Initial Problem

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

Preprocessing

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

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀ for location l5

Found invariant 1 ≤ X₀ for location l1

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀ for location l4

Found invariant 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₄: l0(X₀, X₁, X₄) → l2(X₀, X₁, X₄)
t₁₅: l1(X₀, X₁, X₄) → l3(X₀, X₁, X₄) :|: X₁ < X₄ ∧ 1 ≤ X₀
t₁₆: l1(X₀, X₁, X₄) → l3(X₀, X₁, X₄) :|: X₄ < X₁ ∧ 1 ≤ X₀
t₁₇: l1(X₀, X₁, X₄) → l4(X₀, X₁, X₄) :|: X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₀
t₁₈: l2(X₀, X₁, X₄) → l1(1, 1, X₄)
t₁₉: l3(X₀, X₁, X₄) → l1(X₀+1, X₀*X₁, X₄) :|: 1 ≤ X₀
t₂₀: l4(X₀, X₁, X₄) → l5(X₀, X₁, X₄) :|: X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀

Analysing control-flow refined program

Found invariant X₄ ≤ 0 ∧ 1+X₄ ≤ X₁ ∧ X₁+X₄ ≤ 1 ∧ 1+X₄ ≤ X₀ ∧ X₀+X₄ ≤ 1 ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 2 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___4

Found invariant 2 ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 2 ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l3___5

Found invariant 2 ≤ X₀ for location n_l1___3

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀ for location l5

Found invariant 1+X₁ ≤ X₄ ∧ 2 ≤ X₀ for location n_l3___2

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

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀ for location l4

Found invariant 1+X₄ ≤ X₁ ∧ 2 ≤ X₀ for location n_l3___1

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: inf {Infinity}
t₂₀: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₄: 1 {O(1)}
t₁₅: inf {Infinity}
t₁₆: inf {Infinity}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: inf {Infinity}
t₂₀: 1 {O(1)}

Sizebounds

t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₅, X₄: 2⋅X₄ {O(n)}
t₁₆, X₄: 2⋅X₄ {O(n)}
t₁₇, X₄: 3⋅X₄ {O(n)}
t₁₈, X₀: 1 {O(1)}
t₁₈, X₁: 1 {O(1)}
t₁₈, X₄: X₄ {O(n)}
t₁₉, X₄: 2⋅X₄ {O(n)}
t₂₀, X₄: 3⋅X₄ {O(n)}