KoAT2 Proof Output

Initial Problem

Start: start0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: cut, lbl51, start, start0, stop
Transitions:
t₅: cut(X₀, X₁, X₂, X₃) → lbl51(E, X₁, X₀, X₃) :|: X₀ ≤ 9 ∧ X₀ ≤ 2+X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂
t₃: lbl51(X₀, X₁, X₂, X₃) → cut(X₀, X₁, X₂, X₃) :|: X₀ ≤ 9 ∧ X₂ ≤ 9 ∧ X₀ ≤ 2+X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂
t₁: lbl51(X₀, X₁, X₂, X₃) → stop(X₀, X₁, X₂, X₃) :|: X₂ ≤ 9 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₂
t₂: lbl51(X₀, X₁, X₂, X₃) → stop(X₀, X₁, X₂, X₃) :|: X₂ ≤ 9 ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ X₂
t₄: lbl51(X₀, X₁, X₂, X₃) → stop(X₀, X₁, X₂, X₃) :|: X₂ ≤ 9 ∧ X₀ ≤ 2+X₂ ∧ 1+X₂ ≤ X₀ ∧ 10 ≤ X₀ ∧ 0 ≤ X₂
t₀: start(X₀, X₁, X₂, X₃) → lbl51(E, X₁, 0, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₆: start0(X₀, X₁, X₂, X₃) → start(X₁, X₁, X₃, X₃)

Preprocessing

Found invariant X₂ ≤ 9 ∧ 0 ≤ X₂ for location stop

Found invariant X₂ ≤ 9 ∧ 0 ≤ X₂ for location lbl51

Found invariant X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location start

Found invariant X₂ ≤ 8 ∧ 1+X₂ ≤ X₀ ∧ X₀+X₂ ≤ 17 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 2+X₂ ∧ X₀ ≤ 9 ∧ 1 ≤ X₀ for location cut

Problem after Preprocessing

Start: start0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: cut, lbl51, start, start0, stop
Transitions:
t₅: cut(X₀, X₁, X₂, X₃) → lbl51(E, X₁, X₀, X₃) :|: X₀ ≤ 9 ∧ X₀ ≤ 2+X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₀+X₂ ≤ 17 ∧ X₂ ≤ 8 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂
t₃: lbl51(X₀, X₁, X₂, X₃) → cut(X₀, X₁, X₂, X₃) :|: X₀ ≤ 9 ∧ X₂ ≤ 9 ∧ X₀ ≤ 2+X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂
t₁: lbl51(X₀, X₁, X₂, X₃) → stop(X₀, X₁, X₂, X₃) :|: X₂ ≤ 9 ∧ X₀ ≤ X₂ ∧ 0 ≤ X₂
t₂: lbl51(X₀, X₁, X₂, X₃) → stop(X₀, X₁, X₂, X₃) :|: X₂ ≤ 9 ∧ 3+X₂ ≤ X₀ ∧ 0 ≤ X₂
t₄: lbl51(X₀, X₁, X₂, X₃) → stop(X₀, X₁, X₂, X₃) :|: X₂ ≤ 9 ∧ X₀ ≤ 2+X₂ ∧ 1+X₂ ≤ X₀ ∧ 10 ≤ X₀ ∧ 0 ≤ X₂
t₀: start(X₀, X₁, X₂, X₃) → lbl51(E, X₁, 0, X₃) :|: X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃
t₆: start0(X₀, X₁, X₂, X₃) → start(X₁, X₁, X₃, X₃)

MPRF for transition t₃: lbl51(X₀, X₁, X₂, X₃) → cut(X₀, X₁, X₂, X₃) :|: X₀ ≤ 9 ∧ X₂ ≤ 9 ∧ X₀ ≤ 2+X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ of depth 1:

new bound:

10 {O(1)}

MPRF:

• cut: [9-X₂]
• lbl51: [10-X₂]

MPRF for transition t₅: cut(X₀, X₁, X₂, X₃) → lbl51(E, X₁, X₀, X₃) :|: X₀ ≤ 9 ∧ X₀ ≤ 2+X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₀+X₂ ≤ 17 ∧ X₂ ≤ 8 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ of depth 1:

new bound:

9 {O(1)}

MPRF:

• cut: [9-X₂]
• lbl51: [9-X₂]

All Bounds

Timebounds

Overall timebound:24 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 10 {O(1)}
t₄: 1 {O(1)}
t₅: 9 {O(1)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 24 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 10 {O(1)}
t₄: 1 {O(1)}
t₅: 9 {O(1)}
t₆: 1 {O(1)}

Sizebounds

t₀, X₁: X₁ {O(n)}
t₀, X₂: 0 {O(1)}
t₀, X₃: X₃ {O(n)}
t₁, X₁: 2⋅X₁ {O(n)}
t₁, X₂: 9 {O(1)}
t₁, X₃: 2⋅X₃ {O(n)}
t₂, X₁: 2⋅X₁ {O(n)}
t₂, X₂: 9 {O(1)}
t₂, X₃: 2⋅X₃ {O(n)}
t₃, X₀: 9 {O(1)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: 8 {O(1)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: 11 {O(1)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: 9 {O(1)}
t₄, X₃: X₃ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: 9 {O(1)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₁ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₃ {O(n)}
t₆, X₃: X₃ {O(n)}