Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₈: l1(X₀, X₁, X₂, X₃) → l4(X₀-1, 1, X₂, X₃) :|: 1 ≤ X₀
t₉: l1(X₀, X₁, X₂, X₃) → l4(X₀-1, 0, X₂, X₃) :|: X₀ < 1
t₅: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₇: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₂: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ < 0
t₃: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 < X₁
t₄: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₁: l5(X₀, X₁, X₂, X₃) → l4(X₃, X₂, X₂, X₃)
t₁₀: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
Found invariant X₀ ≤ X₃ for location l2
Found invariant X₀ ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l6
Found invariant X₀ ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l7
Found invariant X₀ ≤ X₃ for location l1
Found invariant X₀ ≤ X₃ for location l4
Found invariant X₀ ≤ X₃ for location l3
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₈: l1(X₀, X₁, X₂, X₃) → l4(X₀-1, 1, X₂, X₃) :|: 1 ≤ X₀ ∧ X₀ ≤ X₃
t₉: l1(X₀, X₁, X₂, X₃) → l4(X₀-1, 0, X₂, X₃) :|: X₀ < 1 ∧ X₀ ≤ X₃
t₅: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃
t₇: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃
t₂: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ < 0 ∧ X₀ ≤ X₃
t₃: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ X₀ ≤ X₃
t₄: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ X₃
t₁: l5(X₀, X₁, X₂, X₃) → l4(X₃, X₂, X₂, X₃)
t₁₀: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁
knowledge_propagation leads to new time bound 1 {O(1)} for transition t₂: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁ < 0 ∧ X₀ ≤ X₃
new bound:
X₃+1 {O(n)}
MPRF:
l3 [X₀+1 ]
l1 [X₀+1 ]
l4 [X₀+1 ]
l2 [X₀+1 ]
new bound:
X₂+1 {O(n)}
MPRF:
l3 [1 ]
l1 [1 ]
l4 [X₁ ]
l2 [1 ]
Found invariant X₀ ≤ X₃ for location l2
Found invariant X₀ ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l6
Found invariant X₀ ≤ X₃ ∧ X₁ ≤ 0 ∧ 0 ≤ X₁ for location l7
Found invariant X₀ ≤ X₃ for location l1
Found invariant X₀ ≤ X₃ for location l4
Found invariant X₀ ≤ X₃ for location l3
Found invariant 1 ≤ 0 for location l2
Found invariant 1 ≤ 0 for location l6
Found invariant 1 ≤ 0 for location l7
Found invariant 1 ≤ 0 for location l1
Found invariant 1 ≤ 0 for location l4
Found invariant 1 ≤ 0 for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₁:
X₀: X₃ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₃+6 {O(n)}
Termination: true
Formula:
relevant size-bounds w.r.t. t₈:
X₀: 2⋅X₃ {O(n)}
Runtime-bound of t₈: X₃+1 {O(n)}
Results in: 4⋅X₃⋅X₃+10⋅X₃+6 {O(n^2)}
relevant size-bounds w.r.t. t₁:
X₀: X₃ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₃+6 {O(n)}
relevant size-bounds w.r.t. t₈:
X₀: 2⋅X₃ {O(n)}
Runtime-bound of t₈: X₃+1 {O(n)}
Results in: 4⋅X₃⋅X₃+10⋅X₃+6 {O(n^2)}
relevant size-bounds w.r.t. t₁:
X₀: X₃ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₃+6 {O(n)}
relevant size-bounds w.r.t. t₈:
X₀: 2⋅X₃ {O(n)}
Runtime-bound of t₈: X₃+1 {O(n)}
Results in: 4⋅X₃⋅X₃+10⋅X₃+6 {O(n^2)}
knowledge_propagation leads to new time bound X₃+2 {O(n)} for transition t₃: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 < X₁ ∧ X₀ ≤ X₃
knowledge_propagation leads to new time bound X₃+3 {O(n)} for transition t₅: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃
knowledge_propagation leads to new time bound X₃+3 {O(n)} for transition t₇: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₃
Overall timebound:4⋅X₃+X₂+15 {O(n)}
t₀: 1 {O(1)}
t₈: X₃+1 {O(n)}
t₉: X₂+1 {O(n)}
t₅: X₃+3 {O(n)}
t₇: X₃+3 {O(n)}
t₂: 1 {O(1)}
t₃: X₃+2 {O(n)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₁₀: 1 {O(1)}
Overall costbound: 4⋅X₃+X₂+15 {O(n)}
t₀: 1 {O(1)}
t₈: X₃+1 {O(n)}
t₉: X₂+1 {O(n)}
t₅: X₃+3 {O(n)}
t₇: X₃+3 {O(n)}
t₂: 1 {O(1)}
t₃: X₃+2 {O(n)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₁₀: 1 {O(1)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₈, X₀: 2⋅X₃ {O(n)}
t₈, X₁: 1 {O(1)}
t₈, X₂: 2⋅X₂ {O(n)}
t₈, X₃: 2⋅X₃ {O(n)}
t₉, X₀: 2⋅X₃+1 {O(n)}
t₉, X₁: 0 {O(1)}
t₉, X₂: 2⋅X₂ {O(n)}
t₉, X₃: 2⋅X₃ {O(n)}
t₅, X₀: 2⋅X₃ {O(n)}
t₅, X₁: 2⋅X₂+1 {O(n)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}
t₇, X₀: 2⋅X₃ {O(n)}
t₇, X₁: 2⋅X₂+1 {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 2⋅X₃ {O(n)}
t₂, X₀: X₃ {O(n)}
t₂, X₁: X₂ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: 2⋅X₃ {O(n)}
t₃, X₁: X₂+1 {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₄, X₀: 3⋅X₃+1 {O(n)}
t₄, X₁: 0 {O(1)}
t₄, X₂: 3⋅X₂ {O(n)}
t₄, X₃: 3⋅X₃ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₂ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁₀, X₀: 3⋅X₃+1 {O(n)}
t₁₀, X₁: 0 {O(1)}
t₁₀, X₂: 3⋅X₂ {O(n)}
t₁₀, X₃: 3⋅X₃ {O(n)}