Initial Problem

Start: f0
Program_Vars: X₀
Temp_Vars: B
Locations: f0, f13, f5
Transitions:
t₀: f0(X₀) → f5(0)
t₂: f5(X₀) → f13(X₀) :|: 1+B ≤ 0 ∧ 2 ≤ X₀
t₃: f5(X₀) → f13(X₀) :|: 2 ≤ X₀
t₁: f5(X₀) → f5(1+X₀) :|: X₀ ≤ 1

Preprocessing

Found invariant X₀ ≤ 2 ∧ 2 ≤ X₀ for location f13

Found invariant X₀ ≤ 2 ∧ 0 ≤ X₀ for location f5

Problem after Preprocessing

Start: f0
Program_Vars: X₀
Temp_Vars: B
Locations: f0, f13, f5
Transitions:
t₀: f0(X₀) → f5(0)
t₂: f5(X₀) → f13(X₀) :|: 1+B ≤ 0 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ X₀
t₃: f5(X₀) → f13(X₀) :|: 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ X₀
t₁: f5(X₀) → f5(1+X₀) :|: X₀ ≤ 1 ∧ X₀ ≤ 2 ∧ 0 ≤ X₀

MPRF for transition t₁: f5(X₀) → f5(1+X₀) :|: X₀ ≤ 1 ∧ X₀ ≤ 2 ∧ 0 ≤ X₀ of depth 1:

new bound:

3 {O(1)}

• f5: [3-X₀]

All Bounds

Timebounds

Overall timebound:6 {O(1)}
t₀: 1 {O(1)}
t₁: 3 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}

Costbounds

Overall costbound: 6 {O(1)}
t₀: 1 {O(1)}
t₁: 3 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}

Sizebounds

t₀, X₀: 0 {O(1)}
t₁, X₀: 2 {O(1)}
t₂, X₀: 2 {O(1)}
t₃, X₀: 2 {O(1)}