Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₃
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₄, X₂, X₃, X₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁, X₂, X₃, X₄) :|: X₀ < X₁ ∧ X₀ < X₁
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₁ ∧ X₁ ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁+1, X₂, X₃, X₄) :|: X₁ ≤ X₀ ∧ X₀ < X₁
t₇: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁+1, X₂, X₃, X₄) :|: X₁ ≤ X₀ ∧ X₁ ≤ X₀
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
Cut unsatisfiable transition t₅: l3→l1
Cut unsatisfiable transition t₆: l3→l1
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ for location l5
Found invariant X₄ ≤ X₁ ∧ X₂ ≤ X₀ for location l1
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ for location l4
Found invariant X₄ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₃ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₄, X₂, X₃, X₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁, X₂, X₃, X₄) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ X₄ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀
t₇: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁+1, X₂, X₃, X₄) :|: X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀
new bound:
X₂+X₃ {O(n)}
MPRF:
l3 [X₃-X₀ ]
l1 [X₃-X₀ ]
new bound:
X₃+X₄ {O(n)}
MPRF:
l3 [X₃-X₁ ]
l1 [X₃-X₁ ]
knowledge_propagation leads to new time bound 2⋅X₃+X₂+X₄+1 {O(n)} for transition t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₃ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₀
Overall timebound:2⋅X₂+2⋅X₄+4⋅X₃+5 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₃+X₂+X₄+1 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₂+X₃ {O(n)}
t₇: X₃+X₄ {O(n)}
t₈: 1 {O(1)}
Overall costbound: 2⋅X₂+2⋅X₄+4⋅X₃+5 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₃+X₂+X₄+1 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₂+X₃ {O(n)}
t₇: X₃+X₄ {O(n)}
t₈: 1 {O(1)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₂, X₀: 2⋅X₂+X₃ {O(n)}
t₂, X₁: 2⋅X₄+X₃ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: 3⋅X₂+X₃ {O(n)}
t₃, X₁: 3⋅X₄+X₃ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₄, X₀: 2⋅X₂+X₃ {O(n)}
t₄, X₁: 2⋅X₄+X₃ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₇, X₀: 2⋅X₂+X₃ {O(n)}
t₇, X₁: 2⋅X₄+X₃ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₈, X₀: 3⋅X₂+X₃ {O(n)}
t₈, X₁: 3⋅X₄+X₃ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}
t₈, X₃: 2⋅X₃ {O(n)}
t₈, X₄: 2⋅X₄ {O(n)}