Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 1 < X₀ ∧ X₀ < 100
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 1
t₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 100 ≤ X₀
t₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₅: l3(X₀, X₁, X₂) → l1((X₀)², X₁, X₂)
t₆: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
Eliminate variables {X₁} that do not contribute to the problem
Found invariant X₀ ≤ 99 ∧ 2 ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₃: l0(X₀, X₁) → l2(X₀, X₁)
t₁₄: l1(X₀, X₁) → l3(X₀, X₁) :|: 1 < X₀ ∧ X₀ < 100
t₁₅: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 1
t₁₆: l1(X₀, X₁) → l4(X₀, X₁) :|: 100 ≤ X₀
t₁₇: l2(X₀, X₁) → l1(X₁, X₁)
t₁₈: l3(X₀, X₁) → l1((X₀)², X₁) :|: X₀ ≤ 99 ∧ 2 ≤ X₀
t₁₉: l4(X₀, X₁) → l5(X₀, X₁)
new bound:
X₁+100 {O(n)}
new bound:
X₁+100 {O(n)}
Overall timebound:2⋅X₁+205 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₁+100 {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: X₁+100 {O(n)}
t₁₉: 1 {O(1)}
Overall costbound: 2⋅X₁+205 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₁+100 {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: X₁+100 {O(n)}
t₁₉: 1 {O(1)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₀: 99 {O(1)}
t₁₄, X₁: X₁ {O(n)}
t₁₅, X₀: X₁+9801 {O(n)}
t₁₅, X₁: 2⋅X₁ {O(n)}
t₁₆, X₀: X₁+9801 {O(n)}
t₁₆, X₁: 2⋅X₁ {O(n)}
t₁₇, X₀: X₁ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₈, X₀: 9801 {O(1)}
t₁₈, X₁: X₁ {O(n)}
t₁₉, X₀: 2⋅X₁+19602 {O(n)}
t₁₉, X₁: 4⋅X₁ {O(n)}