Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₆: l0(X₀, X₁, X₂, X₃, X₄) → l1(F, 0, X₂, 0, F)
t₀: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, 0, F, X₃, X₄) :|: X₀ ≤ 0 ∧ 1 ≤ F
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₀
t₄: l2(X₀, X₁, X₂, X₃, X₄) → l1(F, X₁, X₂, 0, F) :|: X₂ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₂
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₃: l5(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)

Preprocessing

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

Cut unsatisfiable transition t₄: l2→l1

Eliminate variables {X₁,X₃,X₄} that do not contribute to the problem

Found invariant 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l2

Found invariant 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₂
Temp_Vars: F
Locations: l0, l1, l2, l3
Transitions:
t₁₆: l0(X₀, X₂) → l1(F, X₂)
t₁₇: l1(X₀, X₂) → l2(X₀, F) :|: X₀ ≤ 0 ∧ 1 ≤ F
t₁₈: l1(X₀, X₂) → l3(X₀, X₂) :|: 1 ≤ X₀
t₁₉: l2(X₀, X₂) → l2(X₀, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0
t₂₀: l3(X₀, X₂) → l3(X₀, X₂) :|: 1 ≤ X₀

Found invariant 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l2

Found invariant 1 ≤ X₀ for location l3

Analysing control-flow refined program

Found invariant 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l2

Found invariant 1 ≤ X₀ for location l3

Found invariant 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l2

Found invariant 1 ≤ X₀ for location l3

CFR did not improve the program. Rolling back

Found invariant 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l2

Found invariant 1 ≤ X₀ for location l3

Analysing control-flow refined program

Found invariant 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l2

Found invariant 1 ≤ X₀ for location l3

Found invariant 1 ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l2

Found invariant 1 ≤ X₀ for location l3

CFR did not improve the program. Rolling back

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₁₆, X₂: X₂ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₂₀, X₂: X₂ {O(n)}