KoAT2 Proof Output

Initial Problem

Preprocessing

Cut unsatisfiable transition [t₆: lbl82→lbl92]

Found invariant 5 ≤ X₇ ∧ X₀ ≤ X₇ for location stop

Found invariant X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location start

Found invariant X₇ ≤ 4 ∧ X₇ ≤ 3+X₅ ∧ X₅+X₇ ≤ 14 ∧ X₇ ≤ 4+X₁ ∧ X₁+X₇ ≤ 13 ∧ X₀+X₇ ≤ 8 ∧ 3 ≤ X₇ ∧ 4 ≤ X₅+X₇ ∧ X₅ ≤ 7+X₇ ∧ 3 ≤ X₁+X₇ ∧ X₁ ≤ 6+X₇ ∧ X₀ ≤ X₇ ∧ X₅ ≤ 10 ∧ X₅ ≤ 1+X₁ ∧ X₁+X₅ ≤ 19 ∧ X₀+X₅ ≤ 14 ∧ 1 ≤ X₅ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ 3+X₅ ∧ X₁ ≤ 9 ∧ X₀+X₁ ≤ 13 ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 for location lbl82

Found invariant X₇ ≤ 5 ∧ X₇ ≤ 3+X₅ ∧ X₅+X₇ ≤ 15 ∧ X₇ ≤ 1+X₃ ∧ X₃+X₇ ≤ 9 ∧ X₀+X₇ ≤ 9 ∧ 1+X₃ ≤ X₇ ∧ 1+X₀ ≤ X₇ ∧ X₅ ≤ 10 ∧ X₃+X₅ ≤ 14 ∧ X₀+X₅ ≤ 14 ∧ 0 ≤ X₅ ∧ X₃ ≤ 2+X₅ ∧ X₀ ≤ 2+X₅ ∧ X₃ ≤ 4 ∧ X₀+X₃ ≤ 8 ∧ X₀ ≤ X₃ ∧ X₀ ≤ 4 for location lbl92

Problem after Preprocessing

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: lbl82, lbl92, start, start0, stop
Transitions:
t₈: lbl82(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl82(X₀, X₅, X₂, X₃, X₄, 1+X₅, X₆, X₇) :|: X₁ ≤ 9 ∧ X₁ ≤ 8 ∧ X₇ ≤ 4 ∧ X₅ ≤ 1+X₁ ∧ 1+X₁ ≤ X₅ ∧ 3 ≤ X₇ ∧ X₀ ≤ X₇ ∧ 0 ≤ X₁ ∧ X₁+X₅ ≤ 19 ∧ X₀+X₅ ≤ 14 ∧ X₅+X₇ ≤ 14 ∧ X₀+X₁ ≤ 13 ∧ X₁+X₇ ≤ 13 ∧ X₅ ≤ 10 ∧ X₀+X₇ ≤ 8 ∧ X₅ ≤ 7+X₇ ∧ X₁ ≤ 6+X₇ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₇ ≤ 4+X₁ ∧ X₀ ≤ 3+X₅ ∧ X₇ ≤ 3+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₅ ∧ 3 ≤ X₁+X₇ ∧ 4 ≤ X₅+X₇
t₇: lbl82(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl92(X₀, X₁, X₂, X₇, X₄, X₅, X₆, 1+X₇) :|: X₅ ≤ 10 ∧ X₁ ≤ 9 ∧ X₇ ≤ 4 ∧ 3 ≤ X₇ ∧ 9 ≤ X₁ ∧ 10 ≤ X₅ ∧ X₀ ≤ X₇ ∧ X₁+X₅ ≤ 19 ∧ X₀+X₅ ≤ 14 ∧ X₅+X₇ ≤ 14 ∧ X₀+X₁ ≤ 13 ∧ X₁+X₇ ≤ 13 ∧ X₀+X₇ ≤ 8 ∧ X₅ ≤ 7+X₇ ∧ X₁ ≤ 6+X₇ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₇ ≤ 4+X₁ ∧ X₀ ≤ 3+X₅ ∧ X₇ ≤ 3+X₅ ∧ X₅ ≤ 1+X₁ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₅ ∧ 3 ≤ X₁+X₇ ∧ 4 ≤ X₅+X₇ ∧ 0 ≤ X₁
t₅: lbl92(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl82(X₀, 0, X₂, X₃, X₄, 1, X₆, X₇) :|: 5⋅X₃ ≤ 10+X₅ ∧ X₃ ≤ 3 ∧ X₇ ≤ 1+X₃ ∧ 1+X₃ ≤ X₇ ∧ 2 ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₅ ∧ X₅+X₇ ≤ 15 ∧ X₀+X₅ ≤ 14 ∧ X₃+X₅ ≤ 14 ∧ X₅ ≤ 10 ∧ X₀+X₇ ≤ 9 ∧ X₃+X₇ ≤ 9 ∧ X₀+X₃ ≤ 8 ∧ X₇ ≤ 5 ∧ X₀ ≤ 4 ∧ X₃ ≤ 4 ∧ X₇ ≤ 3+X₅ ∧ X₀ ≤ 2+X₅ ∧ X₃ ≤ 2+X₅ ∧ 1+X₀ ≤ X₇
t₄: lbl92(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl92(X₀, X₁, X₂, X₇, X₄, 0, X₆, 1+X₇) :|: 5⋅X₃ ≤ 10+X₅ ∧ X₇ ≤ 1+X₃ ∧ X₃ ≤ 1 ∧ 1+X₃ ≤ X₇ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₅ ∧ X₅+X₇ ≤ 15 ∧ X₀+X₅ ≤ 14 ∧ X₃+X₅ ≤ 14 ∧ X₅ ≤ 10 ∧ X₀+X₇ ≤ 9 ∧ X₃+X₇ ≤ 9 ∧ X₀+X₃ ≤ 8 ∧ X₇ ≤ 5 ∧ X₀ ≤ 4 ∧ X₃ ≤ 4 ∧ X₇ ≤ 3+X₅ ∧ X₀ ≤ 2+X₅ ∧ X₃ ≤ 2+X₅ ∧ 1+X₀ ≤ X₇
t₃: lbl92(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 5⋅X₃ ≤ 10+X₅ ∧ X₇ ≤ 1+X₃ ∧ 1+X₃ ≤ X₇ ∧ 4 ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₅ ∧ X₅+X₇ ≤ 15 ∧ X₀+X₅ ≤ 14 ∧ X₃+X₅ ≤ 14 ∧ X₅ ≤ 10 ∧ X₀+X₇ ≤ 9 ∧ X₃+X₇ ≤ 9 ∧ X₀+X₃ ≤ 8 ∧ X₇ ≤ 5 ∧ X₀ ≤ 4 ∧ X₃ ≤ 4 ∧ X₇ ≤ 3+X₅ ∧ X₀ ≤ 2+X₅ ∧ X₃ ≤ 2+X₅ ∧ 1+X₀ ≤ X₇
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl82(X₀, 0, X₂, X₃, X₄, 1, X₆, X₇) :|: X₀ ≤ 4 ∧ 3 ≤ X₀ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆
t₁: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl92(X₀, X₁, X₂, X₇, X₄, 0, X₆, 1+X₇) :|: X₀ ≤ 2 ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 5 ≤ X₀ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆
t₉: start0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → start(X₀, X₂, X₂, X₄, X₄, X₆, X₆, X₀)

MPRF for transition t₄: lbl92(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl92(X₀, X₁, X₂, X₇, X₄, 0, X₆, 1+X₇) :|: 5⋅X₃ ≤ 10+X₅ ∧ X₇ ≤ 1+X₃ ∧ X₃ ≤ 1 ∧ 1+X₃ ≤ X₇ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₅ ∧ X₅+X₇ ≤ 15 ∧ X₀+X₅ ≤ 14 ∧ X₃+X₅ ≤ 14 ∧ X₅ ≤ 10 ∧ X₀+X₇ ≤ 9 ∧ X₃+X₇ ≤ 9 ∧ X₀+X₃ ≤ 8 ∧ X₇ ≤ 5 ∧ X₀ ≤ 4 ∧ X₃ ≤ 4 ∧ X₇ ≤ 3+X₅ ∧ X₀ ≤ 2+X₅ ∧ X₃ ≤ 2+X₅ ∧ 1+X₀ ≤ X₇ of depth 1:

new bound:

X₀+16 {O(n)}

MPRF:

• lbl82: [5-X₇]
• lbl92: [6-X₇]

MPRF for transition t₅: lbl92(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl82(X₀, 0, X₂, X₃, X₄, 1, X₆, X₇) :|: 5⋅X₃ ≤ 10+X₅ ∧ X₃ ≤ 3 ∧ X₇ ≤ 1+X₃ ∧ 1+X₃ ≤ X₇ ∧ 2 ≤ X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₅ ∧ X₅+X₇ ≤ 15 ∧ X₀+X₅ ≤ 14 ∧ X₃+X₅ ≤ 14 ∧ X₅ ≤ 10 ∧ X₀+X₇ ≤ 9 ∧ X₃+X₇ ≤ 9 ∧ X₀+X₃ ≤ 8 ∧ X₇ ≤ 5 ∧ X₀ ≤ 4 ∧ X₃ ≤ 4 ∧ X₇ ≤ 3+X₅ ∧ X₀ ≤ 2+X₅ ∧ X₃ ≤ 2+X₅ ∧ 1+X₀ ≤ X₇ of depth 1:

new bound:

2⋅X₀+42 {O(n)}

MPRF:

• lbl82: [17-X₀-X₇]
• lbl92: [17-X₀-X₃]

MPRF for transition t₇: lbl82(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl92(X₀, X₁, X₂, X₇, X₄, X₅, X₆, 1+X₇) :|: X₅ ≤ 10 ∧ X₁ ≤ 9 ∧ X₇ ≤ 4 ∧ 3 ≤ X₇ ∧ 9 ≤ X₁ ∧ 10 ≤ X₅ ∧ X₀ ≤ X₇ ∧ X₁+X₅ ≤ 19 ∧ X₀+X₅ ≤ 14 ∧ X₅+X₇ ≤ 14 ∧ X₀+X₁ ≤ 13 ∧ X₁+X₇ ≤ 13 ∧ X₀+X₇ ≤ 8 ∧ X₅ ≤ 7+X₇ ∧ X₁ ≤ 6+X₇ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₇ ≤ 4+X₁ ∧ X₀ ≤ 3+X₅ ∧ X₇ ≤ 3+X₅ ∧ X₅ ≤ 1+X₁ ∧ 1 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₅ ∧ 3 ≤ X₁+X₇ ∧ 4 ≤ X₅+X₇ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₀+49 {O(n)}

MPRF:

• lbl82: [23-X₇]
• lbl92: [22-X₃]

MPRF for transition t₈: lbl82(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl82(X₀, X₅, X₂, X₃, X₄, 1+X₅, X₆, X₇) :|: X₁ ≤ 9 ∧ X₁ ≤ 8 ∧ X₇ ≤ 4 ∧ X₅ ≤ 1+X₁ ∧ 1+X₁ ≤ X₅ ∧ 3 ≤ X₇ ∧ X₀ ≤ X₇ ∧ 0 ≤ X₁ ∧ X₁+X₅ ≤ 19 ∧ X₀+X₅ ≤ 14 ∧ X₅+X₇ ≤ 14 ∧ X₀+X₁ ≤ 13 ∧ X₁+X₇ ≤ 13 ∧ X₅ ≤ 10 ∧ X₀+X₇ ≤ 8 ∧ X₅ ≤ 7+X₇ ∧ X₁ ≤ 6+X₇ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₇ ≤ 4+X₁ ∧ X₀ ≤ 3+X₅ ∧ X₇ ≤ 3+X₅ ∧ 1 ≤ X₁+X₅ ∧ 1 ≤ X₅ ∧ 3 ≤ X₁+X₇ ∧ 4 ≤ X₅+X₇ of depth 1:

new bound:

10⋅X₀+151 {O(n)}

MPRF:

• lbl82: [50-X₁-10⋅X₇]
• lbl92: [51-10⋅X₇]

All Bounds

Timebounds

Overall timebound:14⋅X₀+263 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: X₀+16 {O(n)}
t₅: 2⋅X₀+42 {O(n)}
t₇: X₀+49 {O(n)}
t₈: 10⋅X₀+151 {O(n)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: 14⋅X₀+263 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: X₀+16 {O(n)}
t₅: 2⋅X₀+42 {O(n)}
t₇: X₀+49 {O(n)}
t₈: 10⋅X₀+151 {O(n)}
t₉: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₂ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₄ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₆ {O(n)}
t₀, X₆: X₆ {O(n)}
t₀, X₇: X₀ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₂ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₀ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: 0 {O(1)}
t₁, X₆: X₆ {O(n)}
t₁, X₇: X₀+1 {O(n)}
t₂, X₀: 4 {O(1)}
t₂, X₁: 0 {O(1)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₄ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: 1 {O(1)}
t₂, X₆: X₆ {O(n)}
t₂, X₇: 4 {O(1)}
t₃, X₀: 2⋅X₀+4 {O(n)}
t₃, X₁: 9 {O(1)}
t₃, X₂: 3⋅X₂ {O(n)}
t₃, X₃: 4 {O(1)}
t₃, X₄: 3⋅X₄ {O(n)}
t₃, X₅: 10 {O(1)}
t₃, X₆: 3⋅X₆ {O(n)}
t₃, X₇: 5 {O(1)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: 2⋅X₀+16 {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: 0 {O(1)}
t₄, X₆: X₆ {O(n)}
t₄, X₇: 2⋅X₀+17 {O(n)}
t₅, X₀: 2⋅X₀+4 {O(n)}
t₅, X₁: 0 {O(1)}
t₅, X₂: 3⋅X₂ {O(n)}
t₅, X₃: 3 {O(1)}
t₅, X₄: 3⋅X₄ {O(n)}
t₅, X₅: 1 {O(1)}
t₅, X₆: 3⋅X₆ {O(n)}
t₅, X₇: 4 {O(1)}
t₇, X₀: 2⋅X₀+4 {O(n)}
t₇, X₁: 9 {O(1)}
t₇, X₂: 3⋅X₂ {O(n)}
t₇, X₃: 4 {O(1)}
t₇, X₄: 3⋅X₄ {O(n)}
t₇, X₅: 10 {O(1)}
t₇, X₆: 3⋅X₆ {O(n)}
t₇, X₇: 5 {O(1)}
t₈, X₀: 2⋅X₀+4 {O(n)}
t₈, X₁: 9 {O(1)}
t₈, X₂: 3⋅X₂ {O(n)}
t₈, X₃: X₄+3 {O(n)}
t₈, X₄: 3⋅X₄ {O(n)}
t₈, X₅: 10 {O(1)}
t₈, X₆: 3⋅X₆ {O(n)}
t₈, X₇: 4 {O(1)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₂ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₄ {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: X₆ {O(n)}
t₉, X₆: X₆ {O(n)}
t₉, X₇: X₀ {O(n)}