Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ X₁
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ < X₂
t₁: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₀)
t₄: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1)
t₅: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location l5
Found invariant X₀ ≤ X₂ for location l1
Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location l4
Found invariant X₂ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ X₁ ∧ X₀ ≤ X₂
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ < X₂ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₀)
t₄: l3(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: X₂ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁
t₅: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂
Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location l5
Found invariant X₀ ≤ X₂ for location l1
Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location l4
Found invariant X₂ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₁:
X₁: X₁ {O(n)}
X₂: X₀ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+4 {O(n)}
relevant size-bounds w.r.t. t₁:
X₁: X₁ {O(n)}
X₂: X₀ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+4 {O(n)}
Overall timebound:4⋅X₀+4⋅X₁+12 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₀+2⋅X₁+4 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 2⋅X₀+2⋅X₁+4 {O(n)}
t₅: 1 {O(1)}
Overall costbound: 4⋅X₀+4⋅X₁+12 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₀+2⋅X₁+4 {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: 2⋅X₀+2⋅X₁+4 {O(n)}
t₅: 1 {O(1)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 2⋅X₁+3⋅X₀+4 {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: 2⋅X₁+4⋅X₀+4 {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₀ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: 2⋅X₁+3⋅X₀+4 {O(n)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 2⋅X₁ {O(n)}
t₅, X₂: 2⋅X₁+4⋅X₀+4 {O(n)}