Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₁: l0(X₀, X₁) → l1(X₀, 0)
t₂: l1(X₀, X₁) → l1(X₀-1, X₁) :|: 1 ≤ X₀
t₀: l1(X₀, X₁) → l2(X₀, 1) :|: X₀ ≤ 0

Preprocessing

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

Found invariant X₀ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₀) → l1(X₀)
t₉: l1(X₀) → l1(X₀-1) :|: 1 ≤ X₀
t₈: l1(X₀) → l2(X₀) :|: X₀ ≤ 0

MPRF for transition t₉: l1(X₀) → l1(X₀-1) :|: 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l1 [X₀ ]

All Bounds

Timebounds

Overall timebound:X₀+2 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₀ {O(n)}

Costbounds

Overall costbound: X₀+2 {O(n)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₀ {O(n)}

Sizebounds

t₇, X₀: X₀ {O(n)}
t₈, X₀: 2⋅X₀ {O(n)}
t₉, X₀: X₀ {O(n)}