Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F
Locations: l0, l1, l2
Transitions:
t₁: l0(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄) :|: 2 ≤ X₀ ∧ 2 ≤ X₂
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, F, X₂, X₃, X₄) :|: X₀ ≤ 1
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, 1+X₃, 1+X₄) :|: 0 ≤ X₄ ∧ 2+X₃ ≤ 0
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, 1+X₃, 1+X₄) :|: 2+X₄ ≤ 0 ∧ 2+X₃ ≤ 0
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, F, X₂, X₃, X₄) :|: 0 ≤ 1+X₃
Eliminate variables {F,X₁} that do not contribute to the problem
Found invariant 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2 ≤ X₀ for location l1
Start: l0
Program_Vars: X₀, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₁₄: l0(X₀, X₂, X₃, X₄) → l1(X₀, X₂, X₃, X₄) :|: 2 ≤ X₀ ∧ 2 ≤ X₂
t₁₃: l0(X₀, X₂, X₃, X₄) → l2(X₀, X₂, X₃, X₄) :|: X₀ ≤ 1
t₁₆: l1(X₀, X₂, X₃, X₄) → l1(X₀, X₂, 1+X₃, 1+X₄) :|: 0 ≤ X₄ ∧ 2+X₃ ≤ 0 ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2 ≤ X₀
t₁₇: l1(X₀, X₂, X₃, X₄) → l1(X₀, X₂, 1+X₃, 1+X₄) :|: 2+X₄ ≤ 0 ∧ 2+X₃ ≤ 0 ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2 ≤ X₀
t₁₅: l1(X₀, X₂, X₃, X₄) → l2(X₀, X₂, X₃, X₄) :|: 0 ≤ 1+X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2 ≤ X₀
new bound:
X₃ {O(n)}
MPRF:
l1 [-X₃ ]
new bound:
X₃ {O(n)}
MPRF:
l1 [-X₃ ]
Overall timebound:2⋅X₃+3 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: X₃ {O(n)}
t₁₇: X₃ {O(n)}
Overall costbound: 2⋅X₃+3 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: X₃ {O(n)}
t₁₇: X₃ {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₅, X₀: 3⋅X₀ {O(n)}
t₁₅, X₂: 3⋅X₂ {O(n)}
t₁₅, X₃: 3⋅X₃ {O(n)}
t₁₅, X₄: 3⋅X₄+X₃ {O(n)}
t₁₆, X₀: X₀ {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₄: X₃+X₄ {O(n)}
t₁₇, X₀: X₀ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₄ {O(n)}