Initial Problem

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

Preprocessing

Eliminate variables {X₀} 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:
t₆: l0(X₀) → l1(X₀)
t₇: l1(X₀) → l1(X₀-1) :|: 1 ≤ X₀
t₈: l1(X₀) → l2(X₀) :|: X₀ ≤ 0

MPRF for transition t₇: l1(X₀) → l1(X₀-1) :|: 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

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)}