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) → l3(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ < X₂
t₆: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(2, X₁, X₂, X₃) :|: 0 ≤ X₂
t₁: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ < 0
t₅: l4(X₀, X₁, X₂, X₃) → l1((X₀)², X₁, X₂, X₃)

Preprocessing

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

Found invariant 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1

Found invariant 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₃: l0(X₀, X₁) → l3(X₀, X₁)
t₁₄: l1(X₀, X₁) → l2(X₀, X₁) :|: X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₅: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ < X₁ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₆: l2(X₀, X₁) → l5(X₀, X₁)
t₁₇: l3(X₀, X₁) → l1(2, X₁) :|: 0 ≤ X₁
t₁₈: l3(X₀, X₁) → l2(X₀, X₁) :|: X₁ < 0
t₁₉: l4(X₀, X₁) → l1((X₀)², X₁) :|: 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀

Chain transitions t₁₉: l4→l1 and t₁₅: l1→l4 to t₄₃: l4→l4

Chain transitions t₁₇: l3→l1 and t₁₅: l1→l4 to t₄₄: l3→l4

Chain transitions t₁₇: l3→l1 and t₁₄: l1→l2 to t₄₅: l3→l2

Chain transitions t₁₉: l4→l1 and t₁₄: l1→l2 to t₄₆: l4→l2

Analysing control-flow refined program

Found invariant 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1

Found invariant 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l4

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location n_l4___3

Found invariant 3 ≤ X₁ for location n_l1___2

Found invariant 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location n_l4___1

Found invariant 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location l1

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: inf {Infinity}

Sizebounds

t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₄, X₁: 2⋅X₁ {O(n)}
t₁₅, X₁: X₁ {O(n)}
t₁₆, X₁: 3⋅X₁ {O(n)}
t₁₇, X₀: 2 {O(1)}
t₁₇, X₁: X₁ {O(n)}
t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₉, X₁: X₁ {O(n)}