Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₀, X₇, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₆
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₆ ≤ 0
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ < 0
t₇: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₁
t₈: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂ ≤ (X₁)²+(X₆)⁵
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: (X₁)²+(X₆)⁵ < X₂
t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₃, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₃: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, -2⋅X₁, 3⋅X₂-(X₆)³, X₃, X₄, X₅, X₆, X₇)
Preprocessing
Eliminate variables {X₄,X₅} that do not contribute to the problem
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l2
Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l7
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l5
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l8
Found invariant X₀ ≤ X₃ for location l1
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l4
Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l9
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₂₇: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅)
t₂₈: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ X₀ ≤ X₃
t₂₉: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ X₀ ≤ X₃
t₃₀: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₀, X₅, X₃, X₄, X₅) :|: 0 < X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ 0 ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < 0 ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₃: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₅: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ (X₁)²+(X₄)⁵ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₆: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l8(X₀, X₁, X₂, X₃, X₄, X₅) :|: (X₁)²+(X₄)⁵ < X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₇: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₁, X₂, X₃, X₄, X₅)
t₃₉: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₃ ∧ X₀ ≤ 0
t₄₀: l8(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, -2⋅X₁, 3⋅X₂-(X₄)³, X₃, X₄, X₅) :|: 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
MPRF for transition t₂₈: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ X₀ ≤ X₃ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF for transition t₃₀: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₀, X₅, X₃, X₄, X₅) :|: 0 < X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃+1 {O(n)}
MPRF for transition t₃₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ 0 ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃ {O(n)}
MPRF for transition t₃₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃ {O(n)}
MPRF for transition t₃₅: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ (X₁)²+(X₄)⁵ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃ {O(n)}
MPRF for transition t₃₇: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃ {O(n)}
TWN: t₃₂: l3→l4
cycle: [t₄₀: l8→l3; t₃₆: l4→l8; t₃₂: l3→l4; t₃₃: l3→l4]
loop: (X₁ < 0 ∧ 4⋅(X₁)²+(X₄)⁵+(X₄)³ < 3⋅X₂ ∨ 0 < X₁ ∧ 4⋅(X₁)²+(X₄)⁵+(X₄)³ < 3⋅X₂,(X₁,X₂,X₄) -> (-2⋅X₁,3⋅X₂-(X₄)³,X₄)
order: [X₁; X₄; X₂]
closed-form:
X₁: X₁ * 4^n
X₄: X₄
X₂: X₂ * 9^n + [[n != 0]] * -1/2⋅(X₄)³ * 9^n + [[n != 0]] * 1/2⋅(X₄)³
Termination: true
Formula:
32⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ X₁ < 0
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ X₁ < 0
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ X₁ < 0
∨ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ X₁ < 0
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 2⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ X₁ < 0
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 2⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ X₁ < 0
∨ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 2⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ 0 < X₁
∨ 32⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < X₁
∨ 32⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ 0 < X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < X₁
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ 0 < X₁
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < X₁
∨ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 2⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < X₁
∨ 32⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ 0 < X₁
∨ 32⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < X₁
∨ 32⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ 0 < X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < X₁
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 2⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ 0 < X₁
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 2⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < X₁
∨ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 2⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < X₁
Stabilization-Threshold for: 16⋅(X₁)²+(X₄)⁵+4⋅(X₄)³ < 9⋅X₂
alphas_abs: 18⋅X₂+9⋅(X₄)³+2⋅(X₄)⁵
M: 0
N: 1
Bound: 4⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+18⋅X₄⋅X₄⋅X₄+36⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: 4⋅(X₁)²+(X₄)⁵+(X₄)³ < 3⋅X₂
alphas_abs: 6⋅X₂+3⋅(X₄)³+2⋅(X₄)⁵
M: 0
N: 1
Bound: 4⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+6⋅X₄⋅X₄⋅X₄+12⋅X₂+2 {O(n^5)}
TWN - Lifting for t₃₂: l3→l4 of 16⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+96⋅X₂+21 {O(n^5)}
relevant size-bounds w.r.t. t₃₀:
X₂: X₅ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₃₀: X₃+1 {O(n)}
Results in: 16⋅X₃⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₃⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+96⋅X₃⋅X₅+21⋅X₃+96⋅X₅+21 {O(n^6)}
TWN: t₃₃: l3→l4
TWN - Lifting for t₃₃: l3→l4 of 16⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+96⋅X₂+21 {O(n^5)}
relevant size-bounds w.r.t. t₃₀:
X₂: X₅ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₃₀: X₃+1 {O(n)}
Results in: 16⋅X₃⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₃⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+96⋅X₃⋅X₅+21⋅X₃+96⋅X₅+21 {O(n^6)}
TWN: t₃₆: l4→l8
TWN - Lifting for t₃₆: l4→l8 of 16⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+96⋅X₂+21 {O(n^5)}
relevant size-bounds w.r.t. t₃₀:
X₂: X₅ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₃₀: X₃+1 {O(n)}
Results in: 16⋅X₃⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₃⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+96⋅X₃⋅X₅+21⋅X₃+96⋅X₅+21 {O(n^6)}
TWN: t₄₀: l8→l3
TWN - Lifting for t₄₀: l8→l3 of 16⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+96⋅X₂+21 {O(n^5)}
relevant size-bounds w.r.t. t₃₀:
X₂: X₅ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₃₀: X₃+1 {O(n)}
Results in: 16⋅X₃⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+16⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₃⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+96⋅X₃⋅X₅+21⋅X₃+96⋅X₅+21 {O(n^6)}
Chain transitions t₃₈: l6→l1 and t₂₉: l1→l7 to t₁₀₅: l6→l7
Chain transitions t₃₇: l5→l1 and t₂₉: l1→l7 to t₁₀₆: l5→l7
Chain transitions t₃₇: l5→l1 and t₂₈: l1→l2 to t₁₀₇: l5→l2
Chain transitions t₃₈: l6→l1 and t₂₈: l1→l2 to t₁₀₈: l6→l2
Chain transitions t₁₀₈: l6→l2 and t₃₁: l2→l5 to t₁₀₉: l6→l5
Chain transitions t₁₀₇: l5→l2 and t₃₁: l2→l5 to t₁₁₀: l5→l5
Chain transitions t₁₀₇: l5→l2 and t₃₀: l2→l3 to t₁₁₁: l5→l3
Chain transitions t₁₀₈: l6→l2 and t₃₀: l2→l3 to t₁₁₂: l6→l3
Chain transitions t₄₀: l8→l3 and t₃₄: l3→l5 to t₁₁₃: l8→l5
Chain transitions t₁₁₂: l6→l3 and t₃₄: l3→l5 to t₁₁₄: l6→l5
Chain transitions t₁₁₂: l6→l3 and t₃₃: l3→l4 to t₁₁₅: l6→l4
Chain transitions t₄₀: l8→l3 and t₃₃: l3→l4 to t₁₁₆: l8→l4
Chain transitions t₁₁₁: l5→l3 and t₃₃: l3→l4 to t₁₁₇: l5→l4
Chain transitions t₁₁₁: l5→l3 and t₃₄: l3→l5 to t₁₁₈: l5→l5
Chain transitions t₁₁₁: l5→l3 and t₃₂: l3→l4 to t₁₁₉: l5→l4
Chain transitions t₁₁₂: l6→l3 and t₃₂: l3→l4 to t₁₂₀: l6→l4
Chain transitions t₄₀: l8→l3 and t₃₂: l3→l4 to t₁₂₁: l8→l4
Chain transitions t₁₂₁: l8→l4 and t₃₆: l4→l8 to t₁₂₂: l8→l8
Chain transitions t₁₁₆: l8→l4 and t₃₆: l4→l8 to t₁₂₃: l8→l8
Chain transitions t₁₁₆: l8→l4 and t₃₅: l4→l5 to t₁₂₄: l8→l5
Chain transitions t₁₂₁: l8→l4 and t₃₅: l4→l5 to t₁₂₅: l8→l5
Chain transitions t₁₂₀: l6→l4 and t₃₅: l4→l5 to t₁₂₆: l6→l5
Chain transitions t₁₂₀: l6→l4 and t₃₆: l4→l8 to t₁₂₇: l6→l8
Chain transitions t₁₁₅: l6→l4 and t₃₅: l4→l5 to t₁₂₈: l6→l5
Chain transitions t₁₁₅: l6→l4 and t₃₆: l4→l8 to t₁₂₉: l6→l8
Chain transitions t₁₁₉: l5→l4 and t₃₅: l4→l5 to t₁₃₀: l5→l5
Chain transitions t₁₁₉: l5→l4 and t₃₆: l4→l8 to t₁₃₁: l5→l8
Chain transitions t₁₁₇: l5→l4 and t₃₅: l4→l5 to t₁₃₂: l5→l5
Chain transitions t₁₁₇: l5→l4 and t₃₆: l4→l8 to t₁₃₃: l5→l8
Analysing control-flow refined program
Cut unsatisfiable transition t₁₁₃: l8→l5
Cut unsatisfiable transition t₁₁₄: l6→l5
Cut unsatisfiable transition t₁₁₈: l5→l5
Cut unsatisfiable transition t₁₁₉: l5→l4
Cut unsatisfiable transition t₁₂₀: l6→l4
Cut unsatisfiable transition t₁₂₆: l6→l5
Cut unsatisfiable transition t₁₂₇: l6→l8
Cut unsatisfiable transition t₁₃₀: l5→l5
Cut unsatisfiable transition t₁₃₁: l5→l8
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l2
Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l7
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l5
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l8
Found invariant X₀ ≤ X₃ for location l1
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l4
Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l9
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l3
MPRF for transition t₁₁₀: l5(X₀, X₁, X₂, X₃, X₄, X₅) -{3}> l5(X₀-1, X₁, X₂, X₃, X₄, X₅) :|: 1 < X₀ ∧ X₄ ≤ 0 ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:
new bound:
3⋅X₃ {O(n)}
MPRF for transition t₁₂₄: l8(X₀, X₁, X₂, X₃, X₄, X₅) -{3}> l5(X₀, -2⋅X₁, 3⋅X₂-Temp_Int₁₉₅₅, X₃, X₄, X₅) :|: 2⋅X₁ < 0 ∧ 3⋅X₂ ≤ (X₄)³+4⋅(X₁)²+(X₄)⁵ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:
new bound:
3⋅X₃+2 {O(n)}
MPRF for transition t₁₂₅: l8(X₀, X₁, X₂, X₃, X₄, X₅) -{3}> l5(X₀, -2⋅X₁, 3⋅X₂-Temp_Int₁₉₅₆, X₃, X₄, X₅) :|: 0 < 2⋅X₁ ∧ 3⋅X₂ ≤ (X₄)³+4⋅(X₁)²+(X₄)⁵ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:
new bound:
3⋅X₃+2 {O(n)}
MPRF for transition t₁₃₂: l5(X₀, X₁, X₂, X₃, X₄, X₅) -{5}> l5(X₀-1, X₀-1, X₅, X₃, X₄, X₅) :|: 1 < X₀ ∧ 0 < X₄ ∧ 1 < X₀ ∧ X₅+2⋅X₀ ≤ 1+(X₀)²+(X₄)⁵ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:
new bound:
3⋅X₃ {O(n)}
MPRF for transition t₁₃₃: l5(X₀, X₁, X₂, X₃, X₄, X₅) -{5}> l8(X₀-1, X₀-1, X₅, X₃, X₄, X₅) :|: 1 < X₀ ∧ 0 < X₄ ∧ 1 < X₀ ∧ 1+(X₀)²+(X₄)⁵ < 2⋅X₀+X₅ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:
new bound:
3⋅X₃+3 {O(n)}
TWN: t₁₂₂: l8→l8
cycle: [t₁₂₂: l8→l8; t₁₂₃: l8→l8]
loop: (0 < 2⋅X₁ ∧ 4⋅(X₁)²+(X₄)⁵+(X₄)³ < 3⋅X₂ ∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)²+(X₄)⁵+(X₄)³ < 3⋅X₂,(X₁,X₂,X₄) -> (-2⋅X₁,3⋅X₂-(X₄)³,X₄)
order: [X₁; X₄; X₂]
closed-form:
X₁: X₁ * 4^n
X₄: X₄
X₂: X₂ * 9^n + [[n != 0]] * -1/2⋅(X₄)³ * 9^n + [[n != 0]] * 1/2⋅(X₄)³
Termination: true
Formula:
32⋅(X₁)² < 0 ∧ 4⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² < 0 ∧ 4⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² < 0 ∧ 4⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < 2⋅X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 4⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 4⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 4⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < 2⋅X₁
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 4⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 4⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 4⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² < 0 ∧ 0 < 4⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² < 0 ∧ 0 < 4⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² < 0 ∧ 0 < 4⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < 2⋅X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 4⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 4⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 4⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < 2⋅X₁
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 4⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 4⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 4⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² < 0 ∧ 4⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 4⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 4⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 2⋅X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 4⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 4⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 4⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 2⋅X₁ < 0
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 4⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 4⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0
∨ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 4⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 2⋅X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 0 < 4⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 0 < 4⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 0 < 4⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 2⋅X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 4⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 4⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 4⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 2⋅X₁ < 0
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 4⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 4⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0
∨ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 4⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 2⋅X₁ < 0
Stabilization-Threshold for: 16⋅(X₁)²+(X₄)⁵+4⋅(X₄)³ < 9⋅X₂
alphas_abs: 18⋅X₂+9⋅(X₄)³+2⋅(X₄)⁵
M: 0
N: 1
Bound: 4⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+18⋅X₄⋅X₄⋅X₄+36⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: 4⋅(X₁)²+(X₄)⁵+(X₄)³ < 3⋅X₂
alphas_abs: 6⋅X₂+3⋅(X₄)³+2⋅(X₄)⁵
M: 0
N: 1
Bound: 4⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+6⋅X₄⋅X₄⋅X₄+12⋅X₂+2 {O(n^5)}
loop: (0 < 2⋅X₁ ∧ 4⋅(X₁)²+(X₄)⁵+(X₄)³ < 3⋅X₂ ∨ 2⋅X₁ < 0 ∧ 4⋅(X₁)²+(X₄)⁵+(X₄)³ < 3⋅X₂,(X₁,X₂,X₄) -> (-2⋅X₁,3⋅X₂-(X₄)³,X₄)
order: [X₁; X₄; X₂]
closed-form:
X₁: X₁ * 4^n
X₄: X₄
X₂: X₂ * 9^n + [[n != 0]] * -1/2⋅(X₄)³ * 9^n + [[n != 0]] * 1/2⋅(X₄)³
Termination: true
Formula:
32⋅(X₁)² < 0 ∧ 4⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² < 0 ∧ 4⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² < 0 ∧ 4⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < 2⋅X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 4⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 4⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 4⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < 2⋅X₁
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 4⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 4⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 4⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² < 0 ∧ 0 < 4⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² < 0 ∧ 0 < 4⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² < 0 ∧ 0 < 4⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < 2⋅X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 4⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 4⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 4⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < 2⋅X₁
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 4⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 4⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 4⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 0 < 2⋅X₁
∨ 32⋅(X₁)² < 0 ∧ 4⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 4⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 4⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 2⋅X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 4⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 4⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 4⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 2⋅X₁ < 0
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 4⋅X₁ < 0 ∧ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 4⋅X₁ < 0 ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0
∨ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 4⋅X₁ < 0 ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 2⋅X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 0 < 4⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 0 < 4⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0
∨ 32⋅(X₁)² < 0 ∧ 0 < 4⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 2⋅X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 4⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 4⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0
∨ 9⋅(X₄)³ < 18⋅X₂ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 0 < 4⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 2⋅X₁ < 0
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 4⋅X₁ ∧ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0
∨ 2⋅(X₄)⁵ < (X₄)³ ∧ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 4⋅X₁ ∧ 3⋅(X₄)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0
∨ 32⋅(X₁)² ≤ 0 ∧ 0 ≤ 32⋅(X₁)² ∧ 9⋅(X₄)³ ≤ 18⋅X₂ ∧ 18⋅X₂ ≤ 9⋅(X₄)³ ∧ 0 < 4⋅X₁ ∧ 2⋅(X₄)⁵ < (X₄)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₄)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₄)³ ∧ 2⋅X₁ < 0
Stabilization-Threshold for: 16⋅(X₁)²+(X₄)⁵+4⋅(X₄)³ < 9⋅X₂
alphas_abs: 18⋅X₂+9⋅(X₄)³+2⋅(X₄)⁵
M: 0
N: 1
Bound: 4⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+18⋅X₄⋅X₄⋅X₄+36⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: 4⋅(X₁)²+(X₄)⁵+(X₄)³ < 3⋅X₂
alphas_abs: 6⋅X₂+3⋅(X₄)³+2⋅(X₄)⁵
M: 0
N: 1
Bound: 4⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+6⋅X₄⋅X₄⋅X₄+12⋅X₂+2 {O(n^5)}
TWN - Lifting for t₁₂₂: l8→l8 of 16⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+96⋅X₂+21 {O(n^5)}
relevant size-bounds w.r.t. t₁₂₉:
X₂: X₅ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₁₂₉: 1 {O(1)}
Results in: 16⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+96⋅X₅+21 {O(n^5)}
TWN - Lifting for t₁₂₂: l8→l8 of 16⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+96⋅X₂+21 {O(n^5)}
relevant size-bounds w.r.t. t₁₃₃:
X₂: 7⋅X₅ {O(n)}
X₄: 2⋅X₄ {O(n)}
Runtime-bound of t₁₃₃: 3⋅X₃+3 {O(n)}
Results in: 1536⋅X₃⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+1536⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+1152⋅X₃⋅X₄⋅X₄⋅X₄+1152⋅X₄⋅X₄⋅X₄+2016⋅X₃⋅X₅+2016⋅X₅+63⋅X₃+63 {O(n^6)}
TWN: t₁₂₃: l8→l8
TWN - Lifting for t₁₂₃: l8→l8 of 16⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+96⋅X₂+21 {O(n^5)}
relevant size-bounds w.r.t. t₁₂₉:
X₂: X₅ {O(n)}
X₄: X₄ {O(n)}
Runtime-bound of t₁₂₉: 1 {O(1)}
Results in: 16⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+96⋅X₅+21 {O(n^5)}
TWN - Lifting for t₁₂₃: l8→l8 of 16⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+48⋅X₄⋅X₄⋅X₄+96⋅X₂+21 {O(n^5)}
relevant size-bounds w.r.t. t₁₃₃:
X₂: 7⋅X₅ {O(n)}
X₄: 2⋅X₄ {O(n)}
Runtime-bound of t₁₃₃: 3⋅X₃+3 {O(n)}
Results in: 1536⋅X₃⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+1536⋅X₄⋅X₄⋅X₄⋅X₄⋅X₄+1152⋅X₃⋅X₄⋅X₄⋅X₄+1152⋅X₄⋅X₄⋅X₄+2016⋅X₃⋅X₅+2016⋅X₅+63⋅X₃+63 {O(n^6)}
CFR did not improve the program. Rolling back
CFR did not improve the program. Rolling back
Analysing control-flow refined program
Cut unsatisfiable transition t₃₄: l3→l5
Cut unsatisfiable transition t₄₅₂: n_l3___1→l5
Cut unsatisfiable transition t₄₅₃: n_l3___4→l5
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l2
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location n_l3___4
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location n_l8___2
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___6
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location n_l4___3
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l8___5
Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l7
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l5
Found invariant X₀ ≤ X₃ for location l1
Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l9
Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 5 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___1
Found invariant X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3
knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₄₃₉: l3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₁ ∧ 0 < X₁ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
MPRF for transition t₄₅₄: n_l4___3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ (X₁)²+(X₄)⁵ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃ {O(n)}
MPRF for transition t₄₅₅: n_l4___6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ (X₁)²+(X₄)⁵ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₃ {O(n)}
TWN: t₄₃₇: n_l3___1→n_l4___6
cycle: [t₄₄₂: n_l8___2→n_l3___1; t₄₄₀: n_l4___3→n_l8___2; t₄₃₈: n_l3___4→n_l4___3; t₄₄₃: n_l8___5→n_l3___4; t₄₄₁: n_l4___6→n_l8___5; t₄₃₇: n_l3___1→n_l4___6]
loop: (0 < X₁ ∧ 0 < X₁ ∧ 0 < X₁ ∧ X₁ < 0 ∧ 0 < 2⋅X₁ ∧ 0 < 2⋅X₁ ∧ 0 < 2⋅X₁ ∧ 2⋅X₁ < 0,(X₁) -> (4⋅X₁)
order: [X₁]
closed-form:
X₁: X₁ * 4^n
Termination: true
Formula:
2⋅X₁ < 0 ∧ 0 < 2⋅X₁ ∧ X₁ < 0 ∧ 0 < X₁
TWN - Lifting for t₄₃₇: n_l3___1→n_l4___6 of 6 {O(1)}
relevant size-bounds w.r.t. t₄₃₉:
Runtime-bound of t₄₃₉: X₃+1 {O(n)}
Results in: 6⋅X₃+6 {O(n)}
TWN: t₄₃₈: n_l3___4→n_l4___3
TWN - Lifting for t₄₃₈: n_l3___4→n_l4___3 of 6 {O(1)}
relevant size-bounds w.r.t. t₄₃₉:
Runtime-bound of t₄₃₉: X₃+1 {O(n)}
Results in: 6⋅X₃+6 {O(n)}
TWN: t₄₄₀: n_l4___3→n_l8___2
TWN - Lifting for t₄₄₀: n_l4___3→n_l8___2 of 6 {O(1)}
relevant size-bounds w.r.t. t₄₃₉:
Runtime-bound of t₄₃₉: X₃+1 {O(n)}
Results in: 6⋅X₃+6 {O(n)}
TWN: t₄₄₁: n_l4___6→n_l8___5
TWN - Lifting for t₄₄₁: n_l4___6→n_l8___5 of 6 {O(1)}
relevant size-bounds w.r.t. t₄₃₉:
Runtime-bound of t₄₃₉: X₃+1 {O(n)}
Results in: 6⋅X₃+6 {O(n)}
TWN: t₄₄₂: n_l8___2→n_l3___1
TWN - Lifting for t₄₄₂: n_l8___2→n_l3___1 of 6 {O(1)}
relevant size-bounds w.r.t. t₄₃₉:
Runtime-bound of t₄₃₉: X₃+1 {O(n)}
Results in: 6⋅X₃+6 {O(n)}
TWN: t₄₄₃: n_l8___5→n_l3___4
TWN - Lifting for t₄₄₃: n_l8___5→n_l3___4 of 6 {O(1)}
relevant size-bounds w.r.t. t₄₃₉:
Runtime-bound of t₄₃₉: X₃+1 {O(n)}
Results in: 6⋅X₃+6 {O(n)}
CFR did not improve the program. Rolling back
CFR: Improvement to new bound with the following program:
new bound:
43⋅X₃+39 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: Arg3_P, Arg4_P, NoDet0
Locations: l0, l1, l2, l3, l5, l6, l7, l9, n_l3___1, n_l3___4, n_l4___3, n_l4___6, n_l8___2, n_l8___5
Transitions:
t₂₇: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅)
t₂₈: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₀ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₃
t₂₉: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ 0 ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₃
t₃₀: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₀, X₅, X₃, X₄, X₅) :|: 0 < X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ 0 ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₄₃₉: l3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₁ ∧ 0 < X₁ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₃₇: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₁, X₂, X₃, X₄, X₅)
t₃₉: l7(X₀, X₁, X₂, X₃, X₄, X₅) → l9(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₃ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₃ ∧ X₀ ≤ 0
t₄₃₇: n_l3___1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 < X₁ ∧ 0 < X₁ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 5 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₃₈: n_l3___4(X₀, X₁, X₂, X₃, X₄, X₅) → n_l4___3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < 0 ∧ X₁ < 0 ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀
t₄₅₄: n_l4___3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ (X₁)²+(X₄)⁵ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀
t₄₄₀: n_l4___3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l8___2(X₀, X₁, X₂, Arg3_P, Arg4_P, X₅) :|: X₁ < 0 ∧ 1 ≤ Arg4_P ∧ X₀ ≤ Arg3_P ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀
t₄₅₅: n_l4___6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ (X₁)²+(X₄)⁵ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₄₁: n_l4___6(X₀, X₁, X₂, X₃, X₄, X₅) → n_l8___5(X₀, X₁, X₂, Arg3_P, Arg4_P, X₅) :|: 0 < X₁ ∧ 1 ≤ Arg4_P ∧ X₀ ≤ Arg3_P ∧ X₄ ≤ Arg4_P ∧ Arg4_P ≤ X₄ ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄₄₂: n_l8___2(X₀, X₁, X₂, X₃, X₄, X₅) → n_l3___1(X₀, -2⋅X₁, NoDet0, Arg3_P, X₄, X₅) :|: X₁ < 0 ∧ X₀ ≤ Arg3_P ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3+X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀
t₄₄₃: n_l8___5(X₀, X₁, X₂, X₃, X₄, X₅) → n_l3___4(X₀, -2⋅X₁, NoDet0, Arg3_P, X₄, X₅) :|: 0 < X₁ ∧ X₀ ≤ Arg3_P ∧ X₃ ≤ Arg3_P ∧ Arg3_P ≤ X₃ ∧ 1 ≤ X₄ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:43⋅X₃+43 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: X₃+1 {O(n)}
t₂₉: 1 {O(1)}
t₃₀: X₃+1 {O(n)}
t₃₁: X₃ {O(n)}
t₃₇: X₃ {O(n)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₃₇: 6⋅X₃+6 {O(n)}
t₄₃₈: 6⋅X₃+6 {O(n)}
t₄₃₉: X₃+1 {O(n)}
t₄₄₀: 6⋅X₃+6 {O(n)}
t₄₄₁: 6⋅X₃+6 {O(n)}
t₄₄₂: 6⋅X₃+6 {O(n)}
t₄₄₃: 6⋅X₃+6 {O(n)}
t₄₅₄: X₃ {O(n)}
t₄₅₅: X₃ {O(n)}
Costbounds
Overall costbound: 43⋅X₃+43 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: X₃+1 {O(n)}
t₂₉: 1 {O(1)}
t₃₀: X₃+1 {O(n)}
t₃₁: X₃ {O(n)}
t₃₇: X₃ {O(n)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₃₇: 6⋅X₃+6 {O(n)}
t₄₃₈: 6⋅X₃+6 {O(n)}
t₄₃₉: X₃+1 {O(n)}
t₄₄₀: 6⋅X₃+6 {O(n)}
t₄₄₁: 6⋅X₃+6 {O(n)}
t₄₄₂: 6⋅X₃+6 {O(n)}
t₄₄₃: 6⋅X₃+6 {O(n)}
t₄₅₄: X₃ {O(n)}
t₄₅₅: X₃ {O(n)}
Sizebounds
t₂₇, X₀: X₀ {O(n)}
t₂₇, X₁: X₁ {O(n)}
t₂₇, X₂: X₂ {O(n)}
t₂₇, X₃: X₃ {O(n)}
t₂₇, X₄: X₄ {O(n)}
t₂₇, X₅: X₅ {O(n)}
t₂₈, X₀: X₃ {O(n)}
t₂₈, X₁: 2⋅2^(6⋅X₃+6)⋅2^(6⋅X₃+6)⋅X₃+X₁+X₃ {O(EXP)}
t₂₈, X₃: X₃ {O(n)}
t₂₈, X₄: X₄ {O(n)}
t₂₈, X₅: X₅ {O(n)}
t₂₉, X₀: 2⋅X₃ {O(n)}
t₂₉, X₁: 2⋅2^(6⋅X₃+6)⋅2^(6⋅X₃+6)⋅X₃+2⋅X₁+X₃ {O(EXP)}
t₂₉, X₃: 2⋅X₃ {O(n)}
t₂₉, X₄: 2⋅X₄ {O(n)}
t₂₉, X₅: 2⋅X₅ {O(n)}
t₃₀, X₀: X₃ {O(n)}
t₃₀, X₁: X₃ {O(n)}
t₃₀, X₂: X₅ {O(n)}
t₃₀, X₃: X₃ {O(n)}
t₃₀, X₄: X₄ {O(n)}
t₃₀, X₅: X₅ {O(n)}
t₃₁, X₀: X₃ {O(n)}
t₃₁, X₁: 2⋅2^(6⋅X₃+6)⋅2^(6⋅X₃+6)⋅X₃+X₁+X₃ {O(EXP)}
t₃₁, X₃: X₃ {O(n)}
t₃₁, X₄: X₄ {O(n)}
t₃₁, X₅: X₅ {O(n)}
t₃₇, X₀: X₃ {O(n)}
t₃₇, X₁: 2⋅2^(6⋅X₃+6)⋅2^(6⋅X₃+6)⋅X₃+X₁+X₃ {O(EXP)}
t₃₇, X₃: X₃ {O(n)}
t₃₇, X₄: X₄ {O(n)}
t₃₇, X₅: X₅ {O(n)}
t₃₈, X₀: X₃ {O(n)}
t₃₈, X₁: X₁ {O(n)}
t₃₈, X₂: X₂ {O(n)}
t₃₈, X₃: X₃ {O(n)}
t₃₈, X₄: X₄ {O(n)}
t₃₈, X₅: X₅ {O(n)}
t₃₉, X₀: 2⋅X₃ {O(n)}
t₃₉, X₁: 2⋅2^(6⋅X₃+6)⋅2^(6⋅X₃+6)⋅X₃+2⋅X₁+X₃ {O(EXP)}
t₃₉, X₃: 2⋅X₃ {O(n)}
t₃₉, X₄: 2⋅X₄ {O(n)}
t₃₉, X₅: 2⋅X₅ {O(n)}
t₄₃₇, X₀: X₃ {O(n)}
t₄₃₇, X₁: 2^(6⋅X₃+6)⋅2^(6⋅X₃+6)⋅X₃ {O(EXP)}
t₄₃₇, X₃: X₃ {O(n)}
t₄₃₇, X₄: X₄ {O(n)}
t₄₃₇, X₅: X₅ {O(n)}
t₄₃₈, X₀: X₃ {O(n)}
t₄₃₈, X₁: 2^(6⋅X₃+6)⋅2^(6⋅X₃+6)⋅X₃ {O(EXP)}
t₄₃₈, X₃: X₃ {O(n)}
t₄₃₈, X₄: X₄ {O(n)}
t₄₃₈, X₅: X₅ {O(n)}
t₄₃₉, X₀: X₃ {O(n)}
t₄₃₉, X₁: X₃ {O(n)}
t₄₃₉, X₂: X₅ {O(n)}
t₄₃₉, X₃: X₃ {O(n)}
t₄₃₉, X₄: X₄ {O(n)}
t₄₃₉, X₅: X₅ {O(n)}
t₄₄₀, X₀: X₃ {O(n)}
t₄₄₀, X₁: 2^(6⋅X₃+6)⋅2^(6⋅X₃+6)⋅X₃ {O(EXP)}
t₄₄₀, X₃: X₃ {O(n)}
t₄₄₀, X₄: X₄ {O(n)}
t₄₄₀, X₅: X₅ {O(n)}
t₄₄₁, X₀: X₃ {O(n)}
t₄₄₁, X₁: 2^(6⋅X₃+6)⋅2^(6⋅X₃+6)⋅X₃ {O(EXP)}
t₄₄₁, X₃: X₃ {O(n)}
t₄₄₁, X₄: X₄ {O(n)}
t₄₄₁, X₅: X₅ {O(n)}
t₄₄₂, X₀: X₃ {O(n)}
t₄₄₂, X₁: 2^(6⋅X₃+6)⋅2^(6⋅X₃+6)⋅X₃ {O(EXP)}
t₄₄₂, X₃: X₃ {O(n)}
t₄₄₂, X₄: X₄ {O(n)}
t₄₄₂, X₅: X₅ {O(n)}
t₄₄₃, X₀: X₃ {O(n)}
t₄₄₃, X₁: 2^(6⋅X₃+6)⋅2^(6⋅X₃+6)⋅X₃ {O(EXP)}
t₄₄₃, X₃: X₃ {O(n)}
t₄₄₃, X₄: X₄ {O(n)}
t₄₄₃, X₅: X₅ {O(n)}
t₄₅₄, X₀: X₃ {O(n)}
t₄₅₄, X₁: 2^(6⋅X₃+6)⋅2^(6⋅X₃+6)⋅X₃ {O(EXP)}
t₄₅₄, X₃: X₃ {O(n)}
t₄₅₄, X₄: X₄ {O(n)}
t₄₅₄, X₅: X₅ {O(n)}
t₄₅₅, X₀: X₃ {O(n)}
t₄₅₅, X₁: 2^(6⋅X₃+6)⋅2^(6⋅X₃+6)⋅X₃+X₃ {O(EXP)}
t₄₅₅, X₃: X₃ {O(n)}
t₄₅₅, X₄: X₄ {O(n)}
t₄₅₅, X₅: X₅ {O(n)}