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 X₁ ≤ 0 for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₇: l0(X₁) → l1(X₁)
t₈: l1(X₁) → l1(X₁-1) :|: 1 ≤ X₁
t₉: l1(X₁) → l2(X₁) :|: X₁ ≤ 0

MPRF for transition t₈: l1(X₁) → l1(X₁-1) :|: 1 ≤ X₁ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

l1 [X₁ ]

All Bounds

Timebounds

Overall timebound:X₁+2 {O(n)}
t₇: 1 {O(1)}
t₈: X₁ {O(n)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: X₁+2 {O(n)}
t₇: 1 {O(1)}
t₈: X₁ {O(n)}
t₉: 1 {O(1)}

Sizebounds

t₇, X₁: X₁ {O(n)}
t₈, X₁: X₁ {O(n)}
t₉, X₁: 2⋅X₁ {O(n)}