Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 1 < X₀ ∧ X₀ < X₃
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1((X₀)², X₁, X₂, X₃)
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
Eliminate variables {X₁} that do not contribute to the problem
Found invariant 3 ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₄: l0(X₀, X₂, X₃) → l2(X₀, X₂, X₃)
t₁₅: l1(X₀, X₂, X₃) → l3(X₀, X₂, X₃) :|: 1 < X₀ ∧ X₀ < X₃
t₁₆: l1(X₀, X₂, X₃) → l4(X₀, X₂, X₃) :|: X₀ ≤ 1
t₁₇: l1(X₀, X₂, X₃) → l4(X₀, X₂, X₃) :|: X₃ ≤ X₀
t₁₈: l2(X₀, X₂, X₃) → l1(X₂, X₂, X₃)
t₁₉: l3(X₀, X₂, X₃) → l1((X₀)², X₂, X₃) :|: 3 ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₀
t₂₀: l4(X₀, X₂, X₃) → l5(X₀, X₂, X₃)
new bound:
X₂+X₃ {O(n)}
MPRF:
l3 [X₃-X₀-1 ]
l1 [X₃-X₀ ]
new bound:
X₂+X₃ {O(n)}
MPRF:
l3 [X₃-X₀ ]
l1 [X₃-X₀ ]
Overall timebound:2⋅X₂+2⋅X₃+5 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: X₂+X₃ {O(n)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: X₂+X₃ {O(n)}
t₂₀: 1 {O(1)}
Overall costbound: 2⋅X₂+2⋅X₃+5 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: X₂+X₃ {O(n)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: X₂+X₃ {O(n)}
t₂₀: 1 {O(1)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₆, X₂: 2⋅X₂ {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}
t₁₇, X₂: 2⋅X₂ {O(n)}
t₁₇, X₃: 2⋅X₃ {O(n)}
t₁₈, X₀: X₂ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₂₀, X₂: 4⋅X₂ {O(n)}
t₂₀, X₃: 4⋅X₃ {O(n)}