KoAT2 Proof Output

Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀+X₂, X₁, X₂-1) :|: 1 ≤ X₂
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ 0
t₃: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂-2⋅X₁) :|: 1+X₀ ≤ (X₁)²
t₄: l3(X₀, X₁, X₂) → l4(5⋅X₀, X₁, X₁+X₂)
t₅: l4(X₀, X₁, X₂) → l2(X₀+(X₂)⁴, 2⋅X₁, X₁+X₂)

Preprocessing

Found invariant 1 ≤ X₀ for location l2

Found invariant 1 ≤ X₀ for location l1

Found invariant 5 ≤ X₀ for location l4

Found invariant 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂) :|: 1 ≤ X₀
t₁: l1(X₀, X₁, X₂) → l1(X₀+X₂, X₁, X₂-1) :|: 1 ≤ X₂ ∧ 1 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ 1 ≤ X₀
t₃: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂-2⋅X₁) :|: 1+X₀ ≤ (X₁)² ∧ 1 ≤ X₀
t₄: l3(X₀, X₁, X₂) → l4(5⋅X₀, X₁, X₁+X₂) :|: 1 ≤ X₀
t₅: l4(X₀, X₁, X₂) → l2(X₀+(X₂)⁴, 2⋅X₁, X₁+X₂) :|: 5 ≤ X₀

MPRF for transition t₁: l1(X₀, X₁, X₂) → l1(X₀+X₂, X₁, X₂-1) :|: 1 ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

• l1: [X₂]

TWN: t₄: l3→l4

cycle: [t₄: l3→l4; t₅: l4→l2; t₃: l2→l3]
original loop: (1+X₀ ≤ (X₁)² ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀,(X₀,X₁,X₂) -> (5⋅X₀+6⋅(X₁)²*(X₂)²+(X₁)⁴+(X₂)⁴-4⋅X₁*(X₂)³-4⋅(X₁)³*X₂,2⋅X₁,X₂))
transformed loop: (1+X₀ ≤ (X₁)² ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀,(X₀,X₁,X₂) -> (5⋅X₀+6⋅(X₁)²*(X₂)²+(X₁)⁴+(X₂)⁴-4⋅X₁*(X₂)³-4⋅(X₁)³*X₂,2⋅X₁,X₂))
loop: (1+X₀ ≤ (X₁)² ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀,(X₀,X₁,X₂) -> (5⋅X₀+6⋅(X₁)²*(X₂)²+(X₁)⁴+(X₂)⁴-4⋅X₁*(X₂)³-4⋅(X₁)³*X₂,2⋅X₁,X₂))
order: [X₁; X₂; X₀]
closed-form:

X₁: X₁⋅(2)^n
X₂: X₂
X₀: X₀⋅(5)^n + [[n != 0]]⋅1/11⋅(X₁)⁴⋅(16)^n + [[n != 0]]⋅-4/3⋅(X₁)³*X₂⋅(8)^n + [[n != 0]]⋅(6⋅(X₁)²*(X₂)²+4/3⋅(X₁)³*X₂+1/4⋅(X₂)⁴-4/3⋅X₁*(X₂)³-1/11⋅(X₁)⁴)⋅(5)^n + [[n != 0]]⋅-6⋅(X₁)²*(X₂)²⋅(4)^n + [[n != 0]]⋅4/3⋅X₁*(X₂)³⋅(2)^n + [[n != 0]]⋅-1/4⋅(X₂)⁴

Termination: true
Formula:

(X₂)⁴ ≤ 4 ∧ 1 ≤ X₀ ∧ 4 ≤ (X₂)⁴ ∧ 176⋅X₁*(X₂)³+12⋅(X₁)⁴ ≤ 132⋅X₀+792⋅(X₁)²*(X₂)²+176⋅(X₁)³*X₂+33⋅(X₂)⁴ ∧ 132⋅X₀+792⋅(X₁)²*(X₂)²+176⋅(X₁)³*X₂+33⋅(X₂)⁴ ≤ 176⋅X₁*(X₂)³+12⋅(X₁)⁴ ∧ 0 ≤ X₁*(X₂)³ ∧ X₁*(X₂)³ ≤ 0 ∧ 0 ≤ (X₁)²+6⋅(X₁)²*(X₂)² ∧ (X₁)²+6⋅(X₁)²*(X₂)² ≤ 0 ∧ 0 ≤ (X₁)³*X₂ ∧ (X₁)³*X₂ ≤ 0 ∧ 0 ≤ (X₁)⁴ ∧ (X₁)⁴ ≤ 0
∨ 1 ≤ X₀ ∧ 1+132⋅X₀+792⋅(X₁)²*(X₂)²+176⋅(X₁)³*X₂+33⋅(X₂)⁴ ≤ 176⋅X₁*(X₂)³+12⋅(X₁)⁴ ∧ 0 ≤ (X₁)³*X₂ ∧ (X₁)³*X₂ ≤ 0 ∧ 0 ≤ (X₁)⁴ ∧ (X₁)⁴ ≤ 0
∨ 1 ≤ X₀ ∧ 1+176⋅X₁*(X₂)³ ≤ 0 ∧ 176⋅X₁*(X₂)³+12⋅(X₁)⁴ ≤ 132⋅X₀+792⋅(X₁)²*(X₂)²+176⋅(X₁)³*X₂+33⋅(X₂)⁴ ∧ 132⋅X₀+792⋅(X₁)²*(X₂)²+176⋅(X₁)³*X₂+33⋅(X₂)⁴ ≤ 176⋅X₁*(X₂)³+12⋅(X₁)⁴ ∧ 0 ≤ (X₁)²+6⋅(X₁)²*(X₂)² ∧ (X₁)²+6⋅(X₁)²*(X₂)² ≤ 0 ∧ 0 ≤ (X₁)³*X₂ ∧ (X₁)³*X₂ ≤ 0 ∧ 0 ≤ (X₁)⁴ ∧ (X₁)⁴ ≤ 0
∨ 1 ≤ X₀ ∧ 1 ≤ 132⋅(X₁)²+792⋅(X₁)²*(X₂)² ∧ 176⋅X₁*(X₂)³+12⋅(X₁)⁴ ≤ 132⋅X₀+792⋅(X₁)²*(X₂)²+176⋅(X₁)³*X₂+33⋅(X₂)⁴ ∧ 132⋅X₀+792⋅(X₁)²*(X₂)²+176⋅(X₁)³*X₂+33⋅(X₂)⁴ ≤ 176⋅X₁*(X₂)³+12⋅(X₁)⁴ ∧ 0 ≤ (X₁)³*X₂ ∧ (X₁)³*X₂ ≤ 0 ∧ 0 ≤ (X₁)⁴ ∧ (X₁)⁴ ≤ 0
∨ 1 ≤ X₀ ∧ 1 ≤ 176⋅(X₁)³*X₂ ∧ 0 ≤ (X₁)⁴ ∧ (X₁)⁴ ≤ 0
∨ 1 ≤ X₀ ∧ 1+12⋅(X₁)⁴ ≤ 0
∨ 1 ≤ X₀ ∧ 133 ≤ 33⋅(X₂)⁴ ∧ 176⋅X₁*(X₂)³+12⋅(X₁)⁴ ≤ 132⋅X₀+792⋅(X₁)²*(X₂)²+176⋅(X₁)³*X₂+33⋅(X₂)⁴ ∧ 132⋅X₀+792⋅(X₁)²*(X₂)²+176⋅(X₁)³*X₂+33⋅(X₂)⁴ ≤ 176⋅X₁*(X₂)³+12⋅(X₁)⁴ ∧ 0 ≤ X₁*(X₂)³ ∧ X₁*(X₂)³ ≤ 0 ∧ 0 ≤ (X₁)²+6⋅(X₁)²*(X₂)² ∧ (X₁)²+6⋅(X₁)²*(X₂)² ≤ 0 ∧ 0 ≤ (X₁)³*X₂ ∧ (X₁)³*X₂ ≤ 0 ∧ 0 ≤ (X₁)⁴ ∧ (X₁)⁴ ≤ 0

Stabilization-Threshold for: 1+X₀ ≤ (X₁)²

alphas_abs: 132⋅X₀+176⋅X₁*(X₂)³+132⋅(X₁)²+792⋅(X₁)²*(X₂)²+176⋅(X₁)³*X₂+12⋅(X₁)⁴+33⋅(X₂)⁴
M': 1
N: 3
Bound: 10⋅log(X₂)+12⋅log(X₁)+log(X₀)+62 {O(log(n))}

TWN - Lifting for [3: l2->l3; 4: l3->l4; 5: l4->l2] of 10⋅log(X₂)+12⋅log(X₁)+log(X₀)+64 {O(log(n))}

relevant size-bounds w.r.t. t₂: l1→l2:
X₀: 2⋅X₂⋅X₂+2⋅X₀+2⋅X₂ {O(n^2)}
X₁: 2⋅X₁ {O(n)}
X₂: 2⋅X₂ {O(n)}
Runtime-bound of t₂: 1 {O(1)}
Results in: 12⋅log(X₁)+13⋅log(X₂)+log(X₀)+89 {O(log(n))}

All Bounds

Timebounds

Overall timebound:X₂+3⋅log(X₀)+36⋅log(X₁)+39⋅log(X₂)+269 {O(n)}
t₀: 1 {O(1)}
t₁: X₂ {O(n)}
t₂: 1 {O(1)}
t₃: 12⋅log(X₁)+13⋅log(X₂)+log(X₀)+89 {O(log(n))}
t₄: 12⋅log(X₁)+13⋅log(X₂)+log(X₀)+89 {O(log(n))}
t₅: 12⋅log(X₁)+13⋅log(X₂)+log(X₀)+89 {O(log(n))}

Costbounds

Overall costbound: X₂+3⋅log(X₀)+36⋅log(X₁)+39⋅log(X₂)+269 {O(n)}
t₀: 1 {O(1)}
t₁: X₂ {O(n)}
t₂: 1 {O(1)}
t₃: 12⋅log(X₁)+13⋅log(X₂)+log(X₀)+89 {O(log(n))}
t₄: 12⋅log(X₁)+13⋅log(X₂)+log(X₀)+89 {O(log(n))}
t₅: 12⋅log(X₁)+13⋅log(X₂)+log(X₀)+89 {O(log(n))}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: 2⋅X₂⋅X₂+2⋅X₂+X₀ {O(n^2)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: 2⋅X₂⋅X₂+2⋅X₀+2⋅X₂ {O(n^2)}
t₂, X₁: 2⋅X₁ {O(n)}
t₂, X₂: 2⋅X₂ {O(n)}
t₃, X₀: 146783911423364576743092537299333564210980159306769991919205685720763064069663027716481187399048043939495936⋅2^(3⋅log(X₀))⋅2^(36⋅log(X₁))⋅2^(39⋅log(X₂))⋅2^(9⋅log(X₂))⋅X₁⋅X₂⋅X₂⋅X₂+16^(3⋅log(X₀))⋅16^(36⋅log(X₁))⋅16^(39⋅log(X₂))⋅16^(9⋅log(X₂))⋅7083271603906078757501937199839970337237042072752024044272935252133021449487672037753077279976540494138725768234495819230178699615482523444525217326451885295083794903354995236859949814158861106339793498427520403285563504697437506153794873484561573759163876734171825622767620957924878367969185009358384129424236514293956457858505582263102570156257796764049361854053114869322098725721757629614488965634874516982012228724064256⋅X₁⋅X₁⋅X₁⋅X₁+2019892186194575426780540115025969407571330484284098762047339866778393147250079035691647949930593965271161460040772435601799461984070580683441080871930322246382805889713322725705598883027579923432176608666540048384⋅4^(3⋅log(X₀))⋅4^(36⋅log(X₁))⋅4^(39⋅log(X₂))⋅4^(9⋅log(X₂))⋅X₁⋅X₁⋅X₂⋅X₂+20928724205608062418501896026098772450901672268483862204866806211443468675050137860268213290896704644455256122193127958353647607951976051351184856446717063756692761548634373675691940424248389150981952255142770624729564588051289319992065429687500000⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₁⋅X₁⋅X₂⋅X₂+3088413288990945714607167766096760666649729152895234960279866913260350640380788374205938472006792060778611417607373228628384532735989280347702230834056678923362997806954442769843550227998248540363155634742320939156524772391123850992097524347673943425610505012700786888921103128284156837954503288400970554554866145951744⋅8^(3⋅log(X₀))⋅8^(36⋅log(X₁))⋅8^(39⋅log(X₂))⋅8^(9⋅log(X₂))⋅X₁⋅X₁⋅X₁⋅X₂+3488120700934677069750316004349795408483612044747310367477801035240578112508356310044702215149450774075876020365521326392274601325329341891864142741119510626115460258105728945948656737374731525163658709190461770788260764675214886665344238281250000⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₁⋅X₁⋅X₁⋅X₁+3488120700934677069750316004349795408483612044747310367477801035240578112508356310044702215149450774075876020365521326392274601325329341891864142741119510626115460258105728945948656737374731525163658709190461770788260764675214886665344238281250000⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₂⋅X₂⋅X₂⋅X₂+436015087616834633718789500543724426060451505593413795934725129405072264063544538755587776893681346759484502545690165799034325165666167736483017842639938828264432532263216118243582092171841440645457338648807721348532595584401860833168029785156250⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₀+436015087616834633718789500543724426060451505593413795934725129405072264063544538755587776893681346759484502545690165799034325165666167736483017842639938828264432532263216118243582092171841440645457338648807721348532595584401860833168029785156250⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₂+436015087616834633718789500543724426060451505593413795934725129405072264063544538755587776893681346759484502545690165799034325165666167736483017842639938828264432532263216118243582092171841440645457338648807721348532595584401860833168029785156250⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₂⋅X₂+5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅6976241401869354139500632008699590816967224089494620734955602070481156225016712620089404430298901548151752040731042652784549202650658683783728285482239021252230920516211457891897313474749463050327317418380923541576521529350429773330688476562500000⋅X₁⋅X₁⋅X₁⋅X₂+5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅6976241401869354139500632008699590816967224089494620734955602070481156225016712620089404430298901548151752040731042652784549202650658683783728285482239021252230920516211457891897313474749463050327317418380923541576521529350429773330688476562500000⋅X₁⋅X₂⋅X₂⋅X₂+16⋅X₂⋅X₂⋅X₂⋅X₂ {O(EXP)}
t₃, X₁: 1237940039285380274899124224⋅2^(12⋅log(X₁))⋅2^(13⋅log(X₂))⋅X₀⋅X₁ {O(EXP)}
t₃, X₂: 2⋅X₂ {O(n)}
t₄, X₀: 146783911423364576743092537299333564210980159306769991919205685720763064069663027716481187399048043939495936⋅2^(3⋅log(X₀))⋅2^(36⋅log(X₁))⋅2^(39⋅log(X₂))⋅2^(9⋅log(X₂))⋅X₁⋅X₂⋅X₂⋅X₂+16^(3⋅log(X₀))⋅16^(36⋅log(X₁))⋅16^(39⋅log(X₂))⋅16^(9⋅log(X₂))⋅7083271603906078757501937199839970337237042072752024044272935252133021449487672037753077279976540494138725768234495819230178699615482523444525217326451885295083794903354995236859949814158861106339793498427520403285563504697437506153794873484561573759163876734171825622767620957924878367969185009358384129424236514293956457858505582263102570156257796764049361854053114869322098725721757629614488965634874516982012228724064256⋅X₁⋅X₁⋅X₁⋅X₁+2019892186194575426780540115025969407571330484284098762047339866778393147250079035691647949930593965271161460040772435601799461984070580683441080871930322246382805889713322725705598883027579923432176608666540048384⋅4^(3⋅log(X₀))⋅4^(36⋅log(X₁))⋅4^(39⋅log(X₂))⋅4^(9⋅log(X₂))⋅X₁⋅X₁⋅X₂⋅X₂+20928724205608062418501896026098772450901672268483862204866806211443468675050137860268213290896704644455256122193127958353647607951976051351184856446717063756692761548634373675691940424248389150981952255142770624729564588051289319992065429687500000⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₁⋅X₁⋅X₂⋅X₂+3088413288990945714607167766096760666649729152895234960279866913260350640380788374205938472006792060778611417607373228628384532735989280347702230834056678923362997806954442769843550227998248540363155634742320939156524772391123850992097524347673943425610505012700786888921103128284156837954503288400970554554866145951744⋅8^(3⋅log(X₀))⋅8^(36⋅log(X₁))⋅8^(39⋅log(X₂))⋅8^(9⋅log(X₂))⋅X₁⋅X₁⋅X₁⋅X₂+3488120700934677069750316004349795408483612044747310367477801035240578112508356310044702215149450774075876020365521326392274601325329341891864142741119510626115460258105728945948656737374731525163658709190461770788260764675214886665344238281250000⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₁⋅X₁⋅X₁⋅X₁+3488120700934677069750316004349795408483612044747310367477801035240578112508356310044702215149450774075876020365521326392274601325329341891864142741119510626115460258105728945948656737374731525163658709190461770788260764675214886665344238281250000⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₂⋅X₂⋅X₂⋅X₂+436015087616834633718789500543724426060451505593413795934725129405072264063544538755587776893681346759484502545690165799034325165666167736483017842639938828264432532263216118243582092171841440645457338648807721348532595584401860833168029785156250⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₀+436015087616834633718789500543724426060451505593413795934725129405072264063544538755587776893681346759484502545690165799034325165666167736483017842639938828264432532263216118243582092171841440645457338648807721348532595584401860833168029785156250⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₂+436015087616834633718789500543724426060451505593413795934725129405072264063544538755587776893681346759484502545690165799034325165666167736483017842639938828264432532263216118243582092171841440645457338648807721348532595584401860833168029785156250⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₂⋅X₂+5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅6976241401869354139500632008699590816967224089494620734955602070481156225016712620089404430298901548151752040731042652784549202650658683783728285482239021252230920516211457891897313474749463050327317418380923541576521529350429773330688476562500000⋅X₁⋅X₁⋅X₁⋅X₂+5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅6976241401869354139500632008699590816967224089494620734955602070481156225016712620089404430298901548151752040731042652784549202650658683783728285482239021252230920516211457891897313474749463050327317418380923541576521529350429773330688476562500000⋅X₁⋅X₂⋅X₂⋅X₂+16⋅X₂⋅X₂⋅X₂⋅X₂ {O(EXP)}
t₄, X₁: 1237940039285380274899124224⋅2^(12⋅log(X₁))⋅2^(13⋅log(X₂))⋅X₀⋅X₁ {O(EXP)}
t₄, X₂: 2⋅X₂ {O(n)}
t₅, X₀: 146783911423364576743092537299333564210980159306769991919205685720763064069663027716481187399048043939495936⋅2^(3⋅log(X₀))⋅2^(36⋅log(X₁))⋅2^(39⋅log(X₂))⋅2^(9⋅log(X₂))⋅X₁⋅X₂⋅X₂⋅X₂+16^(3⋅log(X₀))⋅16^(36⋅log(X₁))⋅16^(39⋅log(X₂))⋅16^(9⋅log(X₂))⋅7083271603906078757501937199839970337237042072752024044272935252133021449487672037753077279976540494138725768234495819230178699615482523444525217326451885295083794903354995236859949814158861106339793498427520403285563504697437506153794873484561573759163876734171825622767620957924878367969185009358384129424236514293956457858505582263102570156257796764049361854053114869322098725721757629614488965634874516982012228724064256⋅X₁⋅X₁⋅X₁⋅X₁+2019892186194575426780540115025969407571330484284098762047339866778393147250079035691647949930593965271161460040772435601799461984070580683441080871930322246382805889713322725705598883027579923432176608666540048384⋅4^(3⋅log(X₀))⋅4^(36⋅log(X₁))⋅4^(39⋅log(X₂))⋅4^(9⋅log(X₂))⋅X₁⋅X₁⋅X₂⋅X₂+20928724205608062418501896026098772450901672268483862204866806211443468675050137860268213290896704644455256122193127958353647607951976051351184856446717063756692761548634373675691940424248389150981952255142770624729564588051289319992065429687500000⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₁⋅X₁⋅X₂⋅X₂+3088413288990945714607167766096760666649729152895234960279866913260350640380788374205938472006792060778611417607373228628384532735989280347702230834056678923362997806954442769843550227998248540363155634742320939156524772391123850992097524347673943425610505012700786888921103128284156837954503288400970554554866145951744⋅8^(3⋅log(X₀))⋅8^(36⋅log(X₁))⋅8^(39⋅log(X₂))⋅8^(9⋅log(X₂))⋅X₁⋅X₁⋅X₁⋅X₂+3488120700934677069750316004349795408483612044747310367477801035240578112508356310044702215149450774075876020365521326392274601325329341891864142741119510626115460258105728945948656737374731525163658709190461770788260764675214886665344238281250000⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₁⋅X₁⋅X₁⋅X₁+3488120700934677069750316004349795408483612044747310367477801035240578112508356310044702215149450774075876020365521326392274601325329341891864142741119510626115460258105728945948656737374731525163658709190461770788260764675214886665344238281250000⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₂⋅X₂⋅X₂⋅X₂+436015087616834633718789500543724426060451505593413795934725129405072264063544538755587776893681346759484502545690165799034325165666167736483017842639938828264432532263216118243582092171841440645457338648807721348532595584401860833168029785156250⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₀+436015087616834633718789500543724426060451505593413795934725129405072264063544538755587776893681346759484502545690165799034325165666167736483017842639938828264432532263216118243582092171841440645457338648807721348532595584401860833168029785156250⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₂+436015087616834633718789500543724426060451505593413795934725129405072264063544538755587776893681346759484502545690165799034325165666167736483017842639938828264432532263216118243582092171841440645457338648807721348532595584401860833168029785156250⋅5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅X₂⋅X₂+5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅6976241401869354139500632008699590816967224089494620734955602070481156225016712620089404430298901548151752040731042652784549202650658683783728285482239021252230920516211457891897313474749463050327317418380923541576521529350429773330688476562500000⋅X₁⋅X₁⋅X₁⋅X₂+5^(3⋅log(X₀))⋅5^(36⋅log(X₁))⋅5^(39⋅log(X₂))⋅5^(9⋅log(X₂))⋅6976241401869354139500632008699590816967224089494620734955602070481156225016712620089404430298901548151752040731042652784549202650658683783728285482239021252230920516211457891897313474749463050327317418380923541576521529350429773330688476562500000⋅X₁⋅X₂⋅X₂⋅X₂+16⋅X₂⋅X₂⋅X₂⋅X₂ {O(EXP)}
t₅, X₁: 1237940039285380274899124224⋅2^(12⋅log(X₁))⋅2^(13⋅log(X₂))⋅X₀⋅X₁ {O(EXP)}
t₅, X₂: 2⋅X₂ {O(n)}