Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < X₄
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₅, X₂, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+1, X₁, X₂, X₃, X₄, X₅) :|: X₀ < X₁ ∧ X₀ < X₁
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < X₁ ∧ X₁ ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+1, X₁+1, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₀ ∧ X₀ < X₁
t₇: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁+1, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₀ ∧ X₁ ≤ X₀
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)
Cut unsatisfiable transition t₅: l3→l1
Cut unsatisfiable transition t₆: l3→l1
Eliminate variables {X₂} that do not contribute to the problem
Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₀ for location l5
Found invariant X₅ ≤ X₁ ∧ X₃ ≤ X₀ for location l1
Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₀ for location l4
Found invariant X₅ ≤ X₁ ∧ 1+X₃ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₁, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₈: l0(X₀, X₁, X₃, X₄, X₅) → l2(X₀, X₁, X₃, X₄, X₅)
t₁₉: l1(X₀, X₁, X₃, X₄, X₅) → l3(X₀, X₁, X₃, X₄, X₅) :|: X₀ < X₄ ∧ X₅ ≤ X₁ ∧ X₃ ≤ X₀
t₂₀: l1(X₀, X₁, X₃, X₄, X₅) → l4(X₀, X₁, X₃, X₄, X₅) :|: X₄ ≤ X₀ ∧ X₅ ≤ X₁ ∧ X₃ ≤ X₀
t₂₁: l2(X₀, X₁, X₃, X₄, X₅) → l1(X₃, X₅, X₃, X₄, X₅)
t₂₂: l3(X₀, X₁, X₃, X₄, X₅) → l1(X₀+1, X₁, X₃, X₄, X₅) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ X₅ ≤ X₁ ∧ 1+X₃ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀
t₂₃: l3(X₀, X₁, X₃, X₄, X₅) → l1(X₀, X₁+1, X₃, X₄, X₅) :|: X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₅ ≤ X₁ ∧ 1+X₃ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ X₃ ≤ X₀
t₂₄: l4(X₀, X₁, X₃, X₄, X₅) → l5(X₀, X₁, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₀
new bound:
X₃+X₄ {O(n)}
MPRF:
l3 [X₄-X₀ ]
l1 [X₄-X₀ ]
new bound:
X₄+X₅ {O(n)}
MPRF:
l3 [X₄-X₁ ]
l1 [X₄-X₁ ]
knowledge_propagation leads to new time bound 2⋅X₄+X₃+X₅+1 {O(n)} for transition t₁₉: l1(X₀, X₁, X₃, X₄, X₅) → l3(X₀, X₁, X₃, X₄, X₅) :|: X₀ < X₄ ∧ X₅ ≤ X₁ ∧ X₃ ≤ X₀
Overall timebound:2⋅X₃+2⋅X₅+4⋅X₄+5 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 2⋅X₄+X₃+X₅+1 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: X₃+X₄ {O(n)}
t₂₃: X₄+X₅ {O(n)}
t₂₄: 1 {O(1)}
Overall costbound: 2⋅X₃+2⋅X₅+4⋅X₄+5 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: 2⋅X₄+X₃+X₅+1 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: X₃+X₄ {O(n)}
t₂₃: X₄+X₅ {O(n)}
t₂₄: 1 {O(1)}
t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₉, X₀: 2⋅X₃+X₄ {O(n)}
t₁₉, X₁: 2⋅X₅+X₄ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₂₀, X₀: 3⋅X₃+X₄ {O(n)}
t₂₀, X₁: 3⋅X₅+X₄ {O(n)}
t₂₀, X₃: 2⋅X₃ {O(n)}
t₂₀, X₄: 2⋅X₄ {O(n)}
t₂₀, X₅: 2⋅X₅ {O(n)}
t₂₁, X₀: X₃ {O(n)}
t₂₁, X₁: X₅ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₂, X₀: 2⋅X₃+X₄ {O(n)}
t₂₂, X₁: 2⋅X₅+X₄ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₃, X₀: 2⋅X₃+X₄ {O(n)}
t₂₃, X₁: 2⋅X₅+X₄ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₄, X₀: 3⋅X₃+X₄ {O(n)}
t₂₄, X₁: 3⋅X₅+X₄ {O(n)}
t₂₄, X₃: 2⋅X₃ {O(n)}
t₂₄, X₄: 2⋅X₄ {O(n)}
t₂₄, X₅: 2⋅X₅ {O(n)}