Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 < X₀
t₇: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃) :|: 0 < X₃
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₂, X₃) :|: X₃ < X₀
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: X₀ ≤ X₃
Eliminate variables {X₁} that do not contribute to the problem
Found invariant 1 ≤ X₂ ∧ X₀ ≤ X₁ for location l1
Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l4
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₅: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₁₆: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁
t₁₇: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 0 < X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁
t₁₈: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₁₉: l3(X₀, X₁, X₂) → l1(X₁, X₁, X₂) :|: 0 < X₂
t₂₀: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ 0
t₂₁: l4(X₀, X₁, X₂) → l1(X₂, X₁, X₂) :|: X₂ < X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₂: l4(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
new bound:
X₁ {O(n)}
new bound:
X₁ {O(n)}
new bound:
X₁ {O(n)}
Overall timebound:3⋅X₁+5 {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: X₁ {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₁ {O(n)}
t₂₂: X₁ {O(n)}
Overall costbound: 3⋅X₁+5 {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: X₁ {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₁ {O(n)}
t₂₂: X₁ {O(n)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₆, X₀: 2⋅X₁ {O(n)}
t₁₆, X₁: 2⋅X₁ {O(n)}
t₁₆, X₂: 2⋅X₂ {O(n)}
t₁₇, X₀: X₁ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₈, X₀: 2⋅X₁+X₀ {O(n)}
t₁₈, X₁: 3⋅X₁ {O(n)}
t₁₈, X₂: 3⋅X₂ {O(n)}
t₁₉, X₀: X₁ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₂₀, X₀: X₀ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₁, X₀: X₁ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₂, X₀: X₁ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₂: X₂ {O(n)}