Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 < X₀
t₈: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₃: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: X₀ < X₂
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀-X₂, X₁, X₂, X₃) :|: X₂ ≤ X₀
Eliminate variables {X₁} that do not contribute to the problem
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂ for location l1
Found invariant 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀ for location l4
Start: l0
Program_Vars: X₀, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₈: l0(X₀, X₂, X₃) → l3(X₀, X₂, X₃)
t₂₀: l1(X₀, X₂, X₃) → l2(X₀, X₂, X₃) :|: X₀ ≤ 0 ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂
t₁₉: l1(X₀, X₂, X₃) → l4(X₀, X₂, X₃) :|: 0 < X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀+X₂
t₂₁: l2(X₀, X₂, X₃) → l5(X₀, X₂, X₃)
t₂₂: l3(X₀, X₂, X₃) → l1(X₃, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₂₃: l3(X₀, X₂, X₃) → l2(X₀, X₂, X₃) :|: X₂ ≤ 0
t₂₄: l3(X₀, X₂, X₃) → l2(X₀, X₂, X₃) :|: X₃ ≤ X₂
t₂₅: l4(X₀, X₂, X₃) → l1(X₀-1, X₂, X₃) :|: X₀ < X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀
t₂₆: l4(X₀, X₂, X₃) → l1(X₀-X₂, X₂, X₃) :|: X₂ ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₀
new bound:
X₃ {O(n)}
MPRF:
l4 [X₀-1 ]
l1 [X₀ ]
new bound:
X₃ {O(n)}
MPRF:
l4 [X₀ ]
l1 [X₀ ]
new bound:
X₃ {O(n)}
MPRF:
l4 [X₀ ]
l1 [X₀ ]
Overall timebound:3⋅X₃+6 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: X₃ {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: X₃ {O(n)}
t₂₆: X₃ {O(n)}
Overall costbound: 3⋅X₃+6 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: X₃ {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: X₃ {O(n)}
t₂₆: X₃ {O(n)}
t₁₈, X₀: X₀ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₉, X₀: X₃ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₂₀, X₀: 2⋅X₃ {O(n)}
t₂₀, X₂: 2⋅X₂ {O(n)}
t₂₀, X₃: 2⋅X₃ {O(n)}
t₂₁, X₀: 2⋅X₀+2⋅X₃ {O(n)}
t₂₁, X₂: 4⋅X₂ {O(n)}
t₂₁, X₃: 4⋅X₃ {O(n)}
t₂₂, X₀: X₃ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₃, X₀: X₀ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₄, X₀: X₀ {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₅, X₀: X₃ {O(n)}
t₂₅, X₂: X₂ {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₂₆, X₀: X₃ {O(n)}
t₂₆, X₂: X₂ {O(n)}
t₂₆, X₃: X₃ {O(n)}