Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(1+X₀, X₁, E, X₃) :|: 1 ≤ E ∧ 1+X₀ ≤ X₁
t₂: l1(X₀, X₁, X₂, X₃) → l1(1+X₀, X₁, E, X₃) :|: E+1 ≤ 0 ∧ 1+X₀ ≤ X₁
t₃: l1(X₀, X₁, X₂, X₃) → l1(X₀, X₁-1, 0, X₃) :|: 1+X₀ ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, E) :|: X₁ ≤ X₀
Eliminate variables {X₂,X₃} that do not contribute to the problem
Found invariant X₁ ≤ X₀ for location l2
Start: l0
Program_Vars: X₀, X₁
Temp_Vars: E
Locations: l0, l1, l2
Transitions:
t₁₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁₁: l1(X₀, X₁) → l1(1+X₀, X₁) :|: 1 ≤ E ∧ 1+X₀ ≤ X₁
t₁₂: l1(X₀, X₁) → l1(1+X₀, X₁) :|: E+1 ≤ 0 ∧ 1+X₀ ≤ X₁
t₁₃: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 1+X₀ ≤ X₁
t₁₄: l1(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ X₀
new bound:
X₀+X₁ {O(n)}
new bound:
X₀+X₁ {O(n)}
new bound:
X₀+X₁ {O(n)}
Overall timebound:3⋅X₀+3⋅X₁+2 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₀+X₁ {O(n)}
t₁₂: X₀+X₁ {O(n)}
t₁₃: X₀+X₁ {O(n)}
t₁₄: 1 {O(1)}
Overall costbound: 3⋅X₀+3⋅X₁+2 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₀+X₁ {O(n)}
t₁₂: X₀+X₁ {O(n)}
t₁₃: X₀+X₁ {O(n)}
t₁₄: 1 {O(1)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₁, X₀: 2⋅X₁+3⋅X₀ {O(n)}
t₁₁, X₁: 2⋅X₁+X₀ {O(n)}
t₁₂, X₀: 2⋅X₁+3⋅X₀ {O(n)}
t₁₂, X₁: 2⋅X₁+X₀ {O(n)}
t₁₃, X₀: 2⋅X₁+3⋅X₀ {O(n)}
t₁₃, X₁: 2⋅X₁+X₀ {O(n)}
t₁₄, X₀: 10⋅X₀+6⋅X₁ {O(n)}
t₁₄, X₁: 3⋅X₀+7⋅X₁ {O(n)}