Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀
Temp_Vars: L, M, N
Locations: f0, f18, f24, f32, f34, f37
Transitions:
t₇: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f18(1, X₁, X₂, X₃, X₄, X₅, L, M, X₈, X₉, X₁₀) :|: M ≤ 0
t₈: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f18(1, X₁, X₂, X₃, X₄, X₅, L, 0, 1, M, M) :|: 1 ≤ M ∧ 1 ≤ N
t₉: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f32(1, X₁, X₂, X₃, X₄, X₅, L, 0, 1, M, M) :|: 1 ≤ N ∧ M ≤ 0
t₀: f18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f24(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: X₀ ≤ 0
t₆: f18(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f24(0, X₁, L, X₃, X₄, L, X₆, X₇, X₈, X₉, X₁₀) :|: 1 ≤ X₀
t₃: f24(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f32(X₀, L, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1 ≤ X₀
t₄: f24(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f32(X₀, M, X₂, L, L, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: L ≤ 999+X₂ ∧ X₀ ≤ 0
t₅: f24(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f32(1, M, X₂, L, L, X₅, X₆, X₇, X₈, X₉, X₁₀) :|: 1000+X₂ ≤ L ∧ X₀ ≤ 0
t₁: f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)
t₂: f34(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀) → f37(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀)

Preprocessing

Cut unreachable locations [f34; f37] from the program graph

Cut unsatisfiable transition [t₀: f18→f24; t₃: f24→f32]

Eliminate variables [X₁; X₃; X₄; X₅; X₆; X₇; X₈; X₉; X₁₀] that do not contribute to the problem

Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location f18

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location f24

Found invariant X₀ ≤ 1 ∧ 0 ≤ X₀ for location f32

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars: L, M, N
Locations: f0, f18, f24, f32
Transitions:
t₁₉: f0(X₀, X₁) → f18(1, X₁) :|: M ≤ 0
t₂₀: f0(X₀, X₁) → f18(1, X₁) :|: 1 ≤ M ∧ 1 ≤ N
t₂₁: f0(X₀, X₁) → f32(1, X₁) :|: 1 ≤ N ∧ M ≤ 0
t₂₂: f18(X₀, X₁) → f24(0, L) :|: 1 ≤ X₀ ∧ X₀ ≤ 1
t₂₃: f24(X₀, X₁) → f32(X₀, X₁) :|: L ≤ 999+X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₄: f24(X₀, X₁) → f32(1, X₁) :|: 1000+X₁ ≤ L ∧ X₀ ≤ 0 ∧ 0 ≤ X₀
t₂₅: f32(X₀, X₁) → f32(X₀, X₁) :|: X₀ ≤ 1 ∧ 0 ≤ X₀

Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location f18

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location f24

Found invariant X₀ ≤ 1 ∧ 0 ≤ X₀ for location f32

Found invariant X₀ ≤ 1 ∧ 0 ≤ X₀ for location f32_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)}