Initial Problem

Start: f3
Program_Vars: X₀
Temp_Vars:
Locations: f2, f3
Transitions:
t₁: f2(X₀) → f2(X₀-1) :|: 2 ≤ X₀
t₂: f2(X₀) → f2(X₀-1) :|: X₀ ≤ 1
t₀: f3(X₀) → f2(X₀)

Preprocessing

Problem after Preprocessing

Start: f3
Program_Vars: X₀
Temp_Vars:
Locations: f2, f3
Transitions:
t₁: f2(X₀) → f2(X₀-1) :|: 2 ≤ X₀
t₂: f2(X₀) → f2(X₀-1) :|: X₀ ≤ 1
t₀: f3(X₀) → f2(X₀)

MPRF for transition t₁: f2(X₀) → f2(X₀-1) :|: 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

• f2: [X₀]

Found invariant X₀ ≤ 0 for location f2_v1

Found invariant 1 ≤ X₀ for location f2_v2

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: inf {Infinity}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: X₀ {O(n)}
t₂: inf {Infinity}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₁, X₀: X₀ {O(n)}