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 t₉₅: n_l1___2→l2
Cut unsatisfiable transition t₇₇: 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
new bound:
2⋅X₁+X₂+2 {O(n)}
MPRF:
n_l4___6 [X₁-X₀ ]
n_l1___4 [X₁+1-X₀ ]
new bound:
2⋅X₁+X₂+3 {O(n)}
MPRF:
n_l4___6 [X₁+1-X₀ ]
n_l1___4 [X₁+1-X₀ ]
new bound:
2⋅X₂+4⋅X₁+5 {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
t₇₉: l1(X₀, X₁, X₂) → n_l4___5(X₀, X₁, X₂) :|: X₁ < X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁
t₈₀: 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
t₇₆: 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
t₉₆: n_l1___4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₁
t₇₈: 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
t₈₁: 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
t₈₃: 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
t₈₄: 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:2⋅X₂+4⋅X₁+16 {O(n)}
t₀: 1 {O(1)}
t₅: 1 {O(1)}
t₇₉: 1 {O(1)}
t₈₀: 1 {O(1)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₇₆: 1 {O(1)}
t₇₈: 2⋅X₁+X₂+2 {O(n)}
t₉₆: 1 {O(1)}
t₈₁: 1 {O(1)}
t₈₃: 1 {O(1)}
t₈₄: 2⋅X₁+X₂+3 {O(n)}
Overall costbound: 2⋅X₂+4⋅X₁+16 {O(n)}
t₀: 1 {O(1)}
t₅: 1 {O(1)}
t₇₉: 1 {O(1)}
t₈₀: 1 {O(1)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₇₆: 1 {O(1)}
t₇₈: 2⋅X₁+X₂+2 {O(n)}
t₉₆: 1 {O(1)}
t₈₁: 1 {O(1)}
t₈₃: 1 {O(1)}
t₈₄: 2⋅X₁+X₂+3 {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)}
t₇₉, X₀: X₂ {O(n)}
t₇₉, X₁: X₁ {O(n)}
t₇₉, X₂: X₂ {O(n)}
t₈₀, X₀: X₂ {O(n)}
t₈₀, X₁: X₁ {O(n)}
t₈₀, X₂: X₂ {O(n)}
t₈, X₀: 2⋅X₁+3⋅X₂+X₀+5 {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)}
t₇₆, X₀: 0 {O(1)}
t₇₆, X₁: X₁ {O(n)}
t₇₆, X₂: X₂ {O(n)}
t₇₈, X₀: 2⋅X₁+2⋅X₂+4 {O(n)}
t₇₈, X₁: 2⋅X₁ {O(n)}
t₇₈, X₂: 2⋅X₂ {O(n)}
t₉₆, X₀: 2⋅X₁+2⋅X₂+5 {O(n)}
t₉₆, X₁: 3⋅X₁ {O(n)}
t₉₆, X₂: 3⋅X₂ {O(n)}
t₈₁, X₀: 1 {O(1)}
t₈₁, X₁: X₁ {O(n)}
t₈₁, X₂: X₂ {O(n)}
t₈₃, X₀: 0 {O(1)}
t₈₃, X₁: X₁ {O(n)}
t₈₃, X₂: X₂ {O(n)}
t₈₄, X₀: 2⋅X₁+2⋅X₂+4 {O(n)}
t₈₄, X₁: 2⋅X₁ {O(n)}
t₈₄, X₂: 2⋅X₂ {O(n)}