Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, 0, X₂, X₃) :|: X₀ < 100
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 100 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(0, X₁, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 1 ≤ X₁
t₄: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < 1
t₈: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₇: l5(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)

Preprocessing

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

Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l6

Found invariant 1 ≤ 0 for location l7

Found invariant 1 ≤ 0 for location l5

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

Found invariant 1 ≤ 0 for location l4

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

Cut unsatisfiable transition t₂₀: l1→l4

Cut unsatisfiable transition t₂₃: l3→l5

Cut unsatisfiable transition t₂₄: l4→l7

Cut unsatisfiable transition t₂₅: l5→l1

Cut unreachable locations [l4; l5; l7] from the program graph

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l6
Transitions:
t₁₈: l0(X₀, X₁) → l2(X₀, X₁)
t₁₉: l1(X₀, X₁) → l3(X₀, 0) :|: X₀ < 100 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₁: l2(X₀, X₁) → l1(0, X₁)
t₂₂: l3(X₀, X₁) → l6(X₀, X₁) :|: X₁ < 1 ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₆: l6(X₀, X₁) → l3(X₀, X₁) :|: X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀

Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location l6

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

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

Analysing control-flow refined program

Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l6___1

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

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

Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location n_l6___1

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

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

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: inf {Infinity}
t₂₆: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: inf {Infinity}
t₂₆: inf {Infinity}

Sizebounds

t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₉, X₀: 0 {O(1)}
t₁₉, X₁: 0 {O(1)}
t₂₁, X₀: 0 {O(1)}
t₂₁, X₁: X₁ {O(n)}
t₂₂, X₀: 0 {O(1)}
t₂₂, X₁: 0 {O(1)}
t₂₆, X₀: 0 {O(1)}
t₂₆, X₁: 0 {O(1)}