Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₀ ≤ 0
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < X₀
t₂₂: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₄: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, X₀, X₉, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 ≤ 5+X₈ ∧ X₈ ≤ 5
t₅: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₈+5 < 0
t₆: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 5 < X₈
t₁₂: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, -2⋅X₁, 3⋅X₂-(X₈)³, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₂₀: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l5(X₀, X₁, X₂, -2⋅X₃, 3⋅X₄-(X₈)³, X₅, X₆, X₇, X₈, X₉)
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₁ < 0
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < X₁
t₉: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₁₀: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: (X₁)²+(X₈)⁵ < X₂
t₁₁: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₂ ≤ (X₁)²+(X₈)⁵
t₁₃: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l5(X₀, X₁, X₂, X₀, X₉, X₅, X₆, X₇, X₈, X₉) :|: 0 < X₈
t₁₄: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₈ ≤ 0
t₁₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃ < 0
t₁₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 0 < X₃
t₁₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₃ ≤ 0 ∧ 0 ≤ X₃
t₁₈: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: (X₃)²+(X₈)⁵ < X₄
t₁₉: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₄ ≤ (X₃)²+(X₈)⁵
t₂₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(X₅, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)

Preprocessing

Eliminate variables {X₆,X₇} that do not contribute to the problem

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l11

Found invariant X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l2

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l6

Found invariant X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l12

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l7

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l5

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l13

Found invariant X₀ ≤ X₅ for location l1

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location l10

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l4

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location l9

Found invariant X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₄₇: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉)
t₄₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l10(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₀ ≤ 0 ∧ X₀ ≤ X₅
t₄₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: 0 < X₀ ∧ X₀ ≤ X₅
t₅₀: l10(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₀ ≤ X₅ ∧ X₀ ≤ 0
t₅₁: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l2(X₀, X₀, X₉, X₃, X₄, X₅, X₈, X₉) :|: 0 ≤ 5+X₈ ∧ X₈ ≤ 5 ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₅₂: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₈+5 < 0 ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₅₃: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: 5 < X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₅₄: l12(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l2(X₀, -2⋅X₁, 3⋅X₂-(X₈)³, X₃, X₄, X₅, X₈, X₉) :|: X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₅₅: l13(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l5(X₀, X₁, X₂, -2⋅X₃, 3⋅X₄-(X₈)³, X₅, X₈, X₉) :|: 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₅₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₁ < 0 ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₅₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: 0 < X₁ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₅₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₅₉: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l12(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: (X₁)²+(X₈)⁵ < X₂ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₆₀: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₂ ≤ (X₁)²+(X₈)⁵ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₆₁: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l5(X₀, X₁, X₂, X₀, X₉, X₅, X₈, X₉) :|: 0 < X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₆₂: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₈ ≤ 0 ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₆₃: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₃ < 0 ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₆₄: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: 0 < X₃ ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₆₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₆₆: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l13(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: (X₃)²+(X₈)⁵ < X₄ ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₆₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₄ ≤ (X₃)²+(X₈)⁵ ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₆₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l1(X₀-1, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
t₆₉: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l1(X₅, X₁, X₂, X₃, X₄, X₅, X₈, X₉)

MPRF for transition t₄₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l11(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: 0 < X₀ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

l11 [X₀ ]
l2 [X₀ ]
l12 [X₀ ]
l3 [X₀ ]
l4 [X₀ ]
l5 [X₀ ]
l13 [X₀ ]
l6 [X₀ ]
l7 [X₀ ]
l1 [X₀+1 ]

MPRF for transition t₅₁: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l2(X₀, X₀, X₉, X₃, X₄, X₅, X₈, X₉) :|: 0 ≤ 5+X₈ ∧ X₈ ≤ 5 ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

l11 [X₀ ]
l2 [X₀-1 ]
l12 [X₀-1 ]
l3 [X₀-1 ]
l4 [X₀ ]
l5 [X₀ ]
l13 [X₀ ]
l6 [X₀ ]
l7 [X₀-1 ]
l1 [X₀ ]

MPRF for transition t₅₂: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₈+5 < 0 ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

l11 [X₀+1 ]
l2 [X₀ ]
l12 [X₀ ]
l3 [X₀ ]
l4 [X₀ ]
l5 [X₀ ]
l13 [X₀ ]
l6 [X₀ ]
l7 [X₀ ]
l1 [X₀+1 ]

MPRF for transition t₅₃: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: 5 < X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

l11 [X₀+1 ]
l2 [X₀ ]
l12 [X₀ ]
l3 [X₀ ]
l4 [X₀ ]
l5 [X₀ ]
l13 [X₀ ]
l6 [X₀ ]
l7 [X₀ ]
l1 [X₀+1 ]

MPRF for transition t₅₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

l11 [X₀ ]
l2 [X₀ ]
l12 [X₀ ]
l3 [X₀ ]
l4 [X₀ ]
l5 [X₀ ]
l13 [X₀ ]
l6 [X₀ ]
l7 [X₀-1 ]
l1 [X₀ ]

MPRF for transition t₆₀: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₂ ≤ (X₁)²+(X₈)⁵ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₅ {O(n)}

MPRF:

l11 [X₀+X₅ ]
l2 [X₀+X₅ ]
l12 [X₀+X₅ ]
l3 [X₀+X₅ ]
l4 [X₀+X₅ ]
l5 [X₀+X₅ ]
l13 [X₀+X₅ ]
l6 [X₀+X₅ ]
l7 [X₀+X₅-1 ]
l1 [X₀+X₅ ]

MPRF for transition t₆₁: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l5(X₀, X₁, X₂, X₀, X₉, X₅, X₈, X₉) :|: 0 < X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

l11 [X₀+1 ]
l2 [X₀ ]
l12 [X₀ ]
l3 [X₀ ]
l4 [X₀+1 ]
l5 [X₀ ]
l13 [X₀ ]
l6 [X₀ ]
l7 [X₀ ]
l1 [X₀+1 ]

MPRF for transition t₆₂: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₈ ≤ 0 ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

l11 [X₀ ]
l2 [X₀ ]
l12 [X₀ ]
l3 [X₀ ]
l4 [X₀ ]
l5 [X₀ ]
l13 [X₀ ]
l6 [X₀ ]
l7 [X₀-1 ]
l1 [X₀ ]

MPRF for transition t₆₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ of depth 1:

new bound:

20⋅X₅+X₈+5 {O(n)}

MPRF:

l11 [10⋅X₀+10⋅X₅+X₈+5 ]
l2 [10⋅X₀+10⋅X₅ ]
l12 [10⋅X₀+10⋅X₅ ]
l3 [10⋅X₀+10⋅X₅ ]
l4 [10⋅X₀+10⋅X₅+X₈ ]
l5 [10⋅X₀+10⋅X₅+X₈-4 ]
l13 [10⋅X₀+10⋅X₅+X₈-4 ]
l6 [10⋅X₀+10⋅X₅+X₈-4 ]
l7 [10⋅X₀+10⋅X₅+X₈-5 ]
l1 [10⋅X₀+10⋅X₅+X₈+5 ]

MPRF for transition t₆₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₄ ≤ (X₃)²+(X₈)⁵ ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ of depth 1:

new bound:

10⋅X₅+10⋅X₈ {O(n)}

MPRF:

l11 [10⋅X₀+10⋅X₈ ]
l2 [10⋅X₀+9⋅X₈-5 ]
l12 [10⋅X₀+9⋅X₈-5 ]
l3 [10⋅X₀+9⋅X₈-5 ]
l4 [10⋅X₀+10⋅X₈ ]
l5 [10⋅X₀+10⋅X₈ ]
l13 [10⋅X₀+10⋅X₈ ]
l6 [10⋅X₀+10⋅X₈ ]
l7 [10⋅X₀+10⋅X₈-10 ]
l1 [10⋅X₀+10⋅X₈ ]

MPRF for transition t₆₈: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l1(X₀-1, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₅ {O(n)}

MPRF:

l11 [X₀ ]
l2 [X₀ ]
l12 [X₀ ]
l3 [X₀ ]
l4 [X₀ ]
l5 [X₀ ]
l13 [X₀ ]
l6 [X₀ ]
l7 [X₀ ]
l1 [X₀ ]

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l11

Found invariant X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l2

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l6

Found invariant X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l12

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l7

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l5

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l13

Found invariant X₀ ≤ X₅ for location l1

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location l10

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l4

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location l9

Found invariant X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₅₄ 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}

TWN-Loops:

entry: t₅₁: l11(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l2(X₀, X₀, X₉, X₃, X₄, X₅, X₈, X₉) :|: 0 ≤ 5+X₈ ∧ X₈ ≤ 5 ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
results in twn-loop: twn:Inv: [X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₃,X₄,X₅,X₈,X₉) -> (X₀,-2⋅X₁,3⋅X₂-(X₈)³,X₃,X₄,X₅,X₈,X₉) :|: X₁ < 0 ∧ (X₁)²+(X₈)⁵ < X₂ ∨ 0 < X₁ ∧ (X₁)²+(X₈)⁵ < X₂
order: [X₀; X₁; X₈; X₂; X₅]
closed-form:
X₀: X₀
X₁: X₁ * 4^n
X₈: X₈
X₂: X₂ * 9^n + [[n != 0]] * -1/2⋅(X₈)³ * 9^n + [[n != 0]] * 1/2⋅(X₈)³
X₅: X₅

Termination: true
Formula:

8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ 2⋅(X₁)² < 0 ∧ X₁ < 0
∨ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ (X₈)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ X₁ < 0
∨ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₈)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₈)³ ∧ X₁ < 0
∨ 3⋅(X₈)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ 2⋅(X₁)² < 0 ∧ X₁ < 0
∨ 3⋅(X₈)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ (X₈)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ X₁ < 0
∨ 3⋅(X₈)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₈)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₈)³ ∧ X₁ < 0
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₈)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₈)³ ∧ 0 < 2⋅X₁ ∧ 2⋅(X₁)² < 0 ∧ X₁ < 0
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₈)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₈)³ ∧ 0 < 2⋅X₁ ∧ (X₈)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ X₁ < 0
∨ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₈)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₈)³ ∧ 0 < 2⋅X₁ ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₈)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₈)³ ∧ X₁ < 0
∨ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ 2⋅(X₁)² < 0 ∧ X₁ < 0
∨ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ (X₈)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ X₁ < 0
∨ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₈)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₈)³ ∧ X₁ < 0
∨ 3⋅(X₈)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ 2⋅(X₁)² < 0 ∧ X₁ < 0
∨ 3⋅(X₈)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ (X₈)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ X₁ < 0
∨ 3⋅(X₈)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₈)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₈)³ ∧ X₁ < 0
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₈)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₈)³ ∧ 2⋅X₁ < 0 ∧ 2⋅(X₁)² < 0 ∧ X₁ < 0
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₈)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₈)³ ∧ 2⋅X₁ < 0 ∧ (X₈)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ X₁ < 0
∨ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₈)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₈)³ ∧ 2⋅X₁ < 0 ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₈)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₈)³ ∧ X₁ < 0
∨ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ 2⋅(X₁)² < 0 ∧ 0 < X₁
∨ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ (X₈)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ 0 < X₁
∨ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₈)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₈)³ ∧ 0 < X₁
∨ 3⋅(X₈)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ 2⋅(X₁)² < 0 ∧ 0 < X₁
∨ 3⋅(X₈)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ (X₈)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ 0 < X₁
∨ 3⋅(X₈)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₈)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₈)³ ∧ 0 < X₁
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₈)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₈)³ ∧ 0 < 2⋅X₁ ∧ 2⋅(X₁)² < 0 ∧ 0 < X₁
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₈)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₈)³ ∧ 0 < 2⋅X₁ ∧ (X₈)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ 0 < X₁
∨ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₈)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₈)³ ∧ 0 < 2⋅X₁ ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₈)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₈)³ ∧ 0 < X₁
∨ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ 2⋅(X₁)² < 0 ∧ 0 < X₁
∨ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ (X₈)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ 0 < X₁
∨ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₈)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₈)³ ∧ 0 < X₁
∨ 3⋅(X₈)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ 2⋅(X₁)² < 0 ∧ 0 < X₁
∨ 3⋅(X₈)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ (X₈)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ 0 < X₁
∨ 3⋅(X₈)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₈)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₈)³ ∧ 0 < X₁
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₈)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₈)³ ∧ 2⋅X₁ < 0 ∧ 2⋅(X₁)² < 0 ∧ 0 < X₁
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₈)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₈)³ ∧ 2⋅X₁ < 0 ∧ (X₈)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ 0 < X₁
∨ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₈)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₈)³ ∧ 2⋅X₁ < 0 ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₈)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₈)³ ∧ 0 < X₁

Stabilization-Threshold for: 4⋅(X₁)²+(X₈)⁵+(X₈)³ < 3⋅X₂
alphas_abs: 6⋅X₂+3⋅(X₈)³+2⋅(X₈)⁵
M: 0
N: 1
Bound: 4⋅X₈⋅X₈⋅X₈⋅X₈⋅X₈+6⋅X₈⋅X₈⋅X₈+12⋅X₂+2 {O(n^5)}
Stabilization-Threshold for: (X₁)²+(X₈)⁵ < X₂
alphas_abs: 2⋅X₂+(X₈)³+2⋅(X₈)⁵
M: 0
N: 1
Bound: 4⋅X₈⋅X₈⋅X₈⋅X₈⋅X₈+2⋅X₈⋅X₈⋅X₈+4⋅X₂+2 {O(n^5)}

relevant size-bounds w.r.t. t₅₁:
X₂: X₉ {O(n)}
X₈: 5 {O(1)}
Runtime-bound of t₅₁: X₅ {O(n)}
Results in: 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}

32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l11

Found invariant X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l2

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l6

Found invariant X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l12

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l7

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l5

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l13

Found invariant X₀ ≤ X₅ for location l1

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location l10

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l4

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location l9

Found invariant X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₅₅ 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}

TWN-Loops:

entry: t₆₁: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l5(X₀, X₁, X₂, X₀, X₉, X₅, X₈, X₉) :|: 0 < X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀
results in twn-loop: twn:Inv: [1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₃,X₄,X₅,X₈,X₉) -> (X₀,X₁,X₂,-2⋅X₃,3⋅X₄-(X₈)³,X₅,X₈,X₉) :|: X₃ < 0 ∧ (X₃)²+(X₈)⁵ < X₄ ∨ 0 < X₃ ∧ (X₃)²+(X₈)⁵ < X₄
order: [X₀; X₃; X₈; X₄; X₅]
closed-form:
X₀: X₀
X₃: X₃ * 4^n
X₈: X₈
X₄: X₄ * 9^n + [[n != 0]] * -1/2⋅(X₈)³ * 9^n + [[n != 0]] * 1/2⋅(X₈)³
X₅: X₅

Termination: true
Formula:

8⋅(X₃)² < 0 ∧ 0 < 2⋅X₃ ∧ 2⋅(X₃)² < 0 ∧ X₃ < 0
∨ 8⋅(X₃)² < 0 ∧ 0 < 2⋅X₃ ∧ (X₈)³ < 2⋅X₄ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ X₃ < 0
∨ 8⋅(X₃)² < 0 ∧ 0 < 2⋅X₃ ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ (X₈)³ ≤ 2⋅X₄ ∧ 2⋅X₄ ≤ (X₈)³ ∧ X₃ < 0
∨ 3⋅(X₈)³ < 6⋅X₄ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 0 < 2⋅X₃ ∧ 2⋅(X₃)² < 0 ∧ X₃ < 0
∨ 3⋅(X₈)³ < 6⋅X₄ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 0 < 2⋅X₃ ∧ (X₈)³ < 2⋅X₄ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ X₃ < 0
∨ 3⋅(X₈)³ < 6⋅X₄ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 0 < 2⋅X₃ ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ (X₈)³ ≤ 2⋅X₄ ∧ 2⋅X₄ ≤ (X₈)³ ∧ X₃ < 0
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 3⋅(X₈)³ ≤ 6⋅X₄ ∧ 6⋅X₄ ≤ 3⋅(X₈)³ ∧ 0 < 2⋅X₃ ∧ 2⋅(X₃)² < 0 ∧ X₃ < 0
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 3⋅(X₈)³ ≤ 6⋅X₄ ∧ 6⋅X₄ ≤ 3⋅(X₈)³ ∧ 0 < 2⋅X₃ ∧ (X₈)³ < 2⋅X₄ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ X₃ < 0
∨ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 3⋅(X₈)³ ≤ 6⋅X₄ ∧ 6⋅X₄ ≤ 3⋅(X₈)³ ∧ 0 < 2⋅X₃ ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ (X₈)³ ≤ 2⋅X₄ ∧ 2⋅X₄ ≤ (X₈)³ ∧ X₃ < 0
∨ 8⋅(X₃)² < 0 ∧ 2⋅X₃ < 0 ∧ 2⋅(X₃)² < 0 ∧ X₃ < 0
∨ 8⋅(X₃)² < 0 ∧ 2⋅X₃ < 0 ∧ (X₈)³ < 2⋅X₄ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ X₃ < 0
∨ 8⋅(X₃)² < 0 ∧ 2⋅X₃ < 0 ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ (X₈)³ ≤ 2⋅X₄ ∧ 2⋅X₄ ≤ (X₈)³ ∧ X₃ < 0
∨ 3⋅(X₈)³ < 6⋅X₄ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 2⋅X₃ < 0 ∧ 2⋅(X₃)² < 0 ∧ X₃ < 0
∨ 3⋅(X₈)³ < 6⋅X₄ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 2⋅X₃ < 0 ∧ (X₈)³ < 2⋅X₄ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ X₃ < 0
∨ 3⋅(X₈)³ < 6⋅X₄ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 2⋅X₃ < 0 ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ (X₈)³ ≤ 2⋅X₄ ∧ 2⋅X₄ ≤ (X₈)³ ∧ X₃ < 0
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 3⋅(X₈)³ ≤ 6⋅X₄ ∧ 6⋅X₄ ≤ 3⋅(X₈)³ ∧ 2⋅X₃ < 0 ∧ 2⋅(X₃)² < 0 ∧ X₃ < 0
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 3⋅(X₈)³ ≤ 6⋅X₄ ∧ 6⋅X₄ ≤ 3⋅(X₈)³ ∧ 2⋅X₃ < 0 ∧ (X₈)³ < 2⋅X₄ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ X₃ < 0
∨ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 3⋅(X₈)³ ≤ 6⋅X₄ ∧ 6⋅X₄ ≤ 3⋅(X₈)³ ∧ 2⋅X₃ < 0 ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ (X₈)³ ≤ 2⋅X₄ ∧ 2⋅X₄ ≤ (X₈)³ ∧ X₃ < 0
∨ 8⋅(X₃)² < 0 ∧ 0 < 2⋅X₃ ∧ 2⋅(X₃)² < 0 ∧ 0 < X₃
∨ 8⋅(X₃)² < 0 ∧ 0 < 2⋅X₃ ∧ (X₈)³ < 2⋅X₄ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ 0 < X₃
∨ 8⋅(X₃)² < 0 ∧ 0 < 2⋅X₃ ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ (X₈)³ ≤ 2⋅X₄ ∧ 2⋅X₄ ≤ (X₈)³ ∧ 0 < X₃
∨ 3⋅(X₈)³ < 6⋅X₄ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 0 < 2⋅X₃ ∧ 2⋅(X₃)² < 0 ∧ 0 < X₃
∨ 3⋅(X₈)³ < 6⋅X₄ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 0 < 2⋅X₃ ∧ (X₈)³ < 2⋅X₄ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ 0 < X₃
∨ 3⋅(X₈)³ < 6⋅X₄ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 0 < 2⋅X₃ ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ (X₈)³ ≤ 2⋅X₄ ∧ 2⋅X₄ ≤ (X₈)³ ∧ 0 < X₃
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 3⋅(X₈)³ ≤ 6⋅X₄ ∧ 6⋅X₄ ≤ 3⋅(X₈)³ ∧ 0 < 2⋅X₃ ∧ 2⋅(X₃)² < 0 ∧ 0 < X₃
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 3⋅(X₈)³ ≤ 6⋅X₄ ∧ 6⋅X₄ ≤ 3⋅(X₈)³ ∧ 0 < 2⋅X₃ ∧ (X₈)³ < 2⋅X₄ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ 0 < X₃
∨ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 3⋅(X₈)³ ≤ 6⋅X₄ ∧ 6⋅X₄ ≤ 3⋅(X₈)³ ∧ 0 < 2⋅X₃ ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ (X₈)³ ≤ 2⋅X₄ ∧ 2⋅X₄ ≤ (X₈)³ ∧ 0 < X₃
∨ 8⋅(X₃)² < 0 ∧ 2⋅X₃ < 0 ∧ 2⋅(X₃)² < 0 ∧ 0 < X₃
∨ 8⋅(X₃)² < 0 ∧ 2⋅X₃ < 0 ∧ (X₈)³ < 2⋅X₄ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ 0 < X₃
∨ 8⋅(X₃)² < 0 ∧ 2⋅X₃ < 0 ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ (X₈)³ ≤ 2⋅X₄ ∧ 2⋅X₄ ≤ (X₈)³ ∧ 0 < X₃
∨ 3⋅(X₈)³ < 6⋅X₄ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 2⋅X₃ < 0 ∧ 2⋅(X₃)² < 0 ∧ 0 < X₃
∨ 3⋅(X₈)³ < 6⋅X₄ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 2⋅X₃ < 0 ∧ (X₈)³ < 2⋅X₄ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ 0 < X₃
∨ 3⋅(X₈)³ < 6⋅X₄ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 2⋅X₃ < 0 ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ (X₈)³ ≤ 2⋅X₄ ∧ 2⋅X₄ ≤ (X₈)³ ∧ 0 < X₃
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 3⋅(X₈)³ ≤ 6⋅X₄ ∧ 6⋅X₄ ≤ 3⋅(X₈)³ ∧ 2⋅X₃ < 0 ∧ 2⋅(X₃)² < 0 ∧ 0 < X₃
∨ 2⋅(X₈)⁵ < (X₈)³ ∧ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 3⋅(X₈)³ ≤ 6⋅X₄ ∧ 6⋅X₄ ≤ 3⋅(X₈)³ ∧ 2⋅X₃ < 0 ∧ (X₈)³ < 2⋅X₄ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ 0 < X₃
∨ 8⋅(X₃)² ≤ 0 ∧ 0 ≤ 8⋅(X₃)² ∧ 3⋅(X₈)³ ≤ 6⋅X₄ ∧ 6⋅X₄ ≤ 3⋅(X₈)³ ∧ 2⋅X₃ < 0 ∧ 2⋅(X₈)⁵ < (X₈)³ ∧ 2⋅(X₃)² ≤ 0 ∧ 0 ≤ 2⋅(X₃)² ∧ (X₈)³ ≤ 2⋅X₄ ∧ 2⋅X₄ ≤ (X₈)³ ∧ 0 < X₃

Stabilization-Threshold for: 4⋅(X₃)²+(X₈)⁵+(X₈)³ < 3⋅X₄
alphas_abs: 6⋅X₄
M: 0
N: 1
Bound: 12⋅X₄+2 {O(n)}
Stabilization-Threshold for: (X₃)²+(X₈)⁵ < X₄
alphas_abs: 2⋅X₄
M: 0
N: 1
Bound: 4⋅X₄+2 {O(n)}

relevant size-bounds w.r.t. t₆₁:
X₄: X₉ {O(n)}
Runtime-bound of t₆₁: X₅+1 {O(n)}
Results in: 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}

32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₅₆ 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}

relevant size-bounds w.r.t. t₅₁:
X₂: X₉ {O(n)}
X₈: 5 {O(1)}
Runtime-bound of t₅₁: X₅ {O(n)}
Results in: 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}

32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₅₇ 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}

relevant size-bounds w.r.t. t₅₁:
X₂: X₉ {O(n)}
X₈: 5 {O(1)}
Runtime-bound of t₅₁: X₅ {O(n)}
Results in: 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}

32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₅₉ 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}

relevant size-bounds w.r.t. t₅₁:
X₂: X₉ {O(n)}
X₈: 5 {O(1)}
Runtime-bound of t₅₁: X₅ {O(n)}
Results in: 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}

32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₆₃ 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}

relevant size-bounds w.r.t. t₆₁:
X₄: X₉ {O(n)}
Runtime-bound of t₆₁: X₅+1 {O(n)}
Results in: 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}

32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₆₄ 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}

relevant size-bounds w.r.t. t₆₁:
X₄: X₉ {O(n)}
Runtime-bound of t₆₁: X₅+1 {O(n)}
Results in: 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}

32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₆₆ 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}

relevant size-bounds w.r.t. t₆₁:
X₄: X₉ {O(n)}
Runtime-bound of t₆₁: X₅+1 {O(n)}
Results in: 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}

32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}

Analysing control-flow refined program

Cut unsatisfiable transition t₅₈: l2→l7

Cut unsatisfiable transition t₆₅: l5→l7

Cut unsatisfiable transition t₂₅₈: n_l2___3→l7

Cut unsatisfiable transition t₂₅₉: n_l2___6→l7

Cut unsatisfiable transition t₂₉₂: n_l5___1→l7

Cut unsatisfiable transition t₂₉₃: n_l5___4→l7

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l11

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 3+X₃ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 3+X₃ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2+X₃ ≤ 0 ∧ 3+X₃ ≤ X₀ ∧ 1+X₀+X₃ ≤ 0 ∧ 1 ≤ X₀ for location n_l6___3

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₃+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location n_l6___6

Found invariant X₉ ≤ X₂ ∧ X₂ ≤ X₉ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₁ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₁+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2

Found invariant X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₁+X₈ ≤ 3 ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ X₁ ≤ 3+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 3+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location n_l2___6

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 5 ≤ X₃+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 5 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 4 ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 3+X₀ ≤ X₃ ∧ 1 ≤ X₀ for location n_l5___1

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 3+X₃ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 3+X₃ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2+X₃ ≤ 0 ∧ 3+X₃ ≤ X₀ ∧ 1+X₀+X₃ ≤ 0 ∧ 1 ≤ X₀ for location n_l13___2

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₃+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location n_l13___5

Found invariant X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₁+X₈ ≤ 3 ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ X₁ ≤ 3+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 3+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location n_l3___5

Found invariant X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 1+X₁ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 1+X₁+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 5 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l2___3

Found invariant 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 3+X₃ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 3+X₃ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2+X₃ ≤ 0 ∧ 3+X₃ ≤ X₀ ∧ 1+X₀+X₃ ≤ 0 ∧ 1 ≤ X₀ for location n_l5___4

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l7

Found invariant X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 1+X₁ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 1+X₁+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 5 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l12___1

Found invariant X₉ ≤ X₂ ∧ X₂ ≤ X₉ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₁ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₁+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___8

Found invariant X₉ ≤ X₄ ∧ X₄ ≤ X₉ ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₃+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l5

Found invariant X₉ ≤ X₂ ∧ X₂ ≤ X₉ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₁ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₁+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l12___7

Found invariant X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 1+X₁ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 1+X₁+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 5 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___2

Found invariant X₀ ≤ X₅ for location l1

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location l10

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ for location l4

Found invariant X₀ ≤ X₅ ∧ X₀ ≤ 0 for location l9

Found invariant X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₁+X₈ ≤ 3 ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ X₁ ≤ 3+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 3+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location n_l12___4

knowledge_propagation leads to new time bound X₅ {O(n)} for transition t₂₄₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → n_l3___8(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₈ ≤ 5 ∧ 0 ≤ 5+X₈ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ ∧ 0 < X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₉ ∧ X₉ ≤ X₂ ∧ 0 ≤ 5+X₈ ∧ 1 ≤ X₀ ∧ X₈ ≤ 5 ∧ X₀ ≤ X₅ ∧ 0 ≤ 5+X₈ ∧ 1 ≤ X₀ ∧ X₈ ≤ 5 ∧ X₀ ≤ X₅ ∧ 0 ≤ 5+X₈ ∧ X₈ ≤ 5 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₅ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ 5+X₈ ∧ X₈ ≤ 5 ∧ X₀ ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₉ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₁ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₁+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₅+1 {O(n)} for transition t₂₇₉: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → n_l6___6(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₀ ≤ X₅ ∧ 1 ≤ X₀ ∧ 0 < X₃ ∧ 0 < X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₈ ∧ X₀ ≤ X₅ ∧ X₉ ≤ X₄ ∧ X₄ ≤ X₉ ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₃+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₅ {O(n)} for transition t₂₄₆: n_l3___8(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → n_l12___7(X₀, X₁, X₂, X₃, X₄, Arg5_P, Arg8_P, X₉) :|: X₈ ≤ 5 ∧ 0 ≤ 5+X₈ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₉ ∧ X₉ ≤ X₂ ∧ Arg8_P ≤ 5 ∧ 0 ≤ 5+Arg8_P ∧ X₀ ≤ Arg5_P ∧ 1 ≤ X₀ ∧ X₈ ≤ Arg8_P ∧ Arg8_P ≤ X₈ ∧ X₅ ≤ Arg5_P ∧ Arg5_P ≤ X₅ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₉ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₁ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₁+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₅ {O(n)} for transition t₂₅₇: n_l3___8(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₂ ≤ (X₁)²+(X₈)⁵ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₉ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₁ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₁+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₅ {O(n)} for transition t₂₄₀: n_l12___7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → n_l2___6(X₀, -2⋅X₁, NoDet0, X₃, X₄, Arg5_P, Arg8_P, X₉) :|: X₈ ≤ 5 ∧ 0 ≤ 5+X₈ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₉ ∧ X₉ ≤ X₂ ∧ Arg8_P ≤ 5 ∧ 0 ≤ 5+Arg8_P ∧ X₀ ≤ Arg5_P ∧ 1 ≤ X₀ ∧ X₅ ≤ Arg5_P ∧ Arg5_P ≤ X₅ ∧ X₈ ≤ Arg8_P ∧ Arg8_P ≤ X₈ ∧ X₉ ≤ X₂ ∧ X₂ ≤ X₉ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₁ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₁+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₁+X₅ ∧ X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

MPRF for transition t₂₅₅: n_l3___2(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₂ ≤ (X₁)²+(X₈)⁵ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 1+X₁ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 1+X₁+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 5 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₅ {O(n)}

MPRF:

l11 [X₀+X₅ ]
l2 [X₀+X₅ ]
l4 [X₀+X₅ ]
l5 [X₀+X₅ ]
l1 [X₀+X₅ ]
n_l2___3 [X₀+X₅ ]
n_l2___6 [X₀+X₅ ]
n_l12___1 [X₀+X₅ ]
n_l3___2 [X₀+X₅ ]
n_l12___4 [X₀+X₅ ]
n_l3___5 [X₀+X₅ ]
n_l12___7 [X₁+X₅ ]
n_l3___8 [X₁+X₅ ]
n_l5___1 [X₀+X₅ ]
n_l5___4 [X₀+X₅ ]
n_l13___2 [X₀+X₅ ]
n_l6___3 [X₀+X₅ ]
n_l13___5 [X₀+X₅ ]
n_l6___6 [X₀+X₅ ]
l7 [X₀+X₅-1 ]

MPRF for transition t₂₅₆: n_l3___5(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₂ ≤ (X₁)²+(X₈)⁵ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ ∧ X₈ ≤ 5 ∧ X₈ ≤ 4+X₅ ∧ X₁+X₈ ≤ 3 ∧ X₈ ≤ 4+X₀ ∧ 0 ≤ 5+X₈ ∧ 0 ≤ 4+X₅+X₈ ∧ X₁ ≤ 3+X₈ ∧ 0 ≤ 4+X₀+X₈ ∧ 1 ≤ X₅ ∧ 3+X₁ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₅ {O(n)}

MPRF:

l11 [X₀+X₅ ]
l2 [X₀+X₅ ]
l4 [X₀+X₅ ]
l5 [X₃+X₅ ]
l1 [X₀+X₅ ]
n_l2___3 [X₀+X₅ ]
n_l2___6 [X₀+X₅ ]
n_l12___1 [X₀+X₅ ]
n_l3___2 [X₀+X₅ ]
n_l12___4 [X₀+X₅ ]
n_l3___5 [X₀+X₅ ]
n_l12___7 [X₀+X₅ ]
n_l3___8 [X₁+X₅ ]
n_l5___1 [X₀+X₅ ]
n_l5___4 [X₀+X₅ ]
n_l13___2 [X₀+X₅ ]
n_l6___3 [X₀+X₅ ]
n_l13___5 [X₀+X₅ ]
n_l6___6 [X₀+X₅ ]
l7 [X₀+X₅-1 ]

MPRF for transition t₂₉₀: n_l6___3(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₄ ≤ (X₃)²+(X₈)⁵ ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 3+X₃ ≤ X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 3+X₃ ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 2+X₃ ≤ 0 ∧ 3+X₃ ≤ X₀ ∧ 1+X₀+X₃ ≤ 0 ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₅ {O(n)}

MPRF:

l11 [X₀+X₅ ]
l2 [X₀+X₅ ]
l4 [X₀+X₅ ]
l5 [X₀+X₅ ]
l1 [X₀+X₅ ]
n_l2___3 [X₀+X₅ ]
n_l2___6 [X₀+X₅ ]
n_l12___1 [X₀+X₅ ]
n_l3___2 [X₀+X₅ ]
n_l12___4 [X₀+X₅ ]
n_l3___5 [X₀+X₅ ]
n_l12___7 [X₁+X₅ ]
n_l3___8 [X₀+X₅ ]
n_l5___1 [X₀+X₅ ]
n_l5___4 [X₀+X₅ ]
n_l13___2 [X₀+X₅ ]
n_l6___3 [X₀+X₅ ]
n_l13___5 [X₀+X₅ ]
n_l6___6 [X₀+X₅ ]
l7 [X₀+X₅-1 ]

MPRF for transition t₂₉₁: n_l6___6(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₈, X₉) :|: X₄ ≤ (X₃)²+(X₈)⁵ ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₀ ∧ 1 ≤ X₈ ∧ 2 ≤ X₅+X₈ ∧ 2 ≤ X₃+X₈ ∧ 2 ≤ X₀+X₈ ∧ 1 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:

new bound:

3⋅X₅+4 {O(n)}

MPRF:

l11 [3⋅X₀+4 ]
l2 [3⋅X₁+1 ]
l4 [3⋅X₀+4 ]
l5 [3⋅X₀+4 ]
l1 [3⋅X₀+4 ]
n_l2___3 [3⋅X₀+1 ]
n_l2___6 [3⋅X₀+1 ]
n_l12___1 [3⋅X₀+1 ]
n_l3___2 [3⋅X₀+1 ]
n_l12___4 [3⋅X₀+1 ]
n_l3___5 [3⋅X₀+1 ]
n_l12___7 [3⋅X₀+1 ]
n_l3___8 [3⋅X₁+1 ]
n_l5___1 [3⋅X₀+4 ]
n_l5___4 [3⋅X₀+4 ]
n_l13___2 [3⋅X₀+4 ]
n_l6___3 [3⋅X₀+4 ]
n_l13___5 [3⋅X₀+4 ]
n_l6___6 [3⋅X₀+4 ]
l7 [3⋅X₀+1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:256⋅X₅⋅X₉+11⋅X₈+128⋅X₉+208208⋅X₅+97 {O(n^2)}
t₄₇: 1 {O(1)}
t₄₈: X₅+1 {O(n)}
t₄₉: 1 {O(1)}
t₅₀: 1 {O(1)}
t₅₁: X₅ {O(n)}
t₅₂: X₅+1 {O(n)}
t₅₃: X₅+1 {O(n)}
t₅₄: 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}
t₅₅: 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}
t₅₆: 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}
t₅₇: 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}
t₅₈: X₅ {O(n)}
t₅₉: 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}
t₆₀: 2⋅X₅ {O(n)}
t₆₁: X₅+1 {O(n)}
t₆₂: X₅ {O(n)}
t₆₃: 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}
t₆₄: 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}
t₆₅: 20⋅X₅+X₈+5 {O(n)}
t₆₆: 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}
t₆₇: 10⋅X₅+10⋅X₈ {O(n)}
t₆₈: X₅ {O(n)}
t₆₉: 1 {O(1)}

Costbounds

Overall costbound: 256⋅X₅⋅X₉+11⋅X₈+128⋅X₉+208208⋅X₅+97 {O(n^2)}
t₄₇: 1 {O(1)}
t₄₈: X₅+1 {O(n)}
t₄₉: 1 {O(1)}
t₅₀: 1 {O(1)}
t₅₁: X₅ {O(n)}
t₅₂: X₅+1 {O(n)}
t₅₃: X₅+1 {O(n)}
t₅₄: 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}
t₅₅: 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}
t₅₆: 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}
t₅₇: 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}
t₅₈: X₅ {O(n)}
t₅₉: 32⋅X₅⋅X₉+52021⋅X₅ {O(n^2)}
t₆₀: 2⋅X₅ {O(n)}
t₆₁: X₅+1 {O(n)}
t₆₂: X₅ {O(n)}
t₆₃: 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}
t₆₄: 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}
t₆₅: 20⋅X₅+X₈+5 {O(n)}
t₆₆: 32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21 {O(n^2)}
t₆₇: 10⋅X₅+10⋅X₈ {O(n)}
t₆₈: X₅ {O(n)}
t₆₉: 1 {O(1)}

Sizebounds

t₄₇, X₀: X₀ {O(n)}
t₄₇, X₁: X₁ {O(n)}
t₄₇, X₂: X₂ {O(n)}
t₄₇, X₃: X₃ {O(n)}
t₄₇, X₄: X₄ {O(n)}
t₄₇, X₅: X₅ {O(n)}
t₄₇, X₈: X₈ {O(n)}
t₄₇, X₉: X₉ {O(n)}
t₄₈, X₀: X₅ {O(n)}
t₄₈, X₁: 2⋅2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅+X₁ {O(EXP)}
t₄₈, X₃: 2⋅2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅+X₃ {O(EXP)}
t₄₈, X₅: X₅ {O(n)}
t₄₈, X₈: X₈+10 {O(n)}
t₄₈, X₉: X₉ {O(n)}
t₄₉, X₀: 2⋅X₅ {O(n)}
t₄₉, X₁: 2⋅2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅+2⋅X₁ {O(EXP)}
t₄₉, X₃: 2⋅2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅+2⋅X₃ {O(EXP)}
t₄₉, X₅: 2⋅X₅ {O(n)}
t₄₉, X₈: 2⋅X₈+10 {O(n)}
t₄₉, X₉: 2⋅X₉ {O(n)}
t₅₀, X₀: 2⋅X₅ {O(n)}
t₅₀, X₁: 2⋅2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅+2⋅X₁ {O(EXP)}
t₅₀, X₃: 2⋅2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅+2⋅X₃ {O(EXP)}
t₅₀, X₅: 2⋅X₅ {O(n)}
t₅₀, X₈: 2⋅X₈+10 {O(n)}
t₅₀, X₉: 2⋅X₉ {O(n)}
t₅₁, X₀: X₅ {O(n)}
t₅₁, X₁: X₅ {O(n)}
t₅₁, X₂: X₉ {O(n)}
t₅₁, X₃: 2⋅2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅+X₃ {O(EXP)}
t₅₁, X₅: X₅ {O(n)}
t₅₁, X₈: 5 {O(1)}
t₅₁, X₉: X₉ {O(n)}
t₅₂, X₀: X₅ {O(n)}
t₅₂, X₁: 2⋅2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅+X₁ {O(EXP)}
t₅₂, X₃: 2⋅2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅+X₃ {O(EXP)}
t₅₂, X₅: X₅ {O(n)}
t₅₂, X₈: X₈+10 {O(n)}
t₅₂, X₉: X₉ {O(n)}
t₅₃, X₀: X₅ {O(n)}
t₅₃, X₁: 2⋅2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅+X₁ {O(EXP)}
t₅₃, X₃: 2⋅2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅+X₃ {O(EXP)}
t₅₃, X₅: X₅ {O(n)}
t₅₃, X₈: X₈+10 {O(n)}
t₅₃, X₉: X₉ {O(n)}
t₅₄, X₀: X₅ {O(n)}
t₅₄, X₁: 2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅ {O(EXP)}
t₅₄, X₃: 2⋅2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅+X₃ {O(EXP)}
t₅₄, X₅: X₅ {O(n)}
t₅₄, X₈: 5 {O(1)}
t₅₄, X₉: X₉ {O(n)}
t₅₅, X₀: X₅ {O(n)}
t₅₅, X₁: 2⋅2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅+X₁ {O(EXP)}
t₅₅, X₃: 2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅ {O(EXP)}
t₅₅, X₅: X₅ {O(n)}
t₅₅, X₈: X₈+10 {O(n)}
t₅₅, X₉: X₉ {O(n)}
t₅₆, X₀: X₅ {O(n)}
t₅₆, X₁: 2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅ {O(EXP)}
t₅₆, X₃: 2⋅2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅+X₃ {O(EXP)}
t₅₆, X₅: X₅ {O(n)}
t₅₆, X₈: 5 {O(1)}
t₅₆, X₉: X₉ {O(n)}
t₅₇, X₀: X₅ {O(n)}
t₅₇, X₁: 2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅ {O(EXP)}
t₅₇, X₃: 2⋅2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅+X₃ {O(EXP)}
t₅₇, X₅: X₅ {O(n)}
t₅₇, X₈: 5 {O(1)}
t₅₇, X₉: X₉ {O(n)}
t₅₈, X₀: X₅ {O(n)}
t₅₈, X₁: 0 {O(1)}
t₅₈, X₃: 2⋅2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅+X₃ {O(EXP)}
t₅₈, X₅: X₅ {O(n)}
t₅₈, X₈: 5 {O(1)}
t₅₈, X₉: X₉ {O(n)}
t₅₉, X₀: X₅ {O(n)}
t₅₉, X₁: 2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅ {O(EXP)}
t₅₉, X₃: 2⋅2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅+X₃ {O(EXP)}
t₅₉, X₅: X₅ {O(n)}
t₅₉, X₈: 5 {O(1)}
t₅₉, X₉: X₉ {O(n)}
t₆₀, X₀: X₅ {O(n)}
t₆₀, X₁: 2⋅2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅ {O(EXP)}
t₆₀, X₃: 2⋅2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅+X₃ {O(EXP)}
t₆₀, X₅: X₅ {O(n)}
t₆₀, X₈: 5 {O(1)}
t₆₀, X₉: X₉ {O(n)}
t₆₁, X₀: X₅ {O(n)}
t₆₁, X₁: 2⋅2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅+X₁ {O(EXP)}
t₆₁, X₃: X₅ {O(n)}
t₆₁, X₄: X₉ {O(n)}
t₆₁, X₅: X₅ {O(n)}
t₆₁, X₈: X₈+10 {O(n)}
t₆₁, X₉: X₉ {O(n)}
t₆₂, X₀: X₅ {O(n)}
t₆₂, X₁: 2⋅2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅+X₁ {O(EXP)}
t₆₂, X₃: 2⋅2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅+X₃ {O(EXP)}
t₆₂, X₅: X₅ {O(n)}
t₆₂, X₈: X₈+10 {O(n)}
t₆₂, X₉: X₉ {O(n)}
t₆₃, X₀: X₅ {O(n)}
t₆₃, X₁: 2⋅2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅+X₁ {O(EXP)}
t₆₃, X₃: 2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅ {O(EXP)}
t₆₃, X₅: X₅ {O(n)}
t₆₃, X₈: X₈+10 {O(n)}
t₆₃, X₉: X₉ {O(n)}
t₆₄, X₀: X₅ {O(n)}
t₆₄, X₁: 2⋅2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅+X₁ {O(EXP)}
t₆₄, X₃: 2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅ {O(EXP)}
t₆₄, X₅: X₅ {O(n)}
t₆₄, X₈: X₈+10 {O(n)}
t₆₄, X₉: X₉ {O(n)}
t₆₅, X₀: X₅ {O(n)}
t₆₅, X₁: 2⋅2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅+X₁ {O(EXP)}
t₆₅, X₃: 0 {O(1)}
t₆₅, X₅: X₅ {O(n)}
t₆₅, X₈: X₈+10 {O(n)}
t₆₅, X₉: X₉ {O(n)}
t₆₆, X₀: X₅ {O(n)}
t₆₆, X₁: 2⋅2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅+X₁ {O(EXP)}
t₆₆, X₃: 2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅ {O(EXP)}
t₆₆, X₅: X₅ {O(n)}
t₆₆, X₈: X₈+10 {O(n)}
t₆₆, X₉: X₉ {O(n)}
t₆₇, X₀: X₅ {O(n)}
t₆₇, X₁: 2⋅2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅+X₁ {O(EXP)}
t₆₇, X₃: 2⋅2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅ {O(EXP)}
t₆₇, X₅: X₅ {O(n)}
t₆₇, X₈: X₈+10 {O(n)}
t₆₇, X₉: X₉ {O(n)}
t₆₈, X₀: X₅ {O(n)}
t₆₈, X₁: 2⋅2^(32⋅X₅⋅X₉+52021⋅X₅)⋅X₅+X₁ {O(EXP)}
t₆₈, X₃: 2⋅2^(32⋅X₅⋅X₉+21⋅X₅+32⋅X₉+21)⋅X₅+X₃ {O(EXP)}
t₆₈, X₅: X₅ {O(n)}
t₆₈, X₈: X₈+10 {O(n)}
t₆₈, X₉: X₉ {O(n)}
t₆₉, X₀: X₅ {O(n)}
t₆₉, X₁: X₁ {O(n)}
t₆₉, X₂: X₂ {O(n)}
t₆₉, X₃: X₃ {O(n)}
t₆₉, X₄: X₄ {O(n)}
t₆₉, X₅: X₅ {O(n)}
t₆₉, X₈: X₈ {O(n)}
t₆₉, X₉: X₉ {O(n)}