Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ 0 < X₃
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < X₃
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀-X₃, X₁, X₂, X₃)
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
Eliminate variables {X₁} that do not contribute to the problem
Found invariant X₀ ≤ X₁ for location l5
Found invariant X₀ ≤ X₁ for location l1
Found invariant X₀ ≤ X₁ for location l4
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₃: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₄: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ 0 < X₂ ∧ X₀ ≤ X₁
t₁₅: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ < X₂ ∧ X₀ ≤ X₁
t₁₆: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₂ ≤ 0 ∧ X₀ ≤ X₁
t₁₇: l2(X₀, X₁, X₂) → l1(X₁, X₁, X₂)
t₁₈: l3(X₀, X₁, X₂) → l1(X₀-X₂, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₉: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ X₁
new bound:
X₁ {O(n)}
new bound:
X₁+X₂+1 {O(n)}
Overall timebound:2⋅X₁+X₂+6 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₁ {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: X₁+X₂+1 {O(n)}
t₁₉: 1 {O(1)}
Overall costbound: 2⋅X₁+X₂+6 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₁ {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: X₁+X₂+1 {O(n)}
t₁₉: 1 {O(1)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₄, X₀: X₁ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₅, X₀: 2⋅X₁ {O(n)}
t₁₅, X₁: 2⋅X₁ {O(n)}
t₁₅, X₂: 2⋅X₂ {O(n)}
t₁₆, X₀: X₁ {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₇, X₀: X₁ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₈, X₀: X₁ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₉, X₀: 3⋅X₁ {O(n)}
t₁₉, X₁: 3⋅X₁ {O(n)}
t₁₉, X₂: 3⋅X₂ {O(n)}