Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ < 0
t₃: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀
t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 0 < X₀
t₆: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ 0
t₇: l4(X₀, X₁) → l5(X₀, X₁)
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l5
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ < 0
t₃: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 < X₀
t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₅: l3(X₀, X₁) → l1(X₀-1, X₁) :|: 0 < X₀
t₆: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₀ ≤ 0
t₇: l4(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l5
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Termination: true
Formula:
relevant size-bounds w.r.t. t₁:
X₀: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 4⋅X₁+6 {O(n)}
relevant size-bounds w.r.t. t₁:
X₀: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 4⋅X₁+6 {O(n)}
Found invariant 1 ≤ 0 for location l5
Found invariant 1 ≤ 0 for location l1
Found invariant 1 ≤ 0 for location l4
Found invariant 1 ≤ 0 for location l3
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l5
Found invariant X₀ ≤ X₁ for location l1
Found invariant 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant X₀ ≤ X₁ for location l3
Termination: true
Formula:
relevant size-bounds w.r.t. t₆:
X₀: X₁+1 {O(n)}
Runtime-bound of t₆: 4⋅X₁+6 {O(n)}
Results in: 8⋅X₁⋅X₁+36⋅X₁+36 {O(n^2)}
Termination: true
Formula:
relevant size-bounds w.r.t. t₁:
X₀: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₁+4 {O(n)}
relevant size-bounds w.r.t. t₆:
X₀: X₁+1 {O(n)}
Runtime-bound of t₆: 4⋅X₁+6 {O(n)}
Results in: 8⋅X₁⋅X₁+36⋅X₁+36 {O(n^2)}
relevant size-bounds w.r.t. t₁:
X₀: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₁+4 {O(n)}
Cut unsatisfiable transition t₁₄₈: n_l1___2→n_l3___4
Cut unsatisfiable transition t₁₄₉: n_l1___5→n_l3___3
Cut unreachable locations [n_l3___3] from the program graph
Found invariant 2+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 3+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location n_l3___4
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___6
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___2
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l5
Found invariant 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location n_l1___5
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___1
Found invariant 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l3___7
Found invariant 2+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 3+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location n_l3___4
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___6
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___2
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l5
Found invariant 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location n_l1___5
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___1
Found invariant 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l3___7
Termination: true
Formula:
relevant size-bounds w.r.t. t₁₅₆:
X₀: X₁ {O(n)}
Runtime-bound of t₁₅₆: 1 {O(1)}
Results in: 2⋅X₁+4 {O(n)}
relevant size-bounds w.r.t. t₁₅₆:
X₀: X₁ {O(n)}
Runtime-bound of t₁₅₆: 1 {O(1)}
Results in: 2⋅X₁+4 {O(n)}
Found invariant 2+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 3+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location n_l3___4
Found invariant X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___6
Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l1___2
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l5
Found invariant 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location n_l1___5
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1
Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l4
Found invariant 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___1
Found invariant 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l3___7
Termination: true
Formula:
relevant size-bounds w.r.t. t₁₅₇:
X₀: X₁ {O(n)}
Runtime-bound of t₁₅₇: 1 {O(1)}
Results in: 6⋅X₁+10 {O(n)}
relevant size-bounds w.r.t. t₁₅₇:
X₀: X₁ {O(n)}
Runtime-bound of t₁₅₇: 1 {O(1)}
Results in: 6⋅X₁+10 {O(n)}
new bound:
16⋅X₁+28 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l4, l5, n_l1___2, n_l1___5, n_l3___1, n_l3___4, n_l3___6, n_l3___7
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₄: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₁₅₁: l1(X₀, X₁) → n_l3___6(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₁₅₂: l1(X₀, X₁) → n_l3___7(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₁: l2(X₀, X₁) → l1(X₁, X₁)
t₇: l4(X₀, X₁) → l5(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₆₈: n_l1___2(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₄₇: n_l1___2(X₀, X₁) → n_l3___1(X₀, X₁) :|: 0 < X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₆₉: n_l1___5(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0
t₁₅₀: n_l1___5(X₀, X₁) → n_l3___4(X₀, X₁) :|: X₀ ≤ 1 ∧ X₀ < 0 ∧ 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0
t₁₅₃: n_l3___1(X₀, X₁) → n_l1___2(X₀-1, X₁) :|: 0 < X₀ ∧ 0 < X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₅₅: n_l3___4(X₀, X₁) → n_l1___5(X₀+1, X₁) :|: X₀ < 0 ∧ X₀ ≤ 0 ∧ 2+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 3+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0
t₁₅₆: n_l3___6(X₀, X₁) → n_l1___2(X₀-1, X₁) :|: 0 < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₅₇: n_l3___7(X₀, X₁) → n_l1___5(X₀+1, X₁) :|: X₀ < 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ 0 ∧ 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0
Overall timebound:16⋅X₁+38 {O(n)}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₁₅₁: 1 {O(1)}
t₁₅₂: 1 {O(1)}
t₁: 1 {O(1)}
t₇: 1 {O(1)}
t₁₄₇: 2⋅X₁+4 {O(n)}
t₁₆₈: 1 {O(1)}
t₁₅₀: 6⋅X₁+10 {O(n)}
t₁₆₉: 1 {O(1)}
t₁₅₃: 2⋅X₁+4 {O(n)}
t₁₅₅: 6⋅X₁+10 {O(n)}
t₁₅₆: 1 {O(1)}
t₁₅₇: 1 {O(1)}
Overall costbound: 16⋅X₁+38 {O(n)}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₁₅₁: 1 {O(1)}
t₁₅₂: 1 {O(1)}
t₁: 1 {O(1)}
t₇: 1 {O(1)}
t₁₄₇: 2⋅X₁+4 {O(n)}
t₁₆₈: 1 {O(1)}
t₁₅₀: 6⋅X₁+10 {O(n)}
t₁₆₉: 1 {O(1)}
t₁₅₃: 2⋅X₁+4 {O(n)}
t₁₅₅: 6⋅X₁+10 {O(n)}
t₁₅₆: 1 {O(1)}
t₁₅₇: 1 {O(1)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₄, X₀: 0 {O(1)}
t₄, X₁: X₁ {O(n)}
t₁₅₁, X₀: X₁ {O(n)}
t₁₅₁, X₁: X₁ {O(n)}
t₁₅₂, X₀: X₁ {O(n)}
t₁₅₂, X₁: X₁ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₇, X₀: 0 {O(1)}
t₇, X₁: 5⋅X₁ {O(n)}
t₁₄₇, X₀: X₁ {O(n)}
t₁₄₇, X₁: X₁ {O(n)}
t₁₆₈, X₀: 0 {O(1)}
t₁₆₈, X₁: 2⋅X₁ {O(n)}
t₁₅₀, X₀: X₁ {O(n)}
t₁₅₀, X₁: X₁ {O(n)}
t₁₆₉, X₀: 0 {O(1)}
t₁₆₉, X₁: 2⋅X₁ {O(n)}
t₁₅₃, X₀: X₁ {O(n)}
t₁₅₃, X₁: X₁ {O(n)}
t₁₅₅, X₀: X₁ {O(n)}
t₁₅₅, X₁: X₁ {O(n)}
t₁₅₆, X₀: X₁ {O(n)}
t₁₅₆, X₁: X₁ {O(n)}
t₁₅₇, X₀: X₁ {O(n)}
t₁₅₇, X₁: X₁ {O(n)}