KoAT2 Proof Output

Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < 4⋅(X₁)²+X₀+X₁+X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 4⋅(X₁)²+X₀+X₁+X₂ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(9⋅X₀+8⋅X₀*(X₁)²+16⋅(X₁)³+16⋅(X₁)²*X₂, -43⋅X₁-289⋅(X₀)²-144⋅(X₀)²*(X₁)²-320⋅X₀*(X₁)³-320⋅X₀*(X₁)²*X₂-64⋅(X₀)²*(X₁)⁴-256⋅X₀*(X₁)⁵-256⋅X₀*(X₁)⁴*X₂-256⋅(X₁)⁶-512⋅(X₁)⁵*X₂-256⋅(X₁)⁴*(X₂)²-36⋅X₀*X₁-128⋅(X₁)³*X₂-64⋅(X₁)²*(X₂)²-8⋅X₁*X₂, 57757472⋅(X₀)³*(X₁)³+20770304⋅(X₀)²*(X₁)⁴+1069702144⋅(X₀)³*(X₁)⁵+360895488⋅(X₀)²*(X₁)⁶+1628160⋅(X₀)²*(X₁)⁵*X₂+199268352⋅X₀*(X₁)⁷+642181120⋅X₀*(X₁)⁶*X₂+77824⋅X₀*(X₁)⁵*(X₂)²+808966400⋅X₀*(X₁)⁴*X₂+1050933088⋅(X₀)⁵*(X₁)²+579245760⋅(X₀)⁴*(X₁)³+1480959488⋅(X₀)⁵*(X₁)⁴+3564312576⋅(X₀)⁴*(X₁)⁵+1698422784⋅(X₀)³*(X₁)⁶+450056192⋅(X₀)³*(X₁)⁵*X₂+24908064⋅(X₀)⁴*X₁+193103872⋅(X₀)³*(X₁)³*X₂+952217600⋅(X₀)⁵*(X₁)⁶+4267646976⋅(X₀)⁴*(X₁)⁷+2225569792⋅(X₀)³*(X₁)⁸+1680375808⋅(X₀)³*(X₁)⁷*X₂+5839749120⋅(X₀)²*(X₁)⁹+2734030848⋅(X₀)²*(X₁)⁸*X₂+832077824⋅(X₀)²*(X₁)⁷*(X₂)²+1797652480⋅(X₀)²*(X₁)⁶*X₂+666390528⋅(X₀)²*(X₁)⁵*(X₂)²+916336640⋅(X₀)²*(X₁)⁴*X₂+61593600⋅(X₀)²*(X₁)³*(X₂)²+495501312⋅(X₀)⁵*(X₁)⁸+3145203712⋅(X₀)⁴*(X₁)⁹+1232994304⋅(X₀)³*(X₁)¹⁰+1136918528⋅(X₀)³*(X₁)⁹*X₂+5473566720⋅(X₀)²*(X₁)¹¹+3175350272⋅(X₀)²*(X₁)¹⁰*X₂+1234960384⋅(X₀)²*(X₁)⁹*(X₂)²+320602112⋅X₀*(X₁)¹²+4895801344⋅X₀*(X₁)¹¹*X₂+1744306176⋅X₀*(X₁)¹⁰*(X₂)²+5697699840⋅X₀*(X₁)⁹*X₂+2380464128⋅X₀*(X₁)⁸*(X₂)²+1305509888⋅X₀*(X₁)⁷*X₂+365953024⋅X₀*(X₁)⁹*(X₂)³+573046784⋅X₀*(X₁)⁷*(X₂)³+1274552320⋅X₀*(X₁)⁶*(X₂)²+64618496⋅X₀*(X₁)⁵*(X₂)³+433975232⋅(X₀)²*(X₁)²*X₂+487846912⋅X₀*(X₁)⁴*(X₂)²+144572416⋅(X₀)⁵*(X₁)¹⁰+1194065920⋅(X₀)⁴*(X₁)¹¹+330301440⋅(X₀)³*(X₁)¹²+2002780160⋅(X₀)²*(X₁)¹³+117108736⋅(X₀)²*(X₁)⁷*X₂+4016046080⋅X₀*(X₁)¹⁴+1294336⋅X₀*(X₁)⁸*X₂+26206208⋅X₀*(X₁)⁷*(X₂)²+2680160256⋅(X₁)¹⁵+985661440⋅(X₁)¹⁴*X₂+964689920⋅(X₁)¹³*(X₂)²+293601280⋅(X₁)¹²*(X₂)³+3502243840⋅(X₁)¹¹*(X₂)⁴+1453326336⋅(X₁)⁹*(X₂)⁴+220725248⋅(X₁)⁷*(X₂)⁴+700448768⋅(X₁)¹⁰*(X₂)⁵+274202624⋅(X₁)⁸*(X₂)⁵+30932992⋅(X₁)⁶*(X₂)⁵+11173888⋅(X₁)⁵*(X₂)⁴+567203840⋅X₀*(X₁)⁵*X₂+54166016⋅X₀*(X₁)³*X₂+1632136072⋅(X₀)⁶+476986752⋅(X₀)⁶*(X₁)²+1131883008⋅(X₀)⁵*(X₁)³+1059970560⋅(X₀)⁵*(X₁)²*X₂+355819008⋅(X₀)⁶*(X₁)⁴+1537075200⋅(X₀)⁵*(X₁)⁵+1487198208⋅(X₀)⁵*(X₁)⁴*X₂+3590688768⋅(X₀)⁴*(X₁)⁵*X₂+1686067200⋅(X₀)⁴*(X₁)⁴*(X₂)²+119246688⋅(X₀)⁵*X₁+599774208⋅(X₀)⁴*(X₁)³*X₂+211994112⋅(X₀)⁴*(X₁)²*(X₂)²+26499264⋅(X₀)⁴*X₁*X₂+151732224⋅(X₀)⁶*(X₁)⁶+970653696⋅(X₀)⁵*(X₁)⁷+954728448⋅(X₀)⁵*(X₁)⁶*X₂+4283301888⋅(X₀)⁴*(X₁)⁷*X₂+2090336256⋅(X₀)⁴*(X₁)⁶*(X₂)²+5962072064⋅(X₀)³*(X₁)⁸*X₂+5536481280⋅(X₀)³*(X₁)⁷*(X₂)²+1026457600⋅(X₀)³*(X₁)⁶*X₂+1130643456⋅(X₀)³*(X₁)⁵*(X₂)²+109021184⋅(X₀)³*(X₁)⁴*X₂+1767374848⋅(X₀)³*(X₁)⁶*(X₂)³+284098560⋅(X₀)³*(X₁)⁴*(X₂)³+67473408⋅(X₀)³*(X₁)³*(X₂)²+60260352⋅(X₀)⁶*(X₁)⁸+499777536⋅(X₀)⁵*(X₁)⁹+496238592⋅(X₀)⁵*(X₁)⁸*X₂+3151233024⋅(X₀)⁴*(X₁)⁹*X₂+1561067520⋅(X₀)⁴*(X₁)⁸*(X₂)²+7596933120⋅(X₀)³*(X₁)¹⁰*X₂+6933184512⋅(X₀)³*(X₁)⁹*(X₂)²+2280652800⋅(X₀)³*(X₁)⁸*(X₂)³+7421820928⋅(X₀)²*(X₁)¹¹*X₂+9081716736⋅(X₀)²*(X₁)¹⁰*(X₂)²+1256980480⋅(X₀)²*(X₁)⁹*X₂+2254307328⋅(X₀)²*(X₁)⁸*(X₂)²+5951717376⋅(X₀)²*(X₁)⁹*(X₂)³+1811939328⋅(X₀)²*(X₁)⁷*(X₂)³+261947392⋅(X₀)²*(X₁)⁶*(X₂)²+1454899200⋅(X₀)²*(X₁)⁸*(X₂)⁴+398721024⋅(X₀)²*(X₁)⁶*(X₂)⁴+200638464⋅(X₀)²*(X₁)⁵*(X₂)³+4734976⋅(X₀)³*(X₁)²*X₂+16443392⋅(X₀)²*(X₁)⁴*(X₂)²+28409856⋅(X₀)²*(X₁)⁴*(X₂)⁴+7102464⋅(X₀)²*(X₁)³*(X₂)³+443904⋅(X₀)²*(X₁)²*(X₂)²+14155776⋅(X₀)⁶*(X₁)¹⁰+144703488⋅(X₀)⁵*(X₁)¹¹+144703488⋅(X₀)⁵*(X₁)¹⁰*X₂+767557632⋅(X₀)⁴*(X₁)¹²+1195376640⋅(X₀)⁴*(X₁)¹¹*X₂+597688320⋅(X₀)⁴*(X₁)¹⁰*(X₂)²+2617245696⋅(X₀)³*(X₁)¹³+3925868544⋅(X₀)³*(X₁)¹²*X₂+3774873600⋅(X₀)³*(X₁)¹¹*(X₂)²+1258291200⋅(X₀)³*(X₁)¹⁰*(X₂)³+5259657216⋅(X₀)²*(X₁)¹⁴+6408896512⋅(X₀)²*(X₁)¹³*X₂+8271167488⋅(X₀)²*(X₁)¹²*(X₂)²+5536481280⋅(X₀)²*(X₁)¹¹*(X₂)³+1384120320⋅(X₀)²*(X₁)¹⁰*(X₂)⁴+5335154688⋅X₀*(X₁)¹⁵+4395630592⋅X₀*(X₁)¹⁴*X₂+6777995264⋅X₀*(X₁)¹³*(X₂)²+905969664⋅X₀*(X₁)¹²*X₂+1795162112⋅X₀*(X₁)¹¹*(X₂)²+66584576⋅X₀*(X₁)¹⁰*X₂+6509559808⋅X₀*(X₁)¹²*(X₂)³+2298478592⋅X₀*(X₁)¹⁰*(X₂)³+241696768⋅X₀*(X₁)⁹*(X₂)²+3523215360⋅X₀*(X₁)¹¹*(X₂)⁴+1465909248⋅X₀*(X₁)⁹*(X₂)⁴+411566080⋅X₀*(X₁)⁸*(X₂)³+223346688⋅X₀*(X₁)⁷*(X₂)⁴+37093376⋅X₀*(X₁)⁶*(X₂)³+704643072⋅X₀*(X₁)¹⁰*(X₂)⁵+276824064⋅X₀*(X₁)⁸*(X₂)⁵+31457280⋅X₀*(X₁)⁶*(X₂)⁵+11403264⋅X₀*(X₁)⁵*(X₂)⁴+1376256⋅X₀*(X₁)⁴*(X₂)³+2097152⋅(X₀)⁶*(X₁)¹²+25165824⋅(X₀)⁵*(X₁)¹³+25165824⋅(X₀)⁵*(X₁)¹²*X₂+125829120⋅(X₀)⁴*(X₁)¹⁴+251658240⋅(X₀)⁴*(X₁)¹³*X₂+125829120⋅(X₀)⁴*(X₁)¹²*(X₂)²+335544320⋅(X₀)³*(X₁)¹⁵+1006632960⋅(X₀)³*(X₁)¹⁴*X₂+1006632960⋅(X₀)³*(X₁)¹³*(X₂)²+335544320⋅(X₀)³*(X₁)¹²*(X₂)³+503316480⋅(X₀)²*(X₁)¹⁶+2013265920⋅(X₀)²*(X₁)¹⁵*X₂+3019898880⋅(X₀)²*(X₁)¹⁴*(X₂)²+2013265920⋅(X₀)²*(X₁)¹³*(X₂)³+503316480⋅(X₀)²*(X₁)¹²*(X₂)⁴+402653184⋅X₀*(X₁)¹⁷+2013265920⋅X₀*(X₁)¹⁶*X₂+4026531840⋅X₀*(X₁)¹⁵*(X₂)²+4026531840⋅X₀*(X₁)¹⁴*(X₂)³+2013265920⋅X₀*(X₁)¹³*(X₂)⁴+402653184⋅X₀*(X₁)¹²*(X₂)⁵+134217728⋅(X₁)¹⁸+805306368⋅(X₁)¹⁷*X₂+2013265920⋅(X₁)¹⁶*(X₂)²+2684354560⋅(X₁)¹⁵*(X₂)³+2013265920⋅(X₁)¹⁴*(X₂)⁴+805306368⋅(X₁)¹³*(X₂)⁵+603979776⋅(X₁)¹¹*(X₂)⁵+163577856⋅(X₁)⁹*(X₂)⁵+134217728⋅(X₁)¹²*(X₂)⁶+100663296⋅(X₁)¹⁰*(X₂)⁶+25165824⋅(X₁)⁸*(X₂)⁶+18874368⋅(X₁)⁷*(X₂)⁵+2097152⋅(X₁)⁶*(X₂)⁶+786432⋅(X₁)⁵*(X₂)⁵-21376479⋅X₂-115172⋅X₀*(X₁)²-2420664⋅(X₀)³*X₁-2208704⋅(X₀)²*(X₁)³*X₂-25616⋅(X₀)²*(X₁)²-360960⋅X₀*(X₁)³*(X₂)²-53824⋅X₀*(X₁)²*X₂-3256612⋅(X₀)⁵-20155200⋅(X₀)⁴*(X₁)²*X₂-26340352⋅(X₀)⁴*(X₁)⁴*X₂-30607360⋅(X₀)³*(X₁)⁴*(X₂)²-4308480⋅(X₀)³*(X₁)²*(X₂)²-520064⋅(X₀)³*X₁*X₂-15654912⋅(X₀)⁴*(X₁)⁶*X₂-33734656⋅(X₀)³*(X₁)⁶*(X₂)²-27557888⋅(X₀)²*(X₁)⁶*(X₂)³-5992448⋅(X₀)²*(X₁)⁴*(X₂)³-6062080⋅(X₀)⁴*(X₁)⁸*X₂-19005440⋅(X₀)³*(X₁)⁸*(X₂)²-27525120⋅(X₀)²*(X₁)⁸*(X₂)³-17039360⋅X₀*(X₁)⁸*(X₂)⁴-5505024⋅X₀*(X₁)⁶*(X₂)⁴-475136⋅X₀*(X₁)⁴*(X₂)⁴-114688⋅X₀*(X₁)³*(X₂)³-11776⋅X₀*(X₁)²*(X₂)²-1310720⋅(X₀)⁴*(X₁)¹⁰*X₂-10485760⋅(X₀)³*(X₁)¹¹*X₂-5242880⋅(X₀)³*(X₁)¹⁰*(X₂)²-31457280⋅(X₀)²*(X₁)¹²*X₂-31457280⋅(X₀)²*(X₁)¹¹*(X₂)²-10485760⋅(X₀)²*(X₁)¹⁰*(X₂)³-41943040⋅X₀*(X₁)¹³*X₂-62914560⋅X₀*(X₁)¹²*(X₂)²-41943040⋅X₀*(X₁)¹¹*(X₂)³-10485760⋅X₀*(X₁)¹⁰*(X₂)⁴-217328⋅(X₀)²*X₁*X₂-295936⋅(X₀)²*(X₁)²*(X₂)³-36992⋅(X₀)²*X₁*(X₂)²-32768⋅(X₁)⁴*(X₂)⁵-8192⋅(X₁)³*(X₂)⁴-2124⋅X₀*X₁-576⋅X₀*X₁*X₂, X₃, X₄, X₅)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Problem after Preprocessing

Analysing control-flow refined program

Found invariant X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location n_l3___3

Found invariant X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location l1

CFR did not improve the program. Rolling back

All Bounds

Timebounds

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

Costbounds

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