Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₁, X₃, X₄, X₅, X₆) :|: X₆ < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₀ ≤ X₆
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₄, X₅, X₂, X₃, X₄, X₅, X₆)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₂ ≤ X₆
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ < X₂
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆)
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀-1, X₂, X₂, X₃, X₄, X₅, X₆)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂-1, X₃, X₄, X₅, X₆)

Preprocessing

Eliminate variables {X₃} that do not contribute to the problem

Found invariant 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ for location l6

Found invariant X₀ ≤ X₅ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃ for location l7

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

Found invariant X₁ ≤ X₄ ∧ X₀ ≤ X₃ for location l1

Found invariant X₀ ≤ X₅ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃ for location l4

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₇: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₁₈: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₁, X₃, X₄, X₅) :|: X₅ < X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃
t₁₉: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₅ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃
t₂₀: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₂, X₃, X₄, X₅)
t₂₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₅ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₀ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁
t₂₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ < X₂ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₀ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁
t₂₃: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₅ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃
t₂₄: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₂, X₂, X₃, X₄, X₅) :|: 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₀ ∧ X₂ ≤ X₅ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀
t₂₅: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂-1, X₃, X₄, X₅) :|: 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁

MPRF for transition t₁₈: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₁, X₃, X₄, X₅) :|: X₅ < X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃ of depth 1:

new bound:

X₃+X₅ {O(n)}

MPRF for transition t₂₁: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₂ ≤ X₅ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₀ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₃+X₅ {O(n)}

MPRF for transition t₂₂: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ < X₂ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₀ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₄+X₅ {O(n)}

MPRF for transition t₂₄: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₂, X₂, X₃, X₄, X₅) :|: 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₀ ∧ X₂ ≤ X₅ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ of depth 1:

new bound:

X₃+X₅ {O(n)}

MPRF for transition t₂₅: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂-1, X₃, X₄, X₅) :|: 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₂ ∧ 1+X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₂ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₄+X₅ {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₄+3⋅X₃+5⋅X₅+4 {O(n)}
t₁₇: 1 {O(1)}
t₁₈: X₃+X₅ {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₃+X₅ {O(n)}
t₂₂: X₄+X₅ {O(n)}
t₂₃: 1 {O(1)}
t₂₄: X₃+X₅ {O(n)}
t₂₅: X₄+X₅ {O(n)}

Costbounds

Overall costbound: 2⋅X₄+3⋅X₃+5⋅X₅+4 {O(n)}
t₁₇: 1 {O(1)}
t₁₈: X₃+X₅ {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₃+X₅ {O(n)}
t₂₂: X₄+X₅ {O(n)}
t₂₃: 1 {O(1)}
t₂₄: X₃+X₅ {O(n)}
t₂₅: X₄+X₅ {O(n)}

Sizebounds

t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₇, X₅: X₅ {O(n)}
t₁₈, X₀: 2⋅X₃+X₅ {O(n)}
t₁₈, X₁: 3⋅X₄+X₅ {O(n)}
t₁₈, X₂: 2⋅X₄+X₅ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₉, X₀: 3⋅X₃+X₅ {O(n)}
t₁₉, X₁: 3⋅X₄+X₅ {O(n)}
t₁₉, X₂: 2⋅X₄+X₂+X₅ {O(n)}
t₁₉, X₃: 2⋅X₃ {O(n)}
t₁₉, X₄: 2⋅X₄ {O(n)}
t₁₉, X₅: 2⋅X₅ {O(n)}
t₂₀, X₀: X₃ {O(n)}
t₂₀, X₁: X₄ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₀, X₄: X₄ {O(n)}
t₂₀, X₅: X₅ {O(n)}
t₂₁, X₀: 2⋅X₃+X₅ {O(n)}
t₂₁, X₁: 2⋅X₅+6⋅X₄ {O(n)}
t₂₁, X₂: 2⋅X₄+X₅ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₁, X₅: X₅ {O(n)}
t₂₂, X₀: 2⋅X₃+X₅ {O(n)}
t₂₂, X₁: 3⋅X₄+X₅ {O(n)}
t₂₂, X₂: 2⋅X₄+X₅ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₂, X₄: X₄ {O(n)}
t₂₂, X₅: X₅ {O(n)}
t₂₃, X₀: 3⋅X₃+X₅ {O(n)}
t₂₃, X₁: 3⋅X₄+X₅ {O(n)}
t₂₃, X₂: 2⋅X₄+X₂+X₅ {O(n)}
t₂₃, X₃: 2⋅X₃ {O(n)}
t₂₃, X₄: 2⋅X₄ {O(n)}
t₂₃, X₅: 2⋅X₅ {O(n)}
t₂₄, X₀: 2⋅X₃+X₅ {O(n)}
t₂₄, X₁: 2⋅X₄+X₅ {O(n)}
t₂₄, X₂: 2⋅X₄+X₅ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₄, X₄: X₄ {O(n)}
t₂₄, X₅: X₅ {O(n)}
t₂₅, X₀: 2⋅X₃+X₅ {O(n)}
t₂₅, X₁: 3⋅X₄+X₅ {O(n)}
t₂₅, X₂: 2⋅X₄+X₅ {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₂₅, X₄: X₄ {O(n)}
t₂₅, X₅: X₅ {O(n)}