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