Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₁, X₀, X₂, X₃, X₄) :|: X₁ < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Eliminate variables {X₂} that do not contribute to the problem

Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ for location l1

Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l4

Found invariant X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₉: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₁₀: l1(X₀, X₁, X₂, X₃) → l1(X₁, X₀, X₂, X₃) :|: X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂
t₁₁: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂
t₁₂: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₁₃: l3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₁

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₁₀: l1(X₀, X₁, X₂, X₃) → l1(X₁, X₀, X₂, X₃) :|: X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂

All Bounds

Timebounds

Overall timebound:5 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 5 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}

Sizebounds

t₉, X₀: X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₃ {O(n)}
t₁₀, X₀: X₃ {O(n)}
t₁₀, X₁: X₂ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₁, X₀: X₂+X₃ {O(n)}
t₁₁, X₁: X₂+X₃ {O(n)}
t₁₁, X₂: 2⋅X₂ {O(n)}
t₁₁, X₃: 2⋅X₃ {O(n)}
t₁₂, X₀: X₂ {O(n)}
t₁₂, X₁: X₃ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₃, X₀: X₂+X₃ {O(n)}
t₁₃, X₁: X₂+X₃ {O(n)}
t₁₃, X₂: 2⋅X₂ {O(n)}
t₁₃, X₃: 2⋅X₃ {O(n)}