Initial Problem

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

Preprocessing

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:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₁, X₃, X₄, X₅) :|: X₅ < X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₅ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₂, X₃, X₄, X₅)
t₅: 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
t₄: 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
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₅ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃
t₇: 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
t₆: 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 t₂: 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 t₄: 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 t₅: 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 t₆: 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)}

MPRF for transition t₇: 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)}

All Bounds

Timebounds

Overall timebound:2⋅X₄+3⋅X₃+5⋅X₅+4 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₃+X₅ {O(n)}
t₃: 1 {O(1)}
t₄: X₄+X₅ {O(n)}
t₅: X₃+X₅ {O(n)}
t₆: X₄+X₅ {O(n)}
t₇: X₃+X₅ {O(n)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₄+3⋅X₃+5⋅X₅+4 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₃+X₅ {O(n)}
t₃: 1 {O(1)}
t₄: X₄+X₅ {O(n)}
t₅: X₃+X₅ {O(n)}
t₆: X₄+X₅ {O(n)}
t₇: X₃+X₅ {O(n)}
t₈: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: 2⋅X₃+X₅ {O(n)}
t₂, X₁: 3⋅X₄+X₅ {O(n)}
t₂, X₂: 2⋅X₄+X₅ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 3⋅X₃+X₅ {O(n)}
t₃, X₁: 3⋅X₄+X₅ {O(n)}
t₃, X₂: 2⋅X₄+X₂+X₅ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₄, X₀: 2⋅X₃+X₅ {O(n)}
t₄, X₁: 3⋅X₄+X₅ {O(n)}
t₄, X₂: 2⋅X₄+X₅ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₅, X₀: 2⋅X₃+X₅ {O(n)}
t₅, X₁: 2⋅X₅+6⋅X₄ {O(n)}
t₅, X₂: 2⋅X₄+X₅ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₆, X₀: 2⋅X₃+X₅ {O(n)}
t₆, X₁: 3⋅X₄+X₅ {O(n)}
t₆, X₂: 2⋅X₄+X₅ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₇, X₀: 2⋅X₃+X₅ {O(n)}
t₇, X₁: 2⋅X₄+X₅ {O(n)}
t₇, X₂: 2⋅X₄+X₅ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₅ {O(n)}
t₈, X₀: 3⋅X₃+X₅ {O(n)}
t₈, X₁: 3⋅X₄+X₅ {O(n)}
t₈, X₂: 2⋅X₄+X₂+X₅ {O(n)}
t₈, X₃: 2⋅X₃ {O(n)}
t₈, X₄: 2⋅X₄ {O(n)}
t₈, X₅: 2⋅X₅ {O(n)}