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, X₂, X₃, X₄, X₅) :|: X₀ < 0
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₅, X₂, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₁+1000, X₀+1, X₄, X₅)
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₂, X₂, X₃, X₄, X₅) :|: X₂ < 100
t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 100 ≤ X₂
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂-100, X₃, X₄, X₅)

Preprocessing

Found invariant 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ 1+X₃+X₄ ≤ 0 ∧ 101+X₄ ≤ X₂ ∧ X₄ ≤ 899+X₁ ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ 100+X₃ ≤ X₂ ∧ X₃ ≤ 900+X₁ ∧ X₃ ≤ 1+X₀ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ 1000+X₁ ∧ 100 ≤ X₂ ∧ 0 ≤ 800+X₁+X₂ ∧ 101+X₀ ≤ X₂ ∧ 0 ≤ 900+X₁ ∧ X₀ ≤ 899+X₁ ∧ 1+X₀ ≤ 0 for location l6

Found invariant X₄ ≤ X₀ ∧ 0 ≤ X₀ for location l7

Found invariant 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ 1+X₃+X₄ ≤ 0 ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ X₃ ≤ 1+X₀ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ 1000+X₁ ∧ 1+X₀ ≤ 0 for location l5

Found invariant X₄ ≤ X₀ for location l1

Found invariant X₄ ≤ X₀ ∧ 0 ≤ X₀ for location l4

Found invariant 1+X₄ ≤ 0 ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ 1+X₀ ≤ 0 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, X₂, X₃, X₄, X₅) :|: X₀ < 0 ∧ X₄ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: 0 ≤ X₀ ∧ X₄ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₅, X₂, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₁+1000, X₀+1, X₄, X₅) :|: 1+X₄ ≤ 0 ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ 1+X₀ ≤ 0
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₀ ∧ 0 ≤ X₀
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₂, X₂, X₃, X₄, X₅) :|: X₂ < 100 ∧ 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ 1+X₃+X₄ ≤ 0 ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ X₃ ≤ 1+X₀ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ 1000+X₁ ∧ 1+X₀ ≤ 0
t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 100 ≤ X₂ ∧ 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ 1+X₃+X₄ ≤ 0 ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ X₃ ≤ 1+X₀ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ 1000+X₁ ∧ 1+X₀ ≤ 0
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂-100, X₃, X₄, X₅) :|: 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ 1+X₃+X₄ ≤ 0 ∧ 101+X₄ ≤ X₂ ∧ X₄ ≤ 899+X₁ ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ 100+X₃ ≤ X₂ ∧ X₃ ≤ 900+X₁ ∧ X₃ ≤ 1+X₀ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ 1000+X₁ ∧ 100 ≤ X₂ ∧ 0 ≤ 800+X₁+X₂ ∧ 101+X₀ ≤ X₂ ∧ 0 ≤ 900+X₁ ∧ X₀ ≤ 899+X₁ ∧ 1+X₀ ≤ 0

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < 0 ∧ X₄ ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [-X₀-1 ]
l1 [-X₀ ]
l6 [-X₃ ]
l5 [-X₃ ]

MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₁+1000, X₀+1, X₄, X₅) :|: 1+X₄ ≤ 0 ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ 1+X₀ ≤ 0 of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [-X₀ ]
l1 [-X₀ ]
l6 [-X₃ ]
l5 [-X₀-1 ]

MPRF for transition t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: 100 ≤ X₂ ∧ 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ 1+X₃+X₄ ≤ 0 ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ X₃ ≤ 1+X₀ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ 1000+X₁ ∧ 1+X₀ ≤ 0 of depth 1:

new bound:

1000⋅X₄+X₅+99 {O(n)}

MPRF:

l3 [X₁-1000⋅X₀-99 ]
l1 [X₁-1000⋅X₀-99 ]
l6 [X₂-1000⋅X₀-1199 ]
l5 [X₂-1000⋅X₀-1099 ]

MPRF for transition t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₂, X₂, X₃, X₄, X₅) :|: X₂ < 100 ∧ 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ 1+X₃+X₄ ≤ 0 ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ X₃ ≤ 1+X₀ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ 1000+X₁ ∧ 1+X₀ ≤ 0 of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [-X₀ ]
l1 [-X₀ ]
l6 [-X₀ ]
l5 [1-X₃ ]

MPRF for transition t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂-100, X₃, X₄, X₅) :|: 1+X₄ ≤ 0 ∧ 1+X₄ ≤ X₃ ∧ 1+X₃+X₄ ≤ 0 ∧ 101+X₄ ≤ X₂ ∧ X₄ ≤ 899+X₁ ∧ X₄ ≤ X₀ ∧ 2+X₀+X₄ ≤ 0 ∧ X₃ ≤ 0 ∧ 100+X₃ ≤ X₂ ∧ X₃ ≤ 900+X₁ ∧ X₃ ≤ 1+X₀ ∧ 1+X₀+X₃ ≤ 0 ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ 1000+X₁ ∧ 100 ≤ X₂ ∧ 0 ≤ 800+X₁+X₂ ∧ 101+X₀ ≤ X₂ ∧ 0 ≤ 900+X₁ ∧ X₀ ≤ 899+X₁ ∧ 1+X₀ ≤ 0 of depth 1:

new bound:

1000⋅X₄+X₅+99 {O(n)}

MPRF:

l3 [X₁-1000⋅X₀-99 ]
l1 [X₁-1000⋅X₀-99 ]
l6 [X₂-1000⋅X₃-99 ]
l5 [X₂-1000⋅X₃-99 ]

All Bounds

Timebounds

Overall timebound:2⋅X₅+2003⋅X₄+202 {O(n)}
t₀: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₄ {O(n)}
t₈: 1 {O(1)}
t₅: 1000⋅X₄+X₅+99 {O(n)}
t₆: X₄ {O(n)}
t₇: 1000⋅X₄+X₅+99 {O(n)}

Costbounds

Overall costbound: 2⋅X₅+2003⋅X₄+202 {O(n)}
t₀: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₁: 1 {O(1)}
t₄: X₄ {O(n)}
t₈: 1 {O(1)}
t₅: 1000⋅X₄+X₅+99 {O(n)}
t₆: X₄ {O(n)}
t₇: 1000⋅X₄+X₅+99 {O(n)}

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)}
t₂, X₀: X₄ {O(n)}
t₂, X₁: 1000⋅X₄+X₅ {O(n)}
t₂, X₂: 2⋅X₅+2000⋅X₄+X₂ {O(n)}
t₂, X₃: 2⋅X₄+X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: X₅ {O(n)}
t₃, X₀: 2⋅X₄ {O(n)}
t₃, X₁: 1000⋅X₄+2⋅X₅ {O(n)}
t₃, X₂: 2⋅X₅+2000⋅X₄+X₂ {O(n)}
t₃, X₃: 2⋅X₄+X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₁, X₀: X₄ {O(n)}
t₁, X₁: X₅ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₄, X₀: X₄ {O(n)}
t₄, X₁: 1000⋅X₄+X₅ {O(n)}
t₄, X₂: 1000⋅X₄+X₅ {O(n)}
t₄, X₃: X₄ {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: X₅ {O(n)}
t₈, X₀: 2⋅X₄ {O(n)}
t₈, X₁: 1000⋅X₄+2⋅X₅ {O(n)}
t₈, X₂: 2⋅X₅+2000⋅X₄+X₂ {O(n)}
t₈, X₃: 2⋅X₄+X₃ {O(n)}
t₈, X₄: 2⋅X₄ {O(n)}
t₈, X₅: 2⋅X₅ {O(n)}
t₅, X₀: X₄ {O(n)}
t₅, X₁: 1000⋅X₄+X₅ {O(n)}
t₅, X₂: 1000⋅X₄+X₅ {O(n)}
t₅, X₃: X₄ {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: X₅ {O(n)}
t₆, X₀: X₄ {O(n)}
t₆, X₁: 1000⋅X₄+X₅ {O(n)}
t₆, X₂: 2⋅X₅+2000⋅X₄ {O(n)}
t₆, X₃: 2⋅X₄ {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: X₅ {O(n)}
t₇, X₀: X₄ {O(n)}
t₇, X₁: 1000⋅X₄+X₅ {O(n)}
t₇, X₂: 1000⋅X₄+X₅ {O(n)}
t₇, X₃: X₄ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₅ {O(n)}