Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 100 < X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂ < X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₄, X₅, X₆, X₃, X₄, X₅, X₆, X₇)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₁, X₀+1, X₂-1, X₃, X₄, X₅, X₆, X₇)
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)

Preprocessing

Eliminate variables {X₃,X₇} that do not contribute to the problem

Found invariant X₂ ≤ X₆ for location l5

Found invariant X₂ ≤ X₆ for location l1

Found invariant X₂ ≤ X₆ for location l4

Found invariant X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 100 for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₄: l0(X₀, X₁, X₂, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₄, X₅, X₆)
t₁₅: l1(X₀, X₁, X₂, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₄, X₅, X₆) :|: X₀ ≤ 100 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₆
t₁₆: l1(X₀, X₁, X₂, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₄, X₅, X₆) :|: 100 < X₀ ∧ X₂ ≤ X₆
t₁₇: l1(X₀, X₁, X₂, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₄, X₅, X₆) :|: X₂ < X₁ ∧ X₂ ≤ X₆
t₁₈: l2(X₀, X₁, X₂, X₄, X₅, X₆) → l1(X₄, X₅, X₆, X₄, X₅, X₆)
t₁₉: l3(X₀, X₁, X₂, X₄, X₅, X₆) → l1(X₁, X₀+1, X₂-1, X₄, X₅, X₆) :|: X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 100
t₂₀: l4(X₀, X₁, X₂, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₄, X₅, X₆) :|: X₂ ≤ X₆

Analysing control-flow refined program

Found invariant X₆ ≤ X₂ ∧ X₅ ≤ X₆ ∧ X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₅ ≤ X₂ ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₅ ∧ X₄ ≤ 100 ∧ X₄ ≤ X₀ ∧ X₀+X₄ ≤ 200 ∧ X₀ ≤ X₄ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 100 for location n_l3___3

Found invariant X₅ ≤ X₆ ∧ 1+X₂ ≤ X₆ ∧ X₀ ≤ X₆ ∧ X₄ ≤ 100 ∧ X₁+X₄ ≤ 201 ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 101 for location n_l1___2

Found invariant X₂ ≤ X₆ for location l5

Found invariant X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₄ for location l1

Found invariant X₂ ≤ X₆ for location l4

Found invariant X₅ ≤ X₆ ∧ 1+X₂ ≤ X₆ ∧ 1+X₁ ≤ X₆ ∧ X₀ ≤ X₆ ∧ X₄ ≤ 100 ∧ X₁+X₄ ≤ 201 ∧ X₀+X₄ ≤ 200 ∧ X₁ ≤ X₂ ∧ X₀ ≤ 1+X₂ ∧ X₁ ≤ 101 ∧ X₀+X₁ ≤ 201 ∧ X₀ ≤ 100 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: 1 {O(1)}
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: 1 {O(1)}
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, X₂: X₂ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₄, X₆: X₆ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₅, X₆: X₆ {O(n)}
t₁₆, X₄: 2⋅X₄ {O(n)}
t₁₆, X₅: 2⋅X₅ {O(n)}
t₁₆, X₆: 2⋅X₆ {O(n)}
t₁₇, X₄: 2⋅X₄ {O(n)}
t₁₇, X₅: 2⋅X₅ {O(n)}
t₁₇, X₆: 2⋅X₆ {O(n)}
t₁₈, X₀: X₄ {O(n)}
t₁₈, X₁: X₅ {O(n)}
t₁₈, X₂: X₆ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₈, X₆: X₆ {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₁₉, X₆: X₆ {O(n)}
t₂₀, X₄: 4⋅X₄ {O(n)}
t₂₀, X₅: 4⋅X₅ {O(n)}
t₂₀, X₆: 4⋅X₆ {O(n)}