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
t₇: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₀, X₄, X₃, X₄) :|: 0 < X₀
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁, X₂, X₃, X₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, -2⋅X₁, 3⋅X₂-2⋅(X₃)³, X₃, X₄) :|: (X₁)²+(X₃)⁵ < X₂ ∧ X₁ < 0
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, -2⋅X₁, 3⋅X₂-2⋅(X₃)³, X₃, X₄) :|: (X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁-1, X₂, X₃, X₄) :|: 0 < X₁
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 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
t₇: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
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
t₆: 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) → l3(X₀, -2⋅X₁, 3⋅X₂-2⋅(X₃)³, 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) → l3(X₀, -2⋅X₁, 3⋅X₂-2⋅(X₃)³, X₃, X₄) :|: (X₁)²+(X₃)⁵ < X₂ ∧ 0 < X₁ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 1 ≤ X₀
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁-1, X₂, X₃, X₄) :|: 0 < X₁
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 t₆: 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→l3
cycle: [t₄: l3→l3; t₅: l3→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→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 t₄: 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. 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→l3
TWN - Lifting for t₅: 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. 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→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
Chain transitions t₆: l3→l1 and t₇: l1→l4 to t₉₉: l3→l4
Chain transitions t₀: l0→l1 and t₇: l1→l4 to t₁₀₀: l0→l4
Chain transitions t₀: l0→l1 and t₁: l1→l3 to t₁₀₁: l0→l3
Chain transitions t₆: l3→l1 and t₁: l1→l3 to t₁₀₂: l3→l3
Chain transitions t₀: l0→l1 and t₂: l1→l2 to t₁₀₃: l0→l2
Chain transitions t₆: l3→l1 and t₂: l1→l2 to t₁₀₄: l3→l2
Chain transitions t₁₀₄: l3→l2 and t₃: l2→l3 to t₁₀₅: l3→l3
Chain transitions t₁₀₃: l0→l2 and t₃: l2→l3 to t₁₀₆: l0→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 l3
MPRF for transition t₁₀₂: 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 t₁₀₅: 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)}
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 ∧ X₁ ≤ 3+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location n_l3___2
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 t₂₁₂: l3(X₀, X₁, X₂, X₃, X₄) → n_l3___2(Arg0_P, -2⋅X₁, NoDet0, X₃, X₄) :|: 0 < X₁ ∧ 0 < X₁ ∧ 1 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 5+X₃ ∧ 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 t₂₁₉: 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 {O(n)}
MPRF for transition t₂₂₀: n_l3___2(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: t₂₁₀: n_l3___1→n_l3___2
cycle: [t₂₁₁: n_l3___2→n_l3___1; t₂₁₀: n_l3___1→n_l3___2]
loop: (X₁ < 0 ∧ X₁ < 0 ∧ 2⋅X₁ < 0 ∧ 2⋅X₁ < 0,(X₁) -> (4⋅X₁)
order: [X₁]
closed-form:
X₁: X₁ * 4^n
Termination: true
Formula:
2⋅X₁ < 0 ∧ X₁ < 0
TWN - Lifting for t₂₁₀: n_l3___1→n_l3___2 of 4 {O(1)}
relevant size-bounds w.r.t. t₂₁₂:
Runtime-bound of t₂₁₂: 2⋅X₀ {O(n)}
Results in: 8⋅X₀ {O(n)}
TWN: t₂₁₁: n_l3___2→n_l3___1
TWN - Lifting for t₂₁₁: n_l3___2→n_l3___1 of 4 {O(1)}
relevant size-bounds w.r.t. t₂₁₂:
Runtime-bound of t₂₁₂: 2⋅X₀ {O(n)}
Results in: 8⋅X₀ {O(n)}
CFR did not improve the program. Rolling back
CFR: Improvement to new bound with the following program:
new bound:
24⋅X₀+1 {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, l4, n_l3___1, n_l3___2
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
t₇: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
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
t₆: 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
t₂₁₂: l3(X₀, X₁, X₂, X₃, X₄) → n_l3___2(Arg0_P, -2⋅X₁, NoDet0, X₃, X₄) :|: 0 < X₁ ∧ 0 < X₁ ∧ 1 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 5+X₃ ∧ 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
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁-1, X₂, X₃, X₄) :|: 0 < X₁
t₂₁₉: 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
t₂₁₀: n_l3___1(X₀, X₁, X₂, X₃, X₄) → n_l3___2(Arg0_P, -2⋅X₁, NoDet0, X₃, X₄) :|: 0 < X₁ ∧ 0 < X₁ ∧ 1 ≤ Arg0_P ∧ X₀ ≤ Arg0_P ∧ Arg0_P ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 5+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₂₀: n_l3___2(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
t₂₁₁: n_l3___2(X₀, X₁, X₂, X₃, X₄) → n_l3___1(Arg0_P, -2⋅X₁, NoDet0, Arg3_P, X₄) :|: X₁ < 0 ∧ 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
MPRF for transition t₈: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁-1, X₂, X₃, X₄) :|: 0 < X₁ of depth 1:
new bound:
20⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀+15⋅X₀+X₁ {O(EXP)}
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 ∧ X₁ ≤ 3+X₃ ∧ 0 ≤ 4+X₀+X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location n_l3___2
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
MPRF for transition t₂₉₄: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁-1, X₂, X₃, X₄) :|: 0 < X₁ of depth 1:
new bound:
20⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀+15⋅X₀+X₁ {O(EXP)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:20⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀+39⋅X₀+X₁+3 {O(EXP)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: X₀+1 {O(n)}
t₃: X₀ {O(n)}
t₆: X₀ {O(n)}
t₇: 1 {O(1)}
t₈: 20⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀+15⋅X₀+X₁ {O(EXP)}
t₂₁₀: 8⋅X₀ {O(n)}
t₂₁₁: 8⋅X₀ {O(n)}
t₂₁₂: 2⋅X₀ {O(n)}
t₂₁₉: X₀ {O(n)}
t₂₂₀: X₀ {O(n)}
Costbounds
Overall costbound: 20⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀+39⋅X₀+X₁+3 {O(EXP)}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: X₀+1 {O(n)}
t₃: X₀ {O(n)}
t₆: X₀ {O(n)}
t₇: 1 {O(1)}
t₈: 20⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀+15⋅X₀+X₁ {O(EXP)}
t₂₁₀: 8⋅X₀ {O(n)}
t₂₁₁: 8⋅X₀ {O(n)}
t₂₁₂: 2⋅X₀ {O(n)}
t₂₁₉: X₀ {O(n)}
t₂₂₀: 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)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: 5⋅X₀ {O(n)}
t₆, X₂: 8⋅X₄ {O(n)}
t₆, X₃: X₃+5 {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₀: 4⋅X₀ {O(n)}
t₇, X₁: 20⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀+15⋅X₀+X₁ {O(EXP)}
t₇, X₃: 2⋅X₃+5 {O(n)}
t₇, X₄: 4⋅X₄ {O(n)}
t₈, X₀: 4⋅X₀ {O(n)}
t₈, X₁: 20⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀+15⋅X₀+X₁ {O(EXP)}
t₈, X₃: 2⋅X₃+5 {O(n)}
t₈, X₄: 4⋅X₄ {O(n)}
t₂₁₀, X₀: X₀ {O(n)}
t₂₁₀, X₁: 10⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀ {O(EXP)}
t₂₁₀, X₃: X₃+5 {O(n)}
t₂₁₀, X₄: X₄ {O(n)}
t₂₁₁, X₀: X₀ {O(n)}
t₂₁₁, X₁: 10⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀ {O(EXP)}
t₂₁₁, X₃: X₃+5 {O(n)}
t₂₁₁, X₄: X₄ {O(n)}
t₂₁₂, X₀: X₀ {O(n)}
t₂₁₂, X₁: 10⋅X₀ {O(n)}
t₂₁₂, X₃: X₃+5 {O(n)}
t₂₁₂, X₄: X₄ {O(n)}
t₂₁₉, X₀: X₀ {O(n)}
t₂₁₉, X₁: 10⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀ {O(EXP)}
t₂₁₉, X₃: X₃+5 {O(n)}
t₂₁₉, X₄: X₄ {O(n)}
t₂₂₀, X₀: X₀ {O(n)}
t₂₂₀, X₁: 10⋅2^(8⋅X₀)⋅2^(8⋅X₀)⋅X₀+10⋅X₀ {O(EXP)}
t₂₂₀, X₃: X₃+5 {O(n)}
t₂₂₀, X₄: X₄ {O(n)}