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, X₁, X₂, X₃) :|: X₀ < 100
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, 5, X₂, X₃) :|: 100 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃)
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ < 21
t₆: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: 21 ≤ X₁
t₇: l5(X₀, X₁, X₂, X₃) → l4(X₀, X₁+3, X₂, X₃)
t₈: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
Eliminate variables {X₂,X₃} that do not contribute to the problem
Found invariant 21 ≤ X₁ ∧ 121 ≤ X₀+X₁ ∧ 100 ≤ X₀ for location l6
Found invariant 21 ≤ X₁ ∧ 121 ≤ X₀+X₁ ∧ 100 ≤ X₀ for location l7
Found invariant X₁ ≤ 20 ∧ 80+X₁ ≤ X₀ ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ 100 ≤ X₀ for location l5
Found invariant 0 ≤ X₀ for location l1
Found invariant 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ 100 ≤ X₀ for location l4
Found invariant X₀ ≤ 99 ∧ 0 ≤ X₀ for location l3
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₈: l0(X₀, X₁) → l2(X₀, X₁)
t₁₉: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ < 100 ∧ 0 ≤ X₀
t₂₀: l1(X₀, X₁) → l4(X₀, 5) :|: 100 ≤ X₀ ∧ 0 ≤ X₀
t₂₁: l2(X₀, X₁) → l1(0, X₁)
t₂₂: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ 99 ∧ 0 ≤ X₀
t₂₃: l4(X₀, X₁) → l5(X₀, X₁) :|: X₁ < 21 ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ 100 ≤ X₀
t₂₄: l4(X₀, X₁) → l6(X₀, X₁) :|: 21 ≤ X₁ ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ 100 ≤ X₀
t₂₅: l5(X₀, X₁) → l4(X₀, X₁+3) :|: X₁ ≤ 20 ∧ 80+X₁ ≤ X₀ ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ 100 ≤ X₀
t₂₆: l6(X₀, X₁) → l7(X₀, X₁) :|: 21 ≤ X₁ ∧ 121 ≤ X₀+X₁ ∧ 100 ≤ X₀
Found invariant X₁ ≤ 23 ∧ 77+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 123 ∧ 21 ≤ X₁ ∧ 121 ≤ X₀+X₁ ∧ X₀ ≤ 79+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l6
Found invariant X₁ ≤ 23 ∧ 77+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 123 ∧ 21 ≤ X₁ ∧ 121 ≤ X₀+X₁ ∧ X₀ ≤ 79+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l7
Found invariant X₁ ≤ 20 ∧ 80+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 120 ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ X₀ ≤ 95+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l5
Found invariant X₀ ≤ 100 ∧ 0 ≤ X₀ for location l1
Found invariant X₁ ≤ 23 ∧ 77+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 123 ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ X₀ ≤ 95+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l4
Found invariant X₀ ≤ 99 ∧ 0 ≤ X₀ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₂₁:
Runtime-bound of t₂₁: 1 {O(1)}
Results in: 204 {O(1)}
relevant size-bounds w.r.t. t₂₁:
Runtime-bound of t₂₁: 1 {O(1)}
Results in: 204 {O(1)}
Found invariant X₁ ≤ 23 ∧ 77+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 123 ∧ 21 ≤ X₁ ∧ 121 ≤ X₀+X₁ ∧ X₀ ≤ 79+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l6
Found invariant X₁ ≤ 23 ∧ 77+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 123 ∧ 21 ≤ X₁ ∧ 121 ≤ X₀+X₁ ∧ X₀ ≤ 79+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l7
Found invariant X₁ ≤ 20 ∧ 80+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 120 ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ X₀ ≤ 95+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l5
Found invariant X₀ ≤ 100 ∧ 0 ≤ X₀ for location l1
Found invariant X₁ ≤ 23 ∧ 77+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 123 ∧ 5 ≤ X₁ ∧ 105 ≤ X₀+X₁ ∧ X₀ ≤ 95+X₁ ∧ X₀ ≤ 100 ∧ 100 ≤ X₀ for location l4
Found invariant X₀ ≤ 99 ∧ 0 ≤ X₀ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₂₀:
X₁: 5 {O(1)}
Runtime-bound of t₂₀: 1 {O(1)}
Results in: 56 {O(1)}
relevant size-bounds w.r.t. t₂₀:
X₁: 5 {O(1)}
Runtime-bound of t₂₀: 1 {O(1)}
Results in: 56 {O(1)}
Overall timebound:525 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 204 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 204 {O(1)}
t₂₃: 56 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 56 {O(1)}
t₂₆: 1 {O(1)}
Overall costbound: 525 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 204 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 204 {O(1)}
t₂₃: 56 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 56 {O(1)}
t₂₆: 1 {O(1)}
t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₉, X₀: 99 {O(1)}
t₁₉, X₁: X₁ {O(n)}
t₂₀, X₀: 100 {O(1)}
t₂₀, X₁: 5 {O(1)}
t₂₁, X₀: 0 {O(1)}
t₂₁, X₁: X₁ {O(n)}
t₂₂, X₀: 100 {O(1)}
t₂₂, X₁: X₁ {O(n)}
t₂₃, X₀: 100 {O(1)}
t₂₃, X₁: 20 {O(1)}
t₂₄, X₀: 100 {O(1)}
t₂₄, X₁: 23 {O(1)}
t₂₅, X₀: 100 {O(1)}
t₂₅, X₁: 23 {O(1)}
t₂₆, X₀: 100 {O(1)}
t₂₆, X₁: 23 {O(1)}