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) :|: X₀ < X₂
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₂+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 X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location l5
Found invariant X₂ ≤ X₀ for location l1
Found invariant X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location l4
Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₂: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₃: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₂ ≤ X₀
t₁₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ X₂ ≤ X₀
t₁₅: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₁₆: l3(X₀, X₁, X₂) → l1(X₁+1, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁
t₁₇: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ X₁ ≤ X₀
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₃: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₂ ≤ X₀
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₆: l3(X₀, X₁, X₂) → l1(X₁+1, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁
Overall timebound:6 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
Overall costbound: 6 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₃, X₀: X₂ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₄, X₀: X₁+X₂+1 {O(n)}
t₁₄, X₁: 2⋅X₁ {O(n)}
t₁₄, X₂: 2⋅X₂ {O(n)}
t₁₅, X₀: X₂ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₆, X₀: X₁+1 {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₇, X₀: X₁+X₂+1 {O(n)}
t₁₇, X₁: 2⋅X₁ {O(n)}
t₁₇, X₂: 2⋅X₂ {O(n)}