Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄
Temp_Vars: P, Q
Locations: f0, f21, f29, f41, f43, f46
Transitions:
t₇: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f21(1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, P, P, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: P ≤ 0
t₈: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f21(1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, P, 0, 1, Q, Q, Q, Q) :|: 1 ≤ P ∧ 1 ≤ Q
t₉: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f41(1, X₁, X₂, X₃, X₄, X₅, X₆, X₇, P, 0, 1, Q, Q, Q, Q) :|: 1 ≤ P ∧ Q ≤ 0
t₀: f21(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f29(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₀ ≤ 0
t₆: f21(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f29(0, P, P, X₃, X₄, X₅, 0, P, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₀
t₃: f29(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f41(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1 ≤ X₀
t₄: f29(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f41(X₀, X₁, P, 0, P, P, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: P ≤ 999+X₁ ∧ X₀ ≤ 0
t₅: f29(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f41(1, X₁, P, 0, P, P, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 1000+X₁ ≤ P ∧ X₀ ≤ 0
t₁: f41(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f41(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄)
t₂: f43(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → f46(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄)

Preprocessing

Cut unreachable locations [f43; f46] from the program graph

Cut unsatisfiable transition [t₀: f21→f29; t₃: f29→f41]

Eliminate variables [X₂; X₃; X₄; X₅; X₆; X₇; X₈; X₉; X₁₀; X₁₁; X₁₂; X₁₃; X₁₄] that do not contribute to the problem

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location f29

Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location f21

Found invariant X₀ ≤ 1 ∧ 0 ≤ X₀ for location f41

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars: P, Q
Locations: f0, f21, f29, f41
Transitions:
t₁₉: f0(X₀, X₁) → f21(1, X₁) :|: P ≤ 0
t₂₀: f0(X₀, X₁) → f21(1, X₁) :|: 1 ≤ P ∧ 1 ≤ Q
t₂₁: f0(X₀, X₁) → f41(1, X₁) :|: 1 ≤ P ∧ Q ≤ 0
t₂₂: f21(X₀, X₁) → f29(0, P) :|: 1 ≤ X₀ ∧ X₀ ≤ 1
t₂₃: f29(X₀, X₁) → f41(X₀, X₁) :|: P ≤ 999+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₄: f29(X₀, X₁) → f41(1, X₁) :|: 1000+X₁ ≤ P ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₅: f41(X₀, X₁) → f41(X₀, X₁) :|: X₀ ≤ 1 ∧ 0 ≤ X₀

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location f29

Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location f21

Found invariant X₀ ≤ 1 ∧ 0 ≤ X₀ for location f41

Found invariant X₀ ≤ 1 ∧ 0 ≤ X₀ for location f41_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: inf {Infinity}

Sizebounds

t₁₉, X₀: 1 {O(1)}
t₁₉, X₁: X₁ {O(n)}
t₂₀, X₀: 1 {O(1)}
t₂₀, X₁: X₁ {O(n)}
t₂₁, X₀: 1 {O(1)}
t₂₁, X₁: X₁ {O(n)}
t₂₂, X₀: 0 {O(1)}
t₂₃, X₀: 0 {O(1)}
t₂₄, X₀: 1 {O(1)}
t₂₅, X₀: 1 {O(1)}