Initial Problem

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f2, f3
Transitions:
t₁: f0(X₀, X₁) → f2(X₀, 0)
t₂: f2(X₀, X₁) → f2(X₀-1, X₁) :|: 1 ≤ X₀
t₀: f2(X₀, X₁) → f3(X₀, 1) :|: X₀ ≤ 0

Preprocessing

Eliminate variables [X₁] that do not contribute to the problem

Found invariant X₀ ≤ 0 for location f3

Problem after Preprocessing

Start: f0
Program_Vars: X₀
Temp_Vars:
Locations: f0, f2, f3
Transitions:
t₆: f0(X₀) → f2(X₀)
t₇: f2(X₀) → f2(X₀-1) :|: 1 ≤ X₀
t₈: f2(X₀) → f3(X₀) :|: X₀ ≤ 0

MPRF for transition t₇: f2(X₀) → f2(X₀-1) :|: 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

• f2: [X₀]

All Bounds

Timebounds

Overall timebound:X₀+2 {O(n)}
t₆: 1 {O(1)}
t₇: X₀ {O(n)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: X₀+2 {O(n)}
t₆: 1 {O(1)}
t₇: X₀ {O(n)}
t₈: 1 {O(1)}

Sizebounds

t₆, X₀: X₀ {O(n)}
t₇, X₀: X₀ {O(n)}
t₈, X₀: 2⋅X₀ {O(n)}