Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ (X₀)²+(X₄)⁵
t₆: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: (X₀)²+(X₄)⁵ < X₁ ∧ X₀ < 0
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: (X₀)²+(X₄)⁵ < X₁ ∧ 0 < X₀
t₈: l2(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₃, X₂, X₃, X₄) :|: 0 < X₄
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l1(-2⋅X₀, 3⋅X₁-2⋅(X₄)³, X₂, X₃, X₄)

Preprocessing

Found invariant 1 ≤ X₄ for location l1

Found invariant 1 ≤ X₄ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ (X₀)²+(X₄)⁵ ∧ 1 ≤ X₄
t₆: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₄
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: (X₀)²+(X₄)⁵ < X₁ ∧ X₀ < 0 ∧ 1 ≤ X₄
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: (X₀)²+(X₄)⁵ < X₁ ∧ 0 < X₀ ∧ 1 ≤ X₄
t₈: l2(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₃, X₂, X₃, X₄) :|: 0 < X₄
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ 0
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l1(-2⋅X₀, 3⋅X₁-2⋅(X₄)³, X₂, X₃, X₄) :|: 1 ≤ X₄

TWN: t₃: l1→l4

cycle: [t₃: l1→l4; t₄: l1→l4; t₇: l4→l1]
loop: ((X₀)²+(X₄)⁵ < X₁ ∧ X₀ < 0 ∨ (X₀)²+(X₄)⁵ < X₁ ∧ 0 < X₀,(X₀,X₁,X₄) -> (-2⋅X₀,3⋅X₁-2⋅(X₄)³,X₄)
order: [X₀; X₄; X₁]
closed-form:
X₀: X₀ * 4^n
X₄: X₄
X₁: X₁ * 9^n + [[n != 0]] * -(X₄)³ * 9^n + [[n != 0]] * (X₄)³

Termination: true
Formula:

0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0 ∧ X₀ < 0 ∧ (X₀)² < 0
∨ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0 ∧ X₀ < 0 ∧ (X₄)³ < X₁ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)²
∨ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0 ∧ X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)² ∧ (X₄)³ ≤ X₁ ∧ X₁ ≤ (X₄)³
∨ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ X₀ < 0 ∧ (X₀)² < 0
∨ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ X₀ < 0 ∧ (X₄)³ < X₁ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)²
∨ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)² ∧ (X₄)³ ≤ X₁ ∧ X₁ ≤ (X₄)³
∨ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³ ∧ X₀ < 0 ∧ (X₀)² < 0
∨ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³ ∧ X₀ < 0 ∧ (X₄)³ < X₁ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)²
∨ 0 < 2⋅X₀ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³ ∧ X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)² ∧ (X₄)³ ≤ X₁ ∧ X₁ ≤ (X₄)³
∨ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0 ∧ X₀ < 0 ∧ (X₀)² < 0
∨ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0 ∧ X₀ < 0 ∧ (X₄)³ < X₁ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)²
∨ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0 ∧ X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)² ∧ (X₄)³ ≤ X₁ ∧ X₁ ≤ (X₄)³
∨ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ X₀ < 0 ∧ (X₀)² < 0
∨ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ X₀ < 0 ∧ (X₄)³ < X₁ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)²
∨ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)² ∧ (X₄)³ ≤ X₁ ∧ X₁ ≤ (X₄)³
∨ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³ ∧ X₀ < 0 ∧ (X₀)² < 0
∨ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³ ∧ X₀ < 0 ∧ (X₄)³ < X₁ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)²
∨ 2⋅X₀ < 0 ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³ ∧ X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)² ∧ (X₄)³ ≤ X₁ ∧ X₁ ≤ (X₄)³
∨ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0 ∧ 0 < X₀ ∧ (X₀)² < 0
∨ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0 ∧ 0 < X₀ ∧ (X₄)³ < X₁ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)²
∨ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0 ∧ 0 < X₀ ∧ (X₄)⁵ < (X₄)³ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)² ∧ (X₄)³ ≤ X₁ ∧ X₁ ≤ (X₄)³
∨ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 0 < X₀ ∧ (X₀)² < 0
∨ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 0 < X₀ ∧ (X₄)³ < X₁ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)²
∨ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 0 < X₀ ∧ (X₄)⁵ < (X₄)³ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)² ∧ (X₄)³ ≤ X₁ ∧ X₁ ≤ (X₄)³
∨ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³ ∧ 0 < X₀ ∧ (X₀)² < 0
∨ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³ ∧ 0 < X₀ ∧ (X₄)³ < X₁ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)²
∨ 0 < 2⋅X₀ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³ ∧ 0 < X₀ ∧ (X₄)⁵ < (X₄)³ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)² ∧ (X₄)³ ≤ X₁ ∧ X₁ ≤ (X₄)³
∨ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0 ∧ 0 < X₀ ∧ (X₀)² < 0
∨ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0 ∧ 0 < X₀ ∧ (X₄)³ < X₁ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)²
∨ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0 ∧ 0 < X₀ ∧ (X₄)⁵ < (X₄)³ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)² ∧ (X₄)³ ≤ X₁ ∧ X₁ ≤ (X₄)³
∨ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 0 < X₀ ∧ (X₀)² < 0
∨ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 0 < X₀ ∧ (X₄)³ < X₁ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)²
∨ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 0 < X₀ ∧ (X₄)⁵ < (X₄)³ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)² ∧ (X₄)³ ≤ X₁ ∧ X₁ ≤ (X₄)³
∨ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³ ∧ 0 < X₀ ∧ (X₀)² < 0
∨ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³ ∧ 0 < X₀ ∧ (X₄)³ < X₁ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)²
∨ 2⋅X₀ < 0 ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³ ∧ 0 < X₀ ∧ (X₄)⁵ < (X₄)³ ∧ (X₀)² ≤ 0 ∧ 0 ≤ (X₀)² ∧ (X₄)³ ≤ X₁ ∧ X₁ ≤ (X₄)³

Stabilization-Threshold for: 4⋅(X₀)²+(X₄)⁵+2⋅(X₄)³ < 3⋅X₁
alphas_abs: 3⋅X₁+3⋅(X₄)³+(X₄)⁵
M: 0
N: 1
Bound: 2⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+6⋅X₄⋅X₄⋅X₄+6⋅X₁+2 {O(n^5)}
Stabilization-Threshold for: (X₀)²+(X₄)⁵ < X₁
alphas_abs: X₁+(X₄)³+(X₄)⁵
M: 0
N: 1
Bound: 2⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+2⋅X₄⋅X₄⋅X₄+2⋅X₁+2 {O(n^5)}

TWN - Lifting for t₃: l1→l4 of 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₁+21 {O(n^5)}

relevant size-bounds w.r.t. t₁:
X₁: X₃ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₃+21 {O(n^5)}

TWN: t₄: l1→l4

TWN - Lifting for t₄: l1→l4 of 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₁+21 {O(n^5)}

relevant size-bounds w.r.t. t₁:
X₁: X₃ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₃+21 {O(n^5)}

TWN: t₇: l4→l1

TWN - Lifting for t₇: l4→l1 of 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₁+21 {O(n^5)}

relevant size-bounds w.r.t. t₁:
X₁: X₃ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₃+21 {O(n^5)}

Chain transitions t₇: l4→l1 and t₄: l1→l4 to t₆₆: l4→l4

Chain transitions t₁: l3→l1 and t₄: l1→l4 to t₆₇: l3→l4

Chain transitions t₁: l3→l1 and t₃: l1→l4 to t₆₈: l3→l4

Chain transitions t₇: l4→l1 and t₃: l1→l4 to t₆₉: l4→l4

Chain transitions t₁: l3→l1 and t₆: l1→l2 to t₇₀: l3→l2

Chain transitions t₇: l4→l1 and t₆: l1→l2 to t₇₁: l4→l2

Chain transitions t₁: l3→l1 and t₅: l1→l2 to t₇₂: l3→l2

Chain transitions t₇: l4→l1 and t₅: l1→l2 to t₇₃: l4→l2

Analysing control-flow refined program

Cut unsatisfiable transition t₇₁: l4→l2

Found invariant 1 ≤ X₄ for location l1

Found invariant 1 ≤ X₄ for location l4

TWN: t₆₆: l4→l4

cycle: [t₆₆: l4→l4; t₆₉: l4→l4]
loop: (4⋅(X₀)²+(X₄)⁵+2⋅(X₄)³ < 3⋅X₁ ∧ 2⋅X₀ < 0 ∨ 4⋅(X₀)²+(X₄)⁵+2⋅(X₄)³ < 3⋅X₁ ∧ 0 < 2⋅X₀,(X₀,X₁,X₄) -> (-2⋅X₀,3⋅X₁-2⋅(X₄)³,X₄)
order: [X₀; X₄; X₁]
closed-form:
X₀: X₀ * 4^n
X₄: X₄
X₁: X₁ * 9^n + [[n != 0]] * -(X₄)³ * 9^n + [[n != 0]] * (X₄)³

Termination: true
Formula:

0 < 4⋅X₀ ∧ 16⋅(X₀)² < 0 ∧ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0
∨ 0 < 4⋅X₀ ∧ 16⋅(X₀)² < 0 ∧ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 0 < 4⋅X₀ ∧ 16⋅(X₀)² < 0 ∧ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 0 < 4⋅X₀ ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0
∨ 0 < 4⋅X₀ ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 0 < 4⋅X₀ ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 0 < 4⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0
∨ 0 < 4⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 0 < 4⋅X₀ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² < 0 ∧ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² < 0 ∧ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² < 0 ∧ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 4⋅X₀ < 0 ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0
∨ 4⋅X₀ < 0 ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 4⋅X₀ < 0 ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 4⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0
∨ 4⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 0 < 4⋅X₀ ∧ 16⋅(X₀)² < 0 ∧ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0
∨ 0 < 4⋅X₀ ∧ 16⋅(X₀)² < 0 ∧ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 0 < 4⋅X₀ ∧ 16⋅(X₀)² < 0 ∧ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 0 < 4⋅X₀ ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0
∨ 0 < 4⋅X₀ ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 0 < 4⋅X₀ ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 0 < 4⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0
∨ 0 < 4⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 0 < 4⋅X₀ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² < 0 ∧ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² < 0 ∧ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² < 0 ∧ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 4⋅X₀ < 0 ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0
∨ 4⋅X₀ < 0 ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 4⋅X₀ < 0 ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 4⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0
∨ 4⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³

Stabilization-Threshold for: 16⋅(X₀)²+(X₄)⁵+8⋅(X₄)³ < 9⋅X₁
alphas_abs: 9⋅X₁+9⋅(X₄)³+(X₄)⁵
M: 0
N: 1
Bound: 2⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+18⋅X₄⋅X₄⋅X₄+18⋅X₁+2 {O(n^5)}
Stabilization-Threshold for: 4⋅(X₀)²+(X₄)⁵+2⋅(X₄)³ < 3⋅X₁
alphas_abs: 3⋅X₁+3⋅(X₄)³+(X₄)⁵
M: 0
N: 1
Bound: 2⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+6⋅X₄⋅X₄⋅X₄+6⋅X₁+2 {O(n^5)}
loop: (4⋅(X₀)²+(X₄)⁵+2⋅(X₄)³ < 3⋅X₁ ∧ 2⋅X₀ < 0 ∨ 4⋅(X₀)²+(X₄)⁵+2⋅(X₄)³ < 3⋅X₁ ∧ 0 < 2⋅X₀,(X₀,X₁,X₄) -> (-2⋅X₀,3⋅X₁-2⋅(X₄)³,X₄)
order: [X₀; X₄; X₁]
closed-form:
X₀: X₀ * 4^n
X₄: X₄
X₁: X₁ * 9^n + [[n != 0]] * -(X₄)³ * 9^n + [[n != 0]] * (X₄)³

Termination: true
Formula:

0 < 4⋅X₀ ∧ 16⋅(X₀)² < 0 ∧ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0
∨ 0 < 4⋅X₀ ∧ 16⋅(X₀)² < 0 ∧ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 0 < 4⋅X₀ ∧ 16⋅(X₀)² < 0 ∧ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 0 < 4⋅X₀ ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0
∨ 0 < 4⋅X₀ ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 0 < 4⋅X₀ ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 0 < 4⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0
∨ 0 < 4⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 0 < 4⋅X₀ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² < 0 ∧ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² < 0 ∧ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² < 0 ∧ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 4⋅X₀ < 0 ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0
∨ 4⋅X₀ < 0 ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 4⋅X₀ < 0 ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 4⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 2⋅X₀ < 0 ∧ 4⋅(X₀)² < 0
∨ 4⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 2⋅X₀ < 0 ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 2⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 0 < 4⋅X₀ ∧ 16⋅(X₀)² < 0 ∧ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0
∨ 0 < 4⋅X₀ ∧ 16⋅(X₀)² < 0 ∧ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 0 < 4⋅X₀ ∧ 16⋅(X₀)² < 0 ∧ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 0 < 4⋅X₀ ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0
∨ 0 < 4⋅X₀ ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 0 < 4⋅X₀ ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 0 < 4⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0
∨ 0 < 4⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 0 < 4⋅X₀ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² < 0 ∧ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² < 0 ∧ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² < 0 ∧ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 4⋅X₀ < 0 ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0
∨ 4⋅X₀ < 0 ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 4⋅X₀ < 0 ∧ 9⋅(X₄)³ < 9⋅X₁ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³
∨ 4⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₀ ∧ 4⋅(X₀)² < 0
∨ 4⋅X₀ < 0 ∧ (X₄)⁵ < (X₄)³ ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₀ ∧ 3⋅(X₄)³ < 3⋅X₁ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)²
∨ 4⋅X₀ < 0 ∧ 16⋅(X₀)² ≤ 0 ∧ 0 ≤ 16⋅(X₀)² ∧ 9⋅(X₄)³ ≤ 9⋅X₁ ∧ 9⋅X₁ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₀ ∧ (X₄)⁵ < (X₄)³ ∧ 4⋅(X₀)² ≤ 0 ∧ 0 ≤ 4⋅(X₀)² ∧ 3⋅(X₄)³ ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 3⋅(X₄)³

Stabilization-Threshold for: 16⋅(X₀)²+(X₄)⁵+8⋅(X₄)³ < 9⋅X₁
alphas_abs: 9⋅X₁+9⋅(X₄)³+(X₄)⁵
M: 0
N: 1
Bound: 2⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+18⋅X₄⋅X₄⋅X₄+18⋅X₁+2 {O(n^5)}
Stabilization-Threshold for: 4⋅(X₀)²+(X₄)⁵+2⋅(X₄)³ < 3⋅X₁
alphas_abs: 3⋅X₁+3⋅(X₄)³+(X₄)⁵
M: 0
N: 1
Bound: 2⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+6⋅X₄⋅X₄⋅X₄+6⋅X₁+2 {O(n^5)}

TWN - Lifting for t₆₆: l4→l4 of 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+48⋅X₁+21 {O(n^5)}

relevant size-bounds w.r.t. t₆₈:
X₁: X₃ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₆₈: 1 {O(1)}
Results in: 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+48⋅X₃+21 {O(n^5)}

TWN - Lifting for t₆₆: l4→l4 of 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+48⋅X₁+21 {O(n^5)}

relevant size-bounds w.r.t. t₆₇:
X₁: X₃ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₆₇: 1 {O(1)}
Results in: 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+48⋅X₃+21 {O(n^5)}

TWN: t₆₉: l4→l4

TWN - Lifting for t₆₉: l4→l4 of 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+48⋅X₁+21 {O(n^5)}

relevant size-bounds w.r.t. t₆₈:
X₁: X₃ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₆₈: 1 {O(1)}
Results in: 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+48⋅X₃+21 {O(n^5)}

TWN - Lifting for t₆₉: l4→l4 of 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+48⋅X₁+21 {O(n^5)}

relevant size-bounds w.r.t. t₆₇:
X₁: X₃ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₆₇: 1 {O(1)}
Results in: 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+48⋅X₃+21 {O(n^5)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Cut unsatisfiable transition t₂₀₆: n_l1___1→l2

Cut unsatisfiable transition t₂₀₇: n_l1___2→l2

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location n_l4___3

Found invariant 1 ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location n_l4___4

Found invariant 1 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₀ for location n_l1___2

Found invariant 1 ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

Found invariant 1 ≤ X₄ ∧ 3+X₀ ≤ X₄ ∧ 1+X₀+X₂ ≤ 0 ∧ 2+X₀ ≤ X₂ ∧ 2+X₀ ≤ 0 for location n_l1___1

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:24⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+48⋅X₃+69 {O(n^5)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₃+21 {O(n^5)}
t₄: 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₃+21 {O(n^5)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₃+21 {O(n^5)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: 24⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+48⋅X₃+69 {O(n^5)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₃+21 {O(n^5)}
t₄: 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₃+21 {O(n^5)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₃+21 {O(n^5)}
t₈: 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)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: 2^(8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₃+21)⋅X₂ {O(EXP)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₄, X₀: 2^(8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₃+21)⋅X₂ {O(EXP)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: 2^(8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₃+21)⋅X₂+X₂ {O(EXP)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₆, X₀: 0 {O(1)}
t₆, X₂: 2⋅X₂ {O(n)}
t₆, X₃: 2⋅X₃ {O(n)}
t₆, X₄: 2⋅X₄ {O(n)}
t₇, X₀: 2^(8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₃+21)⋅X₂ {O(EXP)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₈, X₀: 2^(8⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄+16⋅X₃+21)⋅X₂+X₀+X₂ {O(EXP)}
t₈, X₂: 5⋅X₂ {O(n)}
t₈, X₃: 5⋅X₃ {O(n)}
t₈, X₄: 5⋅X₄ {O(n)}