Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₀, X₁, X₄, X₅, X₆, X₇) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₇ < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ < X₁
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ < X₀
t₅: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ X₇
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₅, X₆, X₂, X₃, X₄, X₅, X₆, X₇)
t₇: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₂, X₃, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₃ ≤ X₇
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₇ < X₃
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₈: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₁, X₂-1, X₃-1, X₄, X₅, X₆, X₇)

Preprocessing

Eliminate variables {X₄} that do not contribute to the problem

Found invariant X₁ ≤ X₅ ∧ X₀ ≤ X₄ for location l6

Found invariant 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₃ ∧ 1+X₆ ≤ X₂ ∧ 1+X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5

Found invariant X₁ ≤ X₅ ∧ X₀ ≤ X₄ for location l1

Found invariant X₁ ≤ X₅ ∧ X₀ ≤ X₄ for location l4

Found invariant 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ 1+X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₂₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₀, X₁, X₄, X₅, X₆) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₆ < X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄
t₂₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ < X₁ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄
t₂₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ < X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄
t₂₄: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ X₆ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄
t₂₅: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₄, X₅, X₂, X₃, X₄, X₅, X₆)
t₂₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₂, X₃, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ X₆ ∧ 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ 1+X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₂₇: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ < X₃ ∧ 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ 1+X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₂₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₁ ≤ X₅ ∧ X₀ ≤ X₄
t₂₉: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂-1, X₃-1, X₄, X₅, X₆) :|: 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₃ ∧ 1+X₆ ≤ X₂ ∧ 1+X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₂₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₀, X₁, X₄, X₅, X₆) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₆ < X₀ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₄

MPRF for transition t₂₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₂, X₃, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ X₆ ∧ 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ 1+X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF for transition t₂₇: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ < X₃ ∧ 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ X₆ ≤ X₃ ∧ X₆ ≤ X₂ ∧ 1+X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₅+X₆+1 {O(n)}

MPRF for transition t₂₉: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂-1, X₃-1, X₄, X₅, X₆) :|: 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ 1+X₆ ≤ X₃ ∧ 1+X₆ ≤ X₂ ∧ 1+X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₄ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₄+X₆ {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₅+3⋅X₆+X₄+8 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: X₅+X₆ {O(n)}
t₂₇: X₅+X₆+1 {O(n)}
t₂₈: 1 {O(1)}
t₂₉: X₄+X₆ {O(n)}

Costbounds

Overall costbound: 2⋅X₅+3⋅X₆+X₄+8 {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: X₅+X₆ {O(n)}
t₂₇: X₅+X₆+1 {O(n)}
t₂₈: 1 {O(1)}
t₂₉: X₄+X₆ {O(n)}

Sizebounds

t₂₀, X₀: X₀ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₀, X₄: X₄ {O(n)}
t₂₀, X₅: X₅ {O(n)}
t₂₀, X₆: X₆ {O(n)}
t₂₁, X₀: X₄ {O(n)}
t₂₁, X₁: X₅ {O(n)}
t₂₁, X₂: X₄ {O(n)}
t₂₁, X₃: X₅ {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₁, X₆: X₆ {O(n)}
t₂₂, X₀: X₄ {O(n)}
t₂₂, X₁: X₅ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₂, X₆: X₆ {O(n)}
t₂₃, X₀: X₄ {O(n)}
t₂₃, X₁: X₅ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₃, X₆: X₆ {O(n)}
t₂₄, X₀: 3⋅X₄+X₆ {O(n)}
t₂₄, X₁: 2⋅X₅+X₄+X₆ {O(n)}
t₂₄, X₂: 2⋅X₄+X₂+X₆ {O(n)}
t₂₄, X₃: X₃+X₄+X₅+X₆ {O(n)}
t₂₄, X₄: 2⋅X₄ {O(n)}
t₂₄, X₅: 2⋅X₅ {O(n)}
t₂₄, X₆: 2⋅X₆ {O(n)}
t₂₅, X₀: X₄ {O(n)}
t₂₅, X₁: X₅ {O(n)}
t₂₅, X₂: X₂ {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₂₅, X₄: X₄ {O(n)}
t₂₅, X₅: X₅ {O(n)}
t₂₅, X₆: X₆ {O(n)}
t₂₆, X₀: 2⋅X₄+X₆ {O(n)}
t₂₆, X₁: X₄+X₅+X₆ {O(n)}
t₂₆, X₂: 2⋅X₄+X₆ {O(n)}
t₂₆, X₃: X₄+X₅+X₆ {O(n)}
t₂₆, X₄: X₄ {O(n)}
t₂₆, X₅: X₅ {O(n)}
t₂₆, X₆: X₆ {O(n)}
t₂₇, X₀: X₄ {O(n)}
t₂₇, X₁: X₅ {O(n)}
t₂₇, X₂: 2⋅X₄+X₆ {O(n)}
t₂₇, X₃: X₄+X₅+X₆ {O(n)}
t₂₇, X₄: X₄ {O(n)}
t₂₇, X₅: X₅ {O(n)}
t₂₇, X₆: X₆ {O(n)}
t₂₈, X₀: 5⋅X₄+X₆ {O(n)}
t₂₈, X₁: 4⋅X₅+X₄+X₆ {O(n)}
t₂₈, X₂: 2⋅X₄+3⋅X₂+X₆ {O(n)}
t₂₈, X₃: 3⋅X₃+X₄+X₅+X₆ {O(n)}
t₂₈, X₄: 4⋅X₄ {O(n)}
t₂₈, X₅: 4⋅X₅ {O(n)}
t₂₈, X₆: 4⋅X₆ {O(n)}
t₂₉, X₀: X₄ {O(n)}
t₂₉, X₁: X₅ {O(n)}
t₂₉, X₂: 2⋅X₄+X₆ {O(n)}
t₂₉, X₃: X₄+X₅+X₆ {O(n)}
t₂₉, X₄: X₄ {O(n)}
t₂₉, X₅: X₅ {O(n)}
t₂₉, X₆: X₆ {O(n)}