Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₁: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁+1, X₂, X₃, X₄) :|: X₁+1 ≤ X₀
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₁, X₃, X₄) :|: X₀ ≤ X₁
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂-1, X₃, X₄) :|: 1 ≤ X₂
t₄: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₂, X₄) :|: X₂ ≤ 0
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃+1, X₄) :|: X₃+1 ≤ X₀
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₃) :|: X₀ ≤ X₃
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄-1) :|: 1 ≤ X₄
Found invariant X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l2
Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l4
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₁: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁+1, X₂, X₃, X₄) :|: X₁+1 ≤ X₀
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₁, X₃, X₄) :|: X₀ ≤ X₁
t₃: l2(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂-1, X₃, X₄) :|: 1 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁
t₄: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₂, X₄) :|: X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃+1, X₄) :|: X₃+1 ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₃) :|: X₀ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁
t₇: l4(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄-1) :|: 1 ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁
Found invariant X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l2
Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l4
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₀:
X₀: X₀ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 2⋅X₀+2⋅X₁+4 {O(n)}
Found invariant X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l2
Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l4
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₂:
X₂: 2⋅X₀+4⋅X₁+4 {O(n)}
Runtime-bound of t₂: 1 {O(1)}
Results in: 4⋅X₀+8⋅X₁+12 {O(n)}
Found invariant X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l2
Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l4
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₄:
X₀: 4⋅X₀ {O(n)}
X₃: 4⋅X₀+8⋅X₁+8 {O(n)}
Runtime-bound of t₄: 1 {O(1)}
Results in: 16⋅X₀+16⋅X₁+20 {O(n)}
Found invariant X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l2
Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₂ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l4
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₆:
X₄: 24⋅X₀+32⋅X₁+36 {O(n)}
Runtime-bound of t₆: 1 {O(1)}
Results in: 48⋅X₀+64⋅X₁+76 {O(n)}
Overall timebound:70⋅X₀+90⋅X₁+116 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₀+2⋅X₁+4 {O(n)}
t₂: 1 {O(1)}
t₃: 4⋅X₀+8⋅X₁+12 {O(n)}
t₄: 1 {O(1)}
t₅: 16⋅X₀+16⋅X₁+20 {O(n)}
t₆: 1 {O(1)}
t₇: 48⋅X₀+64⋅X₁+76 {O(n)}
Overall costbound: 70⋅X₀+90⋅X₁+116 {O(n)}
t₀: 1 {O(1)}
t₁: 2⋅X₀+2⋅X₁+4 {O(n)}
t₂: 1 {O(1)}
t₃: 4⋅X₀+8⋅X₁+12 {O(n)}
t₄: 1 {O(1)}
t₅: 16⋅X₀+16⋅X₁+20 {O(n)}
t₆: 1 {O(1)}
t₇: 48⋅X₀+64⋅X₁+76 {O(n)}
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)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 2⋅X₀+3⋅X₁+4 {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₁: 2⋅X₀+4⋅X₁+4 {O(n)}
t₂, X₂: 2⋅X₀+4⋅X₁+4 {O(n)}
t₂, X₃: 2⋅X₃ {O(n)}
t₂, X₄: 2⋅X₄ {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2⋅X₀+4⋅X₁+4 {O(n)}
t₃, X₂: 2⋅X₀+4⋅X₁+4 {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₀: 4⋅X₀ {O(n)}
t₄, X₁: 4⋅X₀+8⋅X₁+8 {O(n)}
t₄, X₂: 4⋅X₀+8⋅X₁+8 {O(n)}
t₄, X₃: 4⋅X₀+8⋅X₁+8 {O(n)}
t₄, X₄: 4⋅X₄ {O(n)}
t₅, X₀: 4⋅X₀ {O(n)}
t₅, X₁: 4⋅X₀+8⋅X₁+8 {O(n)}
t₅, X₂: 4⋅X₀+8⋅X₁+8 {O(n)}
t₅, X₃: 20⋅X₀+24⋅X₁+28 {O(n)}
t₅, X₄: 4⋅X₄ {O(n)}
t₆, X₀: 8⋅X₀ {O(n)}
t₆, X₁: 16⋅X₁+8⋅X₀+16 {O(n)}
t₆, X₂: 16⋅X₁+8⋅X₀+16 {O(n)}
t₆, X₃: 24⋅X₀+32⋅X₁+36 {O(n)}
t₆, X₄: 24⋅X₀+32⋅X₁+36 {O(n)}
t₇, X₀: 8⋅X₀ {O(n)}
t₇, X₁: 16⋅X₁+8⋅X₀+16 {O(n)}
t₇, X₂: 16⋅X₁+8⋅X₀+16 {O(n)}
t₇, X₃: 24⋅X₀+32⋅X₁+36 {O(n)}
t₇, X₄: 24⋅X₀+32⋅X₁+36 {O(n)}