Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < X₂
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₂, X₃)
t₄: l3(X₀, X₁, X₂, X₃) → l1(X₂+1, X₁, X₂, X₃)
t₅: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Preprocessing

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

Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ for location l5

Found invariant X₃ ≤ X₀ for location l1

Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ for location l4

Found invariant 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₂ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₃: l0(X₀, X₂, X₃) → l2(X₀, X₂, X₃)
t₁₄: l1(X₀, X₂, X₃) → l3(X₀, X₂, X₃) :|: X₀ < X₂ ∧ X₃ ≤ X₀
t₁₅: l1(X₀, X₂, X₃) → l4(X₀, X₂, X₃) :|: X₂ ≤ X₀ ∧ X₃ ≤ X₀
t₁₆: l2(X₀, X₂, X₃) → l1(X₃, X₂, X₃)
t₁₇: l3(X₀, X₂, X₃) → l1(X₂+1, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₂
t₁₈: l4(X₀, X₂, X₃) → l5(X₀, X₂, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₄: l1(X₀, X₂, X₃) → l3(X₀, X₂, X₃) :|: X₀ < X₂ ∧ X₃ ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₇: l3(X₀, X₂, X₃) → l1(X₂+1, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₀ ≤ X₂

All Bounds

Timebounds

Overall timebound:6 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}

Costbounds

Overall costbound: 6 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}

Sizebounds

t₁₃, X₀: X₀ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₄, X₀: X₃ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₅, X₀: X₂+X₃+1 {O(n)}
t₁₅, X₂: 2⋅X₂ {O(n)}
t₁₅, X₃: 2⋅X₃ {O(n)}
t₁₆, X₀: X₃ {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₃: X₃ {O(n)}
t₁₇, X₀: X₂+1 {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₈, X₀: X₂+X₃+1 {O(n)}
t₁₈, X₂: 2⋅X₂ {O(n)}
t₁₈, X₃: 2⋅X₃ {O(n)}