Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂
Temp_Vars: D
Locations: f0, f1, f4
Transitions:
t₀: f0(X₀, X₁, X₂) → f1(0, X₁, X₂)
t₁: f1(X₀, X₁, X₂) → f1(X₀, X₁-1, D) :|: 1 ≤ X₁
t₂: f1(X₀, X₁, X₂) → f4(X₀, X₁, D) :|: X₁ ≤ 0
t₃: f4(X₀, X₁, X₂) → f4(1, X₁, D)

Preprocessing

Eliminate variables [D; X₀; X₂] that do not contribute to the problem

Found invariant X₀ ≤ 0 for location f4

Problem after Preprocessing

Start: f0
Program_Vars: X₀
Temp_Vars:
Locations: f0, f1, f4
Transitions:
t₉: f0(X₀) → f1(X₀)
t₁₀: f1(X₀) → f1(X₀-1) :|: 1 ≤ X₀
t₁₁: f1(X₀) → f4(X₀) :|: X₀ ≤ 0
t₁₂: f4(X₀) → f4(X₀) :|: X₀ ≤ 0

MPRF for transition t₁₀: f1(X₀) → f1(X₀-1) :|: 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

• f1: [X₀]

Found invariant X₀ ≤ 0 for location f4

Found invariant X₀ ≤ 0 for location f4_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₉: 1 {O(1)}
t₁₀: X₀ {O(n)}
t₁₁: 1 {O(1)}
t₁₂: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₉: 1 {O(1)}
t₁₀: X₀ {O(n)}
t₁₁: 1 {O(1)}
t₁₂: inf {Infinity}

Sizebounds

t₉, X₀: X₀ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₁, X₀: 2⋅X₀ {O(n)}
t₁₂, X₀: 2⋅X₀ {O(n)}