Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₂: l1(X₀, X₁) → l3(X₀, X₁) :|: 0 ≤ X₀
t₃: l1(X₀, X₁) → l4(X₀, X₁) :|: X₀ < 0
t₁: l2(X₀, X₁) → l1(0, X₁)
t₄: l3(X₀, X₁) → l1(X₀-1, X₁)
t₅: l4(X₀, X₁) → l5(X₀, X₁)

Preprocessing

Eliminate variables {X₁} that do not contribute to the problem

Found invariant 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location l5

Found invariant X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location l1

Found invariant 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀ for location l4

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

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₁: l0(X₀) → l2(X₀)
t₁₂: l1(X₀) → l3(X₀) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₁₃: l1(X₀) → l4(X₀) :|: X₀ < 0 ∧ X₀ ≤ 0 ∧ 0 ≤ 1+X₀
t₁₄: l2(X₀) → l1(0)
t₁₅: l3(X₀) → l1(X₀-1) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₆: l4(X₀) → l5(X₀) :|: 1+X₀ ≤ 0 ∧ 0 ≤ 1+X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₂: l1(X₀) → l3(X₀) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1+X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₅: l3(X₀) → l1(X₀-1) :|: X₀ ≤ 0 ∧ 0 ≤ X₀

All Bounds

Timebounds

Overall timebound:6 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Costbounds

Overall costbound: 6 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}

Sizebounds

t₁₁, X₀: X₀ {O(n)}
t₁₂, X₀: 0 {O(1)}
t₁₃, X₀: 1 {O(1)}
t₁₄, X₀: 0 {O(1)}
t₁₅, X₀: 1 {O(1)}
t₁₆, X₀: 1 {O(1)}