiveXincrXsmarkXsXsactiveXsXheadmarkXheadXheadactiveXheadXtailmarkXtailXtailactiveXtailXactivenatsmarkcons0incrnatsactivenatscons0incrnatsactivenatsincrnatsactivepairsmarkcons0incroddsactivepairscons0incroddsactivepairsincroddsactiveoddsmarkincrpairsactiveoddsincrpairsactiveincrconsXXSmarkconssXincrXSactiveincrconsXXSconssXincrXSactiveincrconsXXSsXactiveincrconsXXSincrXSmarknatsactivenatsmarkconsX1X2activeconsmarkX1X2markconsX1X2consmarkX1X2markconsX1X2markX1mark0active0markincrXactiveincrmarkXmarkincrXincrmarkXmarkincrXmarkXmarkpairsactivepairsmarkoddsactiveoddsmarksXactivesmarkXmarksXsmarkXmarksXmarkXmarkheadXactiveheadmarkXmarkheadXheadmarkXmarkheadXmarkXmarktailXactivetailmarkXmarktailXtailmarkXmarktailXmarkXconsmarkX1X2consX1X2consX1markX2consX1X2consactiveX1X2consX1X2consX1activeX2consX1X2incrmarkXincrXincractiveXincrXsmarkXsXsactiveXsXheadmarkXheadXheadactiveXheadXtailmarkXtailXtailactiveXtailXtruemarkconsX1X2activeconsmarkX1X2activeincrconsXXSmarkconssXincrXSmarkconsX1X2markX1marknatsactivenatsactivenatsmarkcons0incrnatsmarkincrXactiveincrmarkXmarkincrXmarkXmarkpairsactivepairsactivepairsmarkcons0incroddsmarkoddsactiveoddsactiveoddsmarkincrpairsmarksXactivesmarkXmarksXmarkXmarkheadXactiveheadmarkXmarkheadXmarkXmarktailXactivetailmarkXmarktailXmarkXtrue1active111nats00mark111cons21112000incr121pairs00odds00s111head1221tail121mark111active111markconsX1X2activeconsmarkX1X2activeincrconsXXSmarkconssXincrXSmarkconsX1X2markX1marknatsactivenatsactivenatsmarkcons0incrnatsmarkincrXactiveincrmarkXmarkincrXmarkXmarkpairsactivepairsactivepairsmarkcons0incroddsmarkoddsactiveoddsactiveoddsmarkincrpairsmarksXactivesmarkXmarksXmarkXmarkheadXactiveheadmarkXmarktailXactivetailmarkXmarktailXmarkXactivenatsmarkcons0incrnatsactivepairsmarkcons0incroddsactiveoddsmarkincrpairsactiveincrconsXXSmarkconssXincrXSmarknatsactivenatsmarkconsX1X2activeconsmarkX1X2mark0active0markincrXactiveincrmarkXmarkpairsactivepairsmarkoddsactiveoddsmarksXactivesmarkXmarkheadXactiveheadmarkXmarktailXactivetailmarkXconsmarkX1X2consX1X2consX1markX2consX1X2consactiveX1X2consX1X2consX1activeX2consX1X2incrmarkXincrXincractiveXincrXsmarkXsXsactiveXsXheadmarkXheadXheadactiveXheadXtailmarkXtailXtailactiveXtailX1active111nats00mark111cons22112000incr121pairs00odds00s111head111tail1221mark121active121markconsX1X2activeconsmarkX1X2activeincrconsXXSmarkconssXincrXSmarkconsX1X2markX1marknatsactivenatsactivenatsmarkcons0incrnatsmarkincrXactiveincrmarkXmarkincrXmarkXmarkpairsactivepairsactivepairsmarkcons0incroddsmarkoddsactiveoddsactiveoddsmarkincrpairsmarksXactivesmarkXmarksXmarkXmarkheadXactiveheadmarkXmarktailXactivetailmarkXactivenatsmarkcons0incrnatsactivepairsmarkcons0incroddsactiveoddsmarkincrpairsactiveincrconsXXSmarkconssXincrXSmarknatsactivenatsmarkconsX1X2activeconsmarkX1X2mark0active0markincrXactiveincrmarkXmarkpairsactivepairsmarkoddsactiveoddsmarksXactivesmarkXmarkheadXactiveheadmarkXmarktailXactivetailmarkXconsmarkX1X2consX1X2consX1markX2consX1X2consactiveX1X2consX1X2consX1activeX2consX1X2incrmarkXincrXincractiveXincrXsmarkXsXsactiveXsXheadmarkXheadXheadactiveXheadXtailmarkXtailXtailactiveXtailX1nats0110001pairs032odds053head142tail122mark11cons21active11mark11incr11s11nats000pairs0odds0head1tail1active11markconsX1X2activeconsmarkX1X2activeincrconsXXSmarkconssXincrXSmarkconsX1X2markX1marknatsactivenatsmarkincrXactiveincrmarkXmarkincrXmarkXmarkpairsactivepairsmarkoddsactiveoddsmarksXactivesmarkXmarksXmarkXmarkheadXactiveheadmarkXmarktailXactivetailmarkXactiveincrconsXXSmarkconssXincrXSmarkconsX1X2activeconsmarkX1X2markconsX1X2markX1markincrXactiveincrmarkXmarkincrXmarkXmarksXactivesmarkXmarksXmarkXmarkheadXactiveheadmarkXmarktailXactivetailmarkXtrue1cons261head142tail111nats0040032pairs024odds055active11incr11cons21mark11s11mark11head1tail1active11nats000pairs0odds0activeincrconsXXSmarkconssXincrXSmarkconsX1X2activeconsmarkX1X2markincrXactiveincrmarkXmarkincrXmarkXmarksXactivesmarkXmarksXmarkXmarkheadXactiveheadmarkXmarktailXactivetailmarkX1active11mark12cons2-2s10active12mark11incr12head11tail1-2nats00000pairs00odds00activeincrconsXXSmarkconssXincrXSmarkincrXactiveincrmarkXmarkincrXmarkXmarksXmarkXsactiveXsXsmarkXsXincractiveXincrXincrmarkXincrXconsX1markX2consX1X2consmarkX1X2consX1X2consactiveX1X2consX1X2consX1activeX2consX1X2headactiveXheadXheadmarkXheadXtailactiveXtailXtailmarkXtailX1active111cons201incr121active1mark11cons2incr11s11marksXmarkXconsX1markX2consX1X2consmarkX1X2consX1X2consactiveX1X2consX1X2consX1activeX2consX1X21s111mark111marksXmarkXmarksXmarkX1true1marknatsactivenatsfalsemarkpairsactivepairsfalsemarkoddsactiveoddsfalsemark0active0falseactivenatscons0incrnatsfalseactivepairscons0incroddsfalseactiveincrconsXXSconssXincrXSfalsemarkconsX1X2consmarkX1X2falseactivenatsincrnatsfalseactivepairsincroddsfalseactiveoddsincrpairsfalseactiveincrconsXXSincrXSfalsemarkincrXincrmarkXfalseactiveincrconsXXSsXfalsemarksXsmarkXfalsemarkheadXheadmarkXfalsemarktailXtailmarkXfalseconsX1markX2consX1X2consmarkX1X2consX1X2consactiveX1X2consX1X2consX1activeX2consX1X2true1mark111active111cons21112consX1markX2consX1X2consmarkX1X2consX1X2consactiveX1X2consX1X2consX1activeX2consX1X2consX1markX2consX1X21false12true2consmarkX1X2consX1X21true12false2consactiveX1X2consX1X21true12false2consX1activeX2consX1X21false12true2incractiveXincrXincrmarkXincrXtrue1active111mark111incr111incractiveXincrXincrmarkXincrXincractiveXincrX1true1incrmarkXincrX1true1sactiveXsXsmarkXsXtrue1active111mark111s111sactiveXsXsmarkXsXsactiveXsX1true1smarkXsX1true1headactiveXheadXheadmarkXheadXtrue1active111mark111head111headactiveXheadXheadmarkXheadXheadactiveXheadX1true1headmarkXheadX1true1tailactiveXtailXtailmarkXtailXtrue1active111mark111tail111tailactiveXtailXtailmarkXtailXtailactiveXtailX1true1tailmarkXtailX1true1AProVEAProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Statistics for single proof: 100.00 % (23 real / 0 unknown / 0 assumptions / 23 total proof steps)http://aprove.informatik.rwth-aachen.deJohnDoe