Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₂: l1(X₀, X₁, X₂) → l1(X₀, X₁, X₂-1) :|: 2 < X₂
t₃: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₂ ≤ 2
t₁: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₁)
t₄: l3(X₀, X₁, X₂) → l4(X₀, X₁, X₂)

Preprocessing

Eliminate variables {X₀} that do not contribute to the problem

Found invariant X₁ ≤ X₀ for location l1

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ for location l4

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₉: l0(X₀, X₁) → l2(X₀, X₁)
t₁₀: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 2 < X₁ ∧ X₁ ≤ X₀
t₁₁: l1(X₀, X₁) → l3(X₀, X₁) :|: X₁ ≤ 2 ∧ X₁ ≤ X₀
t₁₂: l2(X₀, X₁) → l1(X₀, X₀)
t₁₃: l3(X₀, X₁) → l4(X₀, X₁) :|: X₁ ≤ 2 ∧ X₁ ≤ X₀

MPRF for transition t₁₀: l1(X₀, X₁) → l1(X₀, X₁-1) :|: 2 < X₁ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

All Bounds

Timebounds

Overall timebound:X₀+4 {O(n)}
t₉: 1 {O(1)}
t₁₀: X₀ {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: X₀+4 {O(n)}
t₉: 1 {O(1)}
t₁₀: X₀ {O(n)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}

Sizebounds

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