Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 39
t₃: l1(X₀, X₁) → l5(X₀, X₁) :|: 40 ≤ X₀
t₄: l2(X₀, X₁) → l3(X₀, X₁) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₅: l2(X₀, X₁) → l4(X₀, X₁) :|: X₁+1 ≤ 0
t₆: l2(X₀, X₁) → l4(X₀, X₁) :|: 1 ≤ X₁
t₇: l3(X₀, X₁) → l1(X₀+1, X₁)
t₈: l4(X₀, X₁) → l1(X₀+2, X₁)
t₉: l5(X₀, X₁) → l7(X₀, X₁)
t₁: l6(X₀, X₁) → l1(0, X₁)

Preprocessing

Found invariant X₀ ≤ 39 ∧ 0 ≤ X₀ for location l2

Found invariant 40 ≤ X₀ for location l7

Found invariant 40 ≤ X₀ for location l5

Found invariant 0 ≤ X₀ for location l1

Found invariant X₀ ≤ 39 ∧ 0 ≤ X₀ for location l4

Found invariant X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁) → l6(X₀, X₁)
t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 39 ∧ 0 ≤ X₀
t₃: l1(X₀, X₁) → l5(X₀, X₁) :|: 40 ≤ X₀ ∧ 0 ≤ X₀
t₄: l2(X₀, X₁) → l3(X₀, X₁) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀
t₅: l2(X₀, X₁) → l4(X₀, X₁) :|: X₁+1 ≤ 0 ∧ X₀ ≤ 39 ∧ 0 ≤ X₀
t₆: l2(X₀, X₁) → l4(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀
t₇: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₈: l4(X₀, X₁) → l1(X₀+2, X₁) :|: X₀ ≤ 39 ∧ 0 ≤ X₀
t₉: l5(X₀, X₁) → l7(X₀, X₁) :|: 40 ≤ X₀
t₁: l6(X₀, X₁) → l1(0, X₁)

MPRF for transition t₂: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:

new bound:

1560 {O(1)}

MPRF:

l2 [1521-39⋅X₀ ]
l3 [1521-39⋅X₀ ]
l4 [1521-40⋅X₀ ]
l1 [1560-39⋅X₀ ]

MPRF for transition t₄: l2(X₀, X₁) → l3(X₀, X₁) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:

new bound:

1522 {O(1)}

MPRF:

l2 [1522-39⋅X₀ ]
l3 [1521-39⋅X₀ ]
l4 [1444-37⋅X₀ ]
l1 [1522-39⋅X₀ ]

MPRF for transition t₅: l2(X₀, X₁) → l4(X₀, X₁) :|: X₁+1 ≤ 0 ∧ X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:

new bound:

40 {O(1)}

MPRF:

l2 [40-X₀ ]
l3 [39-X₀ ]
l4 [38-X₀ ]
l1 [40-X₀ ]

MPRF for transition t₆: l2(X₀, X₁) → l4(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:

new bound:

1522 {O(1)}

MPRF:

l2 [1522-39⋅X₀ ]
l3 [1483-38⋅X₀ ]
l4 [1444-39⋅X₀ ]
l1 [1522-39⋅X₀ ]

MPRF for transition t₈: l4(X₀, X₁) → l1(X₀+2, X₁) :|: X₀ ≤ 39 ∧ 0 ≤ X₀ of depth 1:

new bound:

40 {O(1)}

MPRF:

l2 [40-X₀ ]
l3 [39-X₀ ]
l4 [40-X₀ ]
l1 [40-X₀ ]

knowledge_propagation leads to new time bound 1522 {O(1)} for transition t₇: l3(X₀, X₁) → l1(X₀+1, X₁) :|: X₁ ≤ 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀

All Bounds

Timebounds

Overall timebound:6210 {O(1)}
t₀: 1 {O(1)}
t₂: 1560 {O(1)}
t₃: 1 {O(1)}
t₄: 1522 {O(1)}
t₅: 40 {O(1)}
t₆: 1522 {O(1)}
t₇: 1522 {O(1)}
t₈: 40 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}

Costbounds

Overall costbound: 6210 {O(1)}
t₀: 1 {O(1)}
t₂: 1560 {O(1)}
t₃: 1 {O(1)}
t₄: 1522 {O(1)}
t₅: 40 {O(1)}
t₆: 1522 {O(1)}
t₇: 1522 {O(1)}
t₈: 40 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₂, X₀: 39 {O(1)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: 81 {O(1)}
t₃, X₁: X₁ {O(n)}
t₄, X₀: 39 {O(1)}
t₄, X₁: 0 {O(1)}
t₅, X₀: 39 {O(1)}
t₅, X₁: X₁ {O(n)}
t₆, X₀: 39 {O(1)}
t₆, X₁: X₁ {O(n)}
t₇, X₀: 40 {O(1)}
t₇, X₁: 0 {O(1)}
t₈, X₀: 41 {O(1)}
t₈, X₁: X₁ {O(n)}
t₉, X₀: 81 {O(1)}
t₉, X₁: X₁ {O(n)}
t₁, X₀: 0 {O(1)}
t₁, X₁: X₁ {O(n)}