KoAT2 Proof Output

Initial Problem

Start: eval_twn11_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: eval_twn11_bb0_in, eval_twn11_bb1_in, eval_twn11_bb2_in, eval_twn11_bb3_in, eval_twn11_start, eval_twn11_stop
Transitions:
t₁: eval_twn11_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_twn11_bb1_in(X₃, X₄, X₅, X₃, X₄, X₅)
t₂: eval_twn11_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_twn11_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀+X₁+4⋅(X₁)²+X₂
t₃: eval_twn11_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_twn11_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀+X₁+4⋅(X₁)²+X₂ ≤ 0
t₄: eval_twn11_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_twn11_bb1_in(9⋅X₀+8⋅X₀*(X₁)²+16⋅(X₁)²*X₂+16⋅(X₁)³, -36⋅X₀*X₁-320⋅X₀*(X₁)²*X₂-320⋅X₀*(X₁)³-256⋅X₀*(X₁)⁴*X₂-256⋅X₀*(X₁)⁵-289⋅(X₀)²-144⋅(X₀)²*(X₁)²-64⋅(X₀)²*(X₁)⁴-43⋅X₁-8⋅X₁*X₂-64⋅(X₁)²*(X₂)²-128⋅(X₁)³*X₂-256⋅(X₁)⁴*(X₂)²-512⋅(X₁)⁵*X₂-256⋅(X₁)⁶, 54166016⋅X₀*(X₁)³*X₂+808966400⋅X₀*(X₁)⁴*X₂+487846912⋅X₀*(X₁)⁴*(X₂)²+1376256⋅X₀*(X₁)⁴*(X₂)³+567203840⋅X₀*(X₁)⁵*X₂+77824⋅X₀*(X₁)⁵*(X₂)²+64618496⋅X₀*(X₁)⁵*(X₂)³+11403264⋅X₀*(X₁)⁵*(X₂)⁴+642181120⋅X₀*(X₁)⁶*X₂+1274552320⋅X₀*(X₁)⁶*(X₂)²+37093376⋅X₀*(X₁)⁶*(X₂)³+31457280⋅X₀*(X₁)⁶*(X₂)⁵+199268352⋅X₀*(X₁)⁷+1305509888⋅X₀*(X₁)⁷*X₂+26206208⋅X₀*(X₁)⁷*(X₂)²+573046784⋅X₀*(X₁)⁷*(X₂)³+223346688⋅X₀*(X₁)⁷*(X₂)⁴+1294336⋅X₀*(X₁)⁸*X₂+2380464128⋅X₀*(X₁)⁸*(X₂)²+411566080⋅X₀*(X₁)⁸*(X₂)³+276824064⋅X₀*(X₁)⁸*(X₂)⁵+5697699840⋅X₀*(X₁)⁹*X₂+241696768⋅X₀*(X₁)⁹*(X₂)²+365953024⋅X₀*(X₁)⁹*(X₂)³+1465909248⋅X₀*(X₁)⁹*(X₂)⁴+66584576⋅X₀*(X₁)¹⁰*X₂+1744306176⋅X₀*(X₁)¹⁰*(X₂)²+2298478592⋅X₀*(X₁)¹⁰*(X₂)³+704643072⋅X₀*(X₁)¹⁰*(X₂)⁵+4895801344⋅X₀*(X₁)¹¹*X₂+1795162112⋅X₀*(X₁)¹¹*(X₂)²+3523215360⋅X₀*(X₁)¹¹*(X₂)⁴+320602112⋅X₀*(X₁)¹²+905969664⋅X₀*(X₁)¹²*X₂+6509559808⋅X₀*(X₁)¹²*(X₂)³+402653184⋅X₀*(X₁)¹²*(X₂)⁵+6777995264⋅X₀*(X₁)¹³*(X₂)²+2013265920⋅X₀*(X₁)¹³*(X₂)⁴+4016046080⋅X₀*(X₁)¹⁴+4395630592⋅X₀*(X₁)¹⁴*X₂+4026531840⋅X₀*(X₁)¹⁴*(X₂)³+5335154688⋅X₀*(X₁)¹⁵+4026531840⋅X₀*(X₁)¹⁵*(X₂)²+2013265920⋅X₀*(X₁)¹⁶*X₂+402653184⋅X₀*(X₁)¹⁷+433975232⋅(X₀)²*(X₁)²*X₂+443904⋅(X₀)²*(X₁)²*(X₂)²+61593600⋅(X₀)²*(X₁)³*(X₂)²+7102464⋅(X₀)²*(X₁)³*(X₂)³+20770304⋅(X₀)²*(X₁)⁴+916336640⋅(X₀)²*(X₁)⁴*X₂+16443392⋅(X₀)²*(X₁)⁴*(X₂)²+28409856⋅(X₀)²*(X₁)⁴*(X₂)⁴+1628160⋅(X₀)²*(X₁)⁵*X₂+666390528⋅(X₀)²*(X₁)⁵*(X₂)²+200638464⋅(X₀)²*(X₁)⁵*(X₂)³+360895488⋅(X₀)²*(X₁)⁶+1797652480⋅(X₀)²*(X₁)⁶*X₂+261947392⋅(X₀)²*(X₁)⁶*(X₂)²+398721024⋅(X₀)²*(X₁)⁶*(X₂)⁴+117108736⋅(X₀)²*(X₁)⁷*X₂+832077824⋅(X₀)²*(X₁)⁷*(X₂)²+1811939328⋅(X₀)²*(X₁)⁷*(X₂)³+2734030848⋅(X₀)²*(X₁)⁸*X₂+2254307328⋅(X₀)²*(X₁)⁸*(X₂)²+1454899200⋅(X₀)²*(X₁)⁸*(X₂)⁴+5839749120⋅(X₀)²*(X₁)⁹+1256980480⋅(X₀)²*(X₁)⁹*X₂+1234960384⋅(X₀)²*(X₁)⁹*(X₂)²+5951717376⋅(X₀)²*(X₁)⁹*(X₂)³+3175350272⋅(X₀)²*(X₁)¹⁰*X₂+9081716736⋅(X₀)²*(X₁)¹⁰*(X₂)²+1384120320⋅(X₀)²*(X₁)¹⁰*(X₂)⁴+5473566720⋅(X₀)²*(X₁)¹¹+7421820928⋅(X₀)²*(X₁)¹¹*X₂+5536481280⋅(X₀)²*(X₁)¹¹*(X₂)³+8271167488⋅(X₀)²*(X₁)¹²*(X₂)²+503316480⋅(X₀)²*(X₁)¹²*(X₂)⁴+2002780160⋅(X₀)²*(X₁)¹³+6408896512⋅(X₀)²*(X₁)¹³*X₂+2013265920⋅(X₀)²*(X₁)¹³*(X₂)³+5259657216⋅(X₀)²*(X₁)¹⁴+3019898880⋅(X₀)²*(X₁)¹⁴*(X₂)²+2013265920⋅(X₀)²*(X₁)¹⁵*X₂+503316480⋅(X₀)²*(X₁)¹⁶+4734976⋅(X₀)³*(X₁)²*X₂+57757472⋅(X₀)³*(X₁)³+193103872⋅(X₀)³*(X₁)³*X₂+67473408⋅(X₀)³*(X₁)³*(X₂)²+109021184⋅(X₀)³*(X₁)⁴*X₂+284098560⋅(X₀)³*(X₁)⁴*(X₂)³+1069702144⋅(X₀)³*(X₁)⁵+450056192⋅(X₀)³*(X₁)⁵*X₂+1130643456⋅(X₀)³*(X₁)⁵*(X₂)²+1698422784⋅(X₀)³*(X₁)⁶+1026457600⋅(X₀)³*(X₁)⁶*X₂+1767374848⋅(X₀)³*(X₁)⁶*(X₂)³+1680375808⋅(X₀)³*(X₁)⁷*X₂+5536481280⋅(X₀)³*(X₁)⁷*(X₂)²+2225569792⋅(X₀)³*(X₁)⁸+5962072064⋅(X₀)³*(X₁)⁸*X₂+2280652800⋅(X₀)³*(X₁)⁸*(X₂)³+1136918528⋅(X₀)³*(X₁)⁹*X₂+6933184512⋅(X₀)³*(X₁)⁹*(X₂)²+1232994304⋅(X₀)³*(X₁)¹⁰+7596933120⋅(X₀)³*(X₁)¹⁰*X₂+1258291200⋅(X₀)³*(X₁)¹⁰*(X₂)³+3774873600⋅(X₀)³*(X₁)¹¹*(X₂)²+330301440⋅(X₀)³*(X₁)¹²+3925868544⋅(X₀)³*(X₁)¹²*X₂+335544320⋅(X₀)³*(X₁)¹²*(X₂)³+2617245696⋅(X₀)³*(X₁)¹³+1006632960⋅(X₀)³*(X₁)¹³*(X₂)²+1006632960⋅(X₀)³*(X₁)¹⁴*X₂+335544320⋅(X₀)³*(X₁)¹⁵+24908064⋅(X₀)⁴*X₁+26499264⋅(X₀)⁴*X₁*X₂+211994112⋅(X₀)⁴*(X₁)²*(X₂)²+579245760⋅(X₀)⁴*(X₁)³+599774208⋅(X₀)⁴*(X₁)³*X₂+1686067200⋅(X₀)⁴*(X₁)⁴*(X₂)²+3564312576⋅(X₀)⁴*(X₁)⁵+3590688768⋅(X₀)⁴*(X₁)⁵*X₂+2090336256⋅(X₀)⁴*(X₁)⁶*(X₂)²+4267646976⋅(X₀)⁴*(X₁)⁷+4283301888⋅(X₀)⁴*(X₁)⁷*X₂+1561067520⋅(X₀)⁴*(X₁)⁸*(X₂)²+3145203712⋅(X₀)⁴*(X₁)⁹+3151233024⋅(X₀)⁴*(X₁)⁹*X₂+597688320⋅(X₀)⁴*(X₁)¹⁰*(X₂)²+1194065920⋅(X₀)⁴*(X₁)¹¹+1195376640⋅(X₀)⁴*(X₁)¹¹*X₂+767557632⋅(X₀)⁴*(X₁)¹²+125829120⋅(X₀)⁴*(X₁)¹²*(X₂)²+251658240⋅(X₀)⁴*(X₁)¹³*X₂+125829120⋅(X₀)⁴*(X₁)¹⁴+119246688⋅(X₀)⁵*X₁+1050933088⋅(X₀)⁵*(X₁)²+1059970560⋅(X₀)⁵*(X₁)²*X₂+1131883008⋅(X₀)⁵*(X₁)³+1480959488⋅(X₀)⁵*(X₁)⁴+1487198208⋅(X₀)⁵*(X₁)⁴*X₂+1537075200⋅(X₀)⁵*(X₁)⁵+952217600⋅(X₀)⁵*(X₁)⁶+954728448⋅(X₀)⁵*(X₁)⁶*X₂+970653696⋅(X₀)⁵*(X₁)⁷+495501312⋅(X₀)⁵*(X₁)⁸+496238592⋅(X₀)⁵*(X₁)⁸*X₂+499777536⋅(X₀)⁵*(X₁)⁹+144572416⋅(X₀)⁵*(X₁)¹⁰+144703488⋅(X₀)⁵*(X₁)¹⁰*X₂+144703488⋅(X₀)⁵*(X₁)¹¹+25165824⋅(X₀)⁵*(X₁)¹²*X₂+25165824⋅(X₀)⁵*(X₁)¹³+1632136072⋅(X₀)⁶+476986752⋅(X₀)⁶*(X₁)²+355819008⋅(X₀)⁶*(X₁)⁴+151732224⋅(X₀)⁶*(X₁)⁶+60260352⋅(X₀)⁶*(X₁)⁸+14155776⋅(X₀)⁶*(X₁)¹⁰+2097152⋅(X₀)⁶*(X₁)¹²+11173888⋅(X₁)⁵*(X₂)⁴+786432⋅(X₁)⁵*(X₂)⁵+30932992⋅(X₁)⁶*(X₂)⁵+2097152⋅(X₁)⁶*(X₂)⁶+220725248⋅(X₁)⁷*(X₂)⁴+18874368⋅(X₁)⁷*(X₂)⁵+274202624⋅(X₁)⁸*(X₂)⁵+25165824⋅(X₁)⁸*(X₂)⁶+1453326336⋅(X₁)⁹*(X₂)⁴+163577856⋅(X₁)⁹*(X₂)⁵+700448768⋅(X₁)¹⁰*(X₂)⁵+100663296⋅(X₁)¹⁰*(X₂)⁶+3502243840⋅(X₁)¹¹*(X₂)⁴+603979776⋅(X₁)¹¹*(X₂)⁵+293601280⋅(X₁)¹²*(X₂)³+134217728⋅(X₁)¹²*(X₂)⁶+964689920⋅(X₁)¹³*(X₂)²+805306368⋅(X₁)¹³*(X₂)⁵+985661440⋅(X₁)¹⁴*X₂+2013265920⋅(X₁)¹⁴*(X₂)⁴+2680160256⋅(X₁)¹⁵+2684354560⋅(X₁)¹⁵*(X₂)³+2013265920⋅(X₁)¹⁶*(X₂)²+805306368⋅(X₁)¹⁷*X₂+134217728⋅(X₁)¹⁸-2124⋅X₀*X₁-576⋅X₀*X₁*X₂-115172⋅X₀*(X₁)²-53824⋅X₀*(X₁)²*X₂-11776⋅X₀*(X₁)²*(X₂)²-360960⋅X₀*(X₁)³*(X₂)²-114688⋅X₀*(X₁)³*(X₂)³-475136⋅X₀*(X₁)⁴*(X₂)⁴-5505024⋅X₀*(X₁)⁶*(X₂)⁴-17039360⋅X₀*(X₁)⁸*(X₂)⁴-10485760⋅X₀*(X₁)¹⁰*(X₂)⁴-41943040⋅X₀*(X₁)¹¹*(X₂)³-62914560⋅X₀*(X₁)¹²*(X₂)²-41943040⋅X₀*(X₁)¹³*X₂-217328⋅(X₀)²*X₁*X₂-36992⋅(X₀)²*X₁*(X₂)²-25616⋅(X₀)²*(X₁)²-295936⋅(X₀)²*(X₁)²*(X₂)³-2208704⋅(X₀)²*(X₁)³*X₂-5992448⋅(X₀)²*(X₁)⁴*(X₂)³-27557888⋅(X₀)²*(X₁)⁶*(X₂)³-27525120⋅(X₀)²*(X₁)⁸*(X₂)³-10485760⋅(X₀)²*(X₁)¹⁰*(X₂)³-31457280⋅(X₀)²*(X₁)¹¹*(X₂)²-31457280⋅(X₀)²*(X₁)¹²*X₂-2420664⋅(X₀)³*X₁-520064⋅(X₀)³*X₁*X₂-4308480⋅(X₀)³*(X₁)²*(X₂)²-30607360⋅(X₀)³*(X₁)⁴*(X₂)²-33734656⋅(X₀)³*(X₁)⁶*(X₂)²-19005440⋅(X₀)³*(X₁)⁸*(X₂)²-5242880⋅(X₀)³*(X₁)¹⁰*(X₂)²-10485760⋅(X₀)³*(X₁)¹¹*X₂-20155200⋅(X₀)⁴*(X₁)²*X₂-26340352⋅(X₀)⁴*(X₁)⁴*X₂-15654912⋅(X₀)⁴*(X₁)⁶*X₂-6062080⋅(X₀)⁴*(X₁)⁸*X₂-1310720⋅(X₀)⁴*(X₁)¹⁰*X₂-3256612⋅(X₀)⁵-8192⋅(X₁)³*(X₂)⁴-32768⋅(X₁)⁴*(X₂)⁵-21376479⋅X₂, X₃, X₄, X₅)
t₅: eval_twn11_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_twn11_stop(X₀, X₁, X₂, X₃, X₄, X₅)
t₀: eval_twn11_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_twn11_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Problem after Preprocessing

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₅: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: inf {Infinity}
t₃: 1 {O(1)}
t₄: inf {Infinity}
t₅: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₅ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₅, X₅: 2⋅X₅ {O(n)}