KoAT2 Proof Output

Initial Problem

Preprocessing

Cut unsatisfiable transition [t₆: lbl111→lbl121]

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location lbl121

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

Found invariant X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₀ for location lbl6

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

Found invariant 2+X₄ ≤ X₃ ∧ 3+X₄ ≤ X₂ ∧ 3+X₄ ≤ X₁ ∧ 2+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 5 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 3 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location lbl111

Found invariant X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 2+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location cut

Problem after Preprocessing

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: cut, lbl111, lbl121, lbl6, start, start0, stop
Transitions:
t₁₀: cut(X₀, X₁, X₂, X₃, X₄, X₅) → stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₄ ∧ X₄ ≤ 0 ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₄ ∧ 2+X₄ ≤ X₁ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₄ ∧ 2+X₄ ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₂
t₄: lbl111(X₀, X₁, X₂, X₃, X₄, X₅) → cut(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₀ ≤ X₂ ∧ 2 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₄ ∧ X₄ ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 2 ≤ X₀+X₄ ∧ 2+X₄ ≤ X₀ ∧ 2 ≤ X₃ ∧ 2 ≤ X₃+X₄ ∧ 2+X₄ ≤ X₃ ∧ 3 ≤ X₁ ∧ 3 ≤ X₁+X₄ ∧ 3+X₄ ≤ X₁ ∧ 3 ≤ X₂ ∧ 3 ≤ X₂+X₄ ∧ 3+X₄ ≤ X₂ ∧ 4 ≤ X₀+X₃ ∧ 5 ≤ X₀+X₁ ∧ 5 ≤ X₀+X₂ ∧ 5 ≤ X₁+X₃ ∧ 5 ≤ X₂+X₃ ∧ 6 ≤ X₁+X₂
t₅: lbl111(X₀, X₁, X₂, X₃, X₄, X₅) → lbl111(X₀, X₁, X₂, X₃, X₄-1, X₅) :|: 1+X₄ ≤ X₀ ∧ 1+X₀+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2+X₄ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₃ ∧ 2 ≤ X₃+X₄ ∧ 2+X₄ ≤ X₃ ∧ 3 ≤ X₁ ∧ 3 ≤ X₁+X₄ ∧ 3+X₄ ≤ X₁ ∧ 3 ≤ X₂ ∧ 3 ≤ X₂+X₄ ∧ 3+X₄ ≤ X₂ ∧ 4 ≤ X₀+X₃ ∧ 5 ≤ X₀+X₁ ∧ 5 ≤ X₀+X₂ ∧ 5 ≤ X₁+X₃ ∧ 5 ≤ X₂+X₃ ∧ 6 ≤ X₁+X₂
t₇: lbl121(X₀, X₁, X₂, X₃, X₄, X₅) → cut(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₄ ∧ X₄ ≤ 0 ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₂
t₈: lbl121(X₀, X₁, X₂, X₃, X₄, X₅) → lbl111(X₀, X₁, X₂, X₃, X₄-1, X₅) :|: 1 ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀+X₄ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₂
t₉: lbl121(X₀, X₁, X₂, X₃, X₄, X₅) → lbl121(X₀, X₁, X₂, X₃, X₄-X₃, X₅) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀+X₄ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₂
t₃: lbl6(X₀, X₁, X₂, X₃, X₄, X₅) → stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₃
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅) → lbl121(X₀, X₁, X₂, X₃, X₁-X₃, X₅) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₁: start(X₀, X₁, X₂, X₃, X₄, X₅) → lbl6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₀ ∧ X₂ ≤ 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
t₁₁: start0(X₀, X₁, X₂, X₃, X₄, X₅) → start(X₀, X₂, X₂, X₀, X₅, X₅)

MPRF for transition t₉: lbl121(X₀, X₁, X₂, X₃, X₄, X₅) → lbl121(X₀, X₁, X₂, X₃, X₄-X₃, X₅) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀+X₄ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 1+X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₂ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• lbl121: [1+X₄]

MPRF for transition t₅: lbl111(X₀, X₁, X₂, X₃, X₄, X₅) → lbl111(X₀, X₁, X₂, X₃, X₄-1, X₅) :|: 1+X₄ ≤ X₀ ∧ 1+X₀+X₄ ≤ X₂ ∧ 1 ≤ X₄ ∧ 2+X₄ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₃ ∧ 2 ≤ X₃+X₄ ∧ 2+X₄ ≤ X₃ ∧ 3 ≤ X₁ ∧ 3 ≤ X₁+X₄ ∧ 3+X₄ ≤ X₁ ∧ 3 ≤ X₂ ∧ 3 ≤ X₂+X₄ ∧ 3+X₄ ≤ X₂ ∧ 4 ≤ X₀+X₃ ∧ 5 ≤ X₀+X₁ ∧ 5 ≤ X₀+X₂ ∧ 5 ≤ X₁+X₃ ∧ 5 ≤ X₂+X₃ ∧ 6 ≤ X₁+X₂ of depth 1:

new bound:

2⋅X₂+1 {O(n)}

MPRF:

• lbl111: [1+X₄]

All Bounds

Timebounds

Overall timebound:3⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅X₂+1 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₂+1 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: 3⋅X₂+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 2⋅X₂+1 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₂+1 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: 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: X₂ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₀ {O(n)}
t₁, X₄: X₅ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₂ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₀ {O(n)}
t₂, X₄: X₂ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₂ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₀ {O(n)}
t₃, X₄: X₅ {O(n)}
t₃, X₅: X₅ {O(n)}
t₄, X₀: 4⋅X₀ {O(n)}
t₄, X₁: 4⋅X₂ {O(n)}
t₄, X₂: 4⋅X₂ {O(n)}
t₄, X₃: 4⋅X₀ {O(n)}
t₄, X₄: 0 {O(1)}
t₄, X₅: 4⋅X₅ {O(n)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 2⋅X₂ {O(n)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₀ {O(n)}
t₅, X₄: 2⋅X₂ {O(n)}
t₅, X₅: 2⋅X₅ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₂ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₀ {O(n)}
t₇, X₄: 0 {O(1)}
t₇, X₅: X₅ {O(n)}
t₈, X₀: 2⋅X₀ {O(n)}
t₈, X₁: 2⋅X₂ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}
t₈, X₃: 2⋅X₀ {O(n)}
t₈, X₄: 2⋅X₂ {O(n)}
t₈, X₅: 2⋅X₅ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₂ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₀ {O(n)}
t₉, X₄: X₂ {O(n)}
t₉, X₅: X₅ {O(n)}
t₁₀, X₀: 5⋅X₀ {O(n)}
t₁₀, X₁: 5⋅X₂ {O(n)}
t₁₀, X₂: 5⋅X₂ {O(n)}
t₁₀, X₃: 5⋅X₀ {O(n)}
t₁₀, X₄: 0 {O(1)}
t₁₀, X₅: 5⋅X₅ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₂ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₀ {O(n)}
t₁₁, X₄: X₅ {O(n)}
t₁₁, X₅: X₅ {O(n)}