Initial Problem

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

Preprocessing

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

Found invariant 1+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) :|: 0 ≤ X₀
t₈: l1(X₀) → l2(X₀) :|: X₀+1 ≤ 0

MPRF for transition t₇: l1(X₀) → l1(X₀-1) :|: 0 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

All Bounds

Timebounds

Overall timebound:X₀+3 {O(n)}
t₆: 1 {O(1)}
t₇: X₀+1 {O(n)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: X₀+3 {O(n)}
t₆: 1 {O(1)}
t₇: X₀+1 {O(n)}
t₈: 1 {O(1)}

Sizebounds

t₆, X₀: X₀ {O(n)}
t₇, X₀: X₀+1 {O(n)}
t₈, X₀: 2⋅X₀+1 {O(n)}