Initial Problem

Start: f3
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f3, f4
Transitions:
t₁: f0(X₀, X₁) → f0(X₀, X₁-1) :|: 1 ≤ X₁
t₃: f0(X₀, X₁) → f4(-1, X₁) :|: X₁ ≤ 0
t₀: f3(X₀, X₁) → f0(0, X₁)
t₂: f4(X₀, X₁) → f4(X₀, X₁)

Preprocessing

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

Found invariant X₀ ≤ 0 for location f4

Problem after Preprocessing

Start: f3
Program_Vars: X₀
Temp_Vars:
Locations: f0, f3, f4
Transitions:
t₈: f0(X₀) → f0(X₀-1) :|: 1 ≤ X₀
t₉: f0(X₀) → f4(X₀) :|: X₀ ≤ 0
t₁₀: f3(X₀) → f0(X₀)
t₁₁: f4(X₀) → f4(X₀) :|: X₀ ≤ 0

MPRF for transition t₈: f0(X₀) → f0(X₀-1) :|: 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

• f0: [X₀]

Found invariant X₀ ≤ 0 for location f4

Found invariant X₀ ≤ 0 for location f4_v1

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₈: X₀ {O(n)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₈: X₀ {O(n)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: inf {Infinity}

Sizebounds

t₈, X₀: X₀ {O(n)}
t₉, X₀: 2⋅X₀ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₁, X₀: 2⋅X₀ {O(n)}