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) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < X₃
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₃, X₂, X₃) :|: X₃ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃)
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₆: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁
t₇: l5(X₀, X₁, X₂, X₃) → l4(X₀, X₁+1, X₂, X₃)
t₈: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l6
Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l7
Found invariant X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l5
Found invariant X₂ ≤ X₀ for location l1
Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location l4
Found invariant 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ 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) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < X₃ ∧ X₂ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₃, X₂, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀
t₇: l5(X₀, X₁, X₂, X₃) → l4(X₀, X₁+1, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₈: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
new bound:
X₂+X₃ {O(n)}
MPRF:
l3 [X₃-X₀-1 ]
l1 [X₃-X₀ ]
new bound:
X₂+X₃ {O(n)}
MPRF:
l3 [X₃-X₀ ]
l1 [X₃-X₀ ]
new bound:
3⋅X₂+3⋅X₃+1 {O(n)}
MPRF:
l5 [X₀-X₁ ]
l4 [X₀+1-X₁ ]
new bound:
3⋅X₂+3⋅X₃ {O(n)}
MPRF:
l5 [X₀-X₁ ]
l4 [X₀-X₁ ]
Overall timebound:8⋅X₂+8⋅X₃+6 {O(n)}
t₀: 1 {O(1)}
t₂: X₂+X₃ {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₂+X₃ {O(n)}
t₅: 3⋅X₂+3⋅X₃+1 {O(n)}
t₆: 1 {O(1)}
t₇: 3⋅X₂+3⋅X₃ {O(n)}
t₈: 1 {O(1)}
Overall costbound: 8⋅X₂+8⋅X₃+6 {O(n)}
t₀: 1 {O(1)}
t₂: X₂+X₃ {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₂+X₃ {O(n)}
t₅: 3⋅X₂+3⋅X₃+1 {O(n)}
t₆: 1 {O(1)}
t₇: 3⋅X₂+3⋅X₃ {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: 2⋅X₂+X₃ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: 3⋅X₂+X₃ {O(n)}
t₃, X₁: 2⋅X₃ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₄, X₀: 2⋅X₂+X₃ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: 3⋅X₂+X₃ {O(n)}
t₅, X₁: 3⋅X₂+5⋅X₃ {O(n)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}
t₆, X₀: 2⋅X₃+6⋅X₂ {O(n)}
t₆, X₁: 3⋅X₂+7⋅X₃ {O(n)}
t₆, X₂: 4⋅X₂ {O(n)}
t₆, X₃: 4⋅X₃ {O(n)}
t₇, X₀: 3⋅X₂+X₃ {O(n)}
t₇, X₁: 3⋅X₂+5⋅X₃ {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 2⋅X₃ {O(n)}
t₈, X₀: 2⋅X₃+6⋅X₂ {O(n)}
t₈, X₁: 3⋅X₂+7⋅X₃ {O(n)}
t₈, X₂: 4⋅X₂ {O(n)}
t₈, X₃: 4⋅X₃ {O(n)}