Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l1(0, 1+X₁, X₂-1, X₃) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ 0 ∧ 2+X₁ ≤ X₂
t₁: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, E) :|: X₂ ≤ X₁
t₂: l1(X₀, X₁, X₂, X₃) → l2(1, 1+X₁, X₂, E) :|: X₀ ≤ 0 ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1
Eliminate variables {E,X₃} that do not contribute to the problem
Found invariant X₂ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ for location l2
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₉: l0(X₀, X₁, X₂) → l1(0, X₁, X₂)
t₁₂: l1(X₀, X₁, X₂) → l1(0, 1+X₁, X₂-1) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ 0 ∧ 2+X₁ ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₀: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₁: l1(X₀, X₁, X₂) → l2(1, 1+X₁, X₂) :|: X₀ ≤ 0 ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ X₁+1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
Found invariant X₂ ≤ X₁ ∧ X₀ ≤ 1 ∧ 0 ≤ X₀ for location l2
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1
Termination: true
Formula:
relevant size-bounds w.r.t. t₉:
X₁: X₁ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₉: 1 {O(1)}
Results in: 4⋅X₁+4⋅X₂+12 {O(n)}
Overall timebound:4⋅X₁+4⋅X₂+15 {O(n)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 4⋅X₁+4⋅X₂+12 {O(n)}
Overall costbound: 4⋅X₁+4⋅X₂+15 {O(n)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 4⋅X₁+4⋅X₂+12 {O(n)}
t₉, X₀: 0 {O(1)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₁₀, X₀: 0 {O(1)}
t₁₀, X₁: 4⋅X₂+6⋅X₁+12 {O(n)}
t₁₀, X₂: 4⋅X₁+6⋅X₂+12 {O(n)}
t₁₁, X₀: 1 {O(1)}
t₁₁, X₁: 4⋅X₂+6⋅X₁+14 {O(n)}
t₁₁, X₂: 4⋅X₁+6⋅X₂+12 {O(n)}
t₁₂, X₀: 0 {O(1)}
t₁₂, X₁: 4⋅X₂+5⋅X₁+12 {O(n)}
t₁₂, X₂: 4⋅X₁+5⋅X₂+12 {O(n)}