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) :|: 0 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ < 0 ∧ X₁ < 0
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₁-1, X₀-1, X₂, X₃, X₄)
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)

Preprocessing

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

Found invariant 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l5

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₄: l0(X₀, X₁, X₃, X₄) → l2(X₀, X₁, X₃, X₄)
t₁₅: l1(X₀, X₁, X₃, X₄) → l3(X₀, X₁, X₃, X₄) :|: 0 ≤ X₀
t₁₆: l1(X₀, X₁, X₃, X₄) → l3(X₀, X₁, X₃, X₄) :|: 0 ≤ X₁
t₁₇: l1(X₀, X₁, X₃, X₄) → l4(X₀, X₁, X₃, X₄) :|: X₀ < 0 ∧ X₁ < 0
t₁₈: l2(X₀, X₁, X₃, X₄) → l1(X₃, X₄, X₃, X₄)
t₁₉: l3(X₀, X₁, X₃, X₄) → l1(X₁-1, X₀-1, X₃, X₄)
t₂₀: l4(X₀, X₁, X₃, X₄) → l5(X₀, X₁, X₃, X₄) :|: 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0

Analysing control-flow refined program

Found invariant X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₁ for location n_l3___4

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ for location n_l3___5

Found invariant 1+X₁ ≤ 0 ∧ 2+X₀+X₁ ≤ 0 ∧ 1+X₀ ≤ 0 for location l5

Found invariant 0 ≤ X₀ for location n_l3___2

Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location l1

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

Found invariant 0 ≤ X₁ 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, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₅, X₃: 2⋅X₃ {O(n)}
t₁₅, X₄: 2⋅X₄ {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}
t₁₆, X₄: 2⋅X₄ {O(n)}
t₁₇, X₃: 3⋅X₃ {O(n)}
t₁₇, X₄: 3⋅X₄ {O(n)}
t₁₈, X₀: X₃ {O(n)}
t₁₈, X₁: X₄ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₉, X₃: 2⋅X₃ {O(n)}
t₁₉, X₄: 2⋅X₄ {O(n)}
t₂₀, X₃: 3⋅X₃ {O(n)}
t₂₀, X₄: 3⋅X₄ {O(n)}