Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄
Temp_Vars: P, Q
Locations: l0, l1, l2, l3
Transitions:
t₅: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l3(X₀, X₇, X₂, X₃, X₄, X₅, Q, X₇, 2, P, P, P, P, 3, 0) :|: X₇+1 ≤ X₀ ∧ 0 ≤ X₅
t₆: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l3(X₀, X₇, X₂, X₃, X₄, X₅, Q, X₇, 2, P, P, P, P, 3, 0) :|: X₀+1 ≤ X₇ ∧ 0 ≤ X₅
t₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l1(X₀, Q, X₂, 1+X₃, P, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₁+1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l1(X₀, Q, X₂, 1+X₃, P, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l2(X₁, X₁, X₂, X₃, X₄, X₅, P, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₂: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l1(X₀, Q, X₂, 1, P, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 0 ≤ X₅ ∧ X₁+1 ≤ X₀
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l1(X₀, Q, X₂, 1, P, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 0 ≤ X₅ ∧ X₀+1 ≤ X₁

Preprocessing

Eliminate variables {P,X₄,X₆,X₈,X₉,X₁₀,X₁₁,X₁₂,X₁₃,X₁₄} that do not contribute to the problem

Found invariant 0 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Found invariant 0 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃ for location l1

Found invariant X₇ ≤ X₁ ∧ X₁ ≤ X₇ ∧ 0 ≤ X₅ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₅, X₇
Temp_Vars: Q
Locations: l0, l1, l2, l3
Transitions:
t₁₄: l0(X₀, X₁, X₂, X₃, X₅, X₇) → l3(X₀, X₇, X₂, X₃, X₅, X₇) :|: X₇+1 ≤ X₀ ∧ 0 ≤ X₅
t₁₅: l0(X₀, X₁, X₂, X₃, X₅, X₇) → l3(X₀, X₇, X₂, X₃, X₅, X₇) :|: X₀+1 ≤ X₇ ∧ 0 ≤ X₅
t₁₆: l1(X₀, X₁, X₂, X₃, X₅, X₇) → l1(X₀, Q, X₂, 1+X₃, X₅, X₇) :|: X₁+1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃
t₁₇: l1(X₀, X₁, X₂, X₃, X₅, X₇) → l1(X₀, Q, X₂, 1+X₃, X₅, X₇) :|: X₀+1 ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃
t₁₈: l1(X₀, X₁, X₂, X₃, X₅, X₇) → l2(X₁, X₁, X₂, X₃, X₅, X₇) :|: 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₃
t₁₉: l3(X₀, X₁, X₂, X₃, X₅, X₇) → l1(X₀, Q, X₂, 1, X₅, X₇) :|: 0 ≤ X₅ ∧ X₁+1 ≤ X₀ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₇ ∧ 0 ≤ X₅
t₂₀: l3(X₀, X₁, X₂, X₃, X₅, X₇) → l1(X₀, Q, X₂, 1, X₅, X₇) :|: 0 ≤ X₅ ∧ X₀+1 ≤ X₁ ∧ X₇ ≤ X₁ ∧ X₁ ≤ X₇ ∧ 0 ≤ X₅

Analysing control-flow refined program

Found invariant 0 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l2

Found invariant 0 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ X₃ ≤ 1+X₅ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ for location l1

Found invariant X₇ ≤ X₁ ∧ X₁ ≤ X₇ ∧ 0 ≤ X₅ for location l3

Found invariant 0 ≤ X₅ ∧ 2 ≤ X₃+X₅ ∧ 0 ≤ X₂+X₅ ∧ 2 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₂ for location n_l1___1

CFR did not improve the program. Rolling back

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₇ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₄, X₇: X₇ {O(n)}
t₁₅, X₀: X₀ {O(n)}
t₁₅, X₁: X₇ {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₅, X₇: X₇ {O(n)}
t₁₆, X₀: 4⋅X₀ {O(n)}
t₁₆, X₂: 4⋅X₂ {O(n)}
t₁₆, X₅: 4⋅X₅ {O(n)}
t₁₆, X₇: 4⋅X₇ {O(n)}
t₁₇, X₀: 4⋅X₀ {O(n)}
t₁₇, X₂: 4⋅X₂ {O(n)}
t₁₇, X₅: 4⋅X₅ {O(n)}
t₁₇, X₇: 4⋅X₇ {O(n)}
t₁₈, X₀: 10⋅X₀ {O(n)}
t₁₈, X₂: 10⋅X₂ {O(n)}
t₁₈, X₅: 10⋅X₅ {O(n)}
t₁₈, X₇: 10⋅X₇ {O(n)}
t₁₉, X₀: X₀ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: 1 {O(1)}
t₁₉, X₅: X₅ {O(n)}
t₁₉, X₇: X₇ {O(n)}
t₂₀, X₀: X₀ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: 1 {O(1)}
t₂₀, X₅: X₅ {O(n)}
t₂₀, X₇: X₇ {O(n)}