Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₄: l1(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: X₁ < X₂
t₅: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ X₁
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₃: l3(X₀, X₁, X₂) → l1(X₀, nondef.0, X₂)
t₈: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₆: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ < 0
t₇: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 0 < X₀
t₁₀: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₉: l6(X₀, X₁, X₂) → l4(X₀-1, X₁, X₂)
Preprocessing
Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location l6
Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location l4
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₄: l1(X₀, X₁, X₂) → l4(X₂, X₁, X₂) :|: X₁ < X₂
t₅: l1(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₂ ≤ X₁
t₁: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₃: l3(X₀, X₁, X₂) → l1(X₀, nondef.0, X₂)
t₈: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂
t₆: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ < 0 ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂
t₇: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 0 < X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂
t₁₀: l5(X₀, X₁, X₂) → l7(X₀, X₁, X₂)
t₉: l6(X₀, X₁, X₂) → l4(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂
MPRF for transition t₇: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: 0 < X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
l6 [X₀-1 ]
l4 [X₀ ]
Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l6
Found invariant 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ for location l4
Analysing control-flow refined program
Cut unsatisfiable transition t₈₅: n_l4___3→n_l6___2
Cut unsatisfiable transition t₁₀₀: n_l4___5→l5
Cut unreachable locations [n_l6___2] from the program graph
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location n_l6___6
Found invariant 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l6___1
Found invariant 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ 3+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 4+X₀+X₁ ≤ 0 ∧ 2+X₀ ≤ 0 for location n_l6___4
Found invariant 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ for location n_l4___3
Found invariant 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ 3+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 4+X₀+X₁ ≤ 0 ∧ 2+X₀ ≤ 0 for location n_l4___5
Found invariant 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 3+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location n_l6___7
Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l4
MPRF for transition t₈₄: n_l4___3(X₀, X₁, X₂) → n_l6___1(X₀, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 < X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₂+1 {O(n)}
MPRF:
n_l6___1 [X₀ ]
n_l4___3 [X₀+1 ]
MPRF for transition t₈₉: n_l6___1(X₀, X₁, X₂) → n_l4___3(X₀-1, X₁, X₂) :|: 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 < X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:
new bound:
X₂ {O(n)}
MPRF:
n_l6___1 [X₀ ]
n_l4___3 [X₀ ]
Found invariant X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location n_l6___6
Found invariant 2 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location n_l6___1
Found invariant 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ 3+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 4+X₀+X₁ ≤ 0 ∧ 2+X₀ ≤ 0 for location n_l6___4
Found invariant 1 ≤ X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₀ for location n_l4___3
Found invariant 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ 3+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 4+X₀+X₁ ≤ 0 ∧ 2+X₀ ≤ 0 for location n_l4___5
Found invariant 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 3+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location n_l6___7
Found invariant X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location l4
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁: 1 {O(1)}
t₃: 1 {O(1)}
t₆: inf {Infinity}
t₇: X₂ {O(n)}
t₈: 1 {O(1)}
t₁₀: 1 {O(1)}
t₉: inf {Infinity}
Costbounds
Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₁: 1 {O(1)}
t₃: 1 {O(1)}
t₆: inf {Infinity}
t₇: X₂ {O(n)}
t₈: 1 {O(1)}
t₁₀: 1 {O(1)}
t₉: inf {Infinity}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₂: X₂ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₂: X₂ {O(n)}
t₆, X₂: 2⋅X₂ {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₈, X₀: 0 {O(1)}
t₈, X₂: 3⋅X₂ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₂: 4⋅X₂ {O(n)}
t₉, X₂: 2⋅X₂ {O(n)}