Initial Problem

Start: f3
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: f2, f3, f300
Transitions:
t₁: f2(X₀, X₁) → f2(X₀-1, X₁) :|: 1 ≤ X₀
t₂: f2(X₀, X₁) → f300(X₀-1, C) :|: X₀ ≤ 0
t₀: f3(X₀, X₁) → f2(X₀, X₁)

Preprocessing

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

Found invariant 1+X₀ ≤ 0 for location f300

Problem after Preprocessing

Start: f3
Program_Vars: X₀
Temp_Vars:
Locations: f2, f3, f300
Transitions:
t₅: f2(X₀) → f2(X₀-1) :|: 1 ≤ X₀
t₆: f2(X₀) → f300(X₀-1) :|: X₀ ≤ 0
t₇: f3(X₀) → f2(X₀)

MPRF for transition t₅: f2(X₀) → f2(X₀-1) :|: 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

• f2: [X₀]

All Bounds

Timebounds

Overall timebound:X₀+2 {O(n)}
t₅: X₀ {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}

Costbounds

Overall costbound: X₀+2 {O(n)}
t₅: X₀ {O(n)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}

Sizebounds

t₅, X₀: X₀ {O(n)}
t₆, X₀: 2⋅X₀+2 {O(n)}
t₇, X₀: X₀ {O(n)}