Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: l0, l1, l2, l3
Transitions:
t₄: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₃: l1(X₀, X₁, X₂) → l2(X₀, X₁, D) :|: X₁ ≤ 20
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 21 ≤ X₁
t₁: l3(X₀, X₁, X₂) → l1(X₀, X₁-1, X₂) :|: X₀ ≤ 30
t₀: l3(X₀, X₁, X₂) → l3(X₀-1, X₁, X₂) :|: 31 ≤ X₀
Eliminate variables {D,X₂} that do not contribute to the problem
Found invariant X₁ ≤ 20 for location l2
Found invariant 21 ≤ X₁ for location l3
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₁₀: l0(X₀, X₁) → l1(X₀, X₁)
t₁₁: l1(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ 20
t₁₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 21 ≤ X₁
t₁₃: l3(X₀, X₁) → l1(X₀, X₁-1) :|: X₀ ≤ 30 ∧ 21 ≤ X₁
t₁₄: l3(X₀, X₁) → l3(X₀-1, X₁) :|: 31 ≤ X₀ ∧ 21 ≤ X₁
new bound:
X₁+20 {O(n)}
new bound:
X₁+20 {O(n)}
new bound:
X₀ {O(n)}
Overall timebound:2⋅X₁+X₀+42 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: X₁+20 {O(n)}
t₁₃: X₁+20 {O(n)}
t₁₄: X₀ {O(n)}
Overall costbound: 2⋅X₁+X₀+42 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: X₁+20 {O(n)}
t₁₃: X₁+20 {O(n)}
t₁₄: X₀ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₁, X₀: 2⋅X₀ {O(n)}
t₁₁, X₁: 2⋅X₁ {O(n)}
t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}