Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ < 0
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ < 1
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 1 < X₃
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃
t₈: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₁, X₁, X₂, X₃) :|: X₃ ≤ 2⋅X₂
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 2⋅X₂ < X₃
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀+1-2⋅X₂, X₁, X₂, X₃)
Found invariant X₃ ≤ 1 ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₀ for location l4
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ < 0
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ < 1
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 1 < X₃
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃
t₈: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₁, X₁, X₂, X₃) :|: X₃ ≤ 2⋅X₂
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 2⋅X₂ < X₃
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀+1-2⋅X₂, X₁, X₂, X₃) :|: X₃ ≤ 1 ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀+X₃ ∧ 0 ≤ X₀
Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l4___3
Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ for location n_l1___2
Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l4___1
Found invariant X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l1
new bound:
2⋅X₁+2⋅X₂+1 {O(n)}
MPRF:
n_l4___1 [X₀ ]
n_l1___2 [X₀+1 ]
new bound:
2⋅X₁+2⋅X₂+1 {O(n)}
MPRF:
n_l4___1 [X₀+1 ]
n_l1___2 [X₀+1 ]
new bound:
4⋅X₁+4⋅X₂+2 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l5, n_l1___2, n_l4___1, n_l4___3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ < 1 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₆: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 1 < X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₆₁: l1(X₀, X₁, X₂, X₃) → n_l4___3(X₀, X₁, X₂, 1) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₈: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₁, X₁, X₂, X₃) :|: X₃ ≤ 2⋅X₂
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 2⋅X₂ < X₃
t₆₉: n_l1___2(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁
t₆₀: n_l1___2(X₀, X₁, X₂, X₃) → n_l4___1(X₀, X₁, X₂, 1) :|: X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ 1 ≤ X₀+2⋅X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁
t₆₂: n_l4___1(X₀, X₁, X₂, X₃) → n_l1___2(X₀+1-2⋅X₂, X₁, X₂, 1) :|: 1 ≤ X₀+2⋅X₂ ∧ 0 ≤ X₀ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ 0 ≤ X₀ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₆₃: n_l4___3(X₀, X₁, X₂, X₃) → n_l1___2(X₀+1-2⋅X₂, X₁, X₂, 1) :|: 1 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ 0 ≤ X₀ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
Overall timebound:4⋅X₁+4⋅X₂+12 {O(n)}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₆₁: 1 {O(1)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₆₀: 2⋅X₁+2⋅X₂+1 {O(n)}
t₆₉: 1 {O(1)}
t₆₂: 2⋅X₁+2⋅X₂+1 {O(n)}
t₆₃: 1 {O(1)}
Overall costbound: 4⋅X₁+4⋅X₂+12 {O(n)}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₆₁: 1 {O(1)}
t₈: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₆₀: 2⋅X₁+2⋅X₂+1 {O(n)}
t₆₉: 1 {O(1)}
t₆₂: 2⋅X₁+2⋅X₂+1 {O(n)}
t₆₃: 1 {O(1)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₄, X₀: X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₁ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₁ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆₁, X₀: X₁ {O(n)}
t₆₁, X₁: X₁ {O(n)}
t₆₁, X₂: X₂ {O(n)}
t₆₁, X₃: 1 {O(1)}
t₈, X₀: 2⋅2^(2⋅X₁+2⋅X₂+1)⋅X₁+2⋅2^(2⋅X₁+2⋅X₂+1)⋅X₁⋅X₂+2⋅2^(2⋅X₁+2⋅X₂+1)⋅X₂⋅X₂+2^(2⋅X₁+2⋅X₂+1)⋅4⋅X₂+2⋅X₂+5⋅X₁+X₀ {O(EXP)}
t₈, X₁: 6⋅X₁ {O(n)}
t₈, X₂: 6⋅X₂ {O(n)}
t₈, X₃: 4⋅X₃+1 {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₆₀, X₀: 2⋅2^(2⋅X₁+2⋅X₂+1)⋅X₁+2⋅2^(2⋅X₁+2⋅X₂+1)⋅X₁⋅X₂+2⋅2^(2⋅X₁+2⋅X₂+1)⋅X₂⋅X₂+2^(2⋅X₁+2⋅X₂+1)⋅4⋅X₂ {O(EXP)}
t₆₀, X₁: X₁ {O(n)}
t₆₀, X₂: X₂ {O(n)}
t₆₀, X₃: 1 {O(1)}
t₆₉, X₀: 2⋅2^(2⋅X₁+2⋅X₂+1)⋅X₁+2⋅2^(2⋅X₁+2⋅X₂+1)⋅X₁⋅X₂+2⋅2^(2⋅X₁+2⋅X₂+1)⋅X₂⋅X₂+2^(2⋅X₁+2⋅X₂+1)⋅4⋅X₂+2⋅X₁+2⋅X₂ {O(EXP)}
t₆₉, X₁: 2⋅X₁ {O(n)}
t₆₉, X₂: 2⋅X₂ {O(n)}
t₆₉, X₃: 1 {O(1)}
t₆₂, X₀: 2⋅2^(2⋅X₁+2⋅X₂+1)⋅X₁+2⋅2^(2⋅X₁+2⋅X₂+1)⋅X₁⋅X₂+2⋅2^(2⋅X₁+2⋅X₂+1)⋅X₂⋅X₂+2^(2⋅X₁+2⋅X₂+1)⋅4⋅X₂ {O(EXP)}
t₆₂, X₁: X₁ {O(n)}
t₆₂, X₂: X₂ {O(n)}
t₆₂, X₃: 1 {O(1)}
t₆₃, X₀: 2⋅X₁+2⋅X₂ {O(n)}
t₆₃, X₁: X₁ {O(n)}
t₆₃, X₂: X₂ {O(n)}
t₆₃, X₃: 1 {O(1)}