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
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃)
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
Eliminate variables {X₁} that do not contribute to the problem
Found invariant X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l5
Found invariant X₀ ≤ X₁ for location l1
Found invariant X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l4
Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₁: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ < X₀ ∧ X₀ ≤ X₁
t₁₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ X₀ ≤ X₁
t₁₄: l2(X₀, X₁, X₂) → l1(X₁, X₁, X₂)
t₁₅: l3(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁
t₁₆: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ X₀ ≤ X₁
new bound:
X₁+X₂ {O(n)}
new bound:
X₁+X₂ {O(n)}
Overall timebound:2⋅X₁+2⋅X₂+4 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₁+X₂ {O(n)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: X₁+X₂ {O(n)}
t₁₆: 1 {O(1)}
Overall costbound: 2⋅X₁+2⋅X₂+4 {O(n)}
t₁₁: 1 {O(1)}
t₁₂: X₁+X₂ {O(n)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: X₁+X₂ {O(n)}
t₁₆: 1 {O(1)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₂, X₀: 2⋅X₁+X₂ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₃, X₀: 3⋅X₁+X₂ {O(n)}
t₁₃, X₁: 2⋅X₁ {O(n)}
t₁₃, X₂: 2⋅X₂ {O(n)}
t₁₄, X₀: X₁ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₅, X₀: 2⋅X₁+X₂ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₆, X₀: 3⋅X₁+X₂ {O(n)}
t₁₆, X₁: 2⋅X₁ {O(n)}
t₁₆, X₂: 2⋅X₂ {O(n)}