KoAT2 Proof Output

Initial Problem

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: lbl72, start, start0, stop
Transitions:
t₅: lbl72(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, X₁-1, X₂, 1+X₅, X₄, X₃, X₅, X₇) :|: X₀+X₂+X₄ ≤ 101+X₁+X₅ ∧ X₀ ≤ 100 ∧ X₅ ≤ 100 ∧ X₀+X₂+X₄ ≤ 1+X₁+X₅+X₆ ∧ X₅ ≤ 1+X₁ ∧ 1+X₁+X₅+X₆ ≤ X₀+X₂+X₄ ∧ 1+X₁ ≤ X₂ ∧ X₁+X₃+X₅ ≤ X₀+X₂+X₄ ∧ X₀+X₂+X₄ ≤ 2⋅X₁+X₅ ∧ X₀+X₂+X₄ ≤ X₁+X₃+X₅ ∧ X₄ ≤ X₂
t₃: lbl72(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀+X₂+X₄ ≤ 101+X₁+X₅ ∧ X₀ ≤ 100 ∧ X₀+X₂+X₄ ≤ 1+X₁+X₅+X₆ ∧ X₅ ≤ 1+X₁ ∧ 1+X₁+X₅+X₆ ≤ X₀+X₂+X₄ ∧ 1+X₁ ≤ X₂ ∧ 101 ≤ X₅ ∧ X₁+X₃+X₅ ≤ X₀+X₂+X₄ ∧ X₀+X₂+X₄ ≤ X₁+X₃+X₅ ∧ X₄ ≤ X₂
t₄: lbl72(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀+X₂+X₄ ≤ 101+X₁+X₅ ∧ X₀ ≤ 100 ∧ X₀+X₂+X₄ ≤ 1+X₁+X₅+X₆ ∧ X₅ ≤ 1+X₁ ∧ 1+X₁+X₅+X₆ ≤ X₀+X₂+X₄ ∧ 1+2⋅X₁+X₅ ≤ X₀+X₂+X₄ ∧ 1+X₁ ≤ X₂ ∧ X₁+X₃+X₅ ≤ X₀+X₂+X₄ ∧ X₀+X₂+X₄ ≤ X₁+X₃+X₅ ∧ X₄ ≤ X₂
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, X₁-1, X₂, 1+X₅, X₄, X₃, X₅, X₇) :|: X₀ ≤ 100 ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 101 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₂ ≤ X₄ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₆: start0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → start(X₀, X₂, X₂, X₄, X₄, X₀, X₇, X₇)

Preprocessing

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

Found invariant X₁ ≤ X₂ for location stop

Found invariant X₆ ≤ 100 ∧ 1+X₆ ≤ X₃ ∧ X₃+X₆ ≤ 201 ∧ X₀+X₆ ≤ 200 ∧ X₃ ≤ 1+X₆ ∧ X₄ ≤ X₂ ∧ X₃ ≤ 101 ∧ X₀+X₃ ≤ 201 ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ 100 for location lbl72

Problem after Preprocessing

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: lbl72, start, start0, stop
Transitions:
t₅: lbl72(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, X₁-1, X₂, 1+X₅, X₄, X₃, X₅, X₇) :|: X₀+X₂+X₄ ≤ 101+X₁+X₅ ∧ X₀ ≤ 100 ∧ X₅ ≤ 100 ∧ X₀+X₂+X₄ ≤ 1+X₁+X₅+X₆ ∧ X₅ ≤ 1+X₁ ∧ 1+X₁+X₅+X₆ ≤ X₀+X₂+X₄ ∧ 1+X₁ ≤ X₂ ∧ X₁+X₃+X₅ ≤ X₀+X₂+X₄ ∧ X₀+X₂+X₄ ≤ 2⋅X₁+X₅ ∧ X₀+X₂+X₄ ≤ X₁+X₃+X₅ ∧ X₄ ≤ X₂ ∧ X₀+X₃ ≤ 201 ∧ X₃+X₆ ≤ 201 ∧ X₀+X₆ ≤ 200 ∧ X₃ ≤ 101 ∧ X₆ ≤ 100 ∧ X₃ ≤ 1+X₆ ∧ 1+X₆ ≤ X₃
t₃: lbl72(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀+X₂+X₄ ≤ 101+X₁+X₅ ∧ X₀ ≤ 100 ∧ X₀+X₂+X₄ ≤ 1+X₁+X₅+X₆ ∧ X₅ ≤ 1+X₁ ∧ 1+X₁+X₅+X₆ ≤ X₀+X₂+X₄ ∧ 1+X₁ ≤ X₂ ∧ 101 ≤ X₅ ∧ X₁+X₃+X₅ ≤ X₀+X₂+X₄ ∧ X₀+X₂+X₄ ≤ X₁+X₃+X₅ ∧ X₄ ≤ X₂ ∧ X₀+X₃ ≤ 201 ∧ X₃+X₆ ≤ 201 ∧ X₀+X₆ ≤ 200 ∧ X₃ ≤ 101 ∧ X₆ ≤ 100 ∧ X₃ ≤ 1+X₆ ∧ 1+X₆ ≤ X₃
t₄: lbl72(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀+X₂+X₄ ≤ 101+X₁+X₅ ∧ X₀ ≤ 100 ∧ X₀+X₂+X₄ ≤ 1+X₁+X₅+X₆ ∧ X₅ ≤ 1+X₁ ∧ 1+X₁+X₅+X₆ ≤ X₀+X₂+X₄ ∧ 1+2⋅X₁+X₅ ≤ X₀+X₂+X₄ ∧ 1+X₁ ≤ X₂ ∧ X₁+X₃+X₅ ≤ X₀+X₂+X₄ ∧ X₀+X₂+X₄ ≤ X₁+X₃+X₅ ∧ X₄ ≤ X₂ ∧ X₀+X₃ ≤ 201 ∧ X₃+X₆ ≤ 201 ∧ X₀+X₆ ≤ 200 ∧ X₃ ≤ 101 ∧ X₆ ≤ 100 ∧ X₃ ≤ 1+X₆ ∧ 1+X₆ ≤ X₃
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, X₁-1, X₂, 1+X₅, X₄, X₃, X₅, X₇) :|: X₀ ≤ 100 ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 101 ≤ X₀ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₂ ≤ X₄ ∧ X₅ ≤ X₀ ∧ X₀ ≤ X₅ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₆: start0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → start(X₀, X₂, X₂, X₄, X₄, X₀, X₇, X₇)

MPRF for transition t₅: lbl72(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, X₁-1, X₂, 1+X₅, X₄, X₃, X₅, X₇) :|: X₀+X₂+X₄ ≤ 101+X₁+X₅ ∧ X₀ ≤ 100 ∧ X₅ ≤ 100 ∧ X₀+X₂+X₄ ≤ 1+X₁+X₅+X₆ ∧ X₅ ≤ 1+X₁ ∧ 1+X₁+X₅+X₆ ≤ X₀+X₂+X₄ ∧ 1+X₁ ≤ X₂ ∧ X₁+X₃+X₅ ≤ X₀+X₂+X₄ ∧ X₀+X₂+X₄ ≤ 2⋅X₁+X₅ ∧ X₀+X₂+X₄ ≤ X₁+X₃+X₅ ∧ X₄ ≤ X₂ ∧ X₀+X₃ ≤ 201 ∧ X₃+X₆ ≤ 201 ∧ X₀+X₆ ≤ 200 ∧ X₃ ≤ 101 ∧ X₆ ≤ 100 ∧ X₃ ≤ 1+X₆ ∧ 1+X₆ ≤ X₃ of depth 1:

new bound:

X₀+X₄+203 {O(n)}

MPRF:

• lbl72: [202-X₃-X₅]

All Bounds

Timebounds

Overall timebound:X₀+X₄+209 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₀+X₄+203 {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: X₀+X₄+209 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₀+X₄+203 {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: X₀ {O(n)}
t₀, X₆: X₇ {O(n)}
t₀, X₇: X₇ {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: X₀ {O(n)}
t₁, X₆: X₇ {O(n)}
t₁, X₇: X₇ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₂+1 {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₀+1 {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₄ {O(n)}
t₂, X₆: X₀ {O(n)}
t₂, X₇: X₇ {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2⋅X₂+X₀+X₄+205 {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₄+3⋅X₀+205 {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₀+3⋅X₄+204 {O(n)}
t₃, X₆: 2⋅X₀+2⋅X₄+4 {O(n)}
t₃, X₇: 2⋅X₇ {O(n)}
t₄, X₀: 2⋅X₀ {O(n)}
t₄, X₁: 2⋅X₂+X₀+X₄+205 {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₄+3⋅X₀+205 {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₀+3⋅X₄+204 {O(n)}
t₄, X₆: 2⋅X₀+2⋅X₄+4 {O(n)}
t₄, X₇: 2⋅X₇ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₀+X₂+X₄+204 {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: 2⋅X₀+2⋅X₄+204 {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: 2⋅X₀+2⋅X₄+204 {O(n)}
t₅, X₆: 2⋅X₄+X₀+4 {O(n)}
t₅, X₇: X₇ {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: X₀ {O(n)}
t₆, X₆: X₇ {O(n)}
t₆, X₇: X₇ {O(n)}