Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₂: l10(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₂, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ < X₃
t₇: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₀, X₂, X₃) :|: X₃ ≤ X₀
t₈: l7(X₀, X₁, X₂, X₃) → l6(X₀+1, X₁, X₂, X₃)
t₁₀: l8(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₁ ≤ 2
t₉: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: 2 < X₁
t₁₁: l9(X₀, X₁, X₂, X₃) → l8(X₀, X₁-3, X₂, X₃)
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 2 ∧ X₁ ≤ X₀ for location l11
Found invariant X₂ ≤ X₀ for location l6
Found invariant 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ for location l7
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location l8
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 2 ∧ X₁ ≤ X₀ for location l10
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 3 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l9
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₂: l10(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 2 ∧ X₁ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₂, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ < X₃ ∧ X₂ ≤ X₀
t₇: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₀, X₂, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₀
t₈: l7(X₀, X₁, X₂, X₃) → l6(X₀+1, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀
t₁₀: l8(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₁ ≤ 2 ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀
t₉: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: 2 < X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀
t₁₁: l9(X₀, X₁, X₂, X₃) → l8(X₀, X₁-3, X₂, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 3 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 3 ≤ X₀
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 2 ∧ X₁ ≤ X₀ for location l11
Found invariant X₂ ≤ X₀ for location l6
Found invariant 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ for location l7
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location l8
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 2 ∧ X₁ ≤ X₀ for location l10
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 3 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l9
Termination: true
Formula:
relevant size-bounds w.r.t. t₅:
X₀: X₂ {O(n)}
X₃: X₃ {O(n)}
Runtime-bound of t₅: 1 {O(1)}
Results in: 2⋅X₂+2⋅X₃+4 {O(n)}
relevant size-bounds w.r.t. t₅:
X₀: X₂ {O(n)}
X₃: X₃ {O(n)}
Runtime-bound of t₅: 1 {O(1)}
Results in: 2⋅X₂+2⋅X₃+4 {O(n)}
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 2 ∧ X₁ ≤ X₀ for location l11
Found invariant X₂ ≤ X₀ for location l6
Found invariant 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ for location l7
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location l8
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 2 ∧ X₁ ≤ X₀ for location l10
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 3 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location l9
Termination: true
Formula:
relevant size-bounds w.r.t. t₇:
X₁: 2⋅X₃+4⋅X₂+4 {O(n)}
Runtime-bound of t₇: 1 {O(1)}
Results in: 4⋅X₃+8⋅X₂+12 {O(n)}
relevant size-bounds w.r.t. t₇:
X₁: 2⋅X₃+4⋅X₂+4 {O(n)}
Runtime-bound of t₇: 1 {O(1)}
Results in: 4⋅X₃+8⋅X₂+12 {O(n)}
Overall timebound:12⋅X₃+20⋅X₂+41 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 2⋅X₂+2⋅X₃+4 {O(n)}
t₇: 1 {O(1)}
t₈: 2⋅X₂+2⋅X₃+4 {O(n)}
t₉: 4⋅X₃+8⋅X₂+12 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: 4⋅X₃+8⋅X₂+12 {O(n)}
Overall costbound: 12⋅X₃+20⋅X₂+41 {O(n)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 2⋅X₂+2⋅X₃+4 {O(n)}
t₇: 1 {O(1)}
t₈: 2⋅X₂+2⋅X₃+4 {O(n)}
t₉: 4⋅X₃+8⋅X₂+12 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: 4⋅X₃+8⋅X₂+12 {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₁₂, X₀: 4⋅X₃+8⋅X₂+8 {O(n)}
t₁₂, X₁: 4⋅X₃+8⋅X₂+8 {O(n)}
t₁₂, X₂: 4⋅X₂ {O(n)}
t₁₂, X₃: 4⋅X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₂ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: 2⋅X₃+3⋅X₂+4 {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: 2⋅X₃+4⋅X₂+4 {O(n)}
t₇, X₁: 2⋅X₃+4⋅X₂+4 {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 2⋅X₃ {O(n)}
t₈, X₀: 2⋅X₃+3⋅X₂+4 {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₀: 2⋅X₃+4⋅X₂+4 {O(n)}
t₉, X₁: 2⋅X₃+4⋅X₂+4 {O(n)}
t₉, X₂: 2⋅X₂ {O(n)}
t₉, X₃: 2⋅X₃ {O(n)}
t₁₀, X₀: 4⋅X₃+8⋅X₂+8 {O(n)}
t₁₀, X₁: 4⋅X₃+8⋅X₂+8 {O(n)}
t₁₀, X₂: 4⋅X₂ {O(n)}
t₁₀, X₃: 4⋅X₃ {O(n)}
t₁₁, X₀: 2⋅X₃+4⋅X₂+4 {O(n)}
t₁₁, X₁: 2⋅X₃+4⋅X₂+4 {O(n)}
t₁₁, X₂: 2⋅X₂ {O(n)}
t₁₁, X₃: 2⋅X₃ {O(n)}