KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l1

Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₂, X₃, X₄, X₅) :|: 1 ≤ X₅
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅) :|: 1 ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₂, X₄, X₅) :|: X₂ ≤ 0 ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 1 ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₅ ∧ 0 ≤ X₅
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(5⋅X₀+(X₂)², 2⋅X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ (X₁)² ∧ X₃ ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₅ ∧ 0 ≤ X₅

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₂, X₄, X₅) :|: X₂ ≤ 0 ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

• l1: [1+X₅]
• l2: [X₅]

MPRF for transition t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 1 ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

• l1: [1+X₅]
• l2: [1+X₅]

TWN: t₁: l1→l1

cycle: [t₁: l1→l1]
original loop: (1 ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅,(X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀+X₂,X₁,X₂-1,X₃,X₄,X₅))
transformed loop: (1 ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅,(X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀+X₂,X₁,X₂-1,X₃,X₄,X₅))
loop: (1 ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅,(X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀+X₂,X₁,X₂-1,X₃,X₄,X₅))
order: [X₂; X₅; X₄; X₃; X₁; X₀]
closed-form:

X₂: X₂ + [[n != 0]]⋅-1⋅n^1
X₅: X₅
X₄: X₄
X₃: X₃
X₁: X₁
X₀: X₀ + [[n != 0]]⋅X₂⋅n^1 + [[n != 0, n != 1]]⋅-1/2⋅n^2 + [[n != 0, n != 1]]⋅1/2⋅n^1

Termination: true
Formula:

0 ≤ 1 ∧ 0 ≤ 1+2⋅X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ 0 ∧ 1+2⋅X₃ ≤ 2⋅X₀ ∧ 1 ≤ X₂ ∧ 1+2⋅X₂ ≤ 0 ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅
∨ 0 ≤ 1 ∧ 0 ≤ 1+2⋅X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 1+2⋅X₂ ≤ 0 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅
∨ 0 ≤ 1 ∧ 0 ≤ 1+2⋅X₂ ∧ 1 ≤ 0 ∧ 1+2⋅X₃ ≤ 2⋅X₀ ∧ 1+2⋅X₂ ≤ 0 ∧ 2 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅
∨ 0 ≤ 1 ∧ 0 ≤ 1+2⋅X₂ ∧ 1 ≤ 0 ∧ 1+2⋅X₃ ≤ 2⋅X₀ ∧ 1+2⋅X₂ ≤ 0 ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅
∨ 0 ≤ 1 ∧ 0 ≤ 1+2⋅X₂ ∧ 1 ≤ 0 ∧ 1+2⋅X₂ ≤ 0 ∧ 2 ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅
∨ 0 ≤ 1 ∧ 0 ≤ 1+2⋅X₂ ∧ 1 ≤ 0 ∧ 1+2⋅X₂ ≤ 0 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅
∨ 0 ≤ 1 ∧ X₂ ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₅
∨ 0 ≤ 1 ∧ X₂ ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₅
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 2 ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₂ ∧ 0 ≤ X₅
∨ 1 ≤ 0 ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅

Stabilization-Threshold for: X₃ ≤ X₀

alphas_abs: 2+2⋅X₀+2⋅X₂+2⋅X₃
M: 0
N: 2
Bound: 4⋅X₀+4⋅X₂+4⋅X₃+7 {O(n)}

Stabilization-Threshold for: 1 ≤ X₂

alphas_abs: X₂
M: 0
N: 1
Bound: 2⋅X₂+2 {O(n)}

original loop: (1 ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅,(X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀+X₂,X₁,X₂-1,X₃,X₄,X₅))
transformed loop: (1 ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅,(X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀+X₂,X₁,X₂-1,X₃,X₄,X₅))
loop: (1 ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₅,(X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀+X₂,X₁,X₂-1,X₃,X₄,X₅))
order: [X₂; X₅; X₄; X₃; X₁; X₀]
closed-form:

X₂: X₂ + [[n != 0]]⋅-1⋅n^1
X₅: X₅
X₄: X₄
X₃: X₃
X₁: X₁
X₀: X₀ + [[n != 0]]⋅X₂⋅n^1 + [[n != 0, n != 1]]⋅-1/2⋅n^2 + [[n != 0, n != 1]]⋅1/2⋅n^1

Termination: true
Formula:

Stabilization-Threshold for: X₃ ≤ X₀

alphas_abs: 2+2⋅X₀+2⋅X₂+2⋅X₃
M: 0
N: 2
Bound: 4⋅X₀+4⋅X₂+4⋅X₃+7 {O(n)}

Stabilization-Threshold for: 1 ≤ X₂

alphas_abs: X₂
M: 0
N: 1
Bound: 2⋅X₂+2 {O(n)}

TWN - Lifting for [1: l1->l1] of 4⋅X₀+4⋅X₃+6⋅X₂+11 {O(n)}

relevant size-bounds w.r.t. t₀: l0→l1:
X₀: X₃ {O(n)}
X₂: X₂ {O(n)}
X₃: X₃ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 6⋅X₂+8⋅X₃+11 {O(n)}

TWN - Lifting for [1: l1->l1] of 4⋅X₀+4⋅X₃+6⋅X₂+11 {O(n)}

relevant size-bounds w.r.t. t₄: l2→l1:
X₀: 4⋅X₂+4⋅X₅ {O(n)}
X₂: 2⋅X₅ {O(n)}
X₃: 4⋅X₂+4⋅X₅ {O(n)}
Runtime-bound of t₄: X₅+1 {O(n)}
Results in: 32⋅X₂⋅X₅+44⋅X₅⋅X₅+32⋅X₂+55⋅X₅+11 {O(n^2)}

TWN: t₃: l2→l2

cycle: [t₃: l2→l2]
original loop: (1 ≤ X₀ ∧ 1+X₀ ≤ (X₁)² ∧ X₃ ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₅ ∧ 0 ≤ X₅,(X₀,X₁,X₂,X₃,X₅) -> (5⋅X₀+(X₂)²,2⋅X₁,X₂,X₃,X₅))
transformed loop: (1 ≤ X₀ ∧ 1+X₀ ≤ (X₁)² ∧ X₃ ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₅ ∧ 0 ≤ X₅,(X₀,X₁,X₂,X₃,X₅) -> (5⋅X₀+(X₂)²,2⋅X₁,X₂,X₃,X₅))
loop: (1 ≤ X₀ ∧ 1+X₀ ≤ (X₁)² ∧ X₃ ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₅ ∧ 0 ≤ X₅,(X₀,X₁,X₂,X₃,X₅) -> (5⋅X₀+(X₂)²,2⋅X₁,X₂,X₃,X₅))
order: [X₂; X₅; X₃; X₁; X₀]
closed-form:

X₂: X₂
X₅: X₅
X₃: X₃
X₁: X₁⋅(2)^n
X₀: X₀⋅(5)^n + [[n != 0]]⋅1/4⋅(X₂)²⋅(5)^n + [[n != 0]]⋅-1/4⋅(X₂)²

Termination: true
Formula:

(X₂)² ≤ 4 ∧ 1 ≤ X₀ ∧ 4 ≤ (X₂)² ∧ 0 ≤ 4⋅X₀+(X₂)² ∧ 4⋅X₀+(X₂)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₅ ∧ 0 ≤ X₅
∨ 1 ≤ X₀ ∧ 1+4⋅X₀+(X₂)² ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₅ ∧ 0 ≤ X₅
∨ 1 ≤ X₀ ∧ 1 ≤ 4⋅(X₁)² ∧ 0 ≤ 4⋅X₀+(X₂)² ∧ 4⋅X₀+(X₂)² ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₅ ∧ 0 ≤ X₅
∨ 1 ≤ X₀ ∧ 5 ≤ (X₂)² ∧ 0 ≤ 4⋅X₀+(X₂)² ∧ 4⋅X₀+(X₂)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₅ ∧ 0 ≤ X₅

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

alphas_abs: 4⋅(X₁)²+(X₂)²
M': 1
N: 1
Bound: 2⋅log(X₁)+2⋅log(X₂)+5 {O(log(n))}

TWN - Lifting for [3: l2->l2] of 2⋅log(X₁)+2⋅log(X₂)+7 {O(log(n))}

relevant size-bounds w.r.t. t₂: l1→l2:
X₁: 4⋅X₄ {O(n)}
X₂: 2⋅X₂+2⋅X₅ {O(n)}
Runtime-bound of t₂: X₅+1 {O(n)}
Results in: 2⋅X₅⋅log(X₂)+2⋅X₅⋅log(X₄)+2⋅X₅⋅log(X₅)+15⋅X₅+2⋅log(X₂)+2⋅log(X₄)+2⋅log(X₅)+15 {O(log(n)*n)}

Found invariant 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location l1

Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location l2

Found invariant 0 ≤ X₅ ∧ 0 ≤ X₂+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₂ for location l1_v1

All Bounds

Timebounds

Overall timebound:32⋅X₂⋅X₅+44⋅X₅⋅X₅+2⋅X₅⋅log(X₂)+2⋅X₅⋅log(X₄)+2⋅X₅⋅log(X₅)+38⋅X₂+72⋅X₅+8⋅X₃+2⋅log(X₂)+2⋅log(X₄)+2⋅log(X₅)+40 {O(n^2)}
t₀: 1 {O(1)}
t₁: 32⋅X₂⋅X₅+44⋅X₅⋅X₅+38⋅X₂+55⋅X₅+8⋅X₃+22 {O(n^2)}
t₂: X₅+1 {O(n)}
t₃: 2⋅X₅⋅log(X₂)+2⋅X₅⋅log(X₄)+2⋅X₅⋅log(X₅)+15⋅X₅+2⋅log(X₂)+2⋅log(X₄)+2⋅log(X₅)+15 {O(log(n)*n)}
t₄: X₅+1 {O(n)}

Costbounds

Overall costbound: 32⋅X₂⋅X₅+44⋅X₅⋅X₅+2⋅X₅⋅log(X₂)+2⋅X₅⋅log(X₄)+2⋅X₅⋅log(X₅)+38⋅X₂+72⋅X₅+8⋅X₃+2⋅log(X₂)+2⋅log(X₄)+2⋅log(X₅)+40 {O(n^2)}
t₀: 1 {O(1)}
t₁: 32⋅X₂⋅X₅+44⋅X₅⋅X₅+38⋅X₂+55⋅X₅+8⋅X₃+22 {O(n^2)}
t₂: X₅+1 {O(n)}
t₃: 2⋅X₅⋅log(X₂)+2⋅X₅⋅log(X₄)+2⋅X₅⋅log(X₅)+15⋅X₅+2⋅log(X₂)+2⋅log(X₄)+2⋅log(X₅)+15 {O(log(n)*n)}
t₄: X₅+1 {O(n)}

Sizebounds

t₀, X₀: X₃ {O(n)}
t₀, X₁: X₄ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₀: 176⋅X₅⋅X₅⋅X₅+216⋅X₂⋅X₅⋅X₅+64⋅X₂⋅X₂⋅X₅+16⋅X₂⋅X₃+220⋅X₅⋅X₅+262⋅X₂⋅X₅+32⋅X₃⋅X₅+76⋅X₂⋅X₂+50⋅X₂+96⋅X₅+X₃ {O(n^3)}
t₁, X₁: 3⋅X₄ {O(n)}
t₁, X₂: 2⋅X₅+X₂ {O(n)}
t₁, X₃: 4⋅X₂+4⋅X₅+X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: 176⋅X₅⋅X₅⋅X₅+216⋅X₂⋅X₅⋅X₅+64⋅X₂⋅X₂⋅X₅+16⋅X₂⋅X₃+220⋅X₅⋅X₅+262⋅X₂⋅X₅+32⋅X₃⋅X₅+76⋅X₂⋅X₂+2⋅X₃+50⋅X₂+96⋅X₅ {O(n^3)}
t₂, X₁: 4⋅X₄ {O(n)}
t₂, X₂: 2⋅X₂+2⋅X₅ {O(n)}
t₂, X₃: 2⋅X₂+2⋅X₅ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 152587890625000⋅5^(15⋅X₅)⋅5^(2⋅X₅⋅log(X₂))⋅5^(2⋅X₅⋅log(X₄))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅log(X₂))⋅5^(2⋅log(X₄))⋅5^(2⋅log(X₅))⋅5^(2⋅log(X₅))⋅5^(4⋅X₅)⋅X₂⋅X₂+1525878906250000⋅5^(15⋅X₅)⋅5^(2⋅X₅⋅log(X₂))⋅5^(2⋅X₅⋅log(X₄))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅log(X₂))⋅5^(2⋅log(X₄))⋅5^(2⋅log(X₅))⋅5^(2⋅log(X₅))⋅5^(4⋅X₅)⋅X₂⋅X₃+16784667968750000⋅5^(15⋅X₅)⋅5^(2⋅X₅⋅log(X₂))⋅5^(2⋅X₅⋅log(X₄))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅log(X₂))⋅5^(2⋅log(X₄))⋅5^(2⋅log(X₅))⋅5^(2⋅log(X₅))⋅5^(4⋅X₅)⋅X₅⋅X₅⋅X₅+190734863281250⋅5^(15⋅X₅)⋅5^(2⋅X₅⋅log(X₂))⋅5^(2⋅X₅⋅log(X₄))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅log(X₂))⋅5^(2⋅log(X₄))⋅5^(2⋅log(X₅))⋅5^(2⋅log(X₅))⋅5^(4⋅X₅)⋅X₃+20599365234375000⋅5^(15⋅X₅)⋅5^(2⋅X₅⋅log(X₂))⋅5^(2⋅X₅⋅log(X₄))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅log(X₂))⋅5^(2⋅log(X₄))⋅5^(2⋅log(X₅))⋅5^(2⋅log(X₅))⋅5^(4⋅X₅)⋅X₂⋅X₅⋅X₅+21133422851562500⋅5^(15⋅X₅)⋅5^(2⋅X₅⋅log(X₂))⋅5^(2⋅X₅⋅log(X₄))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅log(X₂))⋅5^(2⋅log(X₄))⋅5^(2⋅log(X₅))⋅5^(2⋅log(X₅))⋅5^(4⋅X₅)⋅X₅⋅X₅+25291442871093750⋅5^(15⋅X₅)⋅5^(2⋅X₅⋅log(X₂))⋅5^(2⋅X₅⋅log(X₄))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅log(X₂))⋅5^(2⋅log(X₄))⋅5^(2⋅log(X₅))⋅5^(2⋅log(X₅))⋅5^(4⋅X₅)⋅X₂⋅X₅+3051757812500000⋅5^(15⋅X₅)⋅5^(2⋅X₅⋅log(X₂))⋅5^(2⋅X₅⋅log(X₄))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅log(X₂))⋅5^(2⋅log(X₄))⋅5^(2⋅log(X₅))⋅5^(2⋅log(X₅))⋅5^(4⋅X₅)⋅X₃⋅X₅+4768371582031250⋅5^(15⋅X₅)⋅5^(2⋅X₅⋅log(X₂))⋅5^(2⋅X₅⋅log(X₄))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅log(X₂))⋅5^(2⋅log(X₄))⋅5^(2⋅log(X₅))⋅5^(2⋅log(X₅))⋅5^(4⋅X₅)⋅X₂+5^(15⋅X₅)⋅5^(2⋅X₅⋅log(X₂))⋅5^(2⋅X₅⋅log(X₄))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅log(X₂))⋅5^(2⋅log(X₄))⋅5^(2⋅log(X₅))⋅5^(2⋅log(X₅))⋅5^(4⋅X₅)⋅6103515625000000⋅X₂⋅X₂⋅X₅+5^(15⋅X₅)⋅5^(2⋅X₅⋅log(X₂))⋅5^(2⋅X₅⋅log(X₄))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅log(X₂))⋅5^(2⋅log(X₄))⋅5^(2⋅log(X₅))⋅5^(2⋅log(X₅))⋅5^(4⋅X₅)⋅7247924804687500⋅X₂⋅X₂+5^(15⋅X₅)⋅5^(2⋅X₅⋅log(X₂))⋅5^(2⋅X₅⋅log(X₄))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅X₅⋅log(X₅))⋅5^(2⋅log(X₂))⋅5^(2⋅log(X₄))⋅5^(2⋅log(X₅))⋅5^(2⋅log(X₅))⋅5^(4⋅X₅)⋅9155273437500000⋅X₅+4⋅X₂⋅X₂+4⋅X₅⋅X₅+8⋅X₂⋅X₅ {O(EXP)}
t₃, X₁: 131072⋅2^(15⋅X₅)⋅2^(2⋅X₅⋅log(X₂))⋅2^(2⋅X₅⋅log(X₄))⋅2^(2⋅X₅⋅log(X₅))⋅2^(2⋅log(X₂))⋅2^(2⋅log(X₄))⋅2^(2⋅log(X₅))⋅X₄ {O(EXP)}
t₃, X₂: 2⋅X₂+2⋅X₅ {O(n)}
t₃, X₃: 2⋅X₂+2⋅X₅ {O(n)}
t₃, X₄: X₄ {O(n)}
t₃, X₅: X₅ {O(n)}
t₄, X₀: 4⋅X₂+4⋅X₅ {O(n)}
t₄, X₁: 2⋅X₄ {O(n)}
t₄, X₂: 2⋅X₅ {O(n)}
t₄, X₃: 4⋅X₂+4⋅X₅ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}