Initial Problem

Start: l0
Program_Vars: X₀
Temp_Vars: B
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀) → l3(X₀)
t₂: l1(X₀) → l1(B) :|: B ≤ 2+X₀ ∧ X₀+1 ≤ B ∧ B ≤ 9
t₃: l1(X₀) → l2(X₀) :|: X₀+3 ≤ B
t₄: l1(X₀) → l2(X₀) :|: B ≤ X₀
t₅: l1(X₀) → l2(X₀) :|: 10 ≤ B
t₆: l2(X₀) → l4(X₀)
t₁: l3(X₀) → l1(0)

Preprocessing

Found invariant X₀ ≤ 9 ∧ 0 ≤ X₀ for location l2

Found invariant X₀ ≤ 9 ∧ 0 ≤ X₀ for location l1

Found invariant X₀ ≤ 9 ∧ 0 ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars: B
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀) → l3(X₀)
t₂: l1(X₀) → l1(B) :|: B ≤ 2+X₀ ∧ X₀+1 ≤ B ∧ B ≤ 9 ∧ X₀ ≤ 9 ∧ 0 ≤ X₀
t₃: l1(X₀) → l2(X₀) :|: X₀+3 ≤ B ∧ X₀ ≤ 9 ∧ 0 ≤ X₀
t₄: l1(X₀) → l2(X₀) :|: B ≤ X₀ ∧ X₀ ≤ 9 ∧ 0 ≤ X₀
t₅: l1(X₀) → l2(X₀) :|: 10 ≤ B ∧ X₀ ≤ 9 ∧ 0 ≤ X₀
t₆: l2(X₀) → l4(X₀) :|: X₀ ≤ 9 ∧ 0 ≤ X₀
t₁: l3(X₀) → l1(0)

MPRF for transition t₂: l1(X₀) → l1(B) :|: B ≤ 2+X₀ ∧ X₀+1 ≤ B ∧ B ≤ 9 ∧ X₀ ≤ 9 ∧ 0 ≤ X₀ of depth 1:

new bound:

10 {O(1)}

MPRF:

l1 [10-X₀ ]

All Bounds

Timebounds

Overall timebound:16 {O(1)}
t₀: 1 {O(1)}
t₂: 10 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}

Costbounds

Overall costbound: 16 {O(1)}
t₀: 1 {O(1)}
t₂: 10 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₂, X₀: 9 {O(1)}
t₃, X₀: 9 {O(1)}
t₄, X₀: 9 {O(1)}
t₅, X₀: 9 {O(1)}
t₆, X₀: 9 {O(1)}
t₁, X₀: 0 {O(1)}