KoAT2 Proof Output

Initial Problem

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: lbl101, start, start0, stop
Transitions:
t₄: lbl101(X₀, X₁, X₂, X₃, X₄, X₅) → lbl101(X₀, 1+X₁, X₂, X₃, 1+X₄, X₅) :|: X₁ ≤ 1+X₀ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 2 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₅: lbl101(X₀, X₁, X₂, X₃, X₄, X₅) → lbl101(X₀, 1+X₁, X₂, X₃, X₄-1, X₅) :|: X₁ ≤ 1+X₀ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 2 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₃: lbl101(X₀, X₁, X₂, X₃, X₄, X₅) → stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₀+X₄ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₃
t₁: start(X₀, X₁, X₂, X₃, X₄, X₅) → lbl101(X₀, 2, X₂, X₃, 1, X₅) :|: 1 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅) → lbl101(X₀, 2, X₂, X₃, -1, X₅) :|: 1 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅) → stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₆: start0(X₀, X₁, X₂, X₃, X₄, X₅) → start(X₀, X₂, X₂, X₀, X₅, X₅)

Preprocessing

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

Found invariant X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₁+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1+X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location lbl101

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location stop

Problem after Preprocessing

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: lbl101, start, start0, stop
Transitions:
t₄: lbl101(X₀, X₁, X₂, X₃, X₄, X₅) → lbl101(X₀, 1+X₁, X₂, X₃, 1+X₄, X₅) :|: X₁ ≤ 1+X₀ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 2 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₄ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃
t₅: lbl101(X₀, X₁, X₂, X₃, X₄, X₅) → lbl101(X₀, 1+X₁, X₂, X₃, X₄-1, X₅) :|: X₁ ≤ 1+X₀ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 2 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₄ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃
t₃: lbl101(X₀, X₁, X₂, X₃, X₄, X₅) → stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₀+X₄ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃
t₁: start(X₀, X₁, X₂, X₃, X₄, X₅) → lbl101(X₀, 2, X₂, X₃, 1, X₅) :|: 1 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅) → lbl101(X₀, 2, X₂, X₃, -1, X₅) :|: 1 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅) → stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₆: start0(X₀, X₁, X₂, X₃, X₄, X₅) → start(X₀, X₂, X₂, X₀, X₅, X₅)

MPRF for transition t₄: lbl101(X₀, X₁, X₂, X₃, X₄, X₅) → lbl101(X₀, 1+X₁, X₂, X₃, 1+X₄, X₅) :|: X₁ ≤ 1+X₀ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 2 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₄ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ of depth 1:

new bound:

4⋅X₀+10 {O(n)}

MPRF:

• lbl101: [2+2⋅X₃-X₁-X₄]

MPRF for transition t₅: lbl101(X₀, X₁, X₂, X₃, X₄, X₅) → lbl101(X₀, 1+X₁, X₂, X₃, X₄-1, X₅) :|: X₁ ≤ 1+X₀ ∧ 1 ≤ X₁+X₄ ∧ 1+X₄ ≤ X₁ ∧ 2 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₁ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₄ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ of depth 1:

new bound:

4⋅X₀+8 {O(n)}

MPRF:

• lbl101: [1+2⋅X₀+X₄-X₁]

All Bounds

Timebounds

Overall timebound:8⋅X₀+23 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 4⋅X₀+10 {O(n)}
t₅: 4⋅X₀+8 {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 8⋅X₀+23 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 4⋅X₀+10 {O(n)}
t₅: 4⋅X₀+8 {O(n)}
t₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₂ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₀ {O(n)}
t₀, X₄: X₅ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 2 {O(1)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₀ {O(n)}
t₁, X₄: 1 {O(1)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: 2 {O(1)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₀ {O(n)}
t₂, X₄: 1 {O(1)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 6⋅X₀ {O(n)}
t₃, X₁: 16⋅X₀+48 {O(n)}
t₃, X₂: 6⋅X₂ {O(n)}
t₃, X₃: 6⋅X₀ {O(n)}
t₃, X₄: 16⋅X₀+42 {O(n)}
t₃, X₅: 6⋅X₅ {O(n)}
t₄, X₀: 2⋅X₀ {O(n)}
t₄, X₁: 8⋅X₀+22 {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₀ {O(n)}
t₄, X₄: 8⋅X₀+20 {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 8⋅X₀+22 {O(n)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₀ {O(n)}
t₅, X₄: 8⋅X₀+20 {O(n)}
t₅, X₅: 2⋅X₅ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₂ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₀ {O(n)}
t₆, X₄: X₅ {O(n)}
t₆, X₅: X₅ {O(n)}