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 < 5
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 5 ≤ X₀+X₁
t₁: l2(X₀, X₁, X₂, X₃) → l1(1, 2, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₁, X₀, X₂, X₃)
t₅: 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 ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 3 ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ for location l1

Found invariant 1 ≤ 0 for location l4

Found invariant X₁ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 3 ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ for location l3

Cut unsatisfiable transition t₁₄: l1→l4

Cut unsatisfiable transition t₁₇: 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:
t₁₂: l0(X₀, X₁) → l2(X₀, X₁)
t₁₃: l1(X₀, X₁) → l3(X₀, X₁) :|: X₀+X₁ < 5 ∧ X₁ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 3 ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀
t₁₅: l2(X₀, X₁) → l1(1, 2)
t₁₆: l3(X₀, X₁) → l1(X₁, X₀) :|: X₁ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 3 ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀

Analysing control-flow refined program

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

Found invariant X₁ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 3 ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ for location n_l1___2

Found invariant X₁ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 3 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location l1

Found invariant X₁ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 3 ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ for location n_l3___1

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

Found invariant X₁ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 3 ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ for location n_l1___2

Found invariant X₁ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 3 ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location l1

Found invariant X₁ ≤ 2 ∧ X₁ ≤ 1+X₀ ∧ X₀+X₁ ≤ 3 ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 2 ∧ 1 ≤ X₀ for location n_l3___1

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₂: 1 {O(1)}
t₁₃: inf {Infinity}
t₁₅: 1 {O(1)}
t₁₆: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₂: 1 {O(1)}
t₁₃: inf {Infinity}
t₁₅: 1 {O(1)}
t₁₆: inf {Infinity}

Sizebounds

t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₃, X₀: 2 {O(1)}
t₁₃, X₁: 2 {O(1)}
t₁₅, X₀: 1 {O(1)}
t₁₅, X₁: 2 {O(1)}
t₁₆, X₀: 2 {O(1)}
t₁₆, X₁: 2 {O(1)}