KoAT2 Proof Output

Initial Problem

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: lbl111, lbl91, start, start0, stop
Transitions:
t₉: lbl111(X₀, X₁, X₂, X₃, X₄, X₅) → lbl111(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 41 ∧ X₄ ≤ 39 ∧ 1+X₁ ≤ 0 ∧ 2 ≤ X₄ ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₁₀: lbl111(X₀, X₁, X₂, X₃, X₄, X₅) → lbl111(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 41 ∧ X₄ ≤ 39 ∧ 1 ≤ X₁ ∧ 2 ≤ X₄ ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₈: lbl111(X₀, X₁, X₂, X₃, X₄, X₅) → lbl91(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 41 ∧ X₄ ≤ 39 ∧ 2 ≤ X₄ ∧ 100 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₇: lbl111(X₀, X₁, X₂, X₃, X₄, X₅) → stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 41 ∧ 2 ≤ X₄ ∧ 40 ≤ X₄ ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₅: lbl91(X₀, X₁, X₂, X₃, X₄, X₅) → lbl111(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 40 ∧ X₄ ≤ 39 ∧ 1 ≤ 0 ∧ 1 ≤ X₄ ∧ 100 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₆: lbl91(X₀, X₁, X₂, X₃, X₄, X₅) → lbl111(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 40 ∧ X₄ ≤ 39 ∧ 1 ≤ 0 ∧ 1 ≤ X₄ ∧ 100 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₄: lbl91(X₀, X₁, X₂, X₃, X₄, X₅) → lbl91(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 40 ∧ X₄ ≤ 39 ∧ 1 ≤ X₄ ∧ 100 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₃: lbl91(X₀, X₁, X₂, X₃, X₄, X₅) → stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 40 ∧ 40 ≤ X₄ ∧ 100 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₁: start(X₀, X₁, X₂, X₃, X₄, X₅) → lbl111(X₀, X₁, 100, X₃, 2, X₅) :|: 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅) → lbl111(X₀, X₁, 100, X₃, 2, X₅) :|: 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅) → lbl91(X₀, X₁, 100, X₃, 1, X₅) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₁₁: start0(X₀, X₁, X₂, X₃, X₄, X₅) → start(X₁, X₁, X₃, X₃, X₅, X₅)

Preprocessing

Cut unsatisfiable transition [t₅: lbl91→lbl111; t₆: lbl91→lbl111; t₈: lbl111→lbl91]

Found invariant X₄ ≤ 41 ∧ 59+X₄ ≤ X₂ ∧ X₂+X₄ ≤ 141 ∧ 40 ≤ X₄ ∧ 140 ≤ X₂+X₄ ∧ X₂ ≤ 60+X₄ ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location stop

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

Found invariant X₄ ≤ 41 ∧ 59+X₄ ≤ X₂ ∧ X₂+X₄ ≤ 141 ∧ 2 ≤ X₄ ∧ 102 ≤ X₂+X₄ ∧ X₂ ≤ 98+X₄ ∧ X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location lbl111

Found invariant X₄ ≤ 40 ∧ 60+X₄ ≤ X₂ ∧ X₂+X₄ ≤ 140 ∧ X₄ ≤ 40+X₁ ∧ X₁+X₄ ≤ 40 ∧ X₄ ≤ 40+X₀ ∧ X₀+X₄ ≤ 40 ∧ 1 ≤ X₄ ∧ 101 ≤ X₂+X₄ ∧ X₂ ≤ 99+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₂ ≤ 100 ∧ X₂ ≤ 100+X₁ ∧ X₁+X₂ ≤ 100 ∧ X₂ ≤ 100+X₀ ∧ X₀+X₂ ≤ 100 ∧ 100 ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ 100+X₁ ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ 100+X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ for location lbl91

Problem after Preprocessing

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: lbl111, lbl91, start, start0, stop
Transitions:
t₉: lbl111(X₀, X₁, X₂, X₃, X₄, X₅) → lbl111(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 41 ∧ X₄ ≤ 39 ∧ 1+X₁ ≤ 0 ∧ 2 ≤ X₄ ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂+X₄ ≤ 141 ∧ X₂ ≤ 98+X₄ ∧ 59+X₄ ≤ X₂ ∧ 102 ≤ X₂+X₄
t₁₀: lbl111(X₀, X₁, X₂, X₃, X₄, X₅) → lbl111(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 41 ∧ X₄ ≤ 39 ∧ 1 ≤ X₁ ∧ 2 ≤ X₄ ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂+X₄ ≤ 141 ∧ X₂ ≤ 98+X₄ ∧ 59+X₄ ≤ X₂ ∧ 102 ≤ X₂+X₄
t₇: lbl111(X₀, X₁, X₂, X₃, X₄, X₅) → stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 41 ∧ 2 ≤ X₄ ∧ 40 ≤ X₄ ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂+X₄ ≤ 141 ∧ X₂ ≤ 98+X₄ ∧ 59+X₄ ≤ X₂ ∧ 102 ≤ X₂+X₄
t₄: lbl91(X₀, X₁, X₂, X₃, X₄, X₅) → lbl91(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 40 ∧ X₄ ≤ 39 ∧ 1 ≤ X₄ ∧ 100 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₂+X₄ ≤ 140 ∧ X₂ ≤ 100+X₀ ∧ X₀+X₂ ≤ 100 ∧ X₂ ≤ 100+X₁ ∧ X₁+X₂ ≤ 100 ∧ X₂ ≤ 99+X₄ ∧ X₄ ≤ 40+X₀ ∧ X₀+X₄ ≤ 40 ∧ X₄ ≤ 40+X₁ ∧ X₁+X₄ ≤ 40 ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 60+X₄ ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ 100+X₀ ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ 100+X₁ ≤ X₂ ∧ 101 ≤ X₂+X₄ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀+X₁ ≤ 0
t₃: lbl91(X₀, X₁, X₂, X₃, X₄, X₅) → stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 40 ∧ 40 ≤ X₄ ∧ 100 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₂+X₄ ≤ 140 ∧ X₂ ≤ 100+X₀ ∧ X₀+X₂ ≤ 100 ∧ X₂ ≤ 100+X₁ ∧ X₁+X₂ ≤ 100 ∧ X₂ ≤ 99+X₄ ∧ X₄ ≤ 40+X₀ ∧ X₀+X₄ ≤ 40 ∧ X₄ ≤ 40+X₁ ∧ X₁+X₄ ≤ 40 ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₄ ∧ 60+X₄ ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ 100+X₀ ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ 100+X₁ ≤ X₂ ∧ 101 ≤ X₂+X₄ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀+X₁ ≤ 0
t₁: start(X₀, X₁, X₂, X₃, X₄, X₅) → lbl111(X₀, X₁, 100, X₃, 2, X₅) :|: 1+X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅) → lbl111(X₀, X₁, 100, X₃, 2, X₅) :|: 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅) → lbl91(X₀, X₁, 100, X₃, 1, X₅) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₁₁: start0(X₀, X₁, X₂, X₃, X₄, X₅) → start(X₁, X₁, X₃, X₃, X₅, X₅)

MPRF for transition t₄: lbl91(X₀, X₁, X₂, X₃, X₄, X₅) → lbl91(X₀, X₁, X₂, X₃, 1+X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 40 ∧ X₄ ≤ 39 ∧ 1 ≤ X₄ ∧ 100 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₂+X₄ ≤ 140 ∧ X₂ ≤ 100+X₀ ∧ X₀+X₂ ≤ 100 ∧ X₂ ≤ 100+X₁ ∧ X₁+X₂ ≤ 100 ∧ X₂ ≤ 99+X₄ ∧ X₄ ≤ 40+X₀ ∧ X₀+X₄ ≤ 40 ∧ X₄ ≤ 40+X₁ ∧ X₁+X₄ ≤ 40 ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ 1 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 60+X₄ ≤ X₂ ∧ 100 ≤ X₀+X₂ ∧ 100+X₀ ≤ X₂ ∧ 100 ≤ X₁+X₂ ∧ 100+X₁ ≤ X₂ ∧ 101 ≤ X₂+X₄ ∧ 0 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₀+X₁ ≤ 0 of depth 1:

new bound:

42 {O(1)}

MPRF:

• lbl91: [41-X₄]

MPRF for transition t₉: lbl111(X₀, X₁, X₂, X₃, X₄, X₅) → lbl111(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 41 ∧ X₄ ≤ 39 ∧ 1+X₁ ≤ 0 ∧ 2 ≤ X₄ ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂+X₄ ≤ 141 ∧ X₂ ≤ 98+X₄ ∧ 59+X₄ ≤ X₂ ∧ 102 ≤ X₂+X₄ of depth 1:

new bound:

84 {O(1)}

MPRF:

• lbl111: [40-X₄]

MPRF for transition t₁₀: lbl111(X₀, X₁, X₂, X₃, X₄, X₅) → lbl111(X₀, X₁, X₂, X₃, 2+X₄, X₅) :|: X₂ ≤ 100 ∧ X₄ ≤ 41 ∧ X₄ ≤ 39 ∧ 1 ≤ X₁ ∧ 2 ≤ X₄ ∧ 100 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂+X₄ ≤ 141 ∧ X₂ ≤ 98+X₄ ∧ 59+X₄ ≤ X₂ ∧ 102 ≤ X₂+X₄ of depth 1:

new bound:

1642 {O(1)}

MPRF:

• lbl111: [781-20⋅X₄]

All Bounds

Timebounds

Overall timebound:1774 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 42 {O(1)}
t₇: 1 {O(1)}
t₉: 84 {O(1)}
t₁₀: 1642 {O(1)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: 1774 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 42 {O(1)}
t₇: 1 {O(1)}
t₉: 84 {O(1)}
t₁₀: 1642 {O(1)}
t₁₁: 1 {O(1)}

Sizebounds

t₀, X₀: 0 {O(1)}
t₀, X₁: 0 {O(1)}
t₀, X₂: 100 {O(1)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: 1 {O(1)}
t₀, X₅: X₅ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: 100 {O(1)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: 2 {O(1)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: X₁ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 100 {O(1)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: 2 {O(1)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 0 {O(1)}
t₃, X₁: 0 {O(1)}
t₃, X₂: 100 {O(1)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: 40 {O(1)}
t₃, X₅: X₅ {O(n)}
t₄, X₀: 0 {O(1)}
t₄, X₁: 0 {O(1)}
t₄, X₂: 100 {O(1)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: 40 {O(1)}
t₄, X₅: X₅ {O(n)}
t₇, X₀: 2⋅X₁ {O(n)}
t₇, X₁: 2⋅X₁ {O(n)}
t₇, X₂: 100 {O(1)}
t₇, X₃: 2⋅X₃ {O(n)}
t₇, X₄: 41 {O(1)}
t₇, X₅: 2⋅X₅ {O(n)}
t₉, X₀: X₁ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 100 {O(1)}
t₉, X₃: X₃ {O(n)}
t₉, X₄: 41 {O(1)}
t₉, X₅: X₅ {O(n)}
t₁₀, X₀: X₁ {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: 100 {O(1)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: 41 {O(1)}
t₁₀, X₅: X₅ {O(n)}
t₁₁, X₀: X₁ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₃ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₁, X₄: X₅ {O(n)}
t₁₁, X₅: X₅ {O(n)}