Initial Problem

Start: f2
Program_Vars: X₀, X₁, X₂
Temp_Vars: D, E
Locations: f1, f2, f3
Transitions:
t₁: f1(X₀, X₁, X₂) → f1(1+X₀, X₁, X₂) :|: X₀ ≤ 499
t₀: f1(X₀, X₁, X₂) → f3(X₀, D, X₂) :|: 500 ≤ X₀
t₃: f2(X₀, X₁, X₂) → f1(1+D, X₁, D) :|: D ≤ 499
t₂: f2(X₀, X₁, X₂) → f3(E, D, E) :|: 500 ≤ E

Preprocessing

Eliminate variables [X₁; X₂] that do not contribute to the problem

Found invariant X₀ ≤ 500 for location f1

Found invariant 500 ≤ X₀ for location f3

Problem after Preprocessing

Start: f2
Program_Vars: X₀
Temp_Vars: D, E
Locations: f1, f2, f3
Transitions:
t₆: f1(X₀) → f1(1+X₀) :|: X₀ ≤ 499 ∧ X₀ ≤ 500
t₇: f1(X₀) → f3(X₀) :|: 500 ≤ X₀ ∧ X₀ ≤ 500
t₈: f2(X₀) → f1(1+D) :|: D ≤ 499
t₉: f2(X₀) → f3(E) :|: 500 ≤ E

Found invariant X₀ ≤ 500 for location f1

Found invariant X₀ ≤ 500 for location f1_v1

Found invariant 500 ≤ X₀ for location f3

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₆: inf {Infinity}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₆: inf {Infinity}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}

Sizebounds

t₇, X₀: 500 {O(1)}