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) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < 0
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+X₁, X₁-1, X₂, X₃)
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Preprocessing

Found invariant X₁ ≤ X₃ ∧ 0 ≤ X₀ for location l5

Found invariant X₁ ≤ X₃ for location l1

Found invariant X₁ ≤ X₃ ∧ 0 ≤ X₀ for location l4

Found invariant X₁ ≤ X₃ ∧ 1+X₀ ≤ 0 for location l3

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) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < 0 ∧ X₁ ≤ X₃
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₁ ≤ X₃
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+X₁, X₁-1, X₂, X₃) :|: X₁ ≤ X₃ ∧ 1+X₀ ≤ 0
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 0 ≤ X₀

Chain transitions t₄: l3→l1 and t₃: l1→l4 to t₃₆: l3→l4

Chain transitions t₁: l2→l1 and t₃: l1→l4 to t₃₇: l2→l4

Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₃₈: l2→l3

Chain transitions t₄: l3→l1 and t₂: l1→l3 to t₃₉: l3→l3

Analysing control-flow refined program

Found invariant X₁ ≤ X₃ ∧ 0 ≤ X₀ for location l5

Found invariant X₁ ≤ X₃ for location l1

Found invariant X₁ ≤ X₃ for location l4

Found invariant X₁ ≤ X₃ ∧ 1+X₂ ≤ 0 for location l3

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ X₂ ≤ X₀ ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location n_l3___3

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

Found invariant X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₀ for location l5

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

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

Found invariant 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ 0 ∧ 2+X₀+X₂ ≤ 0 ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location n_l3___1

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}