Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1
t₄: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 0 < 2⋅X₀+X₁
t₅: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₁+2⋅X₀ < 0
t₂: l2(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 1 < X₀ ∧ 0 ≤ 2⋅X₀+X₁ ∧ X₁+2⋅X₀ ≤ 0
t₁₀: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₉: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₂, X₀, X₂, X₃, X₄)
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄)
t₈: l6(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, nondef.0, X₃, X₄)
t₁: l7(X₀, X₁, X₂, X₃, X₄) → l2(X₄, X₃, X₂, X₃, X₄)

Preprocessing

Found invariant X₃ ≤ X₁ for location l2

Found invariant 4+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 8+X₁+X₃ ≤ 0 ∧ 6+X₃ ≤ X₀ ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2 ≤ X₀ for location l6

Found invariant 4+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 8+X₁+X₃ ≤ 0 ∧ 6+X₃ ≤ X₀ ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2 ≤ X₀ for location l5

Found invariant X₃ ≤ X₁ for location l1

Found invariant 4+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 8+X₁+X₃ ≤ 0 ∧ 6+X₃ ≤ X₀ ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2 ≤ X₀ for location l4

Found invariant X₃ ≤ X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1 ∧ X₃ ≤ X₁
t₄: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 0 < 2⋅X₀+X₁ ∧ X₃ ≤ X₁
t₅: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₁+2⋅X₀ < 0 ∧ X₃ ≤ X₁
t₂: l2(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 1 < X₀ ∧ 0 ≤ 2⋅X₀+X₁ ∧ X₁+2⋅X₀ ≤ 0 ∧ X₃ ≤ X₁
t₁₀: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₁
t₉: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₂, X₀, X₂, X₃, X₄) :|: 4+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 8+X₁+X₃ ≤ 0 ∧ 6+X₃ ≤ X₀ ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2 ≤ X₀
t₆: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 4+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 8+X₁+X₃ ≤ 0 ∧ 6+X₃ ≤ X₀ ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2 ≤ X₀
t₈: l6(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, nondef.0, X₃, X₄) :|: 4+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 8+X₁+X₃ ≤ 0 ∧ 6+X₃ ≤ X₀ ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2 ≤ X₀
t₁: l7(X₀, X₁, X₂, X₃, X₄) → l2(X₄, X₃, X₂, X₃, X₄)

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₂: l2(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 1 < X₀ ∧ 0 ≤ 2⋅X₀+X₁ ∧ X₁+2⋅X₀ ≤ 0 ∧ X₃ ≤ X₁

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₆: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 4+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 8+X₁+X₃ ≤ 0 ∧ 6+X₃ ≤ X₀ ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2 ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₈: l6(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, nondef.0, X₃, X₄) :|: 4+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 8+X₁+X₃ ≤ 0 ∧ 6+X₃ ≤ X₀ ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2 ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₉: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₂, X₀, X₂, X₃, X₄) :|: 4+X₃ ≤ 0 ∧ X₃ ≤ X₁ ∧ 8+X₁+X₃ ≤ 0 ∧ 6+X₃ ≤ X₀ ∧ 2+X₀+X₃ ≤ 0 ∧ 4+X₁ ≤ 0 ∧ 6+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ 2 ≤ X₀

All Bounds

Timebounds

Overall timebound:10 {O(1)}
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)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: 10 {O(1)}
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)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₄ {O(n)}
t₂, X₁: X₃ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₁: X₃+X₄ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₁: X₃+X₄ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₅, X₁: X₃+X₄ {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}
t₅, X₄: 2⋅X₄ {O(n)}
t₆, X₀: X₄ {O(n)}
t₆, X₁: X₃ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₈, X₀: X₄ {O(n)}
t₈, X₁: X₃ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₉, X₁: X₄ {O(n)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: X₄ {O(n)}
t₁₀, X₁: 3⋅X₃+3⋅X₄ {O(n)}
t₁₀, X₃: 6⋅X₃ {O(n)}
t₁₀, X₄: 6⋅X₄ {O(n)}