Initial Problem
Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: I
Locations: lbl131, lbl142, lbl91, start, start0, stop
Transitions:
t₁₀: lbl131(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl131(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, X₇) :|: 1 ≤ X₄ ∧ 1+X₄ ≤ X₆ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₆
t₈: lbl131(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl142(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1, X₇) :|: 1 ≤ X₆ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₆ ≤ X₄ ∧ X₄ ≤ X₆
t₉: lbl131(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl91(X₀, I, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₄ ∧ 1+X₄ ≤ X₆ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₆
t₇: lbl142(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl131(X₀, X₁, X₂, X₃, 1, X₅, X₆, X₇) :|: X₄ ≤ 1+X₆ ∧ 1+X₆ ≤ X₄ ∧ 2 ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₄
t₅: lbl142(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl142(X₀, X₁, X₂, X₃, 0, X₅, X₆-1, X₇) :|: X₄ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₆ ∧ X₆ ≤ 0
t₆: lbl142(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl91(X₀, I, X₂, X₃, 0, X₅, X₆, X₇) :|: X₄ ≤ 1+X₆ ∧ 1+X₆ ≤ X₄ ∧ 2 ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₄
t₄: lbl142(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₆ ∧ 1+X₆ ≤ 0 ∧ 0 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₄ ∧ X₄ ≤ 0
t₁₁: lbl91(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl131(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, X₇) :|: 1+X₄ ≤ X₆ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₄
t₃: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl131(X₀, X₁, X₂, X₃, 1, X₅, X₃, X₇) :|: 1 ≤ 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) → lbl142(X₀, X₁, X₂, X₃, 0, X₅, X₃-1, X₇) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0 ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl91(X₀, I, X₂, X₃, 0, X₅, X₃, X₇) :|: 1 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 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, X₃, X₇) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁₂: start0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → start(X₀, X₂, X₂, X₀, X₅, X₅, X₇, X₇)
Preprocessing
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₆ ∧ 2 ≤ X₄+X₆ ∧ X₄ ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location lbl131
Found invariant 1+X₆ ≤ 0 ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location stop
Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location start
Found invariant 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₃ ∧ 1+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₄+X₆ ∧ X₄ ≤ 1+X₆ ∧ 0 ≤ 1+X₃+X₆ ∧ 0 ≤ 1+X₀+X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ for location lbl142
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location lbl91
Problem after Preprocessing
Start: start0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars: I
Locations: lbl131, lbl142, lbl91, start, start0, stop
Transitions:
t₁₀: lbl131(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl131(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, X₇) :|: 1 ≤ X₄ ∧ 1+X₄ ≤ X₆ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₆ ∧ X₄ ≤ X₀ ∧ X₄ ≤ X₃ ∧ X₆ ≤ X₃
t₈: lbl131(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl142(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1, X₇) :|: 1 ≤ X₆ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₆ ≤ X₄ ∧ X₄ ≤ X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₆ ∧ X₄ ≤ X₀ ∧ X₄ ≤ X₃ ∧ X₆ ≤ X₃
t₉: lbl131(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl91(X₀, I, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₄ ∧ 1+X₄ ≤ X₆ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₆ ∧ X₄ ≤ X₀ ∧ X₄ ≤ X₃ ∧ X₆ ≤ X₃
t₇: lbl142(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl131(X₀, X₁, X₂, X₃, 1, X₅, X₆, X₇) :|: X₄ ≤ 1+X₆ ∧ 1+X₆ ≤ X₄ ∧ 2 ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ 1+X₀+X₆ ∧ 0 ≤ 1+X₃+X₆ ∧ 0 ≤ 1+X₄+X₆ ∧ 0 ≤ 1+X₆ ∧ 1+X₆ ≤ X₀ ∧ 1+X₆ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃
t₅: lbl142(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl142(X₀, X₁, X₂, X₃, 0, X₅, X₆-1, X₇) :|: X₄ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₆ ∧ X₆ ≤ 0 ∧ 0 ≤ 1+X₀+X₆ ∧ 0 ≤ 1+X₃+X₆ ∧ 0 ≤ 1+X₄+X₆ ∧ X₄ ≤ 1+X₆ ∧ 0 ≤ 1+X₆ ∧ 1+X₆ ≤ X₀ ∧ 1+X₆ ≤ X₃ ∧ 1+X₆ ≤ X₄ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄
t₆: lbl142(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl91(X₀, I, X₂, X₃, 0, X₅, X₆, X₇) :|: X₄ ≤ 1+X₆ ∧ 1+X₆ ≤ X₄ ∧ 2 ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ 1+X₀+X₆ ∧ 0 ≤ 1+X₃+X₆ ∧ 0 ≤ 1+X₄+X₆ ∧ 0 ≤ 1+X₆ ∧ 1+X₆ ≤ X₀ ∧ 1+X₆ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃
t₄: lbl142(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₆ ∧ 1+X₆ ≤ 0 ∧ 0 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₄ ∧ X₄ ≤ 0 ∧ 0 ≤ 1+X₀+X₆ ∧ 0 ≤ 1+X₃+X₆ ∧ 0 ≤ 1+X₄+X₆ ∧ X₄ ≤ 1+X₆ ∧ 1+X₆ ≤ X₀ ∧ 1+X₆ ≤ X₃ ∧ 1+X₆ ≤ X₄ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃
t₁₁: lbl91(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl131(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, X₇) :|: 1+X₄ ≤ X₆ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₃+X₆ ∧ X₆ ≤ X₃
t₃: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl131(X₀, X₁, X₂, X₃, 1, X₅, X₃, X₇) :|: 1 ≤ 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) → lbl142(X₀, X₁, X₂, X₃, 0, X₅, X₃-1, X₇) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0 ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₂: start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl91(X₀, I, X₂, X₃, 0, X₅, X₃, X₇) :|: 1 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 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, X₃, X₇) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇
t₁₂: start0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → start(X₀, X₂, X₂, X₀, X₅, X₅, X₇, X₇)
MPRF for transition t₅: lbl142(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl142(X₀, X₁, X₂, X₃, 0, X₅, X₆-1, X₇) :|: X₄ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₆ ∧ X₆ ≤ 0 ∧ 0 ≤ 1+X₀+X₆ ∧ 0 ≤ 1+X₃+X₆ ∧ 0 ≤ 1+X₄+X₆ ∧ X₄ ≤ 1+X₆ ∧ 0 ≤ 1+X₆ ∧ 1+X₆ ≤ X₀ ∧ 1+X₆ ≤ X₃ ∧ 1+X₆ ≤ X₄ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ 0 ≤ X₄ of depth 1:
new bound:
4⋅X₀+2 {O(n)}
MPRF:
• lbl131: [1+2⋅X₆]
• lbl142: [1+2⋅X₄]
• lbl91: [1+2⋅X₆]
MPRF for transition t₆: lbl142(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl91(X₀, I, X₂, X₃, 0, X₅, X₆, X₇) :|: X₄ ≤ 1+X₆ ∧ 1+X₆ ≤ X₄ ∧ 2 ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ 1+X₀+X₆ ∧ 0 ≤ 1+X₃+X₆ ∧ 0 ≤ 1+X₄+X₆ ∧ 0 ≤ 1+X₆ ∧ 1+X₆ ≤ X₀ ∧ 1+X₆ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ of depth 1:
new bound:
4⋅X₀+2 {O(n)}
MPRF:
• lbl131: [1+X₃+X₆]
• lbl142: [1+X₃+X₄]
• lbl91: [1+X₃+X₆]
MPRF for transition t₇: lbl142(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl131(X₀, X₁, X₂, X₃, 1, X₅, X₆, X₇) :|: X₄ ≤ 1+X₆ ∧ 1+X₆ ≤ X₄ ∧ 2 ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₄ ∧ 0 ≤ 1+X₀+X₆ ∧ 0 ≤ 1+X₃+X₆ ∧ 0 ≤ 1+X₄+X₆ ∧ 0 ≤ 1+X₆ ∧ 1+X₆ ≤ X₀ ∧ 1+X₆ ≤ X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ X₀+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₄ ≤ X₃ of depth 1:
new bound:
2⋅X₀+2 {O(n)}
MPRF:
• lbl131: [1+X₆]
• lbl142: [1+X₄]
• lbl91: [1+X₆]
MPRF for transition t₈: lbl131(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl142(X₀, X₁, X₂, X₃, X₄, X₅, X₆-1, X₇) :|: 1 ≤ X₆ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₆ ≤ X₄ ∧ X₄ ≤ X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₆ ∧ X₄ ≤ X₀ ∧ X₄ ≤ X₃ ∧ X₆ ≤ X₃ of depth 1:
new bound:
4⋅X₀ {O(n)}
MPRF:
• lbl131: [X₆]
• lbl142: [X₆]
• lbl91: [X₃+X₆-X₀]
MPRF for transition t₉: lbl131(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl91(X₀, I, X₂, X₃, X₄, X₅, X₆, X₇) :|: 1 ≤ X₄ ∧ 1+X₄ ≤ X₆ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₆ ∧ X₄ ≤ X₀ ∧ X₄ ≤ X₃ ∧ X₆ ≤ X₃ of depth 1:
new bound:
8⋅X₀⋅X₀+2⋅X₀+2 {O(n^2)}
MPRF:
• lbl131: [1+X₀-X₄]
• lbl142: [X₀]
• lbl91: [X₀-X₄]
MPRF for transition t₁₀: lbl131(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl131(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, X₇) :|: 1 ≤ X₄ ∧ 1+X₄ ≤ X₆ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₆ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₄+X₆ ∧ X₄ ≤ X₀ ∧ X₄ ≤ X₃ ∧ X₆ ≤ X₃ of depth 1:
new bound:
8⋅X₀⋅X₀+2⋅X₀+2 {O(n^2)}
MPRF:
• lbl131: [1+X₃-X₄]
• lbl142: [X₃]
• lbl91: [X₃-X₄]
MPRF for transition t₁₁: lbl91(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → lbl131(X₀, X₁, X₂, X₃, 1+X₄, X₅, X₆, X₇) :|: 1+X₄ ≤ X₆ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₄ ∧ 1+X₄ ≤ X₃ ∧ 1 ≤ X₄+X₆ ∧ 1 ≤ X₆ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₆ ∧ 2 ≤ X₃+X₆ ∧ X₆ ≤ X₃ of depth 1:
new bound:
8⋅X₀⋅X₀+2⋅X₀+1 {O(n^2)}
MPRF:
• lbl131: [X₆-X₄]
• lbl142: [X₆]
• lbl91: [X₆-X₄]
Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location start
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ X₀ ∧ 2 ≤ X₆ ∧ 3 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 4 ≤ X₃+X₆ ∧ 4 ≤ X₀+X₆ ∧ X₄ ≤ 1 ∧ 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2 ≤ X₀ for location lbl91_v1
Found invariant 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₃ ∧ 1+X₆ ≤ X₀ ∧ 0 ≤ 1+X₆ ∧ 0 ≤ 1+X₄+X₆ ∧ X₄ ≤ 1+X₆ ∧ 0 ≤ 1+X₃+X₆ ∧ 0 ≤ 1+X₀+X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 0 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₀ for location lbl142
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location lbl91
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₆ ∧ 2 ≤ X₄+X₆ ∧ X₄ ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ 1 ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location lbl131_v2
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ X₀ ∧ 1 ≤ X₆ ∧ 2 ≤ X₄+X₆ ∧ X₄ ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ X₄ ≤ 1 ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location lbl131
Found invariant 1+X₆ ≤ 0 ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location stop
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ X₀ ∧ 2 ≤ X₆ ∧ 4 ≤ X₄+X₆ ∧ X₄ ≤ X₆ ∧ 4 ≤ X₃+X₆ ∧ 4 ≤ X₀+X₆ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 4 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2 ≤ X₀ for location lbl131_v1
Found invariant X₆ ≤ X₃ ∧ X₆ ≤ X₀ ∧ 3 ≤ X₆ ∧ 5 ≤ X₄+X₆ ∧ 1+X₄ ≤ X₆ ∧ 6 ≤ X₃+X₆ ∧ 6 ≤ X₀+X₆ ∧ 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₀ ∧ 2 ≤ X₄ ∧ 5 ≤ X₃+X₄ ∧ 5 ≤ X₀+X₄ ∧ X₃ ≤ X₀ ∧ 3 ≤ X₃ ∧ 6 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 3 ≤ X₀ for location lbl91_v2
All Bounds
Timebounds
Overall timebound:24⋅X₀⋅X₀+20⋅X₀+17 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 4⋅X₀+2 {O(n)}
t₆: 4⋅X₀+2 {O(n)}
t₇: 2⋅X₀+2 {O(n)}
t₈: 4⋅X₀ {O(n)}
t₉: 8⋅X₀⋅X₀+2⋅X₀+2 {O(n^2)}
t₁₀: 8⋅X₀⋅X₀+2⋅X₀+2 {O(n^2)}
t₁₁: 8⋅X₀⋅X₀+2⋅X₀+1 {O(n^2)}
t₁₂: 1 {O(1)}
Costbounds
Overall costbound: 24⋅X₀⋅X₀+20⋅X₀+17 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 4⋅X₀+2 {O(n)}
t₆: 4⋅X₀+2 {O(n)}
t₇: 2⋅X₀+2 {O(n)}
t₈: 4⋅X₀ {O(n)}
t₉: 8⋅X₀⋅X₀+2⋅X₀+2 {O(n^2)}
t₁₀: 8⋅X₀⋅X₀+2⋅X₀+2 {O(n^2)}
t₁₁: 8⋅X₀⋅X₀+2⋅X₀+1 {O(n^2)}
t₁₂: 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: X₀ {O(n)}
t₀, X₇: X₇ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: X₂ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: 0 {O(1)}
t₁, X₄: 0 {O(1)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: 1 {O(1)}
t₁, X₇: X₇ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₀ {O(n)}
t₂, X₄: 0 {O(1)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₀ {O(n)}
t₂, X₇: X₇ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₂ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₀ {O(n)}
t₃, X₄: 1 {O(1)}
t₃, X₅: X₅ {O(n)}
t₃, X₆: X₀ {O(n)}
t₃, X₇: X₇ {O(n)}
t₄, X₀: 2⋅X₀ {O(n)}
t₄, X₂: 3⋅X₂ {O(n)}
t₄, X₃: 2⋅X₀ {O(n)}
t₄, X₄: 0 {O(1)}
t₄, X₅: 3⋅X₅ {O(n)}
t₄, X₆: 1 {O(1)}
t₄, X₇: 3⋅X₇ {O(n)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₂: 2⋅X₂ {O(n)}
t₅, X₃: 2⋅X₀ {O(n)}
t₅, X₄: 0 {O(1)}
t₅, X₅: 2⋅X₅ {O(n)}
t₅, X₆: 1 {O(1)}
t₅, X₇: 2⋅X₇ {O(n)}
t₆, X₀: 2⋅X₀ {O(n)}
t₆, X₂: 2⋅X₂ {O(n)}
t₆, X₃: 2⋅X₀ {O(n)}
t₆, X₄: 0 {O(1)}
t₆, X₅: 2⋅X₅ {O(n)}
t₆, X₆: 2⋅X₀ {O(n)}
t₆, X₇: 2⋅X₇ {O(n)}
t₇, X₀: 2⋅X₀ {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 2⋅X₀ {O(n)}
t₇, X₄: 1 {O(1)}
t₇, X₅: 2⋅X₅ {O(n)}
t₇, X₆: 2⋅X₀ {O(n)}
t₇, X₇: 2⋅X₇ {O(n)}
t₈, X₀: 2⋅X₀ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}
t₈, X₃: 2⋅X₀ {O(n)}
t₈, X₄: 32⋅X₀⋅X₀+8⋅X₀+12 {O(n^2)}
t₈, X₅: 2⋅X₅ {O(n)}
t₈, X₆: 2⋅X₀ {O(n)}
t₈, X₇: 2⋅X₇ {O(n)}
t₉, X₀: 2⋅X₀ {O(n)}
t₉, X₂: 2⋅X₂ {O(n)}
t₉, X₃: 2⋅X₀ {O(n)}
t₉, X₄: 16⋅X₀⋅X₀+4⋅X₀+5 {O(n^2)}
t₉, X₅: 2⋅X₅ {O(n)}
t₉, X₆: 2⋅X₀ {O(n)}
t₉, X₇: 2⋅X₇ {O(n)}
t₁₀, X₀: 2⋅X₀ {O(n)}
t₁₀, X₂: 2⋅X₂ {O(n)}
t₁₀, X₃: 2⋅X₀ {O(n)}
t₁₀, X₄: 16⋅X₀⋅X₀+4⋅X₀+5 {O(n^2)}
t₁₀, X₅: 2⋅X₅ {O(n)}
t₁₀, X₆: 2⋅X₀ {O(n)}
t₁₀, X₇: 2⋅X₇ {O(n)}
t₁₁, X₀: 2⋅X₀ {O(n)}
t₁₁, X₂: 2⋅X₂ {O(n)}
t₁₁, X₃: 2⋅X₀ {O(n)}
t₁₁, X₄: 16⋅X₀⋅X₀+4⋅X₀+5 {O(n^2)}
t₁₁, X₅: 2⋅X₅ {O(n)}
t₁₁, X₆: 2⋅X₀ {O(n)}
t₁₁, X₇: 2⋅X₇ {O(n)}
t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₂ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₀ {O(n)}
t₁₂, X₄: X₅ {O(n)}
t₁₂, X₅: X₅ {O(n)}
t₁₂, X₆: X₇ {O(n)}
t₁₂, X₇: X₇ {O(n)}