Initial Problem

Start: f26
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀
Temp_Vars: F1, G1, H1, I1, J1, K1, L1, M1, N1, O1, P1
Locations: f11, f12, f26, f6
Transitions:
t₂: f11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → f11(X₀, X₁, X₀, X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: 1+X₁ ≤ X₀
t₃: f11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → f11(X₀, X₁, X₀, X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: 1+X₀ ≤ X₁
t₀: f12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → f11(X₀, X₁, X₀, X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: 1+X₁ ≤ X₀
t₁: f12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → f11(X₀, X₁, X₀, X₀, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: 1+X₀ ≤ X₁
t₆: f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → f6(X₀, X₁, X₂, X₃, L1, X₅, 1, 4, 1, 4, X₁₀, X₁₁, X₁₂, F1, 2, 3, G1, H1, 4, J1, 0, K1, M1, M1, M1, M1, N1, O1, P1, 4, X₃₀) :|: 1+X₅ ≤ I1
t₇: f26(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → f6(X₀, X₁, X₂, X₃, L1, X₅, 1, 4, 1, 4, X₁₀, X₁₁, X₁₂, F1, 2, 3, G1, H1, 4, J1, 0, K1, M1, M1, M1, M1, N1, O1, P1, 4, X₃₀) :|: 1+I1 ≤ X₅
t₈: f6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → f12(J1, X₁, J1, J1, X₄, X₄, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, F1, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, G1, X₂₆, X₂₇, X₂₈, X₂₉, H1) :|: 1+X₁ ≤ J1 ∧ 1 ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ 0 ≤ X₆
t₉: f6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → f12(J1, X₁, J1, J1, X₄, X₄, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, F1, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, G1, X₂₆, X₂₇, X₂₈, X₂₉, H1) :|: 1+J1 ≤ X₁ ∧ 1 ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ 0 ≤ X₆
t₄: f6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → f6(X₀, X₁, X₂, X₃, H1, X₅, 1+X₆, X₇-1, 1+X₆, X₇-1, F1, G1, X₇-1, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: 1+X₅ ≤ X₄ ∧ 1 ≤ X₇ ∧ 0 ≤ X₆
t₅: f6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) → f6(X₀, X₁, X₂, X₃, H1, X₅, 1+X₆, X₇-1, 1+X₆, X₇-1, F1, G1, X₇-1, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆, X₂₇, X₂₈, X₂₉, X₃₀) :|: 1+X₄ ≤ X₅ ∧ 1 ≤ X₇ ∧ 0 ≤ X₆

Preprocessing

Eliminate variables [F1; G1; K1; M1; N1; O1; P1; X₂; X₃; X₈; X₉; X₁₀; X₁₁; X₁₂; X₁₃; X₁₄; X₁₅; X₁₆; X₁₇; X₁₈; X₁₉; X₂₀; X₂₁; X₂₂; X₂₃; X₂₄; X₂₅; X₂₆; X₂₇; X₂₈; X₂₉; X₃₀] that do not contribute to the problem

Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ for location f6

Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location f11

Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location f12

Problem after Preprocessing

Start: f26
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: H1, I1, J1, L1
Locations: f11, f12, f26, f6
Transitions:
t₂₁: f11(X₀, X₁, X₂, X₃, X₄, X₅) → f11(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₀ ∧ X₄+X₅ ≤ 5 ∧ X₄ ≤ 4 ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄ ≤ 3+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₂₂: f11(X₀, X₁, X₂, X₃, X₄, X₅) → f11(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ X₄+X₅ ≤ 5 ∧ X₄ ≤ 4 ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄ ≤ 3+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₂₃: f12(X₀, X₁, X₂, X₃, X₄, X₅) → f11(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₀ ∧ X₄+X₅ ≤ 5 ∧ X₄ ≤ 4 ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄ ≤ 3+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₂₄: f12(X₀, X₁, X₂, X₃, X₄, X₅) → f11(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ X₄+X₅ ≤ 5 ∧ X₄ ≤ 4 ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄ ≤ 3+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₂₅: f26(X₀, X₁, X₂, X₃, X₄, X₅) → f6(X₀, X₁, L1, X₃, 1, 4) :|: 1+X₃ ≤ I1
t₂₆: f26(X₀, X₁, X₂, X₃, X₄, X₅) → f6(X₀, X₁, L1, X₃, 1, 4) :|: 1+I1 ≤ X₃
t₂₇: f6(X₀, X₁, X₂, X₃, X₄, X₅) → f12(J1, X₁, X₂, X₂, X₄, X₅) :|: 1+X₁ ≤ J1 ∧ 1 ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₄ ∧ X₄ ≤ 5 ∧ X₄ ≤ 5+X₅ ∧ X₄+X₅ ≤ 5 ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ 1 ≤ X₄ ∧ 5 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₂₈: f6(X₀, X₁, X₂, X₃, X₄, X₅) → f12(J1, X₁, X₂, X₂, X₄, X₅) :|: 1+J1 ≤ X₁ ∧ 1 ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₄ ∧ X₄ ≤ 5 ∧ X₄ ≤ 5+X₅ ∧ X₄+X₅ ≤ 5 ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ 1 ≤ X₄ ∧ 5 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₂₉: f6(X₀, X₁, X₂, X₃, X₄, X₅) → f6(X₀, X₁, H1, X₃, 1+X₄, X₅-1) :|: 1+X₃ ≤ X₂ ∧ 1 ≤ X₅ ∧ 0 ≤ X₄ ∧ X₄ ≤ 5 ∧ X₄ ≤ 5+X₅ ∧ X₄+X₅ ≤ 5 ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ 1 ≤ X₄ ∧ 5 ≤ X₄+X₅ ∧ 0 ≤ X₅
t₃₀: f6(X₀, X₁, X₂, X₃, X₄, X₅) → f6(X₀, X₁, H1, X₃, 1+X₄, X₅-1) :|: 1+X₂ ≤ X₃ ∧ 1 ≤ X₅ ∧ 0 ≤ X₄ ∧ X₄ ≤ 5 ∧ X₄ ≤ 5+X₅ ∧ X₄+X₅ ≤ 5 ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ 1 ≤ X₄ ∧ 5 ≤ X₄+X₅ ∧ 0 ≤ X₅

MPRF for transition t₂₉: f6(X₀, X₁, X₂, X₃, X₄, X₅) → f6(X₀, X₁, H1, X₃, 1+X₄, X₅-1) :|: 1+X₃ ≤ X₂ ∧ 1 ≤ X₅ ∧ 0 ≤ X₄ ∧ X₄ ≤ 5 ∧ X₄ ≤ 5+X₅ ∧ X₄+X₅ ≤ 5 ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ 1 ≤ X₄ ∧ 5 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

14 {O(1)}

MPRF:

• f6: [6-X₄]

MPRF for transition t₃₀: f6(X₀, X₁, X₂, X₃, X₄, X₅) → f6(X₀, X₁, H1, X₃, 1+X₄, X₅-1) :|: 1+X₂ ≤ X₃ ∧ 1 ≤ X₅ ∧ 0 ≤ X₄ ∧ X₄ ≤ 5 ∧ X₄ ≤ 5+X₅ ∧ X₄+X₅ ≤ 5 ∧ X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ 1 ≤ X₄ ∧ 5 ≤ X₄+X₅ ∧ 0 ≤ X₅ of depth 1:

new bound:

14 {O(1)}

MPRF:

• f6: [6-X₄]

Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location f11_v2

Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 0 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 5+X₅ ∧ X₄ ≤ 5 ∧ 1 ≤ X₄ for location f6

Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location f11

Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₀ ≤ X₁ for location f11_v1

Found invariant X₅ ≤ 4 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 5 ∧ 1 ≤ X₅ ∧ 5 ≤ X₄+X₅ ∧ X₄ ≤ 3+X₅ ∧ X₄ ≤ 4 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location f12

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₂₁: inf {Infinity}
t₂₂: inf {Infinity}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 14 {O(1)}
t₃₀: 14 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₂₁: inf {Infinity}
t₂₂: inf {Infinity}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₂₉: 14 {O(1)}
t₃₀: 14 {O(1)}

Sizebounds

t₂₁, X₁: 6⋅X₁ {O(n)}
t₂₁, X₄: 4 {O(1)}
t₂₁, X₅: 4 {O(1)}
t₂₂, X₁: 6⋅X₁ {O(n)}
t₂₂, X₄: 4 {O(1)}
t₂₂, X₅: 4 {O(1)}
t₂₃, X₁: 6⋅X₁ {O(n)}
t₂₃, X₄: 4 {O(1)}
t₂₃, X₅: 4 {O(1)}
t₂₄, X₁: 6⋅X₁ {O(n)}
t₂₄, X₄: 4 {O(1)}
t₂₄, X₅: 4 {O(1)}
t₂₅, X₀: X₀ {O(n)}
t₂₅, X₁: X₁ {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₂₅, X₄: 1 {O(1)}
t₂₅, X₅: 4 {O(1)}
t₂₆, X₀: X₀ {O(n)}
t₂₆, X₁: X₁ {O(n)}
t₂₆, X₃: X₃ {O(n)}
t₂₆, X₄: 1 {O(1)}
t₂₆, X₅: 4 {O(1)}
t₂₇, X₁: 6⋅X₁ {O(n)}
t₂₇, X₄: 4 {O(1)}
t₂₇, X₅: 4 {O(1)}
t₂₈, X₁: 6⋅X₁ {O(n)}
t₂₈, X₄: 4 {O(1)}
t₂₈, X₅: 4 {O(1)}
t₂₉, X₀: 2⋅X₀ {O(n)}
t₂₉, X₁: 2⋅X₁ {O(n)}
t₂₉, X₃: 2⋅X₃ {O(n)}
t₂₉, X₄: 5 {O(1)}
t₂₉, X₅: 3 {O(1)}
t₃₀, X₀: 2⋅X₀ {O(n)}
t₃₀, X₁: 2⋅X₁ {O(n)}
t₃₀, X₃: 2⋅X₃ {O(n)}
t₃₀, X₄: 5 {O(1)}
t₃₀, X₅: 3 {O(1)}