KoAT2 Proof Output

Initial Problem

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: lbl71, start, start0, stop
Transitions:
t₅: lbl71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl71(X₀, X₇, X₂, X₃-1, X₄, 1+X₇, X₆, X₅) :|: X₀+X₄+X₆ ≤ 101+X₁+X₃ ∧ X₀ ≤ 100 ∧ X₁ ≤ 100 ∧ X₀+X₄+X₆ ≤ 2+X₁+2⋅X₃ ∧ X₀+X₄+X₆ ≤ 1+X₁+X₃+X₇ ∧ X₅ ≤ 1+X₁ ∧ 1+X₁+X₃+X₇ ≤ X₀+X₄+X₆ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₆ ≤ X₄
t₃: lbl71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 100 ∧ X₁ ≤ 100 ∧ X₀+X₄+X₆ ≤ 2+X₁+2⋅X₃ ∧ X₀+X₄+X₆ ≤ 1+X₁+X₃+X₇ ∧ X₅ ≤ 1+X₁ ∧ 1+X₁+X₃+X₇ ≤ X₀+X₄+X₆ ∧ 1+X₁ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ 102+X₁+X₃ ≤ X₀+X₄+X₆ ∧ X₆ ≤ X₄
t₄: lbl71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 100 ∧ X₁ ≤ 100 ∧ X₀+X₄+X₆ ≤ 2+X₁+2⋅X₃ ∧ X₀+X₄+X₆ ≤ 1+X₁+X₃+X₇ ∧ X₅ ≤ 1+X₁ ∧ 1+X₁+X₃+X₇ ≤ X₀+X₄+X₆ ∧ 1+X₁ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₆ ≤ X₄
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl71(X₀, X₇, X₂, X₃-1, X₄, 1+X₇, X₆, X₅) :|: X₀ ≤ 100 ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 101 ≤ 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) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₄ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆
t₆: start0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → start(X₀, X₂, X₂, X₄, X₄, X₆, X₆, X₀)

Preprocessing

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

Found invariant X₇ ≤ X₄ ∧ X₇ ≤ 1+X₃ ∧ X₆ ≤ X₄ ∧ X₅ ≤ 1+X₁ ∧ 1+X₁ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₀ ≤ 100 for location lbl71

Found invariant X₃ ≤ X₄ for location stop

Problem after Preprocessing

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: lbl71, start, start0, stop
Transitions:
t₅: lbl71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl71(X₀, X₇, X₂, X₃-1, X₄, 1+X₇, X₆, X₅) :|: X₀+X₄+X₆ ≤ 101+X₁+X₃ ∧ X₀ ≤ 100 ∧ X₁ ≤ 100 ∧ X₀+X₄+X₆ ≤ 2+X₁+2⋅X₃ ∧ X₀+X₄+X₆ ≤ 1+X₁+X₃+X₇ ∧ X₅ ≤ 1+X₁ ∧ 1+X₁+X₃+X₇ ≤ X₀+X₄+X₆ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₆ ≤ X₄ ∧ X₇ ≤ 1+X₃ ∧ X₇ ≤ X₄
t₃: lbl71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 100 ∧ X₁ ≤ 100 ∧ X₀+X₄+X₆ ≤ 2+X₁+2⋅X₃ ∧ X₀+X₄+X₆ ≤ 1+X₁+X₃+X₇ ∧ X₅ ≤ 1+X₁ ∧ 1+X₁+X₃+X₇ ≤ X₀+X₄+X₆ ∧ 1+X₁ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ 102+X₁+X₃ ≤ X₀+X₄+X₆ ∧ X₆ ≤ X₄ ∧ X₇ ≤ 1+X₃ ∧ X₇ ≤ X₄
t₄: lbl71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 100 ∧ X₁ ≤ 100 ∧ X₀+X₄+X₆ ≤ 2+X₁+2⋅X₃ ∧ X₀+X₄+X₆ ≤ 1+X₁+X₃+X₇ ∧ X₅ ≤ 1+X₁ ∧ 1+X₁+X₃+X₇ ≤ X₀+X₄+X₆ ∧ 1+X₁ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₆ ≤ X₄ ∧ X₇ ≤ 1+X₃ ∧ X₇ ≤ X₄
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl71(X₀, X₇, X₂, X₃-1, X₄, 1+X₇, X₆, X₅) :|: X₀ ≤ 100 ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 101 ≤ 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) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₄ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₀ ≤ X₇ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₆ ≤ X₅ ∧ X₅ ≤ X₆
t₆: start0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → start(X₀, X₂, X₂, X₄, X₄, X₆, X₆, X₀)

MPRF for transition t₅: lbl71(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl71(X₀, X₇, X₂, X₃-1, X₄, 1+X₇, X₆, X₅) :|: X₀+X₄+X₆ ≤ 101+X₁+X₃ ∧ X₀ ≤ 100 ∧ X₁ ≤ 100 ∧ X₀+X₄+X₆ ≤ 2+X₁+2⋅X₃ ∧ X₀+X₄+X₆ ≤ 1+X₁+X₃+X₇ ∧ X₅ ≤ 1+X₁ ∧ 1+X₁+X₃+X₇ ≤ X₀+X₄+X₆ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₅ ∧ 1+X₃ ≤ X₄ ∧ X₆ ≤ X₄ ∧ X₇ ≤ 1+X₃ ∧ X₇ ≤ X₄ of depth 1:

new bound:

2⋅X₄+X₀+X₆+3 {O(n)}

MPRF:

• lbl71: [1+2⋅X₃-X₁-X₇]

All Bounds

Timebounds

Overall timebound:2⋅X₄+X₀+X₆+9 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅X₄+X₀+X₆+3 {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₄+X₀+X₆+9 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅X₄+X₀+X₆+3 {O(n)}
t₆: 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: X₄ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₆ {O(n)}
t₁, X₆: X₆ {O(n)}
t₁, X₇: X₀ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₀ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₄+1 {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₀+1 {O(n)}
t₂, X₆: X₆ {O(n)}
t₂, X₇: X₆ {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2⋅X₀+2⋅X₆+4 {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 4⋅X₄+X₀+X₆+5 {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₄+2⋅X₆+3⋅X₀+5 {O(n)}
t₃, X₆: 2⋅X₆ {O(n)}
t₃, X₇: 2⋅X₀+2⋅X₄+3⋅X₆+4 {O(n)}
t₄, X₀: 2⋅X₀ {O(n)}
t₄, X₁: 2⋅X₀+2⋅X₆+4 {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 4⋅X₄+X₀+X₆+5 {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₄+2⋅X₆+3⋅X₀+5 {O(n)}
t₄, X₆: 2⋅X₆ {O(n)}
t₄, X₇: 2⋅X₀+2⋅X₄+3⋅X₆+4 {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: 2⋅X₆+X₀+4 {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: 3⋅X₄+X₀+X₆+4 {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: 2⋅X₀+2⋅X₄+2⋅X₆+4 {O(n)}
t₅, X₆: X₆ {O(n)}
t₅, X₇: 2⋅X₀+2⋅X₄+2⋅X₆+4 {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₂ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₄ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₆ {O(n)}
t₆, X₆: X₆ {O(n)}
t₆, X₇: X₀ {O(n)}