Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁
t₄: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₃
t₅: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃)
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃)
t₈: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₁: l6(X₀, X₁, X₂, X₃) → l1(0, 0, X₂, X₃)
Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l7
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1
Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l4
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₄: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₅: l2(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₈: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁: l6(X₀, X₁, X₂, X₃) → l1(0, 0, X₂, X₃)
new bound:
X₃ {O(n)}
MPRF:
l2 [X₃-X₀ ]
l3 [X₃-X₀-1 ]
l4 [X₃-X₀ ]
l1 [X₃-X₀ ]
new bound:
X₂ {O(n)}
MPRF:
l2 [X₂-X₁ ]
l3 [X₂-X₁ ]
l4 [X₂-X₁-1 ]
l1 [X₂-X₁ ]
new bound:
X₃ {O(n)}
MPRF:
l2 [X₃-X₀ ]
l3 [X₃-X₀ ]
l4 [X₃-X₀ ]
l1 [X₃-X₀ ]
new bound:
X₂ {O(n)}
MPRF:
l2 [X₂-X₁ ]
l3 [X₂-X₁ ]
l4 [X₂-X₁ ]
l1 [X₂-X₁ ]
knowledge_propagation leads to new time bound X₂+X₃+1 {O(n)} for transition t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
Overall timebound:3⋅X₂+3⋅X₃+5 {O(n)}
t₀: 1 {O(1)}
t₂: X₂+X₃+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₃ {O(n)}
t₅: X₂ {O(n)}
t₆: X₃ {O(n)}
t₇: X₂ {O(n)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
Overall costbound: 3⋅X₂+3⋅X₃+5 {O(n)}
t₀: 1 {O(1)}
t₂: X₂+X₃+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₃ {O(n)}
t₅: X₂ {O(n)}
t₆: X₃ {O(n)}
t₇: X₂ {O(n)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₂, X₀: X₃ {O(n)}
t₂, X₁: X₂ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₃ {O(n)}
t₃, X₁: X₂ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₄, X₀: X₃ {O(n)}
t₄, X₁: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₃ {O(n)}
t₅, X₁: X₂ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₃ {O(n)}
t₆, X₁: X₂ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₃ {O(n)}
t₇, X₁: X₂ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₃ {O(n)}
t₈, X₁: X₂ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}
t₈, X₃: 2⋅X₃ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: 0 {O(1)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}