Initial Problem

Start: f0
Program_Vars: X₀
Temp_Vars: B
Locations: f0, f11, f3
Transitions:
t₀: f0(X₀) → f3(0)
t₂: f3(X₀) → f11(X₀) :|: 1+B ≤ 0 ∧ 10 ≤ X₀
t₃: f3(X₀) → f11(X₀) :|: 10 ≤ X₀
t₁: f3(X₀) → f3(1+X₀) :|: X₀ ≤ 9

Preprocessing

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location f3

Found invariant X₀ ≤ 10 ∧ 10 ≤ X₀ for location f11

Problem after Preprocessing

Start: f0
Program_Vars: X₀
Temp_Vars: B
Locations: f0, f11, f3
Transitions:
t₀: f0(X₀) → f3(0)
t₂: f3(X₀) → f11(X₀) :|: 1+B ≤ 0 ∧ 10 ≤ X₀ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₃: f3(X₀) → f11(X₀) :|: 10 ≤ X₀ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₁: f3(X₀) → f3(1+X₀) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀

MPRF for transition t₁: f3(X₀) → f3(1+X₀) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

11 {O(1)}

• f3: [11-X₀]

All Bounds

Timebounds

Overall timebound:14 {O(1)}
t₀: 1 {O(1)}
t₁: 11 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}

Costbounds

Overall costbound: 14 {O(1)}
t₀: 1 {O(1)}
t₁: 11 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}

Sizebounds

t₀, X₀: 0 {O(1)}
t₁, X₀: 10 {O(1)}
t₂, X₀: 10 {O(1)}
t₃, X₀: 10 {O(1)}