Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₁, X₃, X₄) :|: X₀ < 10
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: 10 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(0, 3, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: 12 ≤ X₂
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₂ < 12
t₈: l4(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₇: l5(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₂, X₂, X₃, X₄)
t₆: l6(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂+1, X₃, X₄)
Eliminate variables {X₃,X₄} that do not contribute to the problem
Found invariant X₂ ≤ 11 ∧ X₂ ≤ 8+X₁ ∧ X₁+X₂ ≤ 22 ∧ X₂ ≤ 11+X₀ ∧ 3 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ 11 ∧ X₁ ≤ 11+X₀ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l6
Found invariant 3 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 10 ≤ X₀ for location l7
Found invariant 12 ≤ X₂ ∧ 15 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5
Found invariant 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1
Found invariant 3 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 10 ≤ X₀ for location l4
Found invariant 3 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₈: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₉: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₁) :|: X₀ < 10 ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₀: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 10 ≤ X₀ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₁: l2(X₀, X₁, X₂) → l1(0, 3, X₂)
t₂₃: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 12 ≤ X₂ ∧ 3 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₂: l3(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₂ < 12 ∧ 3 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₄: l4(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: 3 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 10 ≤ X₀
t₂₅: l5(X₀, X₁, X₂) → l1(X₀+1, X₂, X₂) :|: 12 ≤ X₂ ∧ 15 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₂₆: l6(X₀, X₁, X₂) → l3(X₀, X₁, X₂+1) :|: X₂ ≤ 11 ∧ X₂ ≤ 8+X₁ ∧ X₁+X₂ ≤ 22 ∧ X₂ ≤ 11+X₀ ∧ 3 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ 11 ∧ X₁ ≤ 11+X₀ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀
new bound:
10 {O(1)}
MPRF:
l5 [9-X₀ ]
l1 [10-X₀ ]
l6 [9-X₀ ]
l3 [9-X₀ ]
new bound:
15 {O(1)}
MPRF:
l5 [12-X₂ ]
l1 [12-X₁ ]
l6 [11-X₂ ]
l3 [12-X₂ ]
new bound:
15 {O(1)}
MPRF:
l5 [12-X₂ ]
l1 [12-X₁ ]
l6 [12-X₂ ]
l3 [12-X₂ ]
knowledge_propagation leads to new time bound 25 {O(1)} for transition t₂₃: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 12 ≤ X₂ ∧ 3 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀
knowledge_propagation leads to new time bound 25 {O(1)} for transition t₂₅: l5(X₀, X₁, X₂) → l1(X₀+1, X₂, X₂) :|: 12 ≤ X₂ ∧ 15 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀
Overall timebound:94 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 10 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 15 {O(1)}
t₂₃: 25 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 25 {O(1)}
t₂₆: 15 {O(1)}
Overall costbound: 94 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 10 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 15 {O(1)}
t₂₃: 25 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 25 {O(1)}
t₂₆: 15 {O(1)}
t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₉, X₀: 9 {O(1)}
t₁₉, X₁: 18 {O(1)}
t₁₉, X₂: 15 {O(1)}
t₂₀, X₀: 19 {O(1)}
t₂₀, X₁: 15 {O(1)}
t₂₀, X₂: 15 {O(1)}
t₂₁, X₀: 0 {O(1)}
t₂₁, X₁: 3 {O(1)}
t₂₁, X₂: X₂ {O(n)}
t₂₂, X₀: 9 {O(1)}
t₂₂, X₁: 11 {O(1)}
t₂₂, X₂: 11 {O(1)}
t₂₃, X₀: 18 {O(1)}
t₂₃, X₁: 29 {O(1)}
t₂₃, X₂: 15 {O(1)}
t₂₄, X₀: 19 {O(1)}
t₂₄, X₁: 15 {O(1)}
t₂₄, X₂: 15 {O(1)}
t₂₅, X₀: 19 {O(1)}
t₂₅, X₁: 15 {O(1)}
t₂₅, X₂: 15 {O(1)}
t₂₆, X₀: 9 {O(1)}
t₂₆, X₁: 11 {O(1)}
t₂₆, X₂: 12 {O(1)}