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, f26, f6
Transitions:
t₀: 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, X₁, X₁, 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: 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, X₁, X₁, 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
t₄: 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, X₄, L1, 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 ≤ X₄
t₅: 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, X₄, L1, 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+X₄ ≤ I1
t₆: 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) → f11(X₀, J1, J1, J1, X₅, X₅, 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 ≤ X₀ ∧ 1 ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ 0 ≤ X₆
t₇: 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) → f11(X₀, J1, J1, J1, X₅, X₅, 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+X₀ ≤ J1 ∧ 1 ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ 0 ≤ X₆
t₂: 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, X₄, H1, 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
t₃: 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, X₄, H1, 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

Problem after Preprocessing

Start: f26
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: H1, I1, J1, L1
Locations: f11, f26, f6
Transitions:
t₁₆: 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
t₁₇: 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
t₁₈: f26(X₀, X₁, X₂, X₃, X₄, X₅) → f6(X₀, X₁, X₂, L1, 1, 4) :|: 1+I1 ≤ X₂
t₁₉: f26(X₀, X₁, X₂, X₃, X₄, X₅) → f6(X₀, X₁, X₂, L1, 1, 4) :|: 1+X₂ ≤ I1
t₂₀: f6(X₀, X₁, X₂, X₃, X₄, X₅) → f11(X₀, J1, X₃, X₃, X₄, X₅) :|: 1+J1 ≤ X₀ ∧ 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
t₂₁: f6(X₀, X₁, X₂, X₃, X₄, X₅) → f11(X₀, J1, X₃, X₃, X₄, X₅) :|: 1+X₀ ≤ 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
t₂₂: f6(X₀, X₁, X₂, X₃, X₄, X₅) → f6(X₀, X₁, X₂, H1, 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
t₂₃: f6(X₀, X₁, X₂, X₃, X₄, X₅) → f6(X₀, X₁, X₂, H1, 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 t₂₂: f6(X₀, X₁, X₂, X₃, X₄, X₅) → f6(X₀, X₁, X₂, H1, 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 t₂₃: f6(X₀, X₁, X₂, X₃, X₄, X₅) → f6(X₀, X₁, X₂, H1, 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

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₆: inf {Infinity}
t₁₇: inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 14 {O(1)}
t₂₃: 14 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₁₆: inf {Infinity}
t₁₇: inf {Infinity}
t₁₈: 1 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 14 {O(1)}
t₂₃: 14 {O(1)}

Sizebounds

t₁₆, X₀: 6⋅X₀ {O(n)}
t₁₆, X₂: 6⋅X₂ {O(n)}
t₁₆, X₄: 4 {O(1)}
t₁₆, X₅: 4 {O(1)}
t₁₇, X₀: 6⋅X₀ {O(n)}
t₁₇, X₂: 6⋅X₂ {O(n)}
t₁₇, X₄: 4 {O(1)}
t₁₇, X₅: 4 {O(1)}
t₁₈, X₀: X₀ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₄: 1 {O(1)}
t₁₈, X₅: 4 {O(1)}
t₁₉, X₀: X₀ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₄: 1 {O(1)}
t₁₉, X₅: 4 {O(1)}
t₂₀, X₀: 6⋅X₀ {O(n)}
t₂₀, X₂: 6⋅X₂ {O(n)}
t₂₀, X₄: 4 {O(1)}
t₂₀, X₅: 4 {O(1)}
t₂₁, X₀: 6⋅X₀ {O(n)}
t₂₁, X₂: 6⋅X₂ {O(n)}
t₂₁, X₄: 4 {O(1)}
t₂₁, X₅: 4 {O(1)}
t₂₂, X₀: 2⋅X₀ {O(n)}
t₂₂, X₁: 2⋅X₁ {O(n)}
t₂₂, X₂: 2⋅X₂ {O(n)}
t₂₂, X₄: 5 {O(1)}
t₂₂, X₅: 3 {O(1)}
t₂₃, X₀: 2⋅X₀ {O(n)}
t₂₃, X₁: 2⋅X₁ {O(n)}
t₂₃, X₂: 2⋅X₂ {O(n)}
t₂₃, X₄: 5 {O(1)}
t₂₃, X₅: 3 {O(1)}