Initial Problem

Start: f3
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: f0, f1, f2, f3, f4
Transitions:
t₁: f0(X₀, X₁, X₂, X₃) → f0(1+X₀, X₁, X₀, X₃) :|: X₀ ≤ 9
t₀: f0(X₀, X₁, X₂, X₃) → f4(X₀, E, X₂, X₃) :|: 10 ≤ X₀
t₂: f1(X₀, X₁, X₂, X₃) → f0(1, X₁, X₂, X₃) :|: E ≤ 9 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
t₃: f2(X₀, X₁, X₂, X₃) → f0(2, X₁, X₂, 2) :|: X₀ ≤ 9
t₄: f3(X₀, X₁, X₂, X₃) → f0(0, X₁, X₂, X₃)

Preprocessing

Cut unreachable locations [f1; f2] from the program graph

Eliminate variables [E; X₁; X₂; X₃] that do not contribute to the problem

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location f0

Found invariant X₀ ≤ 10 ∧ 10 ≤ X₀ for location f4

Problem after Preprocessing

Start: f3
Program_Vars: X₀
Temp_Vars:
Locations: f0, f3, f4
Transitions:
t₈: f0(X₀) → f0(1+X₀) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₉: f0(X₀) → f4(X₀) :|: 10 ≤ X₀ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₁₀: f3(X₀) → f0(0)

MPRF for transition t₈: f0(X₀) → f0(1+X₀) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

11 {O(1)}

• f0: [11-X₀]

All Bounds

Timebounds

Overall timebound:13 {O(1)}
t₈: 11 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: 13 {O(1)}
t₈: 11 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}

Sizebounds

t₈, X₀: 10 {O(1)}
t₉, X₀: 10 {O(1)}
t₁₀, X₀: 0 {O(1)}