Initial Problem

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

Preprocessing

Found invariant X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Found invariant 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ for location l4

Found invariant 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₀, X₄, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ X₃ ≤ 5
t₁: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 0 < X₀ ∧ 0 < X₃
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 0 < X₀ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₇: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, -2⋅X₁, X₂, X₃, X₄) :|: (X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0 ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, -2⋅X₁, X₂, X₃, X₄) :|: (X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, 3⋅X₂-2⋅(X₃)³, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀

TWN. Size Bound: t₆: l4→l3 for X₂

cycle: [t₄: l3→l4; t₅: l3→l4; t₆: l4→l3]
loop: ((X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂ ∧ X₁ < 0 ∨ (X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂ ∧ 0 < X₁,(X₀,X₁,X₂,X₃,X₄) -> (X₀,-2⋅X₁,3⋅X₂-2⋅(X₃)³,X₃,X₄)
order: [X₀; X₁; X₃; X₂; X₄]
closed-form:
X₀: X₀
X₁: X₁ * 4^n
X₃: X₃
X₂: X₂ * 9^n + [[n != 0]] * -(X₃)³ * 9^n + [[n != 0]] * (X₃)³
X₄: X₄
Stabilization-Threshold for: 4⋅(X₁)²+(X₃)⁵+8⋅(X₃)³ < 9⋅X₂
alphas_abs: 9⋅X₂+9⋅(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+18⋅X₃⋅X₃⋅X₃+18⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: (X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂
alphas_abs: 3⋅X₂+3⋅(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+6⋅X₃⋅X₃⋅X₃+6⋅X₂+2 {O(n^5)}
loop: ((X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂ ∧ X₁ < 0 ∨ (X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂ ∧ 0 < X₁,(X₂,X₃) -> (3⋅X₂-2⋅(X₃)³,X₃)
closed-form: X₂ * 3^n + [[n != 0]] * -(X₃)³ * 3^n + [[n != 0]] * (X₃)³
runtime bound: 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+48⋅X₃⋅X₃⋅X₃+48⋅X₂+21 {O(n^5)}

TWN Size Bound - Lifting for t₆: l4→l3 and X₂: 125⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2048⋅X₃⋅X₃⋅X₃+10720⋅X₃⋅X₃+28600⋅X₃+96⋅X₄+31021)+125⋅3^(96⋅X₄+31021)+15⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2048⋅X₃⋅X₃⋅X₃+10720⋅X₃⋅X₃+28600⋅X₃+96⋅X₄+31021)⋅X₃⋅X₃+2⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2048⋅X₃⋅X₃⋅X₃+10720⋅X₃⋅X₃+28600⋅X₃+96⋅X₄+31021)⋅X₄+2⋅3^(96⋅X₄+31021)⋅X₄+3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2048⋅X₃⋅X₃⋅X₃+10720⋅X₃⋅X₃+28600⋅X₃+96⋅X₄+31021)⋅75⋅X₃+3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2048⋅X₃⋅X₃⋅X₃+10720⋅X₃⋅X₃+28600⋅X₃+96⋅X₄+31021)⋅X₃⋅X₃⋅X₃+X₃⋅X₃⋅X₃+15⋅X₃⋅X₃+75⋅X₃+250 {O(EXP)}

Solv. Size Bound: t₇: l3→l1 for X₁

Solv. Size Bound: t₇: l3→l1 for X₂

cycle: [t₇: l3→l1; t₂: l1→l2; t₃: l2→l3]
loop: (0 ≤ 5+X₃ ∧ X₃ ≤ 5 ∧ 1 < X₀,(X₂,X₄) -> (X₄,X₄)
overappr. closed-form: 2⋅X₄ {O(n)}
runtime bound: X₀+1 {O(n)}

Solv. Size Bound - Lifting for t₇: l3→l1 and X₂: 6⋅X₄ {O(n)}

MPRF for transition t₁: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 0 < X₀ ∧ 0 < X₃ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 0 < X₀ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₇: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

TWN: t₄: l3→l4

cycle: [t₄: l3→l4; t₅: l3→l4; t₆: l4→l3]
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0 ∨ (X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁,(X₁,X₂,X₃) -> (-2⋅X₁,3⋅X₂-2⋅(X₃)³,X₃)
order: [X₁; X₃; X₂]
closed-form:
X₁: X₁ * 4^n
X₃: X₃
X₂: X₂ * 9^n + [[n != 0]] * -(X₃)³ * 9^n + [[n != 0]] * (X₃)³

Termination: true
Formula:

0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³

Stabilization-Threshold for: 4⋅(X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂
alphas_abs: 3⋅X₂+3⋅(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+6⋅X₃⋅X₃⋅X₃+6⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: (X₁)²+(X₃)⁵ < X₂
alphas_abs: X₂+(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+2⋅X₃⋅X₃⋅X₃+2⋅X₂+2 {O(n^5)}
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0 ∨ (X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁,(X₁,X₂,X₃) -> (-2⋅X₁,3⋅X₂-2⋅(X₃)³,X₃)
order: [X₁; X₃; X₂]
closed-form:
X₁: X₁ * 4^n
X₃: X₃
X₂: X₂ * 9^n + [[n != 0]] * -(X₃)³ * 9^n + [[n != 0]] * (X₃)³

Termination: true
Formula:

0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³

Stabilization-Threshold for: 4⋅(X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂
alphas_abs: 3⋅X₂+3⋅(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+6⋅X₃⋅X₃⋅X₃+6⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: (X₁)²+(X₃)⁵ < X₂
alphas_abs: X₂+(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+2⋅X₃⋅X₃⋅X₃+2⋅X₂+2 {O(n^5)}

TWN - Lifting for t₄: l3→l4 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

relevant size-bounds w.r.t. t₃:
X₂: 2⋅X₄ {O(n)}
X₃: 5 {O(1)}
Runtime-bound of t₃: X₀ {O(n)}
Results in: 32⋅X₀⋅X₄+27021⋅X₀ {O(n^2)}

TWN - Lifting for t₄: l3→l4 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

relevant size-bounds w.r.t. t₁:
X₂: 2⋅X₄ {O(n)}
X₃: X₃+5 {O(n)}
Runtime-bound of t₁: X₀ {O(n)}
Results in: 8⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₀⋅X₃⋅X₃⋅X₃+10240⋅X₀⋅X₃⋅X₃+26200⋅X₀⋅X₃+32⋅X₀⋅X₄+27021⋅X₀ {O(n^6)}

TWN: t₅: l3→l4

TWN - Lifting for t₅: l3→l4 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

relevant size-bounds w.r.t. t₃:
X₂: 2⋅X₄ {O(n)}
X₃: 5 {O(1)}
Runtime-bound of t₃: X₀ {O(n)}
Results in: 32⋅X₀⋅X₄+27021⋅X₀ {O(n^2)}

TWN - Lifting for t₅: l3→l4 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

relevant size-bounds w.r.t. t₁:
X₂: 2⋅X₄ {O(n)}
X₃: X₃+5 {O(n)}
Runtime-bound of t₁: X₀ {O(n)}
Results in: 8⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₀⋅X₃⋅X₃⋅X₃+10240⋅X₀⋅X₃⋅X₃+26200⋅X₀⋅X₃+32⋅X₀⋅X₄+27021⋅X₀ {O(n^6)}

TWN: t₆: l4→l3

TWN - Lifting for t₆: l4→l3 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

relevant size-bounds w.r.t. t₃:
X₂: 2⋅X₄ {O(n)}
X₃: 5 {O(1)}
Runtime-bound of t₃: X₀ {O(n)}
Results in: 32⋅X₀⋅X₄+27021⋅X₀ {O(n^2)}

TWN - Lifting for t₆: l4→l3 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

relevant size-bounds w.r.t. t₁:
X₂: 2⋅X₄ {O(n)}
X₃: X₃+5 {O(n)}
Runtime-bound of t₁: X₀ {O(n)}
Results in: 8⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃+2016⋅X₀⋅X₃⋅X₃⋅X₃+10240⋅X₀⋅X₃⋅X₃+26200⋅X₀⋅X₃+32⋅X₀⋅X₄+27021⋅X₀ {O(n^6)}

knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₂: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₀, X₄, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ X₃ ≤ 5

TWN Size Bound - Lifting for t₆: l4→l3 and X₂: 125⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2048⋅X₃⋅X₃⋅X₃+10720⋅X₃⋅X₃+28600⋅X₃+96⋅X₄+31021)+125⋅3^(96⋅X₄+31021)+15⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2048⋅X₃⋅X₃⋅X₃+10720⋅X₃⋅X₃+28600⋅X₃+96⋅X₄+31021)⋅X₃⋅X₃+2⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2048⋅X₃⋅X₃⋅X₃+10720⋅X₃⋅X₃+28600⋅X₃+96⋅X₄+31021)⋅X₄+2⋅3^(96⋅X₄+31021)⋅X₄+3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2048⋅X₃⋅X₃⋅X₃+10720⋅X₃⋅X₃+28600⋅X₃+96⋅X₄+31021)⋅75⋅X₃+3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+200⋅X₃⋅X₃⋅X₃⋅X₃+2048⋅X₃⋅X₃⋅X₃+10720⋅X₃⋅X₃+28600⋅X₃+96⋅X₄+31021)⋅X₃⋅X₃⋅X₃+X₃⋅X₃⋅X₃+15⋅X₃⋅X₃+75⋅X₃+250 {O(EXP)}

Chain transitions t₇: l3→l1 and t₁: l1→l3 to t₁₀₃: l3→l3

Chain transitions t₀: l0→l1 and t₁: l1→l3 to t₁₀₄: l0→l3

Chain transitions t₀: l0→l1 and t₂: l1→l2 to t₁₀₅: l0→l2

Chain transitions t₇: l3→l1 and t₂: l1→l2 to t₁₀₆: l3→l2

Chain transitions t₁₀₆: l3→l2 and t₃: l2→l3 to t₁₀₇: l3→l3

Chain transitions t₁₀₅: l0→l2 and t₃: l2→l3 to t₁₀₈: l0→l3

Chain transitions t₅: l3→l4 and t₆: l4→l3 to t₁₀₉: l3→l3

Chain transitions t₄: l3→l4 and t₆: l4→l3 to t₁₁₀: l3→l3

Analysing control-flow refined program

Found invariant X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Found invariant 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ for location l4

Found invariant 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ for location l3

TWN. Size Bound: t₁₀₉: l3→l3 for X₂

cycle: [t₁₀₉: l3→l3; t₁₁₀: l3→l3]
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁ ∨ (X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0,(X₀,X₁,X₂,X₃,X₄) -> (X₀,-2⋅X₁,3⋅X₂-2⋅(X₃)³,X₃,X₄)
order: [X₀; X₁; X₃; X₂; X₄]
closed-form:
X₀: X₀
X₁: X₁ * 4^n
X₃: X₃
X₂: X₂ * 9^n + [[n != 0]] * -(X₃)³ * 9^n + [[n != 0]] * (X₃)³
X₄: X₄
Stabilization-Threshold for: 4⋅(X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂
alphas_abs: 3⋅X₂+3⋅(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+6⋅X₃⋅X₃⋅X₃+6⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: (X₁)²+(X₃)⁵ < X₂
alphas_abs: X₂+(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+2⋅X₃⋅X₃⋅X₃+2⋅X₂+2 {O(n^5)}
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁ ∨ (X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0,(X₂,X₃) -> (3⋅X₂-2⋅(X₃)³,X₃)
closed-form: X₂ * 3^n + [[n != 0]] * -(X₃)³ * 3^n + [[n != 0]] * (X₃)³
runtime bound: 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

TWN Size Bound - Lifting for t₁₀₉: l3→l3 and X₂: 2⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₄+21)⋅X₃⋅X₃⋅X₃+2⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₄+21)⋅X₄+3^(256⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+384⋅X₃⋅X₃⋅X₃+480⋅X₄+21)⋅48⋅X₃⋅X₃⋅X₃+3^(256⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+384⋅X₃⋅X₃⋅X₃+480⋅X₄+21)⋅60⋅X₄+18⋅X₃⋅X₃⋅X₃ {O(EXP)}

TWN. Size Bound: t₁₁₀: l3→l3 for X₂

cycle: [t₁₀₉: l3→l3; t₁₁₀: l3→l3]
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁ ∨ (X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0,(X₀,X₁,X₂,X₃,X₄) -> (X₀,-2⋅X₁,3⋅X₂-2⋅(X₃)³,X₃,X₄)
order: [X₀; X₁; X₃; X₂; X₄]
closed-form:
X₀: X₀
X₁: X₁ * 4^n
X₃: X₃
X₂: X₂ * 9^n + [[n != 0]] * -(X₃)³ * 9^n + [[n != 0]] * (X₃)³
X₄: X₄
Stabilization-Threshold for: 4⋅(X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂
alphas_abs: 3⋅X₂+3⋅(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+6⋅X₃⋅X₃⋅X₃+6⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: (X₁)²+(X₃)⁵ < X₂
alphas_abs: X₂+(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+2⋅X₃⋅X₃⋅X₃+2⋅X₂+2 {O(n^5)}
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁ ∨ (X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0,(X₂,X₃) -> (3⋅X₂-2⋅(X₃)³,X₃)
closed-form: X₂ * 3^n + [[n != 0]] * -(X₃)³ * 3^n + [[n != 0]] * (X₃)³
runtime bound: 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

TWN Size Bound - Lifting for t₁₁₀: l3→l3 and X₂: 2⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₄+21)⋅X₃⋅X₃⋅X₃+2⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₄+21)⋅X₄+3^(256⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+384⋅X₃⋅X₃⋅X₃+480⋅X₄+21)⋅48⋅X₃⋅X₃⋅X₃+3^(256⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+384⋅X₃⋅X₃⋅X₃+480⋅X₄+21)⋅60⋅X₄+18⋅X₃⋅X₃⋅X₃ {O(EXP)}

MPRF for transition t₁₀₃: l3(X₀, X₁, X₂, X₃, X₄) -{2}> l3(X₀-1, X₀-1, X₄, X₃, X₄) :|: 1 < X₀ ∧ 0 < X₃ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀ {O(n)}

MPRF for transition t₁₀₇: l3(X₀, X₁, X₂, X₃, X₄) -{3}> l3(X₀-1, X₀-1, X₄, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ X₃ ≤ 5 ∧ 1 < X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₀ {O(n)}

TWN: t₁₀₉: l3→l3

cycle: [t₁₀₉: l3→l3; t₁₁₀: l3→l3]
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁ ∨ (X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0,(X₁,X₂,X₃) -> (-2⋅X₁,3⋅X₂-2⋅(X₃)³,X₃)
order: [X₁; X₃; X₂]
closed-form:
X₁: X₁ * 4^n
X₃: X₃
X₂: X₂ * 9^n + [[n != 0]] * -(X₃)³ * 9^n + [[n != 0]] * (X₃)³

Termination: true
Formula:

2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³

Stabilization-Threshold for: 4⋅(X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂
alphas_abs: 3⋅X₂+3⋅(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+6⋅X₃⋅X₃⋅X₃+6⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: (X₁)²+(X₃)⁵ < X₂
alphas_abs: X₂+(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+2⋅X₃⋅X₃⋅X₃+2⋅X₂+2 {O(n^5)}
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁ ∨ (X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0,(X₁,X₂,X₃) -> (-2⋅X₁,3⋅X₂-2⋅(X₃)³,X₃)
order: [X₁; X₃; X₂]
closed-form:
X₁: X₁ * 4^n
X₃: X₃
X₂: X₂ * 9^n + [[n != 0]] * -(X₃)³ * 9^n + [[n != 0]] * (X₃)³

Termination: true
Formula:

2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³

Stabilization-Threshold for: 4⋅(X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂
alphas_abs: 3⋅X₂+3⋅(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+6⋅X₃⋅X₃⋅X₃+6⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: (X₁)²+(X₃)⁵ < X₂
alphas_abs: X₂+(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+2⋅X₃⋅X₃⋅X₃+2⋅X₂+2 {O(n^5)}
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁ ∨ (X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0,(X₁,X₂,X₃) -> (-2⋅X₁,3⋅X₂-2⋅(X₃)³,X₃)
order: [X₁; X₃; X₂]
closed-form:
X₁: X₁ * 4^n
X₃: X₃
X₂: X₂ * 9^n + [[n != 0]] * -(X₃)³ * 9^n + [[n != 0]] * (X₃)³

Termination: true
Formula:

2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³

Stabilization-Threshold for: 4⋅(X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂
alphas_abs: 3⋅X₂+3⋅(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+6⋅X₃⋅X₃⋅X₃+6⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: (X₁)²+(X₃)⁵ < X₂
alphas_abs: X₂+(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+2⋅X₃⋅X₃⋅X₃+2⋅X₂+2 {O(n^5)}
loop: ((X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁ ∨ (X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0,(X₁,X₂,X₃) -> (-2⋅X₁,3⋅X₂-2⋅(X₃)³,X₃)
order: [X₁; X₃; X₂]
closed-form:
X₁: X₁ * 4^n
X₃: X₃
X₂: X₂ * 9^n + [[n != 0]] * -(X₃)³ * 9^n + [[n != 0]] * (X₃)³

Termination: true
Formula:

2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ 0 < X₁ ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 2⋅X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² < 0 ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 3⋅(X₃)³ < 3⋅X₂ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₁)² < 0
∨ 0 < 2⋅X₁ ∧ (X₃)⁵ < (X₃)³ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)³ < X₂ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)²
∨ 0 < 2⋅X₁ ∧ 4⋅(X₁)² ≤ 0 ∧ 0 ≤ 4⋅(X₁)² ∧ 3⋅(X₃)³ ≤ 3⋅X₂ ∧ 3⋅X₂ ≤ 3⋅(X₃)³ ∧ X₁ < 0 ∧ (X₃)⁵ < (X₃)³ ∧ (X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₃)³ ≤ X₂ ∧ X₂ ≤ (X₃)³

Stabilization-Threshold for: 4⋅(X₁)²+(X₃)⁵+2⋅(X₃)³ < 3⋅X₂
alphas_abs: 3⋅X₂+3⋅(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+6⋅X₃⋅X₃⋅X₃+6⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: (X₁)²+(X₃)⁵ < X₂
alphas_abs: X₂+(X₃)³+(X₃)⁵
M: 0
N: 1
Bound: 2⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+2⋅X₃⋅X₃⋅X₃+2⋅X₂+2 {O(n^5)}

TWN - Lifting for t₁₀₉: l3→l3 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

relevant size-bounds w.r.t. t₁₀₇:
X₂: 10⋅X₄ {O(n)}
X₃: 2⋅X₃ {O(n)}
Runtime-bound of t₁₀₇: 2⋅X₀ {O(n)}
Results in: 512⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+256⋅X₀⋅X₃⋅X₃⋅X₃+320⋅X₀⋅X₄+42⋅X₀ {O(n^6)}

TWN - Lifting for t₁₀₉: l3→l3 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

relevant size-bounds w.r.t. t₁₀₃:
X₂: 10⋅X₄ {O(n)}
X₃: 2⋅X₃ {O(n)}
Runtime-bound of t₁₀₃: 2⋅X₀ {O(n)}
Results in: 512⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+256⋅X₀⋅X₃⋅X₃⋅X₃+320⋅X₀⋅X₄+42⋅X₀ {O(n^6)}

TWN - Lifting for t₁₀₉: l3→l3 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

relevant size-bounds w.r.t. t₁₀₈:
X₂: X₄ {O(n)}
X₃: X₃ {O(n)}
Runtime-bound of t₁₀₈: 1 {O(1)}
Results in: 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₄+21 {O(n^5)}

TWN - Lifting for t₁₀₉: l3→l3 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

relevant size-bounds w.r.t. t₁₀₄:
X₂: X₄ {O(n)}
X₃: X₃ {O(n)}
Runtime-bound of t₁₀₄: 1 {O(1)}
Results in: 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₄+21 {O(n^5)}

TWN: t₁₁₀: l3→l3

TWN - Lifting for t₁₁₀: l3→l3 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

relevant size-bounds w.r.t. t₁₀₇:
X₂: 10⋅X₄ {O(n)}
X₃: 2⋅X₃ {O(n)}
Runtime-bound of t₁₀₇: 2⋅X₀ {O(n)}
Results in: 512⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+256⋅X₀⋅X₃⋅X₃⋅X₃+320⋅X₀⋅X₄+42⋅X₀ {O(n^6)}

TWN - Lifting for t₁₁₀: l3→l3 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

relevant size-bounds w.r.t. t₁₀₃:
X₂: 10⋅X₄ {O(n)}
X₃: 2⋅X₃ {O(n)}
Runtime-bound of t₁₀₃: 2⋅X₀ {O(n)}
Results in: 512⋅X₀⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+256⋅X₀⋅X₃⋅X₃⋅X₃+320⋅X₀⋅X₄+42⋅X₀ {O(n^6)}

TWN - Lifting for t₁₁₀: l3→l3 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

relevant size-bounds w.r.t. t₁₀₈:
X₂: X₄ {O(n)}
X₃: X₃ {O(n)}
Runtime-bound of t₁₀₈: 1 {O(1)}
Results in: 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₄+21 {O(n^5)}

TWN - Lifting for t₁₁₀: l3→l3 of 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₂+21 {O(n^5)}

relevant size-bounds w.r.t. t₁₀₄:
X₂: X₄ {O(n)}
X₃: X₃ {O(n)}
Runtime-bound of t₁₀₄: 1 {O(1)}
Results in: 8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₄+21 {O(n^5)}

TWN Size Bound - Lifting for t₁₀₉: l3→l3 and X₂: 2⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₄+21)⋅X₃⋅X₃⋅X₃+2⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₄+21)⋅X₄+3^(256⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+384⋅X₃⋅X₃⋅X₃+480⋅X₄+21)⋅48⋅X₃⋅X₃⋅X₃+3^(256⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+384⋅X₃⋅X₃⋅X₃+480⋅X₄+21)⋅60⋅X₄+18⋅X₃⋅X₃⋅X₃ {O(EXP)}

TWN Size Bound - Lifting for t₁₁₀: l3→l3 and X₂: 2⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₄+21)⋅X₃⋅X₃⋅X₃+2⋅3^(8⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16⋅X₃⋅X₃⋅X₃+16⋅X₄+21)⋅X₄+3^(256⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+384⋅X₃⋅X₃⋅X₃+480⋅X₄+21)⋅48⋅X₃⋅X₃⋅X₃+3^(256⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+384⋅X₃⋅X₃⋅X₃+480⋅X₄+21)⋅60⋅X₄+18⋅X₃⋅X₃⋅X₃ {O(EXP)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Found invariant 0 ≤ 5+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___2

Found invariant 0 ≤ 5+X₃ ∧ X₁ ≤ 3+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location n_l4___4

Found invariant 0 ≤ 5+X₃ ∧ X₁ ≤ 3+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location n_l3___3

Found invariant 0 ≤ 5+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___1

Found invariant X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3

knowledge_propagation leads to new time bound 2⋅X₀ {O(n)} for transition t₂₉₆: l3(X₀, X₁, X₂, X₃, X₄) → n_l4___4(X₀, -2⋅X₁, X₂, X₃, X₄) :|: 0 < X₁ ∧ 0 < X₁ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 5+X₃ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

MPRF for transition t₃₀₄: n_l3___1(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀+4 {O(n)}

MPRF for transition t₃₀₅: n_l3___3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ 3+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

TWN: t₂₉₄: n_l3___1→n_l4___4

cycle: [t₂₉₇: n_l4___2→n_l3___1; t₂₉₅: n_l3___3→n_l4___2; t₂₉₈: n_l4___4→n_l3___3; t₂₉₄: n_l3___1→n_l4___4]
loop: (X₁ < 0 ∧ 0 < X₁ ∧ 0 < X₁ ∧ 2⋅X₁ < 0 ∧ 0 < 2⋅X₁ ∧ 0 < 2⋅X₁,(X₁) -> (4⋅X₁)
order: [X₁]
closed-form:
X₁: X₁ * 4^n

Termination: true
Formula:

0 < 2⋅X₁ ∧ 2⋅X₁ < 0 ∧ 0 < X₁ ∧ X₁ < 0

TWN - Lifting for t₂₉₄: n_l3___1→n_l4___4 of 6 {O(1)}

relevant size-bounds w.r.t. t₂₉₆:
Runtime-bound of t₂₉₆: 2⋅X₀ {O(n)}
Results in: 12⋅X₀ {O(n)}

TWN: t₂₉₅: n_l3___3→n_l4___2

TWN - Lifting for t₂₉₅: n_l3___3→n_l4___2 of 6 {O(1)}

relevant size-bounds w.r.t. t₂₉₆:
Runtime-bound of t₂₉₆: 2⋅X₀ {O(n)}
Results in: 12⋅X₀ {O(n)}

TWN: t₂₉₇: n_l4___2→n_l3___1

TWN - Lifting for t₂₉₇: n_l4___2→n_l3___1 of 6 {O(1)}

relevant size-bounds w.r.t. t₂₉₆:
Runtime-bound of t₂₉₆: 2⋅X₀ {O(n)}
Results in: 12⋅X₀ {O(n)}

TWN: t₂₉₈: n_l4___4→n_l3___3

TWN - Lifting for t₂₉₈: n_l4___4→n_l3___3 of 6 {O(1)}

relevant size-bounds w.r.t. t₂₉₆:
Runtime-bound of t₂₉₆: 2⋅X₀ {O(n)}
Results in: 12⋅X₀ {O(n)}

CFR did not improve the program. Rolling back

CFR: Improvement to new bound with the following program:

new bound:

56⋅X₀+5 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: Arg0_P, Arg3_P, NoDet0
Locations: l0, l1, l2, l3, n_l3___1, n_l3___3, n_l4___2, n_l4___4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₀, X₄, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ X₃ ≤ 5
t₁: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 0 < X₀ ∧ 0 < X₃
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 0 < X₀ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 5 ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₇: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₉₆: l3(X₀, X₁, X₂, X₃, X₄) → n_l4___4(X₀, -2⋅X₁, X₂, X₃, X₄) :|: 0 < X₁ ∧ 0 < X₁ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 5+X₃ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₂ ∧ X₂ ≤ X₄ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₃₀₄: n_l3___1(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₉₄: n_l3___1(X₀, X₁, X₂, X₃, X₄) → n_l4___4(X₀, -2⋅X₁, X₂, X₃, X₄) :|: 0 < X₁ ∧ 0 < X₁ ∧ 0 ≤ 5+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 5+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₃₀₅: n_l3___3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄) :|: 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ 3+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀
t₂₉₅: n_l3___3(X₀, X₁, X₂, X₃, X₄) → n_l4___2(X₀, -2⋅X₁, X₂, Arg3_P, X₄) :|: X₁ < 0 ∧ X₁ < 0 ∧ 0 ≤ 5+Arg3_P ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 0 ≤ 5+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ 3+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀
t₂₉₇: n_l4___2(X₀, X₁, X₂, X₃, X₄) → n_l3___1(Arg0_P, X₁, NoDet0, Arg3_P, X₄) :|: 0 < X₁ ∧ 0 ≤ 5+Arg3_P ∧ 1 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 0 ≤ 5+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₉₈: n_l4___4(X₀, X₁, X₂, X₃, X₄) → n_l3___3(Arg0_P, X₁, NoDet0, Arg3_P, X₄) :|: X₁ < 0 ∧ 0 ≤ 5+Arg3_P ∧ 1 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 0 ≤ 5+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ X₁ ≤ 3+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀

All Bounds

Timebounds

Overall timebound:56⋅X₀+6 {O(n)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: X₀+1 {O(n)}
t₃: X₀ {O(n)}
t₇: X₀ {O(n)}
t₂₉₄: 12⋅X₀ {O(n)}
t₂₉₅: 12⋅X₀ {O(n)}
t₂₉₆: 2⋅X₀ {O(n)}
t₂₉₇: 12⋅X₀ {O(n)}
t₂₉₈: 12⋅X₀ {O(n)}
t₃₀₄: X₀+4 {O(n)}
t₃₀₅: X₀ {O(n)}

Costbounds

Overall costbound: 56⋅X₀+6 {O(n)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: X₀+1 {O(n)}
t₃: X₀ {O(n)}
t₇: X₀ {O(n)}
t₂₉₄: 12⋅X₀ {O(n)}
t₂₉₅: 12⋅X₀ {O(n)}
t₂₉₆: 2⋅X₀ {O(n)}
t₂₉₇: 12⋅X₀ {O(n)}
t₂₉₈: 12⋅X₀ {O(n)}
t₃₀₄: X₀+4 {O(n)}
t₃₀₅: X₀ {O(n)}

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: X₀ {O(n)}
t₁, X₁: 4⋅X₀ {O(n)}
t₁, X₂: 4⋅X₄ {O(n)}
t₁, X₃: X₃+5 {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: 4⋅X₀ {O(n)}
t₂, X₂: 4⋅X₄ {O(n)}
t₂, X₃: 5 {O(1)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₀ {O(n)}
t₃, X₂: 4⋅X₄ {O(n)}
t₃, X₃: 5 {O(1)}
t₃, X₄: X₄ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: 5⋅X₀ {O(n)}
t₇, X₂: 8⋅X₄ {O(n)}
t₇, X₃: X₃+5 {O(n)}
t₇, X₄: X₄ {O(n)}
t₂₉₄, X₀: X₀ {O(n)}
t₂₉₄, X₁: 10⋅2^(12⋅X₀)⋅2^(12⋅X₀)⋅X₀ {O(EXP)}
t₂₉₄, X₃: X₃+5 {O(n)}
t₂₉₄, X₄: X₄ {O(n)}
t₂₉₅, X₀: X₀ {O(n)}
t₂₉₅, X₁: 10⋅2^(12⋅X₀)⋅2^(12⋅X₀)⋅X₀ {O(EXP)}
t₂₉₅, X₃: X₃+5 {O(n)}
t₂₉₅, X₄: X₄ {O(n)}
t₂₉₆, X₀: X₀ {O(n)}
t₂₉₆, X₁: 10⋅X₀ {O(n)}
t₂₉₆, X₂: 8⋅X₄ {O(n)}
t₂₉₆, X₃: X₃+5 {O(n)}
t₂₉₆, X₄: X₄ {O(n)}
t₂₉₇, X₀: X₀ {O(n)}
t₂₉₇, X₁: 10⋅2^(12⋅X₀)⋅2^(12⋅X₀)⋅X₀ {O(EXP)}
t₂₉₇, X₃: X₃+5 {O(n)}
t₂₉₇, X₄: X₄ {O(n)}
t₂₉₈, X₀: X₀ {O(n)}
t₂₉₈, X₁: 10⋅2^(12⋅X₀)⋅2^(12⋅X₀)⋅X₀ {O(EXP)}
t₂₉₈, X₃: X₃+5 {O(n)}
t₂₉₈, X₄: X₄ {O(n)}
t₃₀₄, X₀: X₀ {O(n)}
t₃₀₄, X₁: 10⋅2^(12⋅X₀)⋅2^(12⋅X₀)⋅X₀ {O(EXP)}
t₃₀₄, X₃: X₃+5 {O(n)}
t₃₀₄, X₄: X₄ {O(n)}
t₃₀₅, X₀: X₀ {O(n)}
t₃₀₅, X₁: 10⋅2^(12⋅X₀)⋅2^(12⋅X₀)⋅X₀ {O(EXP)}
t₃₀₅, X₃: X₃+5 {O(n)}
t₃₀₅, X₄: X₄ {O(n)}