Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄
Temp_Vars: P, Q
Locations: f0, f1, f2, f3, f4, f6, f7
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄)
t₄: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f2(X₀, 0, X₃, X₃, X₅, X₅, 3, Q, 0, 0, 3, Q, 2, X₁₃, X₁₄) :|: Q ≤ 7 ∧ Q ≤ 3 ∧ 1 ≤ Q
t₅: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f2(X₀, 0, X₃, X₃, X₅, X₅, 3, Q, 0, 0, 3, Q, 2, X₁₃, X₁₄) :|: Q ≤ 7 ∧ 5 ≤ Q
t₆: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f2(X₀, 0, 1+X₃, 1+X₃, 1+X₅, 1+X₅, 3, 4, 1, 0, 3, 4, 2, X₁₃, X₁₄)
t₁: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f7(X₀-1, 1, X₃, X₃, X₅, X₅, Q, P, 0, 1, Q, P, 7, X₁₃, X₁₄) :|: P ≤ 7 ∧ Q ≤ 7 ∧ P ≤ 3 ∧ 1 ≤ P ∧ 1 ≤ Q ∧ 1 ≤ X₀
t₂: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f7(X₀, 1, X₃, X₃, X₅, X₅, Q, P, 0, 1, Q, P, 7, X₁₃, X₁₄) :|: P ≤ 7 ∧ Q ≤ 7 ∧ 1 ≤ Q ∧ 5 ≤ P
t₃: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f7(X₀, 1, 1+X₃, 1+X₃, 1+X₅, 1+X₅, Q, 4, 1, 1, Q, 4, 7, X₁₃, X₁₄) :|: Q ≤ 7 ∧ 1 ≤ Q
t₁₀: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f3(X₀, 0, X₃, X₃, X₅, X₅, Q, P, X₈, 0, Q, P, 3, X₁₃, X₁₄) :|: P ≤ 7 ∧ Q ≤ 7 ∧ P ≤ 3 ∧ 1 ≤ P ∧ 1 ≤ Q
t₁₁: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f3(X₀, 0, X₃, X₃, X₅, X₅, Q, P, X₈, 0, Q, P, 3, X₁₃, X₁₄) :|: P ≤ 7 ∧ Q ≤ 7 ∧ 1 ≤ Q ∧ 5 ≤ P
t₁₂: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f3(X₀, 0, 1+X₃, 1+X₃, 1+X₅, 1+X₅, Q, 4, 1, 0, Q, 4, 3, X₁₃, X₁₄) :|: Q ≤ 7 ∧ 1 ≤ Q
t₇: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f7(X₀, 1, X₃, X₃, X₅, X₅, Q, P, X₈, 1, Q, P, 7, X₁₃, X₁₄) :|: P ≤ 7 ∧ Q ≤ 7 ∧ P ≤ 3 ∧ 1 ≤ P ∧ 1 ≤ Q
t₈: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f7(X₀, 1, X₃, X₃, X₅, X₅, Q, P, X₈, 1, Q, P, 7, X₁₃, X₁₄) :|: P ≤ 7 ∧ Q ≤ 7 ∧ 1 ≤ Q ∧ 5 ≤ P
t₉: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f7(X₀, 1, 1+X₃, 1+X₃, 1+X₅, 1+X₅, Q, 4, 1, 1, Q, 4, 7, X₁₃, X₁₄) :|: Q ≤ 7 ∧ 1 ≤ Q
t₁₃: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f6(X₀, 1, X₃, X₃, X₅, X₅, Q, P, X₈, 1, Q, P, 6, X₁₃, X₁₄) :|: P ≤ 7 ∧ Q ≤ 7 ∧ P ≤ 3 ∧ 1 ≤ P ∧ 1 ≤ Q
t₁₄: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f6(X₀, 1, X₃, X₃, X₅, X₅, Q, P, X₈, 1, Q, P, 6, X₁₃, X₁₄) :|: P ≤ 7 ∧ Q ≤ 7 ∧ 1 ≤ Q ∧ 5 ≤ P
t₁₅: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f6(X₀, 1, 1+X₃, 1+X₃, 1+X₅, 1+X₅, Q, 4, 1, 1, Q, 4, 6, X₁₃, X₁₄) :|: Q ≤ 7 ∧ 1 ≤ Q
t₁₈: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f2(X₀, 0, X₃, X₃, X₅, X₅, Q, P, 1, 0, Q, P, 2, X₁₃, X₁₄) :|: P ≤ 7 ∧ Q ≤ 7 ∧ P ≤ 3 ∧ X₈ ≤ 1 ∧ 1 ≤ P ∧ 1 ≤ Q ∧ 1+X₃ ≤ X₁₄ ∧ 1+X₅ ≤ X₁₃ ∧ 1 ≤ X₈ ∧ 1 ≤ X₁₃ ∧ 1 ≤ X₁₄
t₁₉: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f2(X₀, 0, X₃, X₃, X₅, X₅, Q, P, 1, 0, Q, P, 2, X₁₃, X₁₄) :|: P ≤ 7 ∧ Q ≤ 7 ∧ X₈ ≤ 1 ∧ 1 ≤ Q ∧ 1+X₃ ≤ X₁₄ ∧ 1+X₅ ≤ X₁₃ ∧ 1 ≤ X₈ ∧ 1 ≤ X₁₃ ∧ 1 ≤ X₁₄ ∧ 5 ≤ P
t₂₀: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f2(X₀, 0, 1+X₃, 1+X₃, 1+X₅, 1+X₅, Q, 4, 1, 0, Q, 4, 2, X₁₃, X₁₄) :|: Q ≤ 7 ∧ 1 ≤ Q ∧ 1 ≤ X₁₃ ∧ 1 ≤ X₁₄ ∧ 2+X₃ ≤ X₁₄ ∧ 2+X₅ ≤ X₁₃
t₂₁: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f7(X₀, 0, X₃, X₃, X₅, X₅, Q, P, X₈, 0, Q, P, 7, X₁₃, X₁₄) :|: P ≤ 7 ∧ Q ≤ 7 ∧ P ≤ 3 ∧ 1 ≤ P ∧ 1 ≤ Q ∧ X₁₄ ≤ X₃ ∧ X₁₃ ≤ X₅
t₂₂: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f7(X₀, 0, X₃, X₃, X₅, X₅, Q, P, X₈, 0, Q, P, 7, X₁₃, X₁₄) :|: P ≤ 7 ∧ Q ≤ 7 ∧ 1 ≤ Q ∧ 5 ≤ P ∧ X₁₄ ≤ X₃ ∧ X₁₃ ≤ X₅
t₂₃: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f7(X₀, 0, 1+X₃, 1+X₃, 1+X₅, 1+X₅, Q, 4, 1, 0, Q, 4, 7, X₁₃, X₁₄) :|: Q ≤ 7 ∧ X₁₄ ≤ 1+X₃ ∧ X₁₃ ≤ 1+X₅ ∧ 1 ≤ Q
t₂₄: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f7(X₀, 1, X₃, X₃, X₅, X₅, Q, P, X₈, 1, Q, P, 7, X₁₃, X₁₄) :|: P ≤ 7 ∧ Q ≤ 7 ∧ P ≤ 3 ∧ 1 ≤ P ∧ 1 ≤ Q
t₂₅: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f7(X₀, 1, X₃, X₃, X₅, X₅, Q, P, X₈, 1, Q, P, 7, X₁₃, X₁₄) :|: P ≤ 7 ∧ Q ≤ 7 ∧ 1 ≤ Q ∧ 5 ≤ P
t₂₆: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f7(X₀, 1, 1+X₃, 1+X₃, 1+X₅, 1+X₅, Q, 4, 1, 1, Q, 4, 7, X₁₃, X₁₄) :|: Q ≤ 7 ∧ 1 ≤ Q
t₁₆: f6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f4(X₀, 1, X₃, X₃, X₅, X₅, Q, 2, 0, 1, Q, 2, 4, X₁₃, X₁₄) :|: Q ≤ 7 ∧ 1 ≤ Q
t₁₇: f6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f4(X₀, Q, X₃, X₃, X₅, X₅, P, 7, 1, Q, P, 7, 4, X₁₃, X₁₄) :|: P ≤ 7 ∧ Q ≤ 1 ∧ X₈ ≤ 1 ∧ 1 ≤ P ∧ 1 ≤ X₈ ∧ 0 ≤ Q

Preprocessing

Eliminate variables [X₁; X₂; X₄; X₆; X₇; X₉; X₁₀; X₁₁; X₁₂] that do not contribute to the problem

Found invariant X₃ ≤ 1 ∧ 0 ≤ X₃ for location f6

Found invariant X₃ ≤ 1 ∧ 0 ≤ X₃ for location f3

Found invariant X₃ ≤ 1 ∧ 0 ≤ X₃ for location f2

Found invariant X₃ ≤ 1 ∧ 0 ≤ X₃ for location f4

Found invariant X₃ ≤ 1 ∧ 0 ≤ X₃ for location f7

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: P, Q
Locations: f0, f1, f2, f3, f4, f6, f7
Transitions:
t₅₃: f0(X₀, X₁, X₂, X₃, X₄, X₅) → f1(X₀, X₁, X₂, X₃, X₄, X₅)
t₅₄: f1(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀, X₁, X₂, 0, X₄, X₅) :|: Q ≤ 7 ∧ Q ≤ 3 ∧ 1 ≤ Q
t₅₅: f1(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀, X₁, X₂, 0, X₄, X₅) :|: Q ≤ 7 ∧ 5 ≤ Q
t₅₆: f1(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀, 1+X₁, 1+X₂, 1, X₄, X₅)
t₅₇: f1(X₀, X₁, X₂, X₃, X₄, X₅) → f7(X₀-1, X₁, X₂, 0, X₄, X₅) :|: P ≤ 7 ∧ Q ≤ 7 ∧ P ≤ 3 ∧ 1 ≤ P ∧ 1 ≤ Q ∧ 1 ≤ X₀
t₅₈: f1(X₀, X₁, X₂, X₃, X₄, X₅) → f7(X₀, X₁, X₂, 0, X₄, X₅) :|: P ≤ 7 ∧ Q ≤ 7 ∧ 1 ≤ Q ∧ 5 ≤ P
t₅₉: f1(X₀, X₁, X₂, X₃, X₄, X₅) → f7(X₀, 1+X₁, 1+X₂, 1, X₄, X₅) :|: Q ≤ 7 ∧ 1 ≤ Q
t₆₀: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f3(X₀, X₁, X₂, X₃, X₄, X₅) :|: P ≤ 7 ∧ Q ≤ 7 ∧ P ≤ 3 ∧ 1 ≤ P ∧ 1 ≤ Q ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₆₁: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f3(X₀, X₁, X₂, X₃, X₄, X₅) :|: P ≤ 7 ∧ Q ≤ 7 ∧ 1 ≤ Q ∧ 5 ≤ P ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₆₂: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f3(X₀, 1+X₁, 1+X₂, 1, X₄, X₅) :|: Q ≤ 7 ∧ 1 ≤ Q ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₆₃: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f7(X₀, X₁, X₂, X₃, X₄, X₅) :|: P ≤ 7 ∧ Q ≤ 7 ∧ P ≤ 3 ∧ 1 ≤ P ∧ 1 ≤ Q ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₆₄: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f7(X₀, X₁, X₂, X₃, X₄, X₅) :|: P ≤ 7 ∧ Q ≤ 7 ∧ 1 ≤ Q ∧ 5 ≤ P ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₆₅: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f7(X₀, 1+X₁, 1+X₂, 1, X₄, X₅) :|: Q ≤ 7 ∧ 1 ≤ Q ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₆₆: f3(X₀, X₁, X₂, X₃, X₄, X₅) → f6(X₀, X₁, X₂, X₃, X₄, X₅) :|: P ≤ 7 ∧ Q ≤ 7 ∧ P ≤ 3 ∧ 1 ≤ P ∧ 1 ≤ Q ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₆₇: f3(X₀, X₁, X₂, X₃, X₄, X₅) → f6(X₀, X₁, X₂, X₃, X₄, X₅) :|: P ≤ 7 ∧ Q ≤ 7 ∧ 1 ≤ Q ∧ 5 ≤ P ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₆₈: f3(X₀, X₁, X₂, X₃, X₄, X₅) → f6(X₀, 1+X₁, 1+X₂, 1, X₄, X₅) :|: Q ≤ 7 ∧ 1 ≤ Q ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₆₉: f4(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀, X₁, X₂, 1, X₄, X₅) :|: P ≤ 7 ∧ Q ≤ 7 ∧ P ≤ 3 ∧ X₃ ≤ 1 ∧ 1 ≤ P ∧ 1 ≤ Q ∧ 1+X₁ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 0 ≤ X₃
t₇₀: f4(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀, X₁, X₂, 1, X₄, X₅) :|: P ≤ 7 ∧ Q ≤ 7 ∧ X₃ ≤ 1 ∧ 1 ≤ Q ∧ 1+X₁ ≤ X₅ ∧ 1+X₂ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 5 ≤ P ∧ 0 ≤ X₃
t₇₁: f4(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀, 1+X₁, 1+X₂, 1, X₄, X₅) :|: Q ≤ 7 ∧ 1 ≤ Q ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 2+X₁ ≤ X₅ ∧ 2+X₂ ≤ X₄ ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₇₂: f4(X₀, X₁, X₂, X₃, X₄, X₅) → f7(X₀, X₁, X₂, X₃, X₄, X₅) :|: P ≤ 7 ∧ Q ≤ 7 ∧ P ≤ 3 ∧ 1 ≤ P ∧ 1 ≤ Q ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₇₃: f4(X₀, X₁, X₂, X₃, X₄, X₅) → f7(X₀, X₁, X₂, X₃, X₄, X₅) :|: P ≤ 7 ∧ Q ≤ 7 ∧ 1 ≤ Q ∧ 5 ≤ P ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₂ ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₇₄: f4(X₀, X₁, X₂, X₃, X₄, X₅) → f7(X₀, 1+X₁, 1+X₂, 1, X₄, X₅) :|: Q ≤ 7 ∧ X₅ ≤ 1+X₁ ∧ X₄ ≤ 1+X₂ ∧ 1 ≤ Q ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₇₅: f4(X₀, X₁, X₂, X₃, X₄, X₅) → f7(X₀, X₁, X₂, X₃, X₄, X₅) :|: P ≤ 7 ∧ Q ≤ 7 ∧ P ≤ 3 ∧ 1 ≤ P ∧ 1 ≤ Q ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₇₆: f4(X₀, X₁, X₂, X₃, X₄, X₅) → f7(X₀, X₁, X₂, X₃, X₄, X₅) :|: P ≤ 7 ∧ Q ≤ 7 ∧ 1 ≤ Q ∧ 5 ≤ P ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₇₇: f4(X₀, X₁, X₂, X₃, X₄, X₅) → f7(X₀, 1+X₁, 1+X₂, 1, X₄, X₅) :|: Q ≤ 7 ∧ 1 ≤ Q ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₇₈: f6(X₀, X₁, X₂, X₃, X₄, X₅) → f4(X₀, X₁, X₂, 0, X₄, X₅) :|: Q ≤ 7 ∧ 1 ≤ Q ∧ X₃ ≤ 1 ∧ 0 ≤ X₃
t₇₉: f6(X₀, X₁, X₂, X₃, X₄, X₅) → f4(X₀, X₁, X₂, 1, X₄, X₅) :|: P ≤ 7 ∧ Q ≤ 1 ∧ X₃ ≤ 1 ∧ 1 ≤ P ∧ 1 ≤ X₃ ∧ 0 ≤ Q ∧ 0 ≤ X₃

MPRF for transition t₇₁: f4(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀, 1+X₁, 1+X₂, 1, X₄, X₅) :|: Q ≤ 7 ∧ 1 ≤ Q ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 2+X₁ ≤ X₅ ∧ 2+X₂ ≤ X₄ ∧ X₃ ≤ 1 ∧ 0 ≤ X₃ of depth 1:

new bound:

3⋅X₁+3⋅X₅+4 {O(n)}

• f2: [X₅-1-X₁]
• f3: [X₅-1-X₁]
• f4: [X₅-1-X₁]
• f6: [X₅-1-X₁]

MPRF for transition t₇₈: f6(X₀, X₁, X₂, X₃, X₄, X₅) → f4(X₀, X₁, X₂, 0, X₄, X₅) :|: Q ≤ 7 ∧ 1 ≤ Q ∧ X₃ ≤ 1 ∧ 0 ≤ X₃ of depth 1:

new bound:

9⋅X₁+9⋅X₅+19 {O(n)}

• f2: [2-X₃]
• f3: [2-X₃]
• f4: [X₃]
• f6: [1]

Cut unreachable locations [f4] from the program graph

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ for location f3_v3

Found invariant X₃ ≤ 1 ∧ 1 ≤ X₃ for location f6_v1

Found invariant X₃ ≤ 1 ∧ 0 ≤ X₃ for location f2

Found invariant X₃ ≤ 1 ∧ 0 ≤ X₃ for location f7

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ X₁ ≤ 1+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ X₂ ≤ 1+X₄ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location f4_v8

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ for location f6_v4

Found invariant X₃ ≤ 1 ∧ 1 ≤ X₃ for location f3_v1

Found invariant X₃ ≤ 1 ∧ 0 ≤ X₃ for location f3_v2

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ X₁ ≤ 1+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ X₂ ≤ 1+X₄ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ for location f6_v5

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ for location f2_v1

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ for location f3_v4

Found invariant X₃ ≤ 0 ∧ 0 ≤ X₃ for location f4_v2

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ for location f6_v3

Found invariant X₃ ≤ 1 ∧ 0 ≤ X₃ for location f6_v2

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location f4_v4

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ for location f4_v5

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ for location f4_v3

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ X₃ ≤ X₅ ∧ X₁ ≤ 1+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ X₂ ≤ 1+X₄ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ for location f4_v7

Found invariant X₃ ≤ 1 ∧ 1 ≤ X₃ for location f4_v1

Found invariant 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₃ ≤ 0 ∧ 0 ≤ X₃ for location f4_v6

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₅₃: 1 {O(1)}
t₅₄: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₇: 1 {O(1)}
t₅₈: 1 {O(1)}
t₅₉: 1 {O(1)}
t₆₀: inf {Infinity}
t₆₁: inf {Infinity}
t₆₂: inf {Infinity}
t₆₃: 1 {O(1)}
t₆₄: 1 {O(1)}
t₆₅: 1 {O(1)}
t₆₆: inf {Infinity}
t₆₇: inf {Infinity}
t₆₈: inf {Infinity}
t₆₉: inf {Infinity}
t₇₀: inf {Infinity}
t₇₁: 3⋅X₁+3⋅X₅+4 {O(n)}
t₇₂: 1 {O(1)}
t₇₃: 1 {O(1)}
t₇₄: 1 {O(1)}
t₇₅: 1 {O(1)}
t₇₆: 1 {O(1)}
t₇₇: 1 {O(1)}
t₇₈: 9⋅X₁+9⋅X₅+19 {O(n)}
t₇₉: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₅₃: 1 {O(1)}
t₅₄: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₇: 1 {O(1)}
t₅₈: 1 {O(1)}
t₅₉: 1 {O(1)}
t₆₀: inf {Infinity}
t₆₁: inf {Infinity}
t₆₂: inf {Infinity}
t₆₃: 1 {O(1)}
t₆₄: 1 {O(1)}
t₆₅: 1 {O(1)}
t₆₆: inf {Infinity}
t₆₇: inf {Infinity}
t₆₈: inf {Infinity}
t₆₉: inf {Infinity}
t₇₀: inf {Infinity}
t₇₁: 3⋅X₁+3⋅X₅+4 {O(n)}
t₇₂: 1 {O(1)}
t₇₃: 1 {O(1)}
t₇₄: 1 {O(1)}
t₇₅: 1 {O(1)}
t₇₆: 1 {O(1)}
t₇₇: 1 {O(1)}
t₇₈: 9⋅X₁+9⋅X₅+19 {O(n)}
t₇₉: inf {Infinity}

Sizebounds

t₅₃, X₀: X₀ {O(n)}
t₅₃, X₁: X₁ {O(n)}
t₅₃, X₂: X₂ {O(n)}
t₅₃, X₃: X₃ {O(n)}
t₅₃, X₄: X₄ {O(n)}
t₅₃, X₅: X₅ {O(n)}
t₅₄, X₀: X₀ {O(n)}
t₅₄, X₁: X₁ {O(n)}
t₅₄, X₂: X₂ {O(n)}
t₅₄, X₃: 0 {O(1)}
t₅₄, X₄: X₄ {O(n)}
t₅₄, X₅: X₅ {O(n)}
t₅₅, X₀: X₀ {O(n)}
t₅₅, X₁: X₁ {O(n)}
t₅₅, X₂: X₂ {O(n)}
t₅₅, X₃: 0 {O(1)}
t₅₅, X₄: X₄ {O(n)}
t₅₅, X₅: X₅ {O(n)}
t₅₆, X₀: X₀ {O(n)}
t₅₆, X₁: X₁+1 {O(n)}
t₅₆, X₂: X₂+1 {O(n)}
t₅₆, X₃: 1 {O(1)}
t₅₆, X₄: X₄ {O(n)}
t₅₆, X₅: X₅ {O(n)}
t₅₇, X₀: X₀ {O(n)}
t₅₇, X₁: X₁ {O(n)}
t₅₇, X₂: X₂ {O(n)}
t₅₇, X₃: 0 {O(1)}
t₅₇, X₄: X₄ {O(n)}
t₅₇, X₅: X₅ {O(n)}
t₅₈, X₀: X₀ {O(n)}
t₅₈, X₁: X₁ {O(n)}
t₅₈, X₂: X₂ {O(n)}
t₅₈, X₃: 0 {O(1)}
t₅₈, X₄: X₄ {O(n)}
t₅₈, X₅: X₅ {O(n)}
t₅₉, X₀: X₀ {O(n)}
t₅₉, X₁: X₁+1 {O(n)}
t₅₉, X₂: X₂+1 {O(n)}
t₅₉, X₃: 1 {O(1)}
t₅₉, X₄: X₄ {O(n)}
t₅₉, X₅: X₅ {O(n)}
t₆₀, X₀: 3⋅X₀ {O(n)}
t₆₀, X₃: 1 {O(1)}
t₆₀, X₄: 3⋅X₄ {O(n)}
t₆₀, X₅: 3⋅X₅ {O(n)}
t₆₁, X₀: 3⋅X₀ {O(n)}
t₆₁, X₃: 1 {O(1)}
t₆₁, X₄: 3⋅X₄ {O(n)}
t₆₁, X₅: 3⋅X₅ {O(n)}
t₆₂, X₀: 3⋅X₀ {O(n)}
t₆₂, X₃: 1 {O(1)}
t₆₂, X₄: 3⋅X₄ {O(n)}
t₆₂, X₅: 3⋅X₅ {O(n)}
t₆₃, X₀: 12⋅X₀ {O(n)}
t₆₃, X₃: 1 {O(1)}
t₆₃, X₄: 12⋅X₄ {O(n)}
t₆₃, X₅: 12⋅X₅ {O(n)}
t₆₄, X₀: 12⋅X₀ {O(n)}
t₆₄, X₃: 1 {O(1)}
t₆₄, X₄: 12⋅X₄ {O(n)}
t₆₄, X₅: 12⋅X₅ {O(n)}
t₆₅, X₀: 12⋅X₀ {O(n)}
t₆₅, X₃: 1 {O(1)}
t₆₅, X₄: 12⋅X₄ {O(n)}
t₆₅, X₅: 12⋅X₅ {O(n)}
t₆₆, X₀: 3⋅X₀ {O(n)}
t₆₆, X₃: 1 {O(1)}
t₆₆, X₄: 3⋅X₄ {O(n)}
t₆₆, X₅: 3⋅X₅ {O(n)}
t₆₇, X₀: 3⋅X₀ {O(n)}
t₆₇, X₃: 1 {O(1)}
t₆₇, X₄: 3⋅X₄ {O(n)}
t₆₇, X₅: 3⋅X₅ {O(n)}
t₆₈, X₀: 3⋅X₀ {O(n)}
t₆₈, X₃: 1 {O(1)}
t₆₈, X₄: 3⋅X₄ {O(n)}
t₆₈, X₅: 3⋅X₅ {O(n)}
t₆₉, X₀: 3⋅X₀ {O(n)}
t₆₉, X₃: 1 {O(1)}
t₆₉, X₄: 3⋅X₄ {O(n)}
t₆₉, X₅: 3⋅X₅ {O(n)}
t₇₀, X₀: 3⋅X₀ {O(n)}
t₇₀, X₃: 1 {O(1)}
t₇₀, X₄: 3⋅X₄ {O(n)}
t₇₀, X₅: 3⋅X₅ {O(n)}
t₇₁, X₀: 3⋅X₀ {O(n)}
t₇₁, X₃: 1 {O(1)}
t₇₁, X₄: 3⋅X₄ {O(n)}
t₇₁, X₅: 3⋅X₅ {O(n)}
t₇₂, X₀: 6⋅X₀ {O(n)}
t₇₂, X₃: 1 {O(1)}
t₇₂, X₄: 6⋅X₄ {O(n)}
t₇₂, X₅: 6⋅X₅ {O(n)}
t₇₃, X₀: 6⋅X₀ {O(n)}
t₇₃, X₃: 1 {O(1)}
t₇₃, X₄: 6⋅X₄ {O(n)}
t₇₃, X₅: 6⋅X₅ {O(n)}
t₇₄, X₀: 6⋅X₀ {O(n)}
t₇₄, X₃: 1 {O(1)}
t₇₄, X₄: 6⋅X₄ {O(n)}
t₇₄, X₅: 6⋅X₅ {O(n)}
t₇₅, X₀: 6⋅X₀ {O(n)}
t₇₅, X₃: 1 {O(1)}
t₇₅, X₄: 6⋅X₄ {O(n)}
t₇₅, X₅: 6⋅X₅ {O(n)}
t₇₆, X₀: 6⋅X₀ {O(n)}
t₇₆, X₃: 1 {O(1)}
t₇₆, X₄: 6⋅X₄ {O(n)}
t₇₆, X₅: 6⋅X₅ {O(n)}
t₇₇, X₀: 6⋅X₀ {O(n)}
t₇₇, X₃: 1 {O(1)}
t₇₇, X₄: 6⋅X₄ {O(n)}
t₇₇, X₅: 6⋅X₅ {O(n)}
t₇₈, X₀: 3⋅X₀ {O(n)}
t₇₈, X₃: 0 {O(1)}
t₇₈, X₄: 3⋅X₄ {O(n)}
t₇₈, X₅: 3⋅X₅ {O(n)}
t₇₉, X₀: 3⋅X₀ {O(n)}
t₇₉, X₃: 1 {O(1)}
t₇₉, X₄: 3⋅X₄ {O(n)}
t₇₉, X₅: 3⋅X₅ {O(n)}