Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₄: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ ≤ X₀
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ < X₁
t₆: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₁: l3(X₀, X₁, X₂) → l1(X₂, X₁, X₂) :|: 0 < X₁
t₂: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ ≤ 0
t₅: l4(X₀, X₁, X₂) → l1(X₁+X₀, X₁, X₂)
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₁ for location l1
Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location l4
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₄: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ < X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁
t₆: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₁: l3(X₀, X₁, X₂) → l1(X₂, X₁, X₂) :|: 0 < X₁
t₂: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ ≤ 0
t₅: l4(X₀, X₁, X₂) → l1(X₁+X₀, X₁, X₂) :|: 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₁ for location l1
Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location l4
Termination: true
Formula:
relevant size-bounds w.r.t. t₁:
X₀: X₂ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₁+2⋅X₂+4 {O(n)}
relevant size-bounds w.r.t. t₁:
X₀: X₂ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₁+2⋅X₂+4 {O(n)}
Overall timebound:4⋅X₁+4⋅X₂+13 {O(n)}
t₀: 1 {O(1)}
t₃: 2⋅X₁+2⋅X₂+4 {O(n)}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: 2⋅X₁+2⋅X₂+4 {O(n)}
Overall costbound: 4⋅X₁+4⋅X₂+13 {O(n)}
t₀: 1 {O(1)}
t₃: 2⋅X₁+2⋅X₂+4 {O(n)}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: 2⋅X₁+2⋅X₂+4 {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₃, X₀: 2⋅X₁⋅X₁+2⋅X₁⋅X₂+5⋅X₁+X₂ {O(n^2)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₄, X₀: 2⋅X₁⋅X₁+2⋅X₁⋅X₂+2⋅X₂+5⋅X₁ {O(n^2)}
t₄, X₁: 2⋅X₁ {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₆, X₀: 2⋅X₁⋅X₁+2⋅X₁⋅X₂+2⋅X₂+5⋅X₁+X₀ {O(n^2)}
t₆, X₁: 3⋅X₁ {O(n)}
t₆, X₂: 3⋅X₂ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₅, X₀: 2⋅X₁⋅X₁+2⋅X₁⋅X₂+5⋅X₁+X₂ {O(n^2)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}