Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₀: l10(X₀, X₁, X₂, X₃) → l11(X₀, X₁, 0, 0)
t₁₁: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₂ < X₁
t₁₂: l11(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂
t₁₃: l12(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂+1, X₃+1)
t₁₄: l13(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃) :|: X₃ < X₀
t₁₅: l13(X₀, X₁, X₂, X₃) → l15(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃
t₁₆: l14(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂+1, X₃+1)
t₁₇: l15(X₀, X₁, X₂, X₃) → l16(X₀, X₁, X₂, X₃)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₈: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₉: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃)
Found invariant X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l11
Found invariant X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location l15
Found invariant X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l12
Found invariant X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l13
Found invariant X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location l16
Found invariant X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l14
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, l16, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₀: l10(X₀, X₁, X₂, X₃) → l11(X₀, X₁, 0, 0)
t₁₁: l11(X₀, X₁, X₂, X₃) → l12(X₀, X₁, X₂, X₃) :|: X₂ < X₁ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₂: l11(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂
t₁₃: l12(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂+1, X₃+1) :|: X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₁₄: l13(X₀, X₁, X₂, X₃) → l14(X₀, X₁, X₂, X₃) :|: X₃ < X₀ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂
t₁₅: l13(X₀, X₁, X₂, X₃) → l15(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂
t₁₆: l14(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂+1, X₃+1) :|: X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀
t₁₇: l15(X₀, X₁, X₂, X₃) → l16(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₇: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₈: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₉: l9(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃)
new bound:
X₁ {O(n)}
MPRF:
l12 [X₁-X₃-1 ]
l13 [X₁-X₃ ]
l14 [X₁-X₃ ]
l11 [X₁-X₃ ]
new bound:
X₁ {O(n)}
MPRF:
l12 [X₁-X₂ ]
l13 [X₁-X₃ ]
l14 [X₁-X₃ ]
l11 [X₁-X₃ ]
new bound:
X₀+1 {O(n)}
MPRF:
l12 [X₀+1-X₃ ]
l13 [X₀+1-X₃ ]
l14 [X₀-X₂ ]
l11 [X₀+1-X₂ ]
new bound:
X₀ {O(n)}
MPRF:
l12 [X₀-X₂ ]
l13 [X₀-X₂ ]
l14 [X₀-X₃ ]
l11 [X₀-X₂ ]
Found invariant 1 ≤ 0 for location l11
Found invariant 1 ≤ 0 for location l15
Found invariant 1 ≤ 0 for location l12
Found invariant 1 ≤ 0 for location l13
Found invariant 1 ≤ 0 for location l16
Found invariant 1 ≤ 0 for location l14
Found invariant X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂ for location l11
Found invariant X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location l15
Found invariant X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l12
Found invariant X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ for location l13
Found invariant X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location l16
Found invariant X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l14
knowledge_propagation leads to new time bound X₀+X₁+1 {O(n)} for transition t₁₂: l11(X₀, X₁, X₂, X₃) → l13(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₂
Overall timebound:3⋅X₀+3⋅X₁+15 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: X₁ {O(n)}
t₁₂: X₀+X₁+1 {O(n)}
t₁₃: X₁ {O(n)}
t₁₄: X₀+1 {O(n)}
t₁₅: 1 {O(1)}
t₁₆: X₀ {O(n)}
t₁₇: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
Overall costbound: 3⋅X₀+3⋅X₁+15 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: X₁ {O(n)}
t₁₂: X₀+X₁+1 {O(n)}
t₁₃: X₁ {O(n)}
t₁₄: X₀+1 {O(n)}
t₁₅: 1 {O(1)}
t₁₆: X₀ {O(n)}
t₁₇: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: 0 {O(1)}
t₁₀, X₃: 0 {O(1)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₁ {O(n)}
t₁₁, X₃: X₁ {O(n)}
t₁₂, X₀: 2⋅X₀ {O(n)}
t₁₂, X₁: 2⋅X₁ {O(n)}
t₁₂, X₂: X₀+X₁ {O(n)}
t₁₂, X₃: X₀+X₁ {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₁ {O(n)}
t₁₃, X₃: X₁ {O(n)}
t₁₄, X₀: 2⋅X₀ {O(n)}
t₁₄, X₁: 2⋅X₁ {O(n)}
t₁₄, X₂: X₀+X₁ {O(n)}
t₁₄, X₃: X₀+X₁ {O(n)}
t₁₅, X₀: 2⋅X₀ {O(n)}
t₁₅, X₁: 2⋅X₁ {O(n)}
t₁₅, X₂: X₀+X₁ {O(n)}
t₁₅, X₃: X₀+X₁ {O(n)}
t₁₆, X₀: 2⋅X₀ {O(n)}
t₁₆, X₁: 2⋅X₁ {O(n)}
t₁₆, X₂: X₀+X₁ {O(n)}
t₁₆, X₃: X₀+X₁ {O(n)}
t₁₇, X₀: 2⋅X₀ {O(n)}
t₁₇, X₁: 2⋅X₁ {O(n)}
t₁₇, X₂: X₀+X₁ {O(n)}
t₁₇, X₃: X₀+X₁ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}