Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃
Temp_Vars: O, P
Locations: f0, f11, f23, f26, f32, f36
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f11(100, O, 1, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃)
t₁: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f11(100, O, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃)
t₂: f11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f23(X₀, X₁, 1, 1, 1, 100, O, 1, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: X₂ ≤ 1 ∧ 1 ≤ X₂
t₃: f11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f23(X₀, X₁, 1, 1, 1, 100, O, 0, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: X₂ ≤ 1 ∧ 1 ≤ X₂
t₆: f11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f36(X₀, X₁, X₂, X₂, X₂, X₅, X₆, X₇, X₈, 100, X₁₀, X₁₁, X₁₂, X₁₃) :|: X₂ ≤ 0
t₇: f11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f36(X₀, X₁, X₂, X₂, X₂, X₅, X₆, X₇, X₈, 100, X₁₀, X₁₁, X₁₂, X₁₃) :|: 2 ≤ X₂
t₄: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f26(X₀, X₁, X₂, X₃, X₇, X₅, X₆, X₇, 100, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: X₇ ≤ 0
t₅: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f26(X₀, X₁, X₂, X₃, X₇, X₅, X₆, X₇, 100, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: 2 ≤ X₇
t₈: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f32(X₀, X₁, X₂, X₃, 1, X₅, X₆, 1, X₈, X₉, O, P, X₁₂, X₁₃) :|: X₇ ≤ 1 ∧ 1 ≤ X₇ ∧ 2+O ≤ 0
t₉: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f32(X₀, X₁, X₂, X₃, 1, X₅, X₆, 1, X₈, X₉, O, P, X₁₂, X₁₃) :|: X₇ ≤ 1 ∧ 1 ≤ X₇ ∧ 0 ≤ O
t₁₀: f23(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f32(X₀, X₁, X₂, X₃, 1, X₅, X₆, 1, X₈, X₉, -1, X₁₁, 100, O) :|: X₇ ≤ 1 ∧ 1 ≤ X₇
t₁₃: f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: 1+O ≤ 0
t₁₄: f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃)
t₁₁: f36(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) :|: 1+O ≤ 0
t₁₂: f36(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f32(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃)

Preprocessing

Cut unsatisfiable transition [t₅: f23→f26; t₇: f11→f36]

Eliminate variables [P; X₀; X₁; X₃; X₄; X₅; X₆; X₈; X₉; X₁₀; X₁₁; X₁₂; X₁₃] that do not contribute to the problem

Found invariant X₀ ≤ 0 ∧ 0 ≤ X₀ for location f36

Found invariant X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 2 ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location f23

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

Found invariant X₀ ≤ 1 ∧ 0 ≤ X₀ for location f11

Found invariant X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 1 ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ X₀ ≤ 1+X₁ ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ for location f26

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars: O
Locations: f0, f11, f23, f26, f32, f36
Transitions:
t₃₅: f0(X₀, X₁) → f11(1, X₁)
t₃₆: f0(X₀, X₁) → f11(0, X₁)
t₃₇: f11(X₀, X₁) → f23(1, 1) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 ≤ X₀
t₃₈: f11(X₀, X₁) → f23(1, 0) :|: X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 0 ≤ X₀
t₃₉: f11(X₀, X₁) → f36(X₀, X₁) :|: X₀ ≤ 0 ∧ X₀ ≤ 1 ∧ 0 ≤ X₀
t₄₀: f23(X₀, X₁) → f26(X₀, X₁) :|: X₁ ≤ 0 ∧ X₀+X₁ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₁ ∧ X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₄₁: f23(X₀, X₁) → f32(X₀, 1) :|: X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 2+O ≤ 0 ∧ X₀+X₁ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₄₂: f23(X₀, X₁) → f32(X₀, 1) :|: X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ 0 ≤ O ∧ X₀+X₁ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₄₃: f23(X₀, X₁) → f32(X₀, 1) :|: X₁ ≤ 1 ∧ 1 ≤ X₁ ∧ X₀+X₁ ≤ 2 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₄₄: f26(X₀, X₁) → f32(X₀, X₁) :|: 1+O ≤ 0 ∧ X₀ ≤ 1 ∧ X₀ ≤ 1+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₄₅: f26(X₀, X₁) → f32(X₀, X₁) :|: X₀ ≤ 1 ∧ X₀ ≤ 1+X₁ ∧ X₀+X₁ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₄₆: f36(X₀, X₁) → f32(X₀, X₁) :|: 1+O ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
t₄₇: f36(X₀, X₁) → f32(X₀, X₁) :|: 0 ≤ X₀ ∧ X₀ ≤ 0

All Bounds

Timebounds

Overall timebound:13 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 1 {O(1)}
t₄₁: 1 {O(1)}
t₄₂: 1 {O(1)}
t₄₃: 1 {O(1)}
t₄₄: 1 {O(1)}
t₄₅: 1 {O(1)}
t₄₆: 1 {O(1)}
t₄₇: 1 {O(1)}

Costbounds

Overall costbound: 13 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 1 {O(1)}
t₃₇: 1 {O(1)}
t₃₈: 1 {O(1)}
t₃₉: 1 {O(1)}
t₄₀: 1 {O(1)}
t₄₁: 1 {O(1)}
t₄₂: 1 {O(1)}
t₄₃: 1 {O(1)}
t₄₄: 1 {O(1)}
t₄₅: 1 {O(1)}
t₄₆: 1 {O(1)}
t₄₇: 1 {O(1)}

Sizebounds

t₃₅, X₀: 1 {O(1)}
t₃₅, X₁: X₁ {O(n)}
t₃₆, X₀: 0 {O(1)}
t₃₆, X₁: X₁ {O(n)}
t₃₇, X₀: 1 {O(1)}
t₃₇, X₁: 1 {O(1)}
t₃₈, X₀: 1 {O(1)}
t₃₈, X₁: 0 {O(1)}
t₃₉, X₀: 0 {O(1)}
t₃₉, X₁: X₁ {O(n)}
t₄₀, X₀: 1 {O(1)}
t₄₀, X₁: 0 {O(1)}
t₄₁, X₀: 1 {O(1)}
t₄₁, X₁: 1 {O(1)}
t₄₂, X₀: 1 {O(1)}
t₄₂, X₁: 1 {O(1)}
t₄₃, X₀: 1 {O(1)}
t₄₃, X₁: 1 {O(1)}
t₄₄, X₀: 1 {O(1)}
t₄₄, X₁: 0 {O(1)}
t₄₅, X₀: 1 {O(1)}
t₄₅, X₁: 0 {O(1)}
t₄₆, X₀: 0 {O(1)}
t₄₆, X₁: X₁ {O(n)}
t₄₇, X₀: 0 {O(1)}
t₄₇, X₁: X₁ {O(n)}