Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars: K, L
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₇: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(1, X₁, X₂, X₃, X₄, K, K, X₇, X₈, X₉) :|: K ≤ 0
t₈: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l1(1, X₁, X₂, X₃, X₄, K, 0, 1, L, L) :|: 1 ≤ K ∧ 1 ≤ L
t₉: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(1, X₁, X₂, X₃, X₄, K, 0, 1, L, L) :|: 1 ≤ K ∧ L ≤ 0
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₀ ≤ 0
t₆: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l3(0, X₁, K, X₃, K, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, K, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) :|: 1 ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(X₀, L, X₂, K, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₀ ≤ 0 ∧ K ≤ 999+X₂
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l2(1, L, X₂, K, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₀ ≤ 0 ∧ X₂+1000 ≤ K
t₂: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉)

Preprocessing

Cut unreachable locations [l4; l5] from the program graph

Cut unsatisfiable transition t₀: l1→l3

Cut unsatisfiable transition t₃: l3→l2

Eliminate variables {X₁,X₃,X₄,X₅,X₆,X₇,X₈,X₉} that do not contribute to the problem

Found invariant X₀ ≤ 1 ∧ 0 ≤ X₀ for location l2

Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location l1

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₂
Temp_Vars: K, L
Locations: l0, l1, l2, l3
Transitions:
t₁₉: l0(X₀, X₂) → l1(1, X₂) :|: K ≤ 0
t₂₀: l0(X₀, X₂) → l1(1, X₂) :|: 1 ≤ K ∧ 1 ≤ L
t₂₁: l0(X₀, X₂) → l2(1, X₂) :|: 1 ≤ K ∧ L ≤ 0
t₂₂: l1(X₀, X₂) → l3(0, K) :|: 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₂₃: l2(X₀, X₂) → l2(X₀, X₂) :|: X₀ ≤ 1 ∧ 0 ≤ X₀
t₂₄: l3(X₀, X₂) → l2(X₀, X₂) :|: X₀ ≤ 0 ∧ K ≤ 999+X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₅: l3(X₀, X₂) → l2(1, X₂) :|: X₀ ≤ 0 ∧ X₂+1000 ≤ K ∧ X₀ ≤ 0 ∧ 0 ≤ X₀

Analysing control-flow refined program

Found invariant X₀ ≤ 1 ∧ 0 ≤ X₀ for location l2

Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location l1

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location l3

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: inf {Infinity}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: inf {Infinity}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}

Sizebounds

t₁₉, X₀: 1 {O(1)}
t₁₉, X₂: X₂ {O(n)}
t₂₀, X₀: 1 {O(1)}
t₂₀, X₂: X₂ {O(n)}
t₂₁, X₀: 1 {O(1)}
t₂₁, X₂: X₂ {O(n)}
t₂₂, X₀: 0 {O(1)}
t₂₃, X₀: 1 {O(1)}
t₂₄, X₀: 0 {O(1)}
t₂₅, X₀: 1 {O(1)}