Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₅: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ < X₁
t₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ < X₀
t₈: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₁: l3(X₀, X₁, X₂) → l1(X₂, X₁, X₂) :|: 0 < X₁
t₂: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ ≤ 0
t₆: l4(X₀, X₁, X₂) → l1(0, X₁, X₂) :|: X₁ < X₀
t₇: l4(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₀ ≤ X₁
Found invariant 1 ≤ X₁ for location l1
Found invariant 1 ≤ X₁ for location l4
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₅: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ < X₁ ∧ 1 ≤ X₁
t₄: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₁ < X₀ ∧ 1 ≤ X₁
t₈: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₁: l3(X₀, X₁, X₂) → l1(X₂, X₁, X₂) :|: 0 < X₁
t₂: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ ≤ 0
t₆: l4(X₀, X₁, X₂) → l1(0, X₁, X₂) :|: X₁ < X₀ ∧ 1 ≤ X₁
t₇: l4(X₀, X₁, X₂) → l1(X₀+1, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1 ≤ X₁
Cut unsatisfiable transition t₂₂₉: n_l1___2→l2
Cut unsatisfiable transition t₂₁₁: n_l1___4→n_l4___3
Cut unreachable locations [n_l4___3] from the program graph
Found invariant 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location n_l4___6
Found invariant 1 ≤ X₁ ∧ X₀ ≤ X₁ for location n_l1___4
Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___2
Found invariant X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___5
Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___1
Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ for location l1
Found invariant 3 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___6
Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___4
Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___2
Found invariant X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___5
Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___1
Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ for location l1
Found invariant 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location n_l4___6
Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ for location n_l1___4
Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l1___2
Found invariant X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___5
Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l4___1
Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ for location l1
Termination: true
Formula:
relevant size-bounds w.r.t. t₂₁₅:
X₁: X₁ {O(n)}
Runtime-bound of t₂₁₅: 1 {O(1)}
Results in: 6⋅X₁+11 {O(n)}
Termination: true
Formula:
relevant size-bounds w.r.t. t₂₁₄:
X₀: X₂ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₁₄: 1 {O(1)}
Results in: 6⋅X₁+6⋅X₂+9 {O(n)}
relevant size-bounds w.r.t. t₂₁₅:
X₁: X₁ {O(n)}
Runtime-bound of t₂₁₅: 1 {O(1)}
Results in: 6⋅X₁+11 {O(n)}
relevant size-bounds w.r.t. t₂₁₄:
X₀: X₂ {O(n)}
X₁: X₁ {O(n)}
Runtime-bound of t₂₁₄: 1 {O(1)}
Results in: 6⋅X₁+6⋅X₂+9 {O(n)}
new bound:
12⋅X₂+24⋅X₁+40 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l5, n_l1___2, n_l1___4, n_l4___1, n_l4___5, n_l4___6
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₅: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁
t₂₁₃: l1(X₀, X₁, X₂) → n_l4___5(X₀, X₁, X₂) :|: X₁ < X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁
t₂₁₄: l1(X₀, X₁, X₂) → n_l4___6(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ < X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁
t₈: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₁: l3(X₀, X₁, X₂) → l1(X₂, X₁, X₂) :|: 0 < X₁
t₂: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ ≤ 0
t₂₁₀: n_l1___2(X₀, X₁, X₂) → n_l4___1(X₀, X₁, X₂) :|: X₀ < X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ X₀ < X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₃₀: n_l1___4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁
t₂₁₂: n_l1___4(X₀, X₁, X₂) → n_l4___6(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ X₀ < X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁
t₂₁₅: n_l4___1(X₀, X₁, X₂) → n_l1___4(X₀+1, X₁, X₂) :|: 1 ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₁₇: n_l4___5(X₀, X₁, X₂) → n_l1___2(0, X₁, X₂) :|: X₁ < X₀ ∧ 1 ≤ X₁ ∧ X₁ < X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₂₁₈: n_l4___6(X₀, X₁, X₂) → n_l1___4(X₀+1, X₁, X₂) :|: X₀ < X₁ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁
Overall timebound:12⋅X₂+24⋅X₁+51 {O(n)}
t₀: 1 {O(1)}
t₅: 1 {O(1)}
t₂₁₃: 1 {O(1)}
t₂₁₄: 1 {O(1)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₂₁₀: 1 {O(1)}
t₂₁₂: 12⋅X₁+6⋅X₂+20 {O(n)}
t₂₃₀: 1 {O(1)}
t₂₁₅: 1 {O(1)}
t₂₁₇: 1 {O(1)}
t₂₁₈: 12⋅X₁+6⋅X₂+20 {O(n)}
Overall costbound: 12⋅X₂+24⋅X₁+51 {O(n)}
t₀: 1 {O(1)}
t₅: 1 {O(1)}
t₂₁₃: 1 {O(1)}
t₂₁₄: 1 {O(1)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₂₁₀: 1 {O(1)}
t₂₁₂: 12⋅X₁+6⋅X₂+20 {O(n)}
t₂₃₀: 1 {O(1)}
t₂₁₅: 1 {O(1)}
t₂₁₇: 1 {O(1)}
t₂₁₈: 12⋅X₁+6⋅X₂+20 {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₅, X₀: X₂ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₂₁₃, X₀: X₂ {O(n)}
t₂₁₃, X₁: X₁ {O(n)}
t₂₁₃, X₂: X₂ {O(n)}
t₂₁₄, X₀: X₂ {O(n)}
t₂₁₄, X₁: X₁ {O(n)}
t₂₁₄, X₂: X₂ {O(n)}
t₈, X₀: 12⋅X₁+8⋅X₂+X₀+22 {O(n)}
t₈, X₁: 5⋅X₁ {O(n)}
t₈, X₂: 5⋅X₂ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂₁₀, X₀: 0 {O(1)}
t₂₁₀, X₁: X₁ {O(n)}
t₂₁₀, X₂: X₂ {O(n)}
t₂₁₂, X₀: 12⋅X₁+7⋅X₂+21 {O(n)}
t₂₁₂, X₁: 2⋅X₁ {O(n)}
t₂₁₂, X₂: 2⋅X₂ {O(n)}
t₂₃₀, X₀: 12⋅X₁+7⋅X₂+22 {O(n)}
t₂₃₀, X₁: 3⋅X₁ {O(n)}
t₂₃₀, X₂: 3⋅X₂ {O(n)}
t₂₁₅, X₀: 1 {O(1)}
t₂₁₅, X₁: X₁ {O(n)}
t₂₁₅, X₂: X₂ {O(n)}
t₂₁₇, X₀: 0 {O(1)}
t₂₁₇, X₁: X₁ {O(n)}
t₂₁₇, X₂: X₂ {O(n)}
t₂₁₈, X₀: 12⋅X₁+7⋅X₂+21 {O(n)}
t₂₁₈, X₁: 2⋅X₁ {O(n)}
t₂₁₈, X₂: 2⋅X₂ {O(n)}