Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁+X₀ < 0
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁+X₀
t₆: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃) :|: 2 ≤ X₂
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ < 2
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁-X₀, X₂, X₃)
Found invariant X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2 ≤ X₀ for location l1
Found invariant X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 0 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l4
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁+X₀ < 0 ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁+X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2 ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃) :|: 2 ≤ X₂
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ < 2
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁-X₀, X₂, X₃) :|: X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 0 ≤ X₀+X₁ ∧ 2 ≤ X₀
new bound:
X₂+X₃+1 {O(n)}
MPRF:
l4 [X₀+X₁ ]
l1 [X₀+X₁+1 ]
new bound:
2⋅X₂+X₃+1 {O(n)}
MPRF:
l4 [X₀+X₁+1 ]
l1 [X₀+X₁+X₂-1 ]
Overall timebound:2⋅X₃+3⋅X₂+7 {O(n)}
t₀: 1 {O(1)}
t₃: X₂+X₃+1 {O(n)}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: 2⋅X₂+X₃+1 {O(n)}
Overall costbound: 2⋅X₃+3⋅X₂+7 {O(n)}
t₀: 1 {O(1)}
t₃: X₂+X₃+1 {O(n)}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: 2⋅X₂+X₃+1 {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₃, X₀: 3⋅X₂+X₃+1 {O(n)}
t₃, X₁: 5⋅X₂⋅X₃+6⋅X₂⋅X₂+X₃⋅X₃+4⋅X₃+8⋅X₂+2 {O(n^2)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: 4⋅X₂+X₃+1 {O(n)}
t₄, X₁: 5⋅X₂⋅X₃+6⋅X₂⋅X₂+X₃⋅X₃+5⋅X₃+8⋅X₂+2 {O(n^2)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₆, X₀: 4⋅X₂+X₀+X₃+1 {O(n)}
t₆, X₁: 5⋅X₂⋅X₃+6⋅X₂⋅X₂+X₃⋅X₃+5⋅X₃+8⋅X₂+X₁+2 {O(n^2)}
t₆, X₂: 3⋅X₂ {O(n)}
t₆, X₃: 3⋅X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {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)}
t₅, X₀: 3⋅X₂+X₃+1 {O(n)}
t₅, X₁: 5⋅X₂⋅X₃+6⋅X₂⋅X₂+X₃⋅X₃+4⋅X₃+8⋅X₂+2 {O(n^2)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}