Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₃: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₂, X₂, X₀, X₅, X₅, X₇, X₇)
t₁₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ X₃ ∧ 0 ≤ 1+X₃ ∧ X₃+1 ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₃ ∧ X₃+1 ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆
t₁₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: X₁ ≤ X₇ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₃ ∧ X₃+1 ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₀ ∧ X₃+1 ≤ 0 ∧ 0 ≤ 1+X₃ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₁ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: X₁ ≤ X₇ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃+1 ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ X₁ ≤ X₇+1 ∧ X₄+1 ≤ X₁ ∧ X₁ ≤ X₄+1 ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, 1+X₁, X₂, X₃, X₁, X₅, X₆, X₇) :|: X₁ ≤ X₇ ∧ X₃+1 ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ X₁ ≤ X₇+1 ∧ X₄+1 ≤ X₁ ∧ X₁ ≤ X₄+1 ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆
t₂: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆
t₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆
t₃: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: X₂ ≤ X₇ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆
t₀: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀+1 ≤ 0 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆

Preprocessing

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 l2

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l5

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀ for location l1

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 1+X₃ ≤ 0 ∧ X₃ ≤ X₀ for location l4

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 l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₃: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₂, X₂, X₀, X₅, X₅, X₇, X₇)
t₁₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ X₃ ∧ 0 ≤ 1+X₃ ∧ X₃+1 ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀
t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₃ ∧ X₃+1 ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀
t₁₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: X₁ ≤ X₇ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₃ ∧ X₃+1 ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₀ ∧ X₃+1 ≤ 0 ∧ 0 ≤ 1+X₃ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₁ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀
t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: X₁ ≤ X₇ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃+1 ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ X₁ ≤ X₇+1 ∧ X₄+1 ≤ X₁ ∧ X₁ ≤ X₄+1 ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ 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
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, 1+X₁, X₂, X₃, X₁, X₅, X₆, X₇) :|: X₁ ≤ X₇ ∧ X₃+1 ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ X₁ ≤ X₇+1 ∧ X₄+1 ≤ X₁ ∧ X₁ ≤ X₄+1 ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ 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
t₂: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₃: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: X₂ ≤ X₇ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₀: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀+1 ≤ 0 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂

MPRF for transition t₁₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ 1+X₃ ∧ X₃+1 ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₀+4 {O(n)}

MPRF:

l2 [X₃ ]
l1 [X₃+1 ]
l3 [X₃+1 ]

MPRF for transition t₁₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ X₃ ∧ 0 ≤ 1+X₃ ∧ X₃+1 ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₀+4 {O(n)}

MPRF:

l2 [X₃ ]
l1 [X₃+1 ]
l3 [X₃+1 ]

MPRF for transition t₁₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: X₁ ≤ X₇ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₃ ∧ X₃+1 ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₀+5 {O(n)}

MPRF:

l2 [X₃+1 ]
l1 [X₃+1 ]
l3 [X₃+1 ]

MPRF for transition t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆, X₇) :|: 0 ≤ 1+X₁ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₀+5 {O(n)}

MPRF:

l2 [X₃+1 ]
l1 [X₃+1 ]
l3 [X₃+1 ]

MPRF for transition t₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, 1+X₁, X₂, X₃-1, X₁, X₅, X₆, X₇) :|: X₁ ≤ X₇ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

3⋅X₀+5 {O(n)}

MPRF:

l2 [X₃+1 ]
l1 [X₃+1 ]
l3 [X₃+1 ]

MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃+1 ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ X₁ ≤ X₇+1 ∧ X₄+1 ≤ X₁ ∧ X₁ ≤ X₄+1 ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ 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 of depth 1:

new bound:

3⋅X₀+6 {O(n)}

MPRF:

l2 [X₃+1 ]
l1 [X₃+1 ]
l3 [X₃+2 ]

MPRF for transition t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 ≤ X₁ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

48⋅X₀⋅X₀+48⋅X₀⋅X₇+125⋅X₀+2⋅X₂+81⋅X₇+75 {O(n^2)}

MPRF:

l2 [X₁+X₃+1 ]
l1 [X₁+X₃ ]
l3 [X₃+X₇+1 ]

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, 1+X₁, X₂, X₃, X₁, X₅, X₆, X₇) :|: X₁ ≤ X₇ ∧ X₃+1 ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ X₁ ≤ X₇+1 ∧ X₄+1 ≤ X₁ ∧ X₁ ≤ X₄+1 ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ 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 of depth 1:

new bound:

24⋅X₀⋅X₇+2⋅X₂+35⋅X₇+6⋅X₀+12 {O(n^2)}

MPRF:

l2 [X₇+2 ]
l1 [X₇+1-X₁ ]
l3 [X₇+1-X₄ ]

Analysing control-flow refined program

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 l2

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ for location n_l2___1

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₅ ≤ X₄ ∧ X₄ ≤ X₅ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l5

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ 0 ≤ X₀ for location l1

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ 1+X₃ ≤ 0 ∧ X₃ ≤ X₀ for location l4

Found invariant X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₄ ≤ X₇ ∧ 1+X₂ ≤ X₇ ∧ X₁ ≤ 1+X₇ ∧ X₄ ≤ X₆ ∧ 1+X₂ ≤ X₆ ∧ X₁ ≤ 1+X₆ ∧ 1+X₄ ≤ X₁ ∧ 1+X₂ ≤ X₄ ∧ X₁ ≤ 1+X₄ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ 1+X₃ ∧ 0 ≤ 1+X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₀ for location n_l3___1

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 l3

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₁₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → n_l2___1(X₀, X₁-1, X₂, X₃, X₄, X₅, X₆, X₆) :|: X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₄ ≤ X₅ ∧ X₅ ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₁ ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₆ ≤ X₇ ∧ X₇ ≤ X₆ ∧ X₇ ≤ X₆ ∧ X₆ ≤ X₇ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀

All Bounds

Timebounds

Overall timebound:48⋅X₀⋅X₀+72⋅X₀⋅X₇+116⋅X₇+149⋅X₀+4⋅X₂+122 {O(n^2)}
t₁₃: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 3⋅X₀+4 {O(n)}
t₁₁: 3⋅X₀+4 {O(n)}
t₁₂: 3⋅X₀+5 {O(n)}
t₆: 48⋅X₀⋅X₀+48⋅X₀⋅X₇+125⋅X₀+2⋅X₂+81⋅X₇+75 {O(n^2)}
t₇: 3⋅X₀+5 {O(n)}
t₈: 3⋅X₀+5 {O(n)}
t₄: 3⋅X₀+6 {O(n)}
t₅: 24⋅X₀⋅X₇+2⋅X₂+35⋅X₇+6⋅X₀+12 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}

Costbounds

Overall costbound: 48⋅X₀⋅X₀+72⋅X₀⋅X₇+116⋅X₇+149⋅X₀+4⋅X₂+122 {O(n^2)}
t₁₃: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 3⋅X₀+4 {O(n)}
t₁₁: 3⋅X₀+4 {O(n)}
t₁₂: 3⋅X₀+5 {O(n)}
t₆: 48⋅X₀⋅X₀+48⋅X₀⋅X₇+125⋅X₀+2⋅X₂+81⋅X₇+75 {O(n^2)}
t₇: 3⋅X₀+5 {O(n)}
t₈: 3⋅X₀+5 {O(n)}
t₄: 3⋅X₀+6 {O(n)}
t₅: 24⋅X₀⋅X₇+2⋅X₂+35⋅X₇+6⋅X₀+12 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}

Sizebounds

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)}
t₉, X₀: 25⋅X₀ {O(n)}
t₉, X₁: 72⋅X₀⋅X₇+105⋅X₇+31⋅X₂+36⋅X₀+84 {O(n^2)}
t₉, X₂: 25⋅X₂ {O(n)}
t₉, X₃: 1 {O(1)}
t₉, X₄: 960⋅X₀⋅X₇+1400⋅X₇+420⋅X₂+480⋅X₀+9⋅X₅+1130 {O(n^2)}
t₉, X₅: 25⋅X₅ {O(n)}
t₉, X₆: 25⋅X₇ {O(n)}
t₉, X₇: 25⋅X₇ {O(n)}
t₁₀, X₀: 8⋅X₀ {O(n)}
t₁₀, X₁: 24⋅X₀⋅X₇+10⋅X₂+12⋅X₀+35⋅X₇+28 {O(n^2)}
t₁₀, X₂: 8⋅X₂ {O(n)}
t₁₀, X₃: 8⋅X₀+6 {O(n)}
t₁₀, X₄: 384⋅X₀⋅X₇+168⋅X₂+192⋅X₀+4⋅X₅+560⋅X₇+452 {O(n^2)}
t₁₀, X₅: 8⋅X₅ {O(n)}
t₁₀, X₆: 8⋅X₇ {O(n)}
t₁₀, X₇: 8⋅X₇ {O(n)}
t₁₁, X₀: 8⋅X₀ {O(n)}
t₁₁, X₁: 24⋅X₀⋅X₇+10⋅X₂+12⋅X₀+35⋅X₇+28 {O(n^2)}
t₁₁, X₂: 8⋅X₂ {O(n)}
t₁₁, X₃: 8⋅X₀+6 {O(n)}
t₁₁, X₄: 384⋅X₀⋅X₇+168⋅X₂+192⋅X₀+4⋅X₅+560⋅X₇+452 {O(n^2)}
t₁₁, X₅: 8⋅X₅ {O(n)}
t₁₁, X₆: 8⋅X₇ {O(n)}
t₁₁, X₇: 8⋅X₇ {O(n)}
t₁₂, X₀: 8⋅X₀ {O(n)}
t₁₂, X₁: 24⋅X₀⋅X₇+10⋅X₂+12⋅X₀+35⋅X₇+28 {O(n^2)}
t₁₂, X₂: 8⋅X₂ {O(n)}
t₁₂, X₃: 8⋅X₀+6 {O(n)}
t₁₂, X₄: 72⋅X₀⋅X₇+105⋅X₇+31⋅X₂+36⋅X₀+84 {O(n^2)}
t₁₂, X₅: 8⋅X₅ {O(n)}
t₁₂, X₆: 8⋅X₇ {O(n)}
t₁₂, X₇: 8⋅X₇ {O(n)}
t₆, X₀: 8⋅X₀ {O(n)}
t₆, X₁: 24⋅X₀⋅X₇+10⋅X₂+12⋅X₀+35⋅X₇+28 {O(n^2)}
t₆, X₂: 8⋅X₂ {O(n)}
t₆, X₃: 8⋅X₀+6 {O(n)}
t₆, X₄: 384⋅X₀⋅X₇+168⋅X₂+192⋅X₀+4⋅X₅+560⋅X₇+452 {O(n^2)}
t₆, X₅: 8⋅X₅ {O(n)}
t₆, X₆: 8⋅X₇ {O(n)}
t₆, X₇: 8⋅X₇ {O(n)}
t₇, X₀: 8⋅X₀ {O(n)}
t₇, X₁: 24⋅X₀⋅X₇+10⋅X₂+12⋅X₀+35⋅X₇+28 {O(n^2)}
t₇, X₂: 8⋅X₂ {O(n)}
t₇, X₃: 8⋅X₀+6 {O(n)}
t₇, X₄: 384⋅X₀⋅X₇+168⋅X₂+192⋅X₀+4⋅X₅+560⋅X₇+452 {O(n^2)}
t₇, X₅: 8⋅X₅ {O(n)}
t₇, X₆: 8⋅X₇ {O(n)}
t₇, X₇: 8⋅X₇ {O(n)}
t₈, X₀: 8⋅X₀ {O(n)}
t₈, X₁: 24⋅X₀⋅X₇+10⋅X₂+12⋅X₀+35⋅X₇+28 {O(n^2)}
t₈, X₂: 8⋅X₂ {O(n)}
t₈, X₃: 8⋅X₀+6 {O(n)}
t₈, X₄: 48⋅X₀⋅X₇+21⋅X₂+24⋅X₀+70⋅X₇+57 {O(n^2)}
t₈, X₅: 8⋅X₅ {O(n)}
t₈, X₆: 8⋅X₇ {O(n)}
t₈, X₇: 8⋅X₇ {O(n)}
t₄, X₀: 8⋅X₀ {O(n)}
t₄, X₁: 24⋅X₀⋅X₇+10⋅X₂+12⋅X₀+35⋅X₇+28 {O(n^2)}
t₄, X₂: 8⋅X₂ {O(n)}
t₄, X₃: 8⋅X₀+6 {O(n)}
t₄, X₄: 192⋅X₀⋅X₇+280⋅X₇+84⋅X₂+96⋅X₀+226 {O(n^2)}
t₄, X₅: 8⋅X₅ {O(n)}
t₄, X₆: 8⋅X₇ {O(n)}
t₄, X₇: 8⋅X₇ {O(n)}
t₅, X₀: 8⋅X₀ {O(n)}
t₅, X₁: 24⋅X₀⋅X₇+10⋅X₂+12⋅X₀+35⋅X₇+28 {O(n^2)}
t₅, X₂: 8⋅X₂ {O(n)}
t₅, X₃: 8⋅X₀+6 {O(n)}
t₅, X₄: 72⋅X₀⋅X₇+105⋅X₇+31⋅X₂+36⋅X₀+85 {O(n^2)}
t₅, X₅: 8⋅X₅ {O(n)}
t₅, X₆: 8⋅X₇ {O(n)}
t₅, X₇: 8⋅X₇ {O(n)}
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)}