Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁) → l5(X₀, X₁)
t₅: l1(X₀, X₁) → l2(X₀, X₀) :|: X₀ ≤ X₁+2 ∧ 1+X₁ ≤ X₀ ∧ X₀ < 10
t₆: l1(X₀, X₁) → l4(X₀, X₁) :|: 2+X₁ < X₀
t₇: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ < X₁+1
t₈: l1(X₀, X₁) → l4(X₀, X₁) :|: 10 ≤ X₀
t₂: l2(X₀, X₁) → l3(X₀, X₁)
t₄: l3(X₀, X₁) → l1(nondef.0, X₁)
t₉: l4(X₀, X₁) → l6(X₀, X₁)
t₁: l5(X₀, X₁) → l2(X₀, 0)

Preprocessing

Found invariant X₁ ≤ 9 ∧ 0 ≤ X₁ for location l2

Found invariant 0 ≤ X₁ for location l6

Found invariant 0 ≤ X₁ for location l1

Found invariant 0 ≤ X₁ for location l4

Found invariant 0 ≤ X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6
Transitions:
t₀: l0(X₀, X₁) → l5(X₀, X₁)
t₅: l1(X₀, X₁) → l2(X₀, X₀) :|: X₀ ≤ X₁+2 ∧ 1+X₁ ≤ X₀ ∧ X₀ < 10 ∧ 0 ≤ X₁
t₆: l1(X₀, X₁) → l4(X₀, X₁) :|: 2+X₁ < X₀ ∧ 0 ≤ X₁
t₇: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ < X₁+1 ∧ 0 ≤ X₁
t₈: l1(X₀, X₁) → l4(X₀, X₁) :|: 10 ≤ X₀ ∧ 0 ≤ X₁
t₂: l2(X₀, X₁) → l3(X₀, X₁) :|: X₁ ≤ 9 ∧ 0 ≤ X₁
t₄: l3(X₀, X₁) → l1(nondef.0, X₁) :|: 0 ≤ X₁
t₉: l4(X₀, X₁) → l6(X₀, X₁) :|: 0 ≤ X₁
t₁: l5(X₀, X₁) → l2(X₀, 0)

MPRF for transition t₅: l1(X₀, X₁) → l2(X₀, X₀) :|: X₀ ≤ X₁+2 ∧ 1+X₁ ≤ X₀ ∧ X₀ < 10 ∧ 0 ≤ X₁ of depth 1:

new bound:

9 {O(1)}

MPRF:

l2 [9-X₁ ]
l3 [9-X₁ ]
l1 [9-X₁ ]

MPRF for transition t₂: l2(X₀, X₁) → l3(X₀, X₁) :|: X₁ ≤ 9 ∧ 0 ≤ X₁ of depth 1:

new bound:

10 {O(1)}

MPRF:

l2 [10-X₁ ]
l3 [9-X₁ ]
l1 [9-X₁ ]

knowledge_propagation leads to new time bound 10 {O(1)} for transition t₄: l3(X₀, X₁) → l1(nondef.0, X₁) :|: 0 ≤ X₁

All Bounds

Timebounds

Overall timebound:35 {O(1)}
t₀: 1 {O(1)}
t₅: 9 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₂: 10 {O(1)}
t₄: 10 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}

Costbounds

Overall costbound: 35 {O(1)}
t₀: 1 {O(1)}
t₅: 9 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₂: 10 {O(1)}
t₄: 10 {O(1)}
t₉: 1 {O(1)}
t₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₅, X₀: 9 {O(1)}
t₅, X₁: 9 {O(1)}
t₆, X₁: 9 {O(1)}
t₇, X₁: 9 {O(1)}
t₈, X₁: 9 {O(1)}
t₂, X₀: X₀+9 {O(n)}
t₂, X₁: 9 {O(1)}
t₄, X₁: 9 {O(1)}
t₉, X₁: 27 {O(1)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 0 {O(1)}