Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₁: l0(X₀, X₁, X₂) → l1(X₀, X₁, 1) :|: 1 ≤ X₀
t₃: l0(X₀, X₁, X₂) → l2(X₀, X₁, 0) :|: X₀ ≤ 0
t₂: l2(X₀, X₁, X₂) → l2(X₀, X₁-1, X₂) :|: 1 ≤ X₁
t₀: l2(X₀, X₁, X₂) → l3(X₀, X₁, 1) :|: X₀ ≤ 0 ∧ X₁ ≤ 0
Eliminate variables {X₂} that do not contribute to the problem
Found invariant X₀ ≤ 0 for location l2
Found invariant 1 ≤ X₀ for location l1
Found invariant X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location l3
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₈: l0(X₀, X₁) → l1(X₀, X₁) :|: 1 ≤ X₀
t₉: l0(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 0
t₁₁: l2(X₀, X₁) → l2(X₀, X₁-1) :|: 1 ≤ X₁ ∧ X₀ ≤ 0
t₁₀: l2(X₀, X₁) → l3(X₀, X₁) :|: X₀ ≤ 0 ∧ X₁ ≤ 0 ∧ X₀ ≤ 0
Found invariant X₀ ≤ 0 for location l2
Found invariant 1 ≤ X₀ for location l1
Found invariant X₁ ≤ 0 ∧ X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₉:
X₁: X₁ {O(n)}
Runtime-bound of t₉: 1 {O(1)}
Results in: 2⋅X₁+4 {O(n)}
Overall timebound:2⋅X₁+7 {O(n)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 2⋅X₁+4 {O(n)}
Overall costbound: 2⋅X₁+7 {O(n)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 2⋅X₁+4 {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₁₀, X₀: 2⋅X₀ {O(n)}
t₁₀, X₁: 2⋅X₁ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₁ {O(n)}