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) → l5(X₀, X₁, X₂)
t₇: l1(X₀, X₁, X₂) → l4(X₀+X₁, X₁, X₂)
t₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₆: l3(X₀, X₁, X₂) → l1(X₀, nondef.0, X₂)
t₂: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 0 ≤ X₀
t₃: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ < 0
t₁: l5(X₀, X₁, X₂) → l4(X₂, X₁, X₂)
t₈: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂)

Preprocessing

Found invariant 0 ≤ X₀ for location l2

Found invariant 1+X₀ ≤ 0 for location l6

Found invariant 1+X₀ ≤ 0 for location l7

Found invariant 0 ≤ X₀ for location l1

Found invariant 0 ≤ X₀ for location l3

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) → l5(X₀, X₁, X₂)
t₇: l1(X₀, X₁, X₂) → l4(X₀+X₁, X₁, X₂) :|: 0 ≤ X₀
t₄: l2(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: 0 ≤ X₀
t₆: l3(X₀, X₁, X₂) → l1(X₀, nondef.0, X₂) :|: 0 ≤ X₀
t₂: l4(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 0 ≤ X₀
t₃: l4(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₀ < 0
t₁: l5(X₀, X₁, X₂) → l4(X₂, X₁, X₂)
t₈: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: 1+X₀ ≤ 0

Chain transitions t₆: l3→l1 and t₇: l1→l4 to t₅₁: l3→l4

Chain transitions t₂: l4→l2 and t₄: l2→l3 to t₅₂: l4→l3

Chain transitions t₅₂: l4→l3 and t₅₁: l3→l4 to t₅₃: l4→l4

Chain transitions t₅₂: l4→l3 and t₆: l3→l1 to t₅₄: l4→l1

Analysing control-flow refined program

Eliminate variables {Temp_Int₁₃₁,X₁} that do not contribute to the problem

Found invariant 0 ≤ X₀ for location l2

Found invariant 1+X₀ ≤ 0 for location l6

Found invariant 1+X₀ ≤ 0 for location l7

Found invariant 0 ≤ X₀ for location l1

Found invariant 0 ≤ X₀ 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 X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ for location n_l2___7

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l6

Found invariant 0 ≤ X₂ ∧ X₁ ≤ X₀ for location n_l4___4

Found invariant X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ for location n_l3___6

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location n_l2___3

Found invariant X₀ ≤ X₂ ∧ 1+X₀ ≤ 0 for location l7

Found invariant X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₀ for location n_l1___5

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀ for location n_l3___2

Found invariant X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l4

Found invariant 0 ≤ X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₀ for location n_l1___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}
t₆: inf {Infinity}
t₇: inf {Infinity}
t₈: 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}
t₆: inf {Infinity}
t₇: inf {Infinity}
t₈: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₂: X₂ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₆, X₂: X₂ {O(n)}
t₇, X₂: X₂ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}