Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 < (X₀)²
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: (X₀)² ≤ 1
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁*X₂ ≤ 0
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 < X₁*X₂
t₇: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₃, X₄, X₂, X₃, X₄, X₅, X₆)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(3⋅X₀-4⋅X₁, 4⋅X₀-3⋅X₁, X₂, X₃, X₄, X₅, X₆)

Preprocessing

Eliminate variables {X₅,X₆} that do not contribute to the problem

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₁₆: l0(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₁₇: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1 < (X₀)²
t₁₈: l2(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: (X₀)² ≤ 1
t₂₀: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₁*X₂ ≤ 0
t₁₉: l3(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₁*X₂
t₂₁: l4(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₂₂: l5(X₀, X₁, X₂, X₃, X₄) → l2(X₃, X₄, X₂, X₃, X₄)
t₂₃: l6(X₀, X₁, X₂, X₃, X₄) → l2(3⋅X₀-4⋅X₁, 4⋅X₀-3⋅X₁, X₂, X₃, X₄)

Analysing control-flow refined program

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location l2

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location n_l6___4

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location n_l3___5

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: inf {Infinity}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: inf {Infinity}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: inf {Infinity}

Sizebounds

t₁₆, X₀: X₀ {O(n)}
t₁₆, X₁: X₁ {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₄: X₄ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₈, X₂: 2⋅X₂ {O(n)}
t₁₈, X₃: 2⋅X₃ {O(n)}
t₁₈, X₄: 2⋅X₄ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₀, X₄: X₄ {O(n)}
t₂₁, X₂: 3⋅X₂ {O(n)}
t₂₁, X₃: 3⋅X₃ {O(n)}
t₂₁, X₄: 3⋅X₄ {O(n)}
t₂₂, X₀: X₃ {O(n)}
t₂₂, X₁: X₄ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₄: X₄ {O(n)}