Initial Problem

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+X₁ < 0
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀+X₁
t₆: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₃, X₂, X₂, X₃) :|: X₂ < 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 ≤ X₂
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₁-1, X₂, X₃)

Preprocessing

Found invariant X₃ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 2+X₁+X₂ ≤ 0 ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ 0 for location l1

Found invariant X₃ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 2+X₁+X₂ ≤ 0 ∧ 2+X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

Problem after Preprocessing

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+X₁ < 0 ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 2+X₁+X₂ ≤ 0 ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ 0
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀+X₁ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 2+X₁+X₂ ≤ 0 ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ 0
t₆: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₃, X₂, X₂, X₃) :|: X₂ < 0
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 ≤ X₂
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀-X₁, X₁-1, X₂, X₃) :|: X₃ ≤ X₀ ∧ 1+X₂ ≤ 0 ∧ 2+X₁+X₂ ≤ 0 ∧ 2+X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 1 ≤ X₀

Analysing control-flow refined program

Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 2+X₁+X₂ ≤ 0 ∧ 2+X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ 1+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l4___3

Found invariant 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ 3+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 2+X₁ ≤ 0 ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___2

Found invariant 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ 0 ∧ 3+X₁+X₂ ≤ 0 ∧ 3+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 2+X₁ ≤ 0 ∧ 4+X₁ ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l4___1

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₂ ≤ X₁ ∧ 2+X₁+X₂ ≤ 0 ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ 0 for location l1

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₃: inf {Infinity}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₃: inf {Infinity}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₃ {O(n)}
t₄, X₁: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₆, X₀: X₀+X₃ {O(n)}
t₆, X₁: X₁+X₂ {O(n)}
t₆, X₂: 2⋅X₂ {O(n)}
t₆, X₃: 2⋅X₃ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₂ {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)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}