Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂+1 ≤ X₀
t₃: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ X₂
t₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂+1 ≤ X₁
t₅: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ ≤ X₂
t₆: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1)
t₇: l4(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂)
t₈: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₁: l6(X₀, X₁, X₂) → l1(X₁, X₂, X₀)
Found invariant 1+X₂ ≤ X₀ for location l2
Found invariant X₀ ≤ X₂ for location l7
Found invariant X₀ ≤ X₂ for location l5
Found invariant 1+X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l4
Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l6(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂+1 ≤ X₀
t₃: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ X₂
t₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂+1 ≤ X₁ ∧ 1+X₂ ≤ X₀
t₅: l2(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 1+X₂ ≤ X₀
t₆: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀
t₇: l4(X₀, X₁, X₂) → l1(X₀, X₁+1, X₂) :|: 1+X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₈: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₀ ≤ X₂
t₁: l6(X₀, X₁, X₂) → l1(X₁, X₂, X₀)
new bound:
X₀+X₁ {O(n)}
MPRF:
l2 [X₀-X₂ ]
l3 [X₀-X₂-1 ]
l4 [X₀-X₂ ]
l1 [X₀-X₂ ]
new bound:
X₁+X₂ {O(n)}
MPRF:
l2 [X₀-X₁ ]
l3 [X₀-X₁ ]
l4 [X₀-X₁-1 ]
l1 [X₀-X₁ ]
new bound:
X₀+X₁ {O(n)}
MPRF:
l2 [X₀-X₂ ]
l3 [X₀-X₂ ]
l4 [X₀-X₂ ]
l1 [X₀-X₂ ]
new bound:
X₁+X₂ {O(n)}
MPRF:
l2 [X₀-X₁ ]
l3 [X₀-X₁ ]
l4 [X₀-X₁ ]
l1 [X₀-X₁ ]
Found invariant 1+X₂ ≤ X₀ for location l2
Found invariant X₀ ≤ X₂ for location l7
Found invariant X₀ ≤ X₂ for location l5
Found invariant 1+X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l4
Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ for location l3
Found invariant 1 ≤ 0 for location l2
Found invariant 1 ≤ 0 for location l7
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
knowledge_propagation leads to new time bound 2⋅X₁+X₀+X₂+1 {O(n)} for transition t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂+1 ≤ X₀
Overall timebound:3⋅X₀+3⋅X₂+6⋅X₁+5 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₁+X₀+X₂+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀+X₁ {O(n)}
t₅: X₁+X₂ {O(n)}
t₆: X₀+X₁ {O(n)}
t₇: X₁+X₂ {O(n)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
Overall costbound: 3⋅X₀+3⋅X₂+6⋅X₁+5 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₁+X₀+X₂+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₀+X₁ {O(n)}
t₅: X₁+X₂ {O(n)}
t₆: X₀+X₁ {O(n)}
t₇: X₁+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)}
t₂, X₀: X₁ {O(n)}
t₂, X₁: 2⋅X₂+X₁ {O(n)}
t₂, X₂: 2⋅X₀+X₁ {O(n)}
t₃, X₀: 2⋅X₁ {O(n)}
t₃, X₁: 3⋅X₂+X₁ {O(n)}
t₃, X₂: 3⋅X₀+X₁ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: 2⋅X₂+X₁ {O(n)}
t₄, X₂: 2⋅X₀+X₁ {O(n)}
t₅, X₀: X₁ {O(n)}
t₅, X₁: 2⋅X₂+X₁ {O(n)}
t₅, X₂: 2⋅X₀+X₁ {O(n)}
t₆, X₀: X₁ {O(n)}
t₆, X₁: 2⋅X₂+X₁ {O(n)}
t₆, X₂: 2⋅X₀+X₁ {O(n)}
t₇, X₀: X₁ {O(n)}
t₇, X₁: 2⋅X₂+X₁ {O(n)}
t₇, X₂: 2⋅X₀+X₁ {O(n)}
t₈, X₀: 2⋅X₁ {O(n)}
t₈, X₁: 3⋅X₂+X₁ {O(n)}
t₈, X₂: 3⋅X₀+X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₂ {O(n)}
t₁, X₂: X₀ {O(n)}