Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₁: l10(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃+1) :|: X₃ < X₀ ∧ X₃ < X₀
t₁₂: l10(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂+1, X₃+1) :|: X₃ < X₀ ∧ X₀ ≤ X₃
t₁₃: l10(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₃ < X₀
t₁₄: l10(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂+1, X₃) :|: X₀ ≤ X₃ ∧ X₀ ≤ X₃
t₁₅: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₈: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, 0, 0)
t₉: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₂ < X₁
t₁₀: l9(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂
Cut unsatisfiable transition t₁₂: l10→l9
Cut unsatisfiable transition t₁₃: l10→l9
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l11
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l12
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l10
Found invariant 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ for location l9
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₁: l10(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃+1) :|: X₃ < X₀ ∧ X₃ < X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₄: l10(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂+1, X₃) :|: X₀ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₅: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₈: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, 0, 0)
t₉: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₂ < X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂
t₁₀: l9(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂
new bound:
X₀ {O(n)}
new bound:
X₁ {O(n)}
knowledge_propagation leads to new time bound X₀+X₁+1 {O(n)} for transition t₉: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₂ < X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₂
Overall timebound:2⋅X₀+2⋅X₁+12 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₀+X₁+1 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₀ {O(n)}
t₁₄: X₁ {O(n)}
t₁₅: 1 {O(1)}
Overall costbound: 2⋅X₀+2⋅X₁+12 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₀+X₁+1 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₀ {O(n)}
t₁₄: X₁ {O(n)}
t₁₅: 1 {O(1)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 0 {O(1)}
t₈, X₃: 0 {O(1)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₁ {O(n)}
t₉, X₃: X₀ {O(n)}
t₁₀, X₀: 2⋅X₀ {O(n)}
t₁₀, X₁: 2⋅X₁ {O(n)}
t₁₀, X₂: X₁ {O(n)}
t₁₀, X₃: X₀ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₁ {O(n)}
t₁₁, X₃: X₀ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₁ {O(n)}
t₁₄, X₃: X₀ {O(n)}
t₁₅, X₀: 2⋅X₀ {O(n)}
t₁₅, X₁: 2⋅X₁ {O(n)}
t₁₅, X₂: X₁ {O(n)}
t₁₅, X₃: X₀ {O(n)}