Initial Problem

Start: f23
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
Temp_Vars: B1, C1, D1, E1, F1, G1, H1, I1, J1
Locations: f2, f23, f8
Transitions:
t₂: f2(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) → f2(X₀, X₁, X₂, X₃, X₄, B1, X₆-1, 1+X₇, 1+X₇, X₆-1, C1, D1, X₆-1, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+X₅ ≤ X₄ ∧ 1 ≤ X₆ ∧ 0 ≤ X₇
t₃: f2(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) → f2(X₀, X₁, X₂, X₃, X₄, B1, X₆-1, 1+X₇, 1+X₇, X₆-1, C1, D1, X₆-1, X₁₃, X₁₄, X₁₅, X₁₆, X₁₇, X₁₈, X₁₉, X₂₀, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, X₂₆) :|: 1+X₄ ≤ X₅ ∧ 1 ≤ X₆ ∧ 0 ≤ X₇
t₆: f2(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) → f8(X₀, C1, C1, C1, X₅, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, B1, X₁₇, X₁₈, X₁₉, D1, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, F1) :|: 1+C1 ≤ X₀ ∧ 1 ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ 0 ≤ X₇
t₇: f2(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) → f8(X₀, C1, C1, C1, X₅, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, B1, X₁₇, X₁₈, X₁₉, D1, X₂₁, X₂₂, X₂₃, X₂₄, X₂₅, F1) :|: 1+X₀ ≤ C1 ∧ 1 ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ 0 ≤ X₇
t₄: f23(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) → f2(X₀, X₁, X₂, X₃, X₄, B1, 2, 1, 1, 2, X₁₀, X₁₁, X₁₂, 2, C1, D1, F1, G1, G1, G1, G1, H1, I1, 2, J1, 0, X₂₆) :|: 1+E1 ≤ X₄
t₅: f23(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) → f2(X₀, X₁, X₂, X₃, X₄, B1, 2, 1, 1, 2, X₁₀, X₁₁, X₁₂, 2, C1, D1, F1, G1, G1, G1, G1, H1, I1, 2, J1, 0, X₂₆) :|: 1+X₄ ≤ E1
t₀: f8(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) → f8(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) :|: 1+X₁ ≤ X₀
t₁: f8(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) → f8(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) :|: 1+X₀ ≤ X₁

Preprocessing

Eliminate variables [D1; F1; G1; H1; I1; J1; X₂; X₃; X₈; X₉; X₁₀; X₁₁; X₁₂; X₁₃; X₁₄; X₁₅; X₁₆; X₁₇; X₁₈; X₁₉; X₂₀; X₂₁; X₂₂; X₂₃; X₂₄; X₂₅; X₂₆] that do not contribute to the problem

Found invariant X₅ ≤ 2 ∧ X₅ ≤ 1+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location f8

Found invariant X₅ ≤ 3 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 0 ≤ X₄ for location f2

Problem after Preprocessing

Start: f23
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: B1, C1, E1
Locations: f2, f23, f8
Transitions:
t₁₉: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀, X₁, X₂, B1, X₄-1, 1+X₅) :|: 1+X₃ ≤ X₂ ∧ 1 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ X₄ ≤ 2 ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 0 ≤ X₄
t₂₀: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀, X₁, X₂, B1, X₄-1, 1+X₅) :|: 1+X₂ ≤ X₃ ∧ 1 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ X₄ ≤ 2 ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 0 ≤ X₄
t₂₁: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f8(X₀, C1, X₃, X₃, X₄, X₅) :|: 1+C1 ≤ X₀ ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₅ ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ X₄ ≤ 2 ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 0 ≤ X₄
t₂₂: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f8(X₀, C1, X₃, X₃, X₄, X₅) :|: 1+X₀ ≤ C1 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₅ ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ X₄ ≤ 2 ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 0 ≤ X₄
t₂₃: f23(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀, X₁, X₂, B1, 2, 1) :|: 1+E1 ≤ X₂
t₂₄: f23(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀, X₁, X₂, B1, 2, 1) :|: 1+X₂ ≤ E1
t₂₅: f8(X₀, X₁, X₂, X₃, X₄, X₅) → f8(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₀ ∧ X₄+X₅ ≤ 3 ∧ X₄ ≤ 2 ∧ X₅ ≤ 2 ∧ X₅ ≤ 1+X₄ ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₂₆: f8(X₀, X₁, X₂, X₃, X₄, X₅) → f8(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₁ ∧ X₄+X₅ ≤ 3 ∧ X₄ ≤ 2 ∧ X₅ ≤ 2 ∧ X₅ ≤ 1+X₄ ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃

MPRF for transition t₁₉: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀, X₁, X₂, B1, X₄-1, 1+X₅) :|: 1+X₃ ≤ X₂ ∧ 1 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ X₄ ≤ 2 ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 0 ≤ X₄ of depth 1:

new bound:

6 {O(1)}

• f2: [1+X₄]

MPRF for transition t₂₀: f2(X₀, X₁, X₂, X₃, X₄, X₅) → f2(X₀, X₁, X₂, B1, X₄-1, 1+X₅) :|: 1+X₂ ≤ X₃ ∧ 1 ≤ X₄ ∧ 0 ≤ X₅ ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ X₅ ≤ 3 ∧ X₄ ≤ 2 ∧ X₄ ≤ 1+X₅ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 0 ≤ X₄ of depth 1:

new bound:

6 {O(1)}

• f2: [1+X₄]

Found invariant X₅ ≤ 2 ∧ X₅ ≤ 1+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₀ ≤ X₁ for location f8_v1

Found invariant X₅ ≤ 2 ∧ X₅ ≤ 1+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location f8_v2

Found invariant X₅ ≤ 2 ∧ X₅ ≤ 1+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 1 ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ for location f8

Found invariant X₅ ≤ 3 ∧ X₅ ≤ 3+X₄ ∧ X₄+X₅ ≤ 3 ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ X₄ ≤ 1+X₅ ∧ X₄ ≤ 2 ∧ 0 ≤ X₄ for location f2

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₁₉: 6 {O(1)}
t₂₀: 6 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: inf {Infinity}
t₂₆: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₁₉: 6 {O(1)}
t₂₀: 6 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: inf {Infinity}
t₂₆: inf {Infinity}

Sizebounds

t₁₉, X₀: 2⋅X₀ {O(n)}
t₁₉, X₁: 2⋅X₁ {O(n)}
t₁₉, X₂: 2⋅X₂ {O(n)}
t₁₉, X₄: 1 {O(1)}
t₁₉, X₅: 3 {O(1)}
t₂₀, X₀: 2⋅X₀ {O(n)}
t₂₀, X₁: 2⋅X₁ {O(n)}
t₂₀, X₂: 2⋅X₂ {O(n)}
t₂₀, X₄: 1 {O(1)}
t₂₀, X₅: 3 {O(1)}
t₂₁, X₀: 6⋅X₀ {O(n)}
t₂₁, X₂: 6⋅X₂ {O(n)}
t₂₁, X₄: 2 {O(1)}
t₂₁, X₅: 2 {O(1)}
t₂₂, X₀: 6⋅X₀ {O(n)}
t₂₂, X₂: 6⋅X₂ {O(n)}
t₂₂, X₄: 2 {O(1)}
t₂₂, X₅: 2 {O(1)}
t₂₃, X₀: X₀ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₄: 2 {O(1)}
t₂₃, X₅: 1 {O(1)}
t₂₄, X₀: X₀ {O(n)}
t₂₄, X₁: X₁ {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₄: 2 {O(1)}
t₂₄, X₅: 1 {O(1)}
t₂₅, X₀: 6⋅X₀ {O(n)}
t₂₅, X₂: 6⋅X₂ {O(n)}
t₂₅, X₄: 2 {O(1)}
t₂₅, X₅: 2 {O(1)}
t₂₆, X₀: 6⋅X₀ {O(n)}
t₂₆, X₂: 6⋅X₂ {O(n)}
t₂₆, X₄: 2 {O(1)}
t₂₆, X₅: 2 {O(1)}