Initial Problem

Start: f2
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: f1, f2, f300
Transitions:
t₂: f2(X₀, X₁) → f300(X₀, X₁)
t₀: f300(X₀, X₁) → f1(X₀, C) :|: 1+X₀ ≤ 0
t₁: f300(X₀, X₁) → f300(X₀-1, X₁) :|: 0 ≤ X₀

Preprocessing

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

Found invariant 1+X₀ ≤ 0 for location f1

Problem after Preprocessing

Start: f2
Program_Vars: X₀
Temp_Vars:
Locations: f1, f2, f300
Transitions:
t₆: f2(X₀) → f300(X₀)
t₇: f300(X₀) → f1(X₀) :|: 1+X₀ ≤ 0
t₈: f300(X₀) → f300(X₀-1) :|: 0 ≤ X₀

MPRF for transition t₈: f300(X₀) → f300(X₀-1) :|: 0 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

• f300: [1+X₀]

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

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