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 ≤ X₆ ∧ X₀ ≤ X₅ for location l6

Found invariant 1+X₇ ≤ X₆ ∧ 1+X₇ ≤ X₅ ∧ 1+X₇ ≤ X₃ ∧ 1+X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₇ ≤ X₀ ∧ X₃ ≤ X₆ ∧ X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₆ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5

Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l1

Found invariant X₁ ≤ X₆ ∧ X₀ ≤ X₅ for location l4

Found invariant 1+X₇ ≤ X₆ ∧ 1+X₇ ≤ X₅ ∧ X₇ ≤ X₃ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₇ ≤ X₀ ∧ X₃ ≤ X₆ ∧ X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₆ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 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, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₂₁: l0(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₅, X₆, X₇)
t₂₂: l1(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l3(X₀, X₁, X₀, X₁, X₅, X₆, X₇) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₇ < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₃: l1(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₅, X₆, X₇) :|: X₀ < X₁ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₄: l1(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₅, X₆, X₇) :|: X₁ < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₅: l1(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₅, X₆, X₇) :|: X₀ ≤ X₇ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₂₆: l2(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l1(X₅, X₆, X₂, X₃, X₅, X₆, X₇)
t₂₈: l3(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l1(X₂, X₃, X₂, X₃, X₅, X₆, X₇) :|: X₃ ≤ X₇ ∧ 1+X₇ ≤ X₆ ∧ 1+X₇ ≤ X₅ ∧ X₇ ≤ X₃ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₇ ≤ X₀ ∧ X₃ ≤ X₆ ∧ X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₆ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₂₇: l3(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₅, X₆, X₇) :|: X₇ < X₃ ∧ 1+X₇ ≤ X₆ ∧ 1+X₇ ≤ X₅ ∧ X₇ ≤ X₃ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₇ ≤ X₀ ∧ X₃ ≤ X₆ ∧ X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₆ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₂₉: l4(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₅, X₆, X₇) :|: X₁ ≤ X₆ ∧ X₀ ≤ X₅
t₃₀: l5(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l3(X₀, X₁, X₂-1, X₃-1, X₅, X₆, X₇) :|: 1+X₇ ≤ X₆ ∧ 1+X₇ ≤ X₅ ∧ 1+X₇ ≤ X₃ ∧ 1+X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₇ ≤ X₀ ∧ X₃ ≤ X₆ ∧ X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₆ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 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 t₂₂: l1(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l3(X₀, X₁, X₀, X₁, X₅, X₆, X₇) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₇ < X₀ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₅

MPRF for transition t₂₇: l3(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₅, X₆, X₇) :|: X₇ < X₃ ∧ 1+X₇ ≤ X₆ ∧ 1+X₇ ≤ X₅ ∧ X₇ ≤ X₃ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₇ ≤ X₀ ∧ X₃ ≤ X₆ ∧ X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₆ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₆+X₇+1 {O(n)}

MPRF:

l1 [X₁+1-X₇ ]
l5 [X₂-X₇ ]
l3 [X₃+1-X₇ ]

MPRF for transition t₂₈: l3(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l1(X₂, X₃, X₂, X₃, X₅, X₆, X₇) :|: X₃ ≤ X₇ ∧ 1+X₇ ≤ X₆ ∧ 1+X₇ ≤ X₅ ∧ X₇ ≤ X₃ ∧ X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₇ ≤ X₀ ∧ X₃ ≤ X₆ ∧ X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₆ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₆+X₇ {O(n)}

MPRF:

l1 [X₁-X₇ ]
l5 [1 ]
l3 [1 ]

MPRF for transition t₃₀: l5(X₀, X₁, X₂, X₃, X₅, X₆, X₇) → l3(X₀, X₁, X₂-1, X₃-1, X₅, X₆, X₇) :|: 1+X₇ ≤ X₆ ∧ 1+X₇ ≤ X₅ ∧ 1+X₇ ≤ X₃ ∧ 1+X₇ ≤ X₂ ∧ 1+X₇ ≤ X₁ ∧ 1+X₇ ≤ X₀ ∧ X₃ ≤ X₆ ∧ X₂ ≤ X₆ ∧ X₁ ≤ X₆ ∧ X₀ ≤ X₆ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₅+X₇ {O(n)}

MPRF:

l1 [X₀-X₇ ]
l5 [X₂-X₇ ]
l3 [X₂-X₇ ]

All Bounds

Timebounds

Overall timebound:2⋅X₆+3⋅X₇+X₅+8 {O(n)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: X₆+X₇+1 {O(n)}
t₂₈: X₆+X₇ {O(n)}
t₂₉: 1 {O(1)}
t₃₀: X₅+X₇ {O(n)}

Costbounds

Overall costbound: 2⋅X₆+3⋅X₇+X₅+8 {O(n)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: X₆+X₇+1 {O(n)}
t₂₈: X₆+X₇ {O(n)}
t₂₉: 1 {O(1)}
t₃₀: X₅+X₇ {O(n)}

Sizebounds

t₂₁, X₀: X₀ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₁, X₆: X₆ {O(n)}
t₂₁, X₇: X₇ {O(n)}
t₂₂, X₀: X₅ {O(n)}
t₂₂, X₁: X₆ {O(n)}
t₂₂, X₂: X₅ {O(n)}
t₂₂, X₃: X₆ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₂, X₆: X₆ {O(n)}
t₂₂, X₇: X₇ {O(n)}
t₂₃, X₀: X₅ {O(n)}
t₂₃, X₁: X₆ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₅: X₅ {O(n)}
t₂₃, X₆: X₆ {O(n)}
t₂₃, X₇: X₇ {O(n)}
t₂₄, X₀: X₅ {O(n)}
t₂₄, X₁: X₆ {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₄, X₅: X₅ {O(n)}
t₂₄, X₆: X₆ {O(n)}
t₂₄, X₇: X₇ {O(n)}
t₂₅, X₀: 3⋅X₅+X₇ {O(n)}
t₂₅, X₁: 2⋅X₆+X₅+X₇ {O(n)}
t₂₅, X₂: 2⋅X₅+X₂+X₇ {O(n)}
t₂₅, X₃: X₃+X₅+X₆+X₇ {O(n)}
t₂₅, X₅: 2⋅X₅ {O(n)}
t₂₅, X₆: 2⋅X₆ {O(n)}
t₂₅, X₇: 2⋅X₇ {O(n)}
t₂₆, X₀: X₅ {O(n)}
t₂₆, X₁: X₆ {O(n)}
t₂₆, X₂: X₂ {O(n)}
t₂₆, X₃: X₃ {O(n)}
t₂₆, X₅: X₅ {O(n)}
t₂₆, X₆: X₆ {O(n)}
t₂₆, X₇: X₇ {O(n)}
t₂₇, X₀: X₅ {O(n)}
t₂₇, X₁: X₆ {O(n)}
t₂₇, X₂: 2⋅X₅+X₇ {O(n)}
t₂₇, X₃: X₅+X₆+X₇ {O(n)}
t₂₇, X₅: X₅ {O(n)}
t₂₇, X₆: X₆ {O(n)}
t₂₇, X₇: X₇ {O(n)}
t₂₈, X₀: 2⋅X₅+X₇ {O(n)}
t₂₈, X₁: X₅+X₆+X₇ {O(n)}
t₂₈, X₂: 2⋅X₅+X₇ {O(n)}
t₂₈, X₃: X₅+X₆+X₇ {O(n)}
t₂₈, X₅: X₅ {O(n)}
t₂₈, X₆: X₆ {O(n)}
t₂₈, X₇: X₇ {O(n)}
t₂₉, X₀: 5⋅X₅+X₇ {O(n)}
t₂₉, X₁: 4⋅X₆+X₅+X₇ {O(n)}
t₂₉, X₂: 2⋅X₅+3⋅X₂+X₇ {O(n)}
t₂₉, X₃: 3⋅X₃+X₅+X₆+X₇ {O(n)}
t₂₉, X₅: 4⋅X₅ {O(n)}
t₂₉, X₆: 4⋅X₆ {O(n)}
t₂₉, X₇: 4⋅X₇ {O(n)}
t₃₀, X₀: X₅ {O(n)}
t₃₀, X₁: X₆ {O(n)}
t₃₀, X₂: 2⋅X₅+X₇ {O(n)}
t₃₀, X₃: X₅+X₆+X₇ {O(n)}
t₃₀, X₅: X₅ {O(n)}
t₃₀, X₆: X₆ {O(n)}
t₃₀, X₇: X₇ {O(n)}