Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars: nondef.0, nondef.1
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₇: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l4(X₀, X₁, X₂, X₀+X₂, X₄, X₅, X₆, X₇, X₈) :|: X₂ < 0
t₈: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l4(X₀, X₁, X₂, X₀-X₂, X₄, X₅, X₆, X₇, X₈) :|: 0 ≤ X₂
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l1(X₀, X₁, nondef.0, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l5(X₀, X₁, X₂, X₃, nondef.1, X₅, X₆, X₇, X₈)
t₁₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₃, X₁+1-X₄, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₄ < 0
t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₃, X₁+X₄+1, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 0 ≤ X₄
t₂: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₁ ≤ X₀
t₃: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₀ < X₁+1
t₁: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l6(X₅, X₆, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₃: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)

Preprocessing

Eliminate variables {X₇,X₈} that do not contribute to the problem

Found invariant 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₁ ≤ X₀ for location l2

Found invariant X₆ ≤ X₁ ∧ X₀ ≤ X₅ for location l6

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

Found invariant X₆ ≤ X₁ ∧ X₀ ≤ X₅ ∧ X₀ ≤ X₁ for location l8

Found invariant 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₁ ≤ X₀ for location l1

Found invariant 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l4

Found invariant X₆ ≤ X₁ ∧ X₀ ≤ X₅ ∧ X₀ ≤ X₁ for location l9

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0, nondef.1
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₂₅: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂₆: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₀+X₂, X₄, X₅, X₆) :|: X₂ < 0 ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₁ ≤ X₀
t₂₇: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₀-X₂, X₄, X₅, X₆) :|: 0 ≤ X₂ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₁ ≤ X₀
t₂₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₁ ≤ X₀
t₂₉: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, nondef.0, X₃, X₄, X₅, X₆) :|: 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₁ ≤ X₀
t₃₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, nondef.1, X₅, X₆) :|: 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₃₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₃, X₁+1-X₄, X₂, X₃, X₄, X₅, X₆) :|: X₄ < 0 ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₃₂: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₃, X₁+X₄+1, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₄ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₃₃: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₁ ≤ X₀ ∧ X₆ ≤ X₁ ∧ X₀ ≤ X₅
t₃₄: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ < X₁+1 ∧ X₆ ≤ X₁ ∧ X₀ ≤ X₅
t₃₅: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₅, X₆, X₂, X₃, X₄, X₅, X₆)
t₃₆: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ X₁ ∧ X₀ ≤ X₅ ∧ X₀ ≤ X₁

MPRF for transition t₂₆: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₀+X₂, X₄, X₅, X₆) :|: X₂ < 0 ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF for transition t₂₇: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₀-X₂, X₄, X₅, X₆) :|: 0 ≤ X₂ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF for transition t₂₈: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF for transition t₂₉: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀, X₁, nondef.0, X₃, X₄, X₅, X₆) :|: 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF for transition t₃₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, nondef.1, X₅, X₆) :|: 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF for transition t₃₁: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₃, X₁+1-X₄, X₂, X₃, X₄, X₅, X₆) :|: X₄ < 0 ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF for transition t₃₂: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₃, X₁+X₄+1, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₄ ∧ 1+X₆ ≤ X₅ ∧ X₆ ≤ X₁ ∧ 1+X₆ ≤ X₀ ∧ X₃ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₅+X₆ {O(n)}

MPRF for transition t₃₃: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₁ ≤ X₀ ∧ X₆ ≤ X₁ ∧ X₀ ≤ X₅ of depth 1:

new bound:

X₅+X₆ {O(n)}

All Bounds

Timebounds

Overall timebound:8⋅X₅+8⋅X₆+4 {O(n)}
t₂₅: 1 {O(1)}
t₂₆: X₅+X₆ {O(n)}
t₂₇: X₅+X₆ {O(n)}
t₂₈: X₅+X₆ {O(n)}
t₂₉: X₅+X₆ {O(n)}
t₃₀: X₅+X₆ {O(n)}
t₃₁: X₅+X₆ {O(n)}
t₃₂: X₅+X₆ {O(n)}
t₃₃: X₅+X₆ {O(n)}
t₃₄: 1 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 1 {O(1)}

Costbounds

Overall costbound: 8⋅X₅+8⋅X₆+4 {O(n)}
t₂₅: 1 {O(1)}
t₂₆: X₅+X₆ {O(n)}
t₂₇: X₅+X₆ {O(n)}
t₂₈: X₅+X₆ {O(n)}
t₂₉: X₅+X₆ {O(n)}
t₃₀: X₅+X₆ {O(n)}
t₃₁: X₅+X₆ {O(n)}
t₃₂: X₅+X₆ {O(n)}
t₃₃: X₅+X₆ {O(n)}
t₃₄: 1 {O(1)}
t₃₅: 1 {O(1)}
t₃₆: 1 {O(1)}

Sizebounds

t₂₅, X₀: X₀ {O(n)}
t₂₅, X₁: X₁ {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, X₅: X₅ {O(n)}
t₂₆, X₆: X₆ {O(n)}
t₂₇, X₅: X₅ {O(n)}
t₂₇, X₆: X₆ {O(n)}
t₂₈, X₅: X₅ {O(n)}
t₂₈, X₆: X₆ {O(n)}
t₂₉, X₅: X₅ {O(n)}
t₂₉, X₆: X₆ {O(n)}
t₃₀, X₅: X₅ {O(n)}
t₃₀, X₆: X₆ {O(n)}
t₃₁, X₅: X₅ {O(n)}
t₃₁, X₆: X₆ {O(n)}
t₃₂, X₅: X₅ {O(n)}
t₃₂, X₆: X₆ {O(n)}
t₃₃, X₅: X₅ {O(n)}
t₃₃, X₆: X₆ {O(n)}
t₃₄, X₅: 3⋅X₅ {O(n)}
t₃₄, X₆: 3⋅X₆ {O(n)}
t₃₅, X₀: X₅ {O(n)}
t₃₅, X₁: X₆ {O(n)}
t₃₅, X₂: X₂ {O(n)}
t₃₅, X₃: X₃ {O(n)}
t₃₅, X₄: X₄ {O(n)}
t₃₅, X₅: X₅ {O(n)}
t₃₅, X₆: X₆ {O(n)}
t₃₆, X₅: 3⋅X₅ {O(n)}
t₃₆, X₆: 3⋅X₆ {O(n)}