KoAT2 Proof Output

Initial Problem

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: cut, lbl42, lbl72, start, start0, stop
Transitions:
t₁₁: cut(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → cut(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁₀: cut(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl42(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁₂: cut(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₇ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₉: cut(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₃ ∧ 1+X₃ ≤ 0 ∧ 0 ≤ X₀ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₇: lbl42(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → cut(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₆: lbl42(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl42(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₈: lbl42(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: 0 ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₇ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₄: lbl72(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → cut(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ 1+X₄ ∧ X₁ ≤ 1+X₇ ∧ 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₅: lbl72(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, 1+X₁, X₂, X₃, X₁, X₅, X₆, X₇) :|: X₁ ≤ 1+X₄ ∧ X₁ ≤ 1+X₇ ∧ 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → cut(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl42(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₃: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: 0 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁₃: start0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → start(X₀, X₂, X₂, X₀, X₅, X₅, X₇, X₇)

Preprocessing

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 1+X₃ ≤ 0 ∧ X₃ ≤ X₀ for location stop

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₁ ≤ 1+X₇ ∧ X₄ ≤ X₆ ∧ X₁ ≤ 1+X₆ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ 1+X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀ for location lbl72

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

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀ for location cut

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ for location lbl42

Problem after Preprocessing

Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: cut, lbl42, lbl72, start, start0, stop
Transitions:
t₁₁: cut(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → cut(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀
t₁₀: cut(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl42(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀
t₁₂: cut(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₇ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀
t₉: cut(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₃ ∧ 1+X₃ ≤ 0 ∧ 0 ≤ X₀ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₃ ∧ 1+X₃ ≤ X₀
t₇: lbl42(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → cut(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃
t₆: lbl42(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl42(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃
t₈: lbl42(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: 0 ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₇ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃
t₄: lbl72(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → cut(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ 1+X₄ ∧ X₁ ≤ 1+X₇ ∧ 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₃ ∧ X₁ ≤ 1+X₆ ∧ 0 ≤ X₀ ∧ X₄ ≤ X₆ ∧ X₄ ≤ X₇
t₅: lbl72(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, 1+X₁, X₂, X₃, X₁, X₅, X₆, X₇) :|: X₁ ≤ 1+X₄ ∧ X₁ ≤ 1+X₇ ∧ 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₃ ∧ X₁ ≤ 1+X₆ ∧ 0 ≤ X₀ ∧ X₄ ≤ X₆ ∧ X₄ ≤ X₇
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → cut(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl42(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₃: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: 0 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₀: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁₃: start0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → start(X₀, X₂, X₂, X₀, X₅, X₅, X₇, X₇)

MPRF for transition t₄: lbl72(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → cut(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ 1+X₄ ∧ X₁ ≤ 1+X₇ ∧ 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₃ ∧ X₁ ≤ 1+X₆ ∧ 0 ≤ X₀ ∧ X₄ ≤ X₆ ∧ X₄ ≤ X₇ of depth 1:

new bound:

3⋅X₀+6 {O(n)}

MPRF:

• cut: [1+X₃]
• lbl42: [1+X₃]
• lbl72: [2+X₃]

MPRF for transition t₇: lbl42(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → cut(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ of depth 1:

new bound:

3⋅X₀+5 {O(n)}

MPRF:

• cut: [1+X₃]
• lbl42: [1+X₃]
• lbl72: [1+X₃]

MPRF for transition t₈: lbl42(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: 0 ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₇ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ of depth 1:

new bound:

3⋅X₀+5 {O(n)}

MPRF:

• cut: [1+X₃]
• lbl42: [1+X₃]
• lbl72: [1+X₃]

MPRF for transition t₁₀: cut(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl42(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₀+4 {O(n)}

MPRF:

• cut: [1+X₃]
• lbl42: [X₃]
• lbl72: [1+X₃]

MPRF for transition t₁₁: cut(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → cut(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₀+4 {O(n)}

MPRF:

• cut: [1+X₃]
• lbl42: [X₃]
• lbl72: [1+X₃]

MPRF for transition t₁₂: cut(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₇ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₀+4 {O(n)}

MPRF:

• cut: [1+X₃]
• lbl42: [X₃]
• lbl72: [1+X₃]

MPRF for transition t₅: lbl72(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl72(X₀, 1+X₁, X₂, X₃, X₁, X₅, X₆, X₇) :|: X₁ ≤ 1+X₄ ∧ X₁ ≤ 1+X₇ ∧ 0 ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₃ ∧ X₁ ≤ 1+X₆ ∧ 0 ≤ X₀ ∧ X₄ ≤ X₆ ∧ X₄ ≤ X₇ of depth 1:

new bound:

9⋅X₀⋅X₇+15⋅X₇+2⋅X₂+3⋅X₀+7 {O(n^2)}

MPRF:

• cut: [X₇-X₁]
• lbl42: [1+X₇]
• lbl72: [1+X₇-X₁]

MPRF for transition t₆: lbl42(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl42(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ of depth 1:

new bound:

18⋅X₀⋅X₇+12⋅X₀+2⋅X₂+28⋅X₇+24 {O(n^2)}

MPRF:

• cut: [1+X₁]
• lbl42: [2+X₁]
• lbl72: [2+X₆]

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 1+X₃ ≤ 0 ∧ X₃ ≤ X₀ for location stop

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ for location lbl42_v1

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₄ ≤ X₇ ∧ X₁ ≤ 1+X₇ ∧ X₄ ≤ X₆ ∧ X₁ ≤ 1+X₆ ∧ 1+X₄ ≤ X₁ ∧ X₁ ≤ 1+X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀ for location lbl72_v1

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

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀ for location cut

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ for location lbl42

All Bounds

Timebounds

Overall timebound:27⋅X₀⋅X₇+33⋅X₀+4⋅X₂+43⋅X₇+65 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 3⋅X₀+6 {O(n)}
t₅: 9⋅X₀⋅X₇+15⋅X₇+2⋅X₂+3⋅X₀+7 {O(n^2)}
t₆: 18⋅X₀⋅X₇+12⋅X₀+2⋅X₂+28⋅X₇+24 {O(n^2)}
t₇: 3⋅X₀+5 {O(n)}
t₈: 3⋅X₀+5 {O(n)}
t₉: 1 {O(1)}
t₁₀: 3⋅X₀+4 {O(n)}
t₁₁: 3⋅X₀+4 {O(n)}
t₁₂: 3⋅X₀+4 {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 27⋅X₀⋅X₇+33⋅X₀+4⋅X₂+43⋅X₇+65 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 3⋅X₀+6 {O(n)}
t₅: 9⋅X₀⋅X₇+15⋅X₇+2⋅X₂+3⋅X₀+7 {O(n^2)}
t₆: 18⋅X₀⋅X₇+12⋅X₀+2⋅X₂+28⋅X₇+24 {O(n^2)}
t₇: 3⋅X₀+5 {O(n)}
t₈: 3⋅X₀+5 {O(n)}
t₉: 1 {O(1)}
t₁₀: 3⋅X₀+4 {O(n)}
t₁₁: 3⋅X₀+4 {O(n)}
t₁₂: 3⋅X₀+4 {O(n)}
t₁₃: 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)}
t₀, X₆: X₇ {O(n)}
t₀, X₇: X₇ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₂+1 {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₀ {O(n)}
t₁, X₄: X₅ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₇ {O(n)}
t₁, X₇: X₇ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₂ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₀+1 {O(n)}
t₂, X₄: X₅ {O(n)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₇ {O(n)}
t₂, X₇: X₇ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₂+1 {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₀+1 {O(n)}
t₃, X₄: X₂ {O(n)}
t₃, X₅: X₅ {O(n)}
t₃, X₆: X₇ {O(n)}
t₃, X₇: X₇ {O(n)}
t₄, X₀: 3⋅X₀ {O(n)}
t₄, X₁: 9⋅X₀⋅X₇+15⋅X₇+5⋅X₂+9⋅X₀+19 {O(n^2)}
t₄, X₂: 3⋅X₂ {O(n)}
t₄, X₃: 3⋅X₀+3 {O(n)}
t₄, X₄: 72⋅X₀⋅X₇+120⋅X₇+44⋅X₂+72⋅X₀+154 {O(n^2)}
t₄, X₅: 3⋅X₅ {O(n)}
t₄, X₆: 3⋅X₇ {O(n)}
t₄, X₇: 3⋅X₇ {O(n)}
t₅, X₀: 3⋅X₀ {O(n)}
t₅, X₁: 9⋅X₀⋅X₇+15⋅X₇+5⋅X₂+9⋅X₀+19 {O(n^2)}
t₅, X₂: 3⋅X₂ {O(n)}
t₅, X₃: 3⋅X₀+3 {O(n)}
t₅, X₄: 27⋅X₀⋅X₇+16⋅X₂+27⋅X₀+45⋅X₇+58 {O(n^2)}
t₅, X₅: 3⋅X₅ {O(n)}
t₅, X₆: 3⋅X₇ {O(n)}
t₅, X₇: 3⋅X₇ {O(n)}
t₆, X₀: 3⋅X₀ {O(n)}
t₆, X₁: 9⋅X₀⋅X₇+15⋅X₇+5⋅X₂+9⋅X₀+19 {O(n^2)}
t₆, X₂: 3⋅X₂ {O(n)}
t₆, X₃: 3⋅X₀+3 {O(n)}
t₆, X₄: 72⋅X₀⋅X₇+120⋅X₇+2⋅X₅+44⋅X₂+72⋅X₀+154 {O(n^2)}
t₆, X₅: 3⋅X₅ {O(n)}
t₆, X₆: 3⋅X₇ {O(n)}
t₆, X₇: 3⋅X₇ {O(n)}
t₇, X₀: 3⋅X₀ {O(n)}
t₇, X₁: 9⋅X₀⋅X₇+15⋅X₇+5⋅X₂+9⋅X₀+19 {O(n^2)}
t₇, X₂: 3⋅X₂ {O(n)}
t₇, X₃: 3⋅X₀+3 {O(n)}
t₇, X₄: 72⋅X₀⋅X₇+120⋅X₇+2⋅X₅+44⋅X₂+72⋅X₀+154 {O(n^2)}
t₇, X₅: 3⋅X₅ {O(n)}
t₇, X₆: 3⋅X₇ {O(n)}
t₇, X₇: 3⋅X₇ {O(n)}
t₈, X₀: 3⋅X₀ {O(n)}
t₈, X₁: 9⋅X₀⋅X₇+15⋅X₇+5⋅X₂+9⋅X₀+19 {O(n^2)}
t₈, X₂: 3⋅X₂ {O(n)}
t₈, X₃: 3⋅X₀+3 {O(n)}
t₈, X₄: 18⋅X₀⋅X₇+11⋅X₂+18⋅X₀+30⋅X₇+39 {O(n^2)}
t₈, X₅: 3⋅X₅ {O(n)}
t₈, X₆: 3⋅X₇ {O(n)}
t₈, X₇: 3⋅X₇ {O(n)}
t₉, X₀: 10⋅X₀ {O(n)}
t₉, X₁: 27⋅X₀⋅X₇+16⋅X₂+27⋅X₀+45⋅X₇+57 {O(n^2)}
t₉, X₂: 10⋅X₂ {O(n)}
t₉, X₃: 1 {O(1)}
t₉, X₄: 216⋅X₀⋅X₇+132⋅X₂+216⋅X₀+360⋅X₇+5⋅X₅+462 {O(n^2)}
t₉, X₅: 10⋅X₅ {O(n)}
t₉, X₆: 10⋅X₇ {O(n)}
t₉, X₇: 10⋅X₇ {O(n)}
t₁₀, X₀: 3⋅X₀ {O(n)}
t₁₀, X₁: 9⋅X₀⋅X₇+15⋅X₇+5⋅X₂+9⋅X₀+19 {O(n^2)}
t₁₀, X₂: 3⋅X₂ {O(n)}
t₁₀, X₃: 3⋅X₀+3 {O(n)}
t₁₀, X₄: 72⋅X₀⋅X₇+120⋅X₇+2⋅X₅+44⋅X₂+72⋅X₀+154 {O(n^2)}
t₁₀, X₅: 3⋅X₅ {O(n)}
t₁₀, X₆: 3⋅X₇ {O(n)}
t₁₀, X₇: 3⋅X₇ {O(n)}
t₁₁, X₀: 3⋅X₀ {O(n)}
t₁₁, X₁: 9⋅X₀⋅X₇+15⋅X₇+5⋅X₂+9⋅X₀+19 {O(n^2)}
t₁₁, X₂: 3⋅X₂ {O(n)}
t₁₁, X₃: 3⋅X₀+3 {O(n)}
t₁₁, X₄: 72⋅X₀⋅X₇+120⋅X₇+2⋅X₅+44⋅X₂+72⋅X₀+154 {O(n^2)}
t₁₁, X₅: 3⋅X₅ {O(n)}
t₁₁, X₆: 3⋅X₇ {O(n)}
t₁₁, X₇: 3⋅X₇ {O(n)}
t₁₂, X₀: 3⋅X₀ {O(n)}
t₁₂, X₁: 9⋅X₀⋅X₇+15⋅X₇+5⋅X₂+9⋅X₀+19 {O(n^2)}
t₁₂, X₂: 3⋅X₂ {O(n)}
t₁₂, X₃: 3⋅X₀+3 {O(n)}
t₁₂, X₄: 27⋅X₀⋅X₇+16⋅X₂+27⋅X₀+45⋅X₇+57 {O(n^2)}
t₁₂, X₅: 3⋅X₅ {O(n)}
t₁₂, X₆: 3⋅X₇ {O(n)}
t₁₂, X₇: 3⋅X₇ {O(n)}
t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₂ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₀ {O(n)}
t₁₃, X₄: X₅ {O(n)}
t₁₃, X₅: X₅ {O(n)}
t₁₃, X₆: X₇ {O(n)}
t₁₃, X₇: X₇ {O(n)}