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) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, 1000, X₂, X₃) :|: X₀ ≤ 10
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 10 < X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1
t₄: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 1 < X₁
t₈: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₇: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l3(X₀, X₁-1, X₂, X₃)
Eliminate variables {X₃} that do not contribute to the problem
Found invariant X₂ ≤ 10 ∧ X₂ ≤ 8+X₁ ∧ X₁+X₂ ≤ 1010 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 20 ∧ X₁ ≤ 1000 ∧ X₀+X₁ ≤ 1010 ∧ 2 ≤ X₁ ∧ X₀ ≤ 8+X₁ ∧ X₀ ≤ 10 for location l6
Found invariant X₂ ≤ X₀ ∧ 11 ≤ X₀ for location l7
Found invariant X₂ ≤ 10 ∧ X₁+X₂ ≤ 11 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 20 ∧ X₁ ≤ 1 ∧ X₀+X₁ ≤ 11 ∧ X₀ ≤ 10 for location l5
Found invariant X₂ ≤ X₀ for location l1
Found invariant X₂ ≤ X₀ ∧ 11 ≤ X₀ for location l4
Found invariant X₂ ≤ 10 ∧ X₁+X₂ ≤ 1010 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 20 ∧ X₁ ≤ 1000 ∧ X₀+X₁ ≤ 1010 ∧ X₀ ≤ 10 for location l3
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₈: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₉: l1(X₀, X₁, X₂) → l3(X₀, 1000, X₂) :|: X₀ ≤ 10 ∧ X₂ ≤ X₀
t₂₀: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 10 < X₀ ∧ X₂ ≤ X₀
t₂₁: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₂₃: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 1 ∧ X₂ ≤ 10 ∧ X₁+X₂ ≤ 1010 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 20 ∧ X₁ ≤ 1000 ∧ X₀+X₁ ≤ 1010 ∧ X₀ ≤ 10
t₂₂: l3(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 1 < X₁ ∧ X₂ ≤ 10 ∧ X₁+X₂ ≤ 1010 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 20 ∧ X₁ ≤ 1000 ∧ X₀+X₁ ≤ 1010 ∧ X₀ ≤ 10
t₂₄: l4(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ ≤ X₀ ∧ 11 ≤ X₀
t₂₅: l5(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₂ ≤ 10 ∧ X₁+X₂ ≤ 11 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 20 ∧ X₁ ≤ 1 ∧ X₀+X₁ ≤ 11 ∧ X₀ ≤ 10
t₂₆: l6(X₀, X₁, X₂) → l3(X₀, X₁-1, X₂) :|: X₂ ≤ 10 ∧ X₂ ≤ 8+X₁ ∧ X₁+X₂ ≤ 1010 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 20 ∧ X₁ ≤ 1000 ∧ X₀+X₁ ≤ 1010 ∧ 2 ≤ X₁ ∧ X₀ ≤ 8+X₁ ∧ X₀ ≤ 10
new bound:
X₂+11 {O(n)}
MPRF:
l5 [10-X₀ ]
l1 [11-X₀ ]
l6 [10-X₀ ]
l3 [10-X₀ ]
new bound:
X₂+11 {O(n)}
MPRF:
l5 [10-X₀ ]
l1 [11-X₀ ]
l6 [11-X₀ ]
l3 [11-X₀ ]
new bound:
X₂+11 {O(n)}
MPRF:
l5 [11-X₀ ]
l1 [11-X₀ ]
l6 [11-X₀ ]
l3 [11-X₀ ]
Found invariant X₂ ≤ 10 ∧ X₂ ≤ 8+X₁ ∧ X₁+X₂ ≤ 1010 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 20 ∧ X₁ ≤ 1000 ∧ X₀+X₁ ≤ 1010 ∧ 2 ≤ X₁ ∧ X₀ ≤ 8+X₁ ∧ X₀ ≤ 10 for location l6
Found invariant X₂ ≤ X₀ ∧ 11 ≤ X₀ for location l7
Found invariant X₂ ≤ 10 ∧ X₂ ≤ 9+X₁ ∧ X₁+X₂ ≤ 11 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 20 ∧ X₁ ≤ 1 ∧ X₀+X₁ ≤ 11 ∧ 1 ≤ X₁ ∧ X₀ ≤ 9+X₁ ∧ X₀ ≤ 10 for location l5
Found invariant X₂ ≤ X₀ for location l1
Found invariant X₂ ≤ X₀ ∧ 11 ≤ X₀ for location l4
Found invariant X₂ ≤ 10 ∧ X₂ ≤ 9+X₁ ∧ X₁+X₂ ≤ 1010 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 20 ∧ X₁ ≤ 1000 ∧ X₀+X₁ ≤ 1010 ∧ 1 ≤ X₁ ∧ X₀ ≤ 9+X₁ ∧ X₀ ≤ 10 for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₁₉:
X₁: 1000 {O(1)}
Runtime-bound of t₁₉: X₂+11 {O(n)}
Results in: 2004⋅X₂+22044 {O(n)}
relevant size-bounds w.r.t. t₁₉:
X₁: 1000 {O(1)}
Runtime-bound of t₁₉: X₂+11 {O(n)}
Results in: 2004⋅X₂+22044 {O(n)}
Overall timebound:4011⋅X₂+44125 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: X₂+11 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 2004⋅X₂+22044 {O(n)}
t₂₃: X₂+11 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₂+11 {O(n)}
t₂₆: 2004⋅X₂+22044 {O(n)}
Overall costbound: 4011⋅X₂+44125 {O(n)}
t₁₈: 1 {O(1)}
t₁₉: X₂+11 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 2004⋅X₂+22044 {O(n)}
t₂₃: X₂+11 {O(n)}
t₂₄: 1 {O(1)}
t₂₅: X₂+11 {O(n)}
t₂₆: 2004⋅X₂+22044 {O(n)}
t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₉, X₀: 2⋅X₂+11 {O(n)}
t₁₉, X₁: 1000 {O(1)}
t₁₉, X₂: X₂ {O(n)}
t₂₀, X₀: 3⋅X₂+11 {O(n)}
t₂₀, X₁: X₁+999 {O(n)}
t₂₀, X₂: 2⋅X₂ {O(n)}
t₂₁, X₀: X₂ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₂, X₀: 2⋅X₂+11 {O(n)}
t₂₂, X₁: 1000 {O(1)}
t₂₂, X₂: X₂ {O(n)}
t₂₃, X₀: 2⋅X₂+11 {O(n)}
t₂₃, X₁: 999 {O(1)}
t₂₃, X₂: X₂ {O(n)}
t₂₄, X₀: 3⋅X₂+11 {O(n)}
t₂₄, X₁: X₁+999 {O(n)}
t₂₄, X₂: 2⋅X₂ {O(n)}
t₂₅, X₀: 2⋅X₂+11 {O(n)}
t₂₅, X₁: 999 {O(1)}
t₂₅, X₂: X₂ {O(n)}
t₂₆, X₀: 2⋅X₂+11 {O(n)}
t₂₆, X₁: 999 {O(1)}
t₂₆, X₂: X₂ {O(n)}