KoAT2 Proof Output

Initial Problem

Start: f8
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃
Temp_Vars: O, P
Locations: f1, f2, f3, f4, f6, f7, f8
Transitions:
t₄: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f2(0, X₂, X₂, X₄, X₄, 3, P, 0, 0, 3, P, 2, X₁₂, X₁₃) :|: P ≤ 7 ∧ P ≤ 3 ∧ 1 ≤ P
t₅: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f2(0, X₂, X₂, X₄, X₄, 3, P, 0, 0, 3, P, 2, X₁₂, X₁₃) :|: P ≤ 7 ∧ 5 ≤ P
t₆: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f2(0, 1+X₂, 1+X₂, 1+X₄, 1+X₄, 3, 4, 1, 0, 3, 4, 2, X₁₂, X₁₃)
t₁: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f7(1, X₂, X₂, X₄, X₄, P, O, 0, 1, P, O, 7, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ 1 ≤ O ∧ 1 ≤ P
t₂: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f7(1, X₂, X₂, X₄, X₄, P, O, 0, 1, P, O, 7, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 7 ∧ 1 ≤ P ∧ 5 ≤ O
t₃: f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f7(1, 1+X₂, 1+X₂, 1+X₄, 1+X₄, P, 4, 1, 1, P, 4, 7, X₁₂, X₁₃) :|: P ≤ 7 ∧ 1 ≤ P
t₁₀: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f3(0, X₂, X₂, X₄, X₄, P, O, X₇, 0, P, O, 3, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ 1 ≤ O ∧ 1 ≤ P
t₁₁: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f3(0, X₂, X₂, X₄, X₄, P, O, X₇, 0, P, O, 3, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 7 ∧ 1 ≤ P ∧ 5 ≤ O
t₁₂: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f3(0, 1+X₂, 1+X₂, 1+X₄, 1+X₄, P, 4, 1, 0, P, 4, 3, X₁₂, X₁₃) :|: P ≤ 7 ∧ 1 ≤ P
t₇: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f7(1, X₂, X₂, X₄, X₄, P, O, X₇, 1, P, O, 7, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ 1 ≤ O ∧ 1 ≤ P
t₈: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f7(1, X₂, X₂, X₄, X₄, P, O, X₇, 1, P, O, 7, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 7 ∧ 1 ≤ P ∧ 5 ≤ O
t₉: f2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f7(1, 1+X₂, 1+X₂, 1+X₄, 1+X₄, P, 4, 1, 1, P, 4, 7, X₁₂, X₁₃) :|: P ≤ 7 ∧ 1 ≤ P
t₁₃: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f6(1, X₂, X₂, X₄, X₄, P, O, X₇, 1, P, O, 6, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ 1 ≤ O ∧ 1 ≤ P
t₁₄: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f6(1, X₂, X₂, X₄, X₄, P, O, X₇, 1, P, O, 6, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 7 ∧ 1 ≤ P ∧ 5 ≤ O
t₁₅: f3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f6(1, 1+X₂, 1+X₂, 1+X₄, 1+X₄, P, 4, 1, 1, P, 4, 6, X₁₂, X₁₃) :|: P ≤ 7 ∧ 1 ≤ P
t₁₈: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f2(0, X₂, X₂, X₄, X₄, P, O, 0, 0, P, O, 2, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ X₇ ≤ 1 ∧ 1 ≤ O ∧ 1 ≤ P ∧ 1+X₂ ≤ X₁₃ ∧ 1+X₄ ≤ X₁₂ ∧ 1 ≤ X₇ ∧ 1 ≤ X₁₂ ∧ 1 ≤ X₁₃
t₁₉: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f2(0, X₂, X₂, X₄, X₄, P, O, 0, 0, P, O, 2, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 7 ∧ X₇ ≤ 1 ∧ 1 ≤ P ∧ 1+X₂ ≤ X₁₃ ∧ 1+X₄ ≤ X₁₂ ∧ 1 ≤ X₇ ∧ 1 ≤ X₁₂ ∧ 1 ≤ X₁₃ ∧ 5 ≤ O
t₂₀: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f2(0, 1+X₂, 1+X₂, 1+X₄, 1+X₄, P, 4, 0, 0, P, 4, 2, X₁₂, X₁₃) :|: P ≤ 7 ∧ 1 ≤ P ∧ 1 ≤ X₁₂ ∧ 1 ≤ X₁₃ ∧ 2+X₂ ≤ X₁₃ ∧ 2+X₄ ≤ X₁₂
t₂₁: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f7(0, X₂, X₂, X₄, X₄, P, O, X₇, 0, P, O, 7, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ 1 ≤ O ∧ 1 ≤ P ∧ X₁₃ ≤ X₂ ∧ X₁₂ ≤ X₄
t₂₂: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f7(0, X₂, X₂, X₄, X₄, P, O, X₇, 0, P, O, 7, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 7 ∧ 1 ≤ P ∧ 5 ≤ O ∧ X₁₃ ≤ X₂ ∧ X₁₂ ≤ X₄
t₂₃: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f7(0, 1+X₂, 1+X₂, 1+X₄, 1+X₄, P, 4, 1, 0, P, 4, 7, X₁₂, X₁₃) :|: P ≤ 7 ∧ X₁₃ ≤ 1+X₂ ∧ X₁₂ ≤ 1+X₄ ∧ 1 ≤ P
t₂₄: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f7(1, X₂, X₂, X₄, X₄, P, O, X₇, 1, P, O, 7, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ 1 ≤ O ∧ 1 ≤ P
t₂₅: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f7(1, X₂, X₂, X₄, X₄, P, O, X₇, 1, P, O, 7, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 7 ∧ 1 ≤ P ∧ 5 ≤ O
t₂₆: f4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f7(1, 1+X₂, 1+X₂, 1+X₄, 1+X₄, P, 4, 1, 1, P, 4, 7, X₁₂, X₁₃) :|: P ≤ 7 ∧ 1 ≤ P
t₁₆: f6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f4(P, X₂, X₂, X₄, X₄, O, 2, 0, P, O, 2, 4, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 1 ∧ 1 ≤ O ∧ 0 ≤ P
t₁₇: f6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f4(P, X₂, X₂, X₄, X₄, O, 7, 1, P, O, 7, 4, X₁₂, X₁₃) :|: O ≤ 7 ∧ P ≤ 1 ∧ X₇ ≤ 1 ∧ 1 ≤ O ∧ 1 ≤ X₇ ∧ 0 ≤ P
t₀: f8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃) → f1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃)

Preprocessing

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

Found invariant X₂ ≤ 1 ∧ 0 ≤ X₂ for location f6

Found invariant X₂ ≤ 1 ∧ 0 ≤ X₂ for location f3

Found invariant X₂ ≤ 1 ∧ 0 ≤ X₂ for location f2

Found invariant X₂ ≤ 1 ∧ 0 ≤ X₂ for location f4

Found invariant X₂ ≤ 1 ∧ 0 ≤ X₂ for location f7

Problem after Preprocessing

Start: f8
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: O, P
Locations: f1, f2, f3, f4, f6, f7, f8
Transitions:
t₅₃: f1(X₀, X₁, X₂, X₃, X₄) → f2(X₀, X₁, 0, X₃, X₄) :|: P ≤ 7 ∧ P ≤ 3 ∧ 1 ≤ P
t₅₄: f1(X₀, X₁, X₂, X₃, X₄) → f2(X₀, X₁, 0, X₃, X₄) :|: P ≤ 7 ∧ 5 ≤ P
t₅₅: f1(X₀, X₁, X₂, X₃, X₄) → f2(1+X₀, 1+X₁, 1, X₃, X₄)
t₅₆: f1(X₀, X₁, X₂, X₃, X₄) → f7(X₀, X₁, 0, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ 1 ≤ O ∧ 1 ≤ P
t₅₇: f1(X₀, X₁, X₂, X₃, X₄) → f7(X₀, X₁, 0, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ 1 ≤ P ∧ 5 ≤ O
t₅₈: f1(X₀, X₁, X₂, X₃, X₄) → f7(1+X₀, 1+X₁, 1, X₃, X₄) :|: P ≤ 7 ∧ 1 ≤ P
t₅₉: f2(X₀, X₁, X₂, X₃, X₄) → f3(X₀, X₁, X₂, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ 1 ≤ O ∧ 1 ≤ P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₆₀: f2(X₀, X₁, X₂, X₃, X₄) → f3(X₀, X₁, X₂, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ 1 ≤ P ∧ 5 ≤ O ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₆₁: f2(X₀, X₁, X₂, X₃, X₄) → f3(1+X₀, 1+X₁, 1, X₃, X₄) :|: P ≤ 7 ∧ 1 ≤ P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₆₂: f2(X₀, X₁, X₂, X₃, X₄) → f7(X₀, X₁, X₂, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ 1 ≤ O ∧ 1 ≤ P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₆₃: f2(X₀, X₁, X₂, X₃, X₄) → f7(X₀, X₁, X₂, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ 1 ≤ P ∧ 5 ≤ O ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₆₄: f2(X₀, X₁, X₂, X₃, X₄) → f7(1+X₀, 1+X₁, 1, X₃, X₄) :|: P ≤ 7 ∧ 1 ≤ P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₆₅: f3(X₀, X₁, X₂, X₃, X₄) → f6(X₀, X₁, X₂, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ 1 ≤ O ∧ 1 ≤ P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₆₆: f3(X₀, X₁, X₂, X₃, X₄) → f6(X₀, X₁, X₂, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ 1 ≤ P ∧ 5 ≤ O ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₆₇: f3(X₀, X₁, X₂, X₃, X₄) → f6(1+X₀, 1+X₁, 1, X₃, X₄) :|: P ≤ 7 ∧ 1 ≤ P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₆₈: f4(X₀, X₁, X₂, X₃, X₄) → f2(X₀, X₁, 0, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ X₂ ≤ 1 ∧ 1 ≤ O ∧ 1 ≤ P ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 0 ≤ X₂
t₆₉: f4(X₀, X₁, X₂, X₃, X₄) → f2(X₀, X₁, 0, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ X₂ ≤ 1 ∧ 1 ≤ P ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 5 ≤ O ∧ 0 ≤ X₂
t₇₀: f4(X₀, X₁, X₂, X₃, X₄) → f2(1+X₀, 1+X₁, 0, X₃, X₄) :|: P ≤ 7 ∧ 1 ≤ P ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₃ ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₇₁: f4(X₀, X₁, X₂, X₃, X₄) → f7(X₀, X₁, X₂, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ 1 ≤ O ∧ 1 ≤ P ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₇₂: f4(X₀, X₁, X₂, X₃, X₄) → f7(X₀, X₁, X₂, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ 1 ≤ P ∧ 5 ≤ O ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₇₃: f4(X₀, X₁, X₂, X₃, X₄) → f7(1+X₀, 1+X₁, 1, X₃, X₄) :|: P ≤ 7 ∧ X₄ ≤ 1+X₀ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₇₄: f4(X₀, X₁, X₂, X₃, X₄) → f7(X₀, X₁, X₂, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ 1 ≤ O ∧ 1 ≤ P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₇₅: f4(X₀, X₁, X₂, X₃, X₄) → f7(X₀, X₁, X₂, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ 1 ≤ P ∧ 5 ≤ O ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₇₆: f4(X₀, X₁, X₂, X₃, X₄) → f7(1+X₀, 1+X₁, 1, X₃, X₄) :|: P ≤ 7 ∧ 1 ≤ P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₇₇: f6(X₀, X₁, X₂, X₃, X₄) → f4(X₀, X₁, 0, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 1 ∧ 1 ≤ O ∧ 0 ≤ P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂
t₇₈: f6(X₀, X₁, X₂, X₃, X₄) → f4(X₀, X₁, 1, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 1 ∧ X₂ ≤ 1 ∧ 1 ≤ O ∧ 1 ≤ X₂ ∧ 0 ≤ P ∧ 0 ≤ X₂
t₇₉: f8(X₀, X₁, X₂, X₃, X₄) → f1(X₀, X₁, X₂, X₃, X₄)

MPRF for transition t₆₈: f4(X₀, X₁, X₂, X₃, X₄) → f2(X₀, X₁, 0, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ X₂ ≤ 1 ∧ 1 ≤ O ∧ 1 ≤ P ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 0 ≤ X₂ of depth 1:

new bound:

3⋅X₀+3⋅X₄+5 {O(n)}

MPRF:

• f2: [X₂+X₄-1-X₀]
• f3: [X₂+X₄-1-X₀]
• f4: [X₂+X₄-1-X₀]
• f6: [X₂+X₄-1-X₀]

MPRF for transition t₆₉: f4(X₀, X₁, X₂, X₃, X₄) → f2(X₀, X₁, 0, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ X₂ ≤ 1 ∧ 1 ≤ P ∧ 1+X₀ ≤ X₄ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 5 ≤ O ∧ 0 ≤ X₂ of depth 1:

new bound:

3⋅X₀+3⋅X₄+2 {O(n)}

MPRF:

• f2: [X₂+X₄-X₀]
• f3: [X₂+X₄-X₀]
• f4: [X₂+X₄-X₀]
• f6: [X₂+X₄-X₀]

MPRF for transition t₇₀: f4(X₀, X₁, X₂, X₃, X₄) → f2(1+X₀, 1+X₁, 0, X₃, X₄) :|: P ≤ 7 ∧ 1 ≤ P ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 2+X₁ ≤ X₃ ∧ X₂ ≤ 1 ∧ 0 ≤ X₂ of depth 1:

new bound:

3⋅X₁+3⋅X₃+4 {O(n)}

MPRF:

• f2: [X₃-1-X₁]
• f3: [X₃-1-X₁]
• f4: [X₃-1-X₁]
• f6: [X₃-1-X₁]

knowledge_propagation leads to new time bound 3⋅X₁+3⋅X₃+6⋅X₀+6⋅X₄+14 {O(n)} for transition t₅₉: f2(X₀, X₁, X₂, X₃, X₄) → f3(X₀, X₁, X₂, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ 1 ≤ O ∧ 1 ≤ P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂

knowledge_propagation leads to new time bound 3⋅X₁+3⋅X₃+6⋅X₀+6⋅X₄+14 {O(n)} for transition t₆₀: f2(X₀, X₁, X₂, X₃, X₄) → f3(X₀, X₁, X₂, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ 1 ≤ P ∧ 5 ≤ O ∧ X₂ ≤ 1 ∧ 0 ≤ X₂

knowledge_propagation leads to new time bound 3⋅X₁+3⋅X₃+6⋅X₀+6⋅X₄+14 {O(n)} for transition t₆₁: f2(X₀, X₁, X₂, X₃, X₄) → f3(1+X₀, 1+X₁, 1, X₃, X₄) :|: P ≤ 7 ∧ 1 ≤ P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂

knowledge_propagation leads to new time bound 18⋅X₀+18⋅X₄+9⋅X₁+9⋅X₃+42 {O(n)} for transition t₆₅: f3(X₀, X₁, X₂, X₃, X₄) → f6(X₀, X₁, X₂, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ O ≤ 3 ∧ 1 ≤ O ∧ 1 ≤ P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂

knowledge_propagation leads to new time bound 18⋅X₀+18⋅X₄+9⋅X₁+9⋅X₃+42 {O(n)} for transition t₆₆: f3(X₀, X₁, X₂, X₃, X₄) → f6(X₀, X₁, X₂, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 7 ∧ 1 ≤ P ∧ 5 ≤ O ∧ X₂ ≤ 1 ∧ 0 ≤ X₂

knowledge_propagation leads to new time bound 18⋅X₀+18⋅X₄+9⋅X₁+9⋅X₃+42 {O(n)} for transition t₆₇: f3(X₀, X₁, X₂, X₃, X₄) → f6(1+X₀, 1+X₁, 1, X₃, X₄) :|: P ≤ 7 ∧ 1 ≤ P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂

knowledge_propagation leads to new time bound 27⋅X₁+27⋅X₃+54⋅X₀+54⋅X₄+126 {O(n)} for transition t₇₇: f6(X₀, X₁, X₂, X₃, X₄) → f4(X₀, X₁, 0, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 1 ∧ 1 ≤ O ∧ 0 ≤ P ∧ X₂ ≤ 1 ∧ 0 ≤ X₂

knowledge_propagation leads to new time bound 27⋅X₁+27⋅X₃+54⋅X₀+54⋅X₄+126 {O(n)} for transition t₇₈: f6(X₀, X₁, X₂, X₃, X₄) → f4(X₀, X₁, 1, X₃, X₄) :|: O ≤ 7 ∧ P ≤ 1 ∧ X₂ ≤ 1 ∧ 1 ≤ O ∧ 1 ≤ X₂ ∧ 0 ≤ P ∧ 0 ≤ X₂

All Bounds

Timebounds

Overall timebound:186⋅X₀+186⋅X₄+93⋅X₁+93⋅X₃+447 {O(n)}
t₅₃: 1 {O(1)}
t₅₄: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₇: 1 {O(1)}
t₅₈: 1 {O(1)}
t₅₉: 3⋅X₁+3⋅X₃+6⋅X₀+6⋅X₄+14 {O(n)}
t₆₀: 3⋅X₁+3⋅X₃+6⋅X₀+6⋅X₄+14 {O(n)}
t₆₁: 3⋅X₁+3⋅X₃+6⋅X₀+6⋅X₄+14 {O(n)}
t₆₂: 1 {O(1)}
t₆₃: 1 {O(1)}
t₆₄: 1 {O(1)}
t₆₅: 18⋅X₀+18⋅X₄+9⋅X₁+9⋅X₃+42 {O(n)}
t₆₆: 18⋅X₀+18⋅X₄+9⋅X₁+9⋅X₃+42 {O(n)}
t₆₇: 18⋅X₀+18⋅X₄+9⋅X₁+9⋅X₃+42 {O(n)}
t₆₈: 3⋅X₀+3⋅X₄+5 {O(n)}
t₆₉: 3⋅X₀+3⋅X₄+2 {O(n)}
t₇₀: 3⋅X₁+3⋅X₃+4 {O(n)}
t₇₁: 1 {O(1)}
t₇₂: 1 {O(1)}
t₇₃: 1 {O(1)}
t₇₄: 1 {O(1)}
t₇₅: 1 {O(1)}
t₇₆: 1 {O(1)}
t₇₇: 27⋅X₁+27⋅X₃+54⋅X₀+54⋅X₄+126 {O(n)}
t₇₈: 27⋅X₁+27⋅X₃+54⋅X₀+54⋅X₄+126 {O(n)}
t₇₉: 1 {O(1)}

Costbounds

Overall costbound: 186⋅X₀+186⋅X₄+93⋅X₁+93⋅X₃+447 {O(n)}
t₅₃: 1 {O(1)}
t₅₄: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₇: 1 {O(1)}
t₅₈: 1 {O(1)}
t₅₉: 3⋅X₁+3⋅X₃+6⋅X₀+6⋅X₄+14 {O(n)}
t₆₀: 3⋅X₁+3⋅X₃+6⋅X₀+6⋅X₄+14 {O(n)}
t₆₁: 3⋅X₁+3⋅X₃+6⋅X₀+6⋅X₄+14 {O(n)}
t₆₂: 1 {O(1)}
t₆₃: 1 {O(1)}
t₆₄: 1 {O(1)}
t₆₅: 18⋅X₀+18⋅X₄+9⋅X₁+9⋅X₃+42 {O(n)}
t₆₆: 18⋅X₀+18⋅X₄+9⋅X₁+9⋅X₃+42 {O(n)}
t₆₇: 18⋅X₀+18⋅X₄+9⋅X₁+9⋅X₃+42 {O(n)}
t₆₈: 3⋅X₀+3⋅X₄+5 {O(n)}
t₆₉: 3⋅X₀+3⋅X₄+2 {O(n)}
t₇₀: 3⋅X₁+3⋅X₃+4 {O(n)}
t₇₁: 1 {O(1)}
t₇₂: 1 {O(1)}
t₇₃: 1 {O(1)}
t₇₄: 1 {O(1)}
t₇₅: 1 {O(1)}
t₇₆: 1 {O(1)}
t₇₇: 27⋅X₁+27⋅X₃+54⋅X₀+54⋅X₄+126 {O(n)}
t₇₈: 27⋅X₁+27⋅X₃+54⋅X₀+54⋅X₄+126 {O(n)}
t₇₉: 1 {O(1)}

Sizebounds

t₅₃, X₀: X₀ {O(n)}
t₅₃, X₁: X₁ {O(n)}
t₅₃, X₂: 0 {O(1)}
t₅₃, X₃: X₃ {O(n)}
t₅₃, X₄: X₄ {O(n)}
t₅₄, X₀: X₀ {O(n)}
t₅₄, X₁: X₁ {O(n)}
t₅₄, X₂: 0 {O(1)}
t₅₄, X₃: X₃ {O(n)}
t₅₄, X₄: X₄ {O(n)}
t₅₅, X₀: X₀+1 {O(n)}
t₅₅, X₁: X₁+1 {O(n)}
t₅₅, X₂: 1 {O(1)}
t₅₅, X₃: X₃ {O(n)}
t₅₅, X₄: X₄ {O(n)}
t₅₆, X₀: X₀ {O(n)}
t₅₆, X₁: X₁ {O(n)}
t₅₆, X₂: 0 {O(1)}
t₅₆, X₃: X₃ {O(n)}
t₅₆, X₄: X₄ {O(n)}
t₅₇, X₀: X₀ {O(n)}
t₅₇, X₁: X₁ {O(n)}
t₅₇, X₂: 0 {O(1)}
t₅₇, X₃: X₃ {O(n)}
t₅₇, X₄: X₄ {O(n)}
t₅₈, X₀: X₀+1 {O(n)}
t₅₈, X₁: X₁+1 {O(n)}
t₅₈, X₂: 1 {O(1)}
t₅₈, X₃: X₃ {O(n)}
t₅₈, X₄: X₄ {O(n)}
t₅₉, X₀: 15⋅X₁+15⋅X₃+24⋅X₄+27⋅X₀+61 {O(n)}
t₅₉, X₁: 15⋅X₃+18⋅X₁+24⋅X₀+24⋅X₄+61 {O(n)}
t₅₉, X₂: 1 {O(1)}
t₅₉, X₃: 3⋅X₃ {O(n)}
t₅₉, X₄: 3⋅X₄ {O(n)}
t₆₀, X₀: 15⋅X₁+15⋅X₃+24⋅X₄+27⋅X₀+61 {O(n)}
t₆₀, X₁: 15⋅X₃+18⋅X₁+24⋅X₀+24⋅X₄+61 {O(n)}
t₆₀, X₂: 1 {O(1)}
t₆₀, X₃: 3⋅X₃ {O(n)}
t₆₀, X₄: 3⋅X₄ {O(n)}
t₆₁, X₀: 15⋅X₁+15⋅X₃+24⋅X₄+27⋅X₀+61 {O(n)}
t₆₁, X₁: 15⋅X₃+18⋅X₁+24⋅X₀+24⋅X₄+61 {O(n)}
t₆₁, X₂: 1 {O(1)}
t₆₁, X₃: 3⋅X₃ {O(n)}
t₆₁, X₄: 3⋅X₄ {O(n)}
t₆₂, X₀: 45⋅X₁+45⋅X₃+72⋅X₄+84⋅X₀+184 {O(n)}
t₆₂, X₁: 45⋅X₃+57⋅X₁+72⋅X₀+72⋅X₄+184 {O(n)}
t₆₂, X₂: 1 {O(1)}
t₆₂, X₃: 12⋅X₃ {O(n)}
t₆₂, X₄: 12⋅X₄ {O(n)}
t₆₃, X₀: 45⋅X₁+45⋅X₃+72⋅X₄+84⋅X₀+184 {O(n)}
t₆₃, X₁: 45⋅X₃+57⋅X₁+72⋅X₀+72⋅X₄+184 {O(n)}
t₆₃, X₂: 1 {O(1)}
t₆₃, X₃: 12⋅X₃ {O(n)}
t₆₃, X₄: 12⋅X₄ {O(n)}
t₆₄, X₀: 45⋅X₁+45⋅X₃+72⋅X₄+84⋅X₀+190 {O(n)}
t₆₄, X₁: 45⋅X₃+57⋅X₁+72⋅X₀+72⋅X₄+190 {O(n)}
t₆₄, X₂: 1 {O(1)}
t₆₄, X₃: 12⋅X₃ {O(n)}
t₆₄, X₄: 12⋅X₄ {O(n)}
t₆₅, X₀: 15⋅X₁+15⋅X₃+24⋅X₄+27⋅X₀+61 {O(n)}
t₆₅, X₁: 15⋅X₃+18⋅X₁+24⋅X₀+24⋅X₄+61 {O(n)}
t₆₅, X₂: 1 {O(1)}
t₆₅, X₃: 3⋅X₃ {O(n)}
t₆₅, X₄: 3⋅X₄ {O(n)}
t₆₆, X₀: 15⋅X₁+15⋅X₃+24⋅X₄+27⋅X₀+61 {O(n)}
t₆₆, X₁: 15⋅X₃+18⋅X₁+24⋅X₀+24⋅X₄+61 {O(n)}
t₆₆, X₂: 1 {O(1)}
t₆₆, X₃: 3⋅X₃ {O(n)}
t₆₆, X₄: 3⋅X₄ {O(n)}
t₆₇, X₀: 15⋅X₁+15⋅X₃+24⋅X₄+27⋅X₀+61 {O(n)}
t₆₇, X₁: 15⋅X₃+18⋅X₁+24⋅X₀+24⋅X₄+61 {O(n)}
t₆₇, X₂: 1 {O(1)}
t₆₇, X₃: 3⋅X₃ {O(n)}
t₆₇, X₄: 3⋅X₄ {O(n)}
t₆₈, X₀: 15⋅X₁+15⋅X₃+24⋅X₄+27⋅X₀+61 {O(n)}
t₆₈, X₁: 15⋅X₃+18⋅X₁+24⋅X₀+24⋅X₄+61 {O(n)}
t₆₈, X₂: 0 {O(1)}
t₆₈, X₃: 3⋅X₃ {O(n)}
t₆₈, X₄: 3⋅X₄ {O(n)}
t₆₉, X₀: 15⋅X₁+15⋅X₃+24⋅X₄+27⋅X₀+61 {O(n)}
t₆₉, X₁: 15⋅X₃+18⋅X₁+24⋅X₀+24⋅X₄+61 {O(n)}
t₆₉, X₂: 0 {O(1)}
t₆₉, X₃: 3⋅X₃ {O(n)}
t₆₉, X₄: 3⋅X₄ {O(n)}
t₇₀, X₀: 15⋅X₁+15⋅X₃+24⋅X₄+27⋅X₀+61 {O(n)}
t₇₀, X₁: 15⋅X₃+18⋅X₁+24⋅X₀+24⋅X₄+61 {O(n)}
t₇₀, X₂: 0 {O(1)}
t₇₀, X₃: 3⋅X₃ {O(n)}
t₇₀, X₄: 3⋅X₄ {O(n)}
t₇₁, X₀: 30⋅X₁+30⋅X₃+48⋅X₄+54⋅X₀+122 {O(n)}
t₇₁, X₁: 30⋅X₃+36⋅X₁+48⋅X₀+48⋅X₄+122 {O(n)}
t₇₁, X₂: 1 {O(1)}
t₇₁, X₃: 6⋅X₃ {O(n)}
t₇₁, X₄: 6⋅X₄ {O(n)}
t₇₂, X₀: 30⋅X₁+30⋅X₃+48⋅X₄+54⋅X₀+122 {O(n)}
t₇₂, X₁: 30⋅X₃+36⋅X₁+48⋅X₀+48⋅X₄+122 {O(n)}
t₇₂, X₂: 1 {O(1)}
t₇₂, X₃: 6⋅X₃ {O(n)}
t₇₂, X₄: 6⋅X₄ {O(n)}
t₇₃, X₀: 30⋅X₁+30⋅X₃+48⋅X₄+54⋅X₀+124 {O(n)}
t₇₃, X₁: 30⋅X₃+36⋅X₁+48⋅X₀+48⋅X₄+124 {O(n)}
t₇₃, X₂: 1 {O(1)}
t₇₃, X₃: 6⋅X₃ {O(n)}
t₇₃, X₄: 6⋅X₄ {O(n)}
t₇₄, X₀: 30⋅X₁+30⋅X₃+48⋅X₄+54⋅X₀+122 {O(n)}
t₇₄, X₁: 30⋅X₃+36⋅X₁+48⋅X₀+48⋅X₄+122 {O(n)}
t₇₄, X₂: 1 {O(1)}
t₇₄, X₃: 6⋅X₃ {O(n)}
t₇₄, X₄: 6⋅X₄ {O(n)}
t₇₅, X₀: 30⋅X₁+30⋅X₃+48⋅X₄+54⋅X₀+122 {O(n)}
t₇₅, X₁: 30⋅X₃+36⋅X₁+48⋅X₀+48⋅X₄+122 {O(n)}
t₇₅, X₂: 1 {O(1)}
t₇₅, X₃: 6⋅X₃ {O(n)}
t₇₅, X₄: 6⋅X₄ {O(n)}
t₇₆, X₀: 30⋅X₁+30⋅X₃+48⋅X₄+54⋅X₀+124 {O(n)}
t₇₆, X₁: 30⋅X₃+36⋅X₁+48⋅X₀+48⋅X₄+124 {O(n)}
t₇₆, X₂: 1 {O(1)}
t₇₆, X₃: 6⋅X₃ {O(n)}
t₇₆, X₄: 6⋅X₄ {O(n)}
t₇₇, X₀: 15⋅X₁+15⋅X₃+24⋅X₄+27⋅X₀+61 {O(n)}
t₇₇, X₁: 15⋅X₃+18⋅X₁+24⋅X₀+24⋅X₄+61 {O(n)}
t₇₇, X₂: 0 {O(1)}
t₇₇, X₃: 3⋅X₃ {O(n)}
t₇₇, X₄: 3⋅X₄ {O(n)}
t₇₈, X₀: 15⋅X₁+15⋅X₃+24⋅X₄+27⋅X₀+61 {O(n)}
t₇₈, X₁: 15⋅X₃+18⋅X₁+24⋅X₀+24⋅X₄+61 {O(n)}
t₇₈, X₂: 1 {O(1)}
t₇₈, X₃: 3⋅X₃ {O(n)}
t₇₈, X₄: 3⋅X₄ {O(n)}
t₇₉, X₀: X₀ {O(n)}
t₇₉, X₁: X₁ {O(n)}
t₇₉, X₂: X₂ {O(n)}
t₇₉, X₃: X₃ {O(n)}
t₇₉, X₄: X₄ {O(n)}