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
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ 0 < X₃
t₈: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃) :|: X₂ < 0
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃) :|: 0 < X₂
t₃: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 0 ≤ X₂
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀-X₃, X₁, X₂, X₃)
Eliminate variables {X₁} that do not contribute to the problem
Found invariant X₀ ≤ X₂ for location l1
Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 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 ∧ X₀ ≤ X₂
t₂₁: l1(X₀, X₂, X₃) → l2(X₀, X₂, X₃) :|: X₃ ≤ 0 ∧ X₀ ≤ X₂
t₁₉: l1(X₀, X₂, X₃) → l4(X₀, X₂, X₃) :|: 0 < X₀ ∧ 0 < X₃ ∧ X₀ ≤ X₂
t₂₂: l2(X₀, X₂, X₃) → l5(X₀, X₂, X₃)
t₂₃: l3(X₀, X₂, X₃) → l1(X₂, X₂, X₃) :|: X₂ < 0
t₂₄: l3(X₀, X₂, X₃) → l1(X₂, X₂, X₃) :|: 0 < X₂
t₂₅: l3(X₀, X₂, X₃) → l2(X₀, X₂, X₃) :|: X₂ ≤ 0 ∧ 0 ≤ X₂
t₂₆: l4(X₀, X₂, X₃) → l1(X₀-X₃, X₂, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
new bound:
X₂ {O(n)}
MPRF:
l4 [X₀-1 ]
l1 [X₀ ]
new bound:
X₂+X₃+1 {O(n)}
MPRF:
l4 [X₀ ]
l1 [X₀+X₃-1 ]
Overall timebound:2⋅X₂+X₃+8 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: X₂ {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: X₂+X₃+1 {O(n)}
Overall costbound: 2⋅X₂+X₃+8 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: X₂ {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: X₂+X₃+1 {O(n)}
t₁₈, X₀: X₀ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₉, X₀: X₂+X₃ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₂₀, X₀: 2⋅X₂+X₃ {O(n)}
t₂₀, X₂: 2⋅X₂ {O(n)}
t₂₀, X₃: 2⋅X₃ {O(n)}
t₂₁, X₀: 2⋅X₂ {O(n)}
t₂₁, X₂: 2⋅X₂ {O(n)}
t₂₁, X₃: 2⋅X₃ {O(n)}
t₂₂, X₀: 4⋅X₂+X₀+X₃ {O(n)}
t₂₂, X₂: 4⋅X₂ {O(n)}
t₂₂, X₃: 5⋅X₃ {O(n)}
t₂₃, X₀: X₂ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₄, X₀: X₂ {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₅, X₀: X₀ {O(n)}
t₂₅, X₂: 0 {O(1)}
t₂₅, X₃: X₃ {O(n)}
t₂₆, X₀: X₂+X₃ {O(n)}
t₂₆, X₂: X₂ {O(n)}
t₂₆, X₃: X₃ {O(n)}