Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₁+1, X₂, X₃)
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
Found invariant X₃ ≤ X₁ ∧ X₀ ≤ 0 for location l5
Found invariant X₃ ≤ X₁ for location l1
Found invariant X₃ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ X₃ ≤ X₁
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₃ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₁+1, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1 ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₀ ≤ 0
Found invariant X₃ ≤ X₁ ∧ X₀ ≤ 0 for location l5
Found invariant X₃ ≤ X₁ for location l1
Found invariant X₃ ≤ X₁ ∧ X₀ ≤ 0 for location l4
Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₀ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₁:
X₀: X₂ {O(n)}
X₁: X₃ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 4⋅X₂+4⋅X₃+7 {O(n)}
relevant size-bounds w.r.t. t₁:
X₀: X₂ {O(n)}
X₁: X₃ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 4⋅X₂+4⋅X₃+7 {O(n)}
Overall timebound:8⋅X₂+8⋅X₃+18 {O(n)}
t₀: 1 {O(1)}
t₂: 4⋅X₂+4⋅X₃+7 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 4⋅X₂+4⋅X₃+7 {O(n)}
t₅: 1 {O(1)}
Overall costbound: 8⋅X₂+8⋅X₃+18 {O(n)}
t₀: 1 {O(1)}
t₂: 4⋅X₂+4⋅X₃+7 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 4⋅X₂+4⋅X₃+7 {O(n)}
t₅: 1 {O(1)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₂, X₀: 16⋅X₂⋅X₂+20⋅X₃⋅X₃+36⋅X₂⋅X₃+61⋅X₂+68⋅X₃+56 {O(n^2)}
t₂, X₁: 4⋅X₂+5⋅X₃+7 {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: 16⋅X₂⋅X₂+20⋅X₃⋅X₃+36⋅X₂⋅X₃+62⋅X₂+68⋅X₃+56 {O(n^2)}
t₃, X₁: 4⋅X₂+6⋅X₃+7 {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₄, X₀: 16⋅X₂⋅X₂+20⋅X₃⋅X₃+36⋅X₂⋅X₃+61⋅X₂+68⋅X₃+56 {O(n^2)}
t₄, X₁: 4⋅X₂+5⋅X₃+7 {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: 16⋅X₂⋅X₂+20⋅X₃⋅X₃+36⋅X₂⋅X₃+62⋅X₂+68⋅X₃+56 {O(n^2)}
t₅, X₁: 4⋅X₂+6⋅X₃+7 {O(n)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}