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 ≤ X₁
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(0, 0, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+2, X₂, X₃) :|: X₁ < X₀+1
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Preprocessing

Eliminate variables {X₂,X₃} that do not contribute to the problem

Found invariant 1 ≤ 0 for location l5

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

Found invariant 1 ≤ 0 for location l4

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

Cut unsatisfiable transition t₁₆: l1→l4

Cut unsatisfiable transition t₂₀: l4→l5

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₁₄: l0(X₀, X₁) → l2(X₀, X₁)
t₁₅: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₇: l2(X₀, X₁) → l1(0, 0)
t₁₈: l3(X₀, X₁) → l1(X₀+1, X₁+2) :|: X₁ < X₀+1 ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₉: l3(X₀, X₁) → l1(X₀+1, X₁) :|: 1+X₀ ≤ X₁ ∧ X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀

Chain transitions t₁₉: l3→l1 and t₁₅: l1→l3 to t₅₆: l3→l3

Chain transitions t₁₈: l3→l1 and t₁₅: l1→l3 to t₅₇: l3→l3

Chain transitions t₁₇: l2→l1 and t₁₅: l1→l3 to t₅₈: l2→l3

Analysing control-flow refined program

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

Found invariant X₁ ≤ 1+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 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 X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___4

Found invariant X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___3

Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l3___5

Found invariant X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l1___2

Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ 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}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}
t₁₉: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: inf {Infinity}
t₁₉: inf {Infinity}

Sizebounds

t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₇, X₀: 0 {O(1)}
t₁₇, X₁: 0 {O(1)}