Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₂ ∧ X₁ < X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁+1, X₂, X₃, X₄)
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ for location l5
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ for location l1
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ for location l4
Found invariant 1+X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₂ ∧ X₁ < X₂ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁+1, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₃ ≤ X₀
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ for location l5
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ for location l1
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ for location l4
Found invariant 1+X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₁:
X₀: X₃ {O(n)}
X₁: X₄ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₃+2⋅X₄+4⋅X₂+6 {O(n)}
relevant size-bounds w.r.t. t₁:
X₀: X₃ {O(n)}
X₁: X₄ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₃+2⋅X₄+4⋅X₂+6 {O(n)}
Overall timebound:4⋅X₃+4⋅X₄+8⋅X₂+17 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₃+2⋅X₄+4⋅X₂+6 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₅: 2⋅X₃+2⋅X₄+4⋅X₂+6 {O(n)}
t₆: 1 {O(1)}
Overall costbound: 4⋅X₃+4⋅X₄+8⋅X₂+17 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₃+2⋅X₄+4⋅X₂+6 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₅: 2⋅X₃+2⋅X₄+4⋅X₂+6 {O(n)}
t₆: 1 {O(1)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₂, X₀: 2⋅X₄+3⋅X₃+4⋅X₂+6 {O(n)}
t₂, X₁: 2⋅X₃+3⋅X₄+4⋅X₂+6 {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: 2⋅X₄+4⋅X₂+4⋅X₃+6 {O(n)}
t₃, X₁: 2⋅X₃+4⋅X₂+4⋅X₄+6 {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₀: 2⋅X₄+4⋅X₂+4⋅X₃+6 {O(n)}
t₄, X₁: 2⋅X₃+4⋅X₂+4⋅X₄+6 {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₅, X₀: 2⋅X₄+3⋅X₃+4⋅X₂+6 {O(n)}
t₅, X₁: 2⋅X₃+3⋅X₄+4⋅X₂+6 {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: 4⋅X₄+8⋅X₂+8⋅X₃+12 {O(n)}
t₆, X₁: 4⋅X₃+8⋅X₂+8⋅X₄+12 {O(n)}
t₆, X₂: 4⋅X₂ {O(n)}
t₆, X₃: 4⋅X₃ {O(n)}
t₆, X₄: 4⋅X₄ {O(n)}