Initial Problem

Start: f3
Program_Vars: X₀
Temp_Vars:
Locations: f1, f3
Transitions:
t₁: f1(X₀) → f1(X₀-1) :|: 1 ≤ X₀
t₀: f3(X₀) → f1(X₀) :|: 0 ≤ X₀

Preprocessing

Found invariant 0 ≤ X₀ for location f1

Problem after Preprocessing

Start: f3
Program_Vars: X₀
Temp_Vars:
Locations: f1, f3
Transitions:
t₁: f1(X₀) → f1(X₀-1) :|: 1 ≤ X₀ ∧ 0 ≤ X₀
t₀: f3(X₀) → f1(X₀) :|: 0 ≤ X₀

MPRF for transition t₁: f1(X₀) → f1(X₀-1) :|: 1 ≤ X₀ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

• f1: [1+X₀]

All Bounds

Timebounds

Overall timebound:X₀+2 {O(n)}
t₀: 1 {O(1)}
t₁: X₀+1 {O(n)}

Costbounds

Overall costbound: X₀+2 {O(n)}
t₀: 1 {O(1)}
t₁: X₀+1 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₁, X₀: X₀ {O(n)}