Initial Problem

Start: f0
Program_Vars: X₀
Temp_Vars: B
Locations: f0, f13, f3
Transitions:
t₀: f0(X₀) → f3(0)
t₃: f3(X₀) → f13(X₀) :|: 42 ≤ X₀
t₁: f3(X₀) → f3(1+X₀) :|: X₀ ≤ 41
t₂: f3(X₀) → f3(1+X₀) :|: X₀ ≤ 41 ∧ 1+B ≤ 0

Preprocessing

Found invariant X₀ ≤ 42 ∧ 42 ≤ X₀ for location f13

Found invariant X₀ ≤ 42 ∧ 0 ≤ X₀ for location f3

Problem after Preprocessing

Start: f0
Program_Vars: X₀
Temp_Vars: B
Locations: f0, f13, f3
Transitions:
t₀: f0(X₀) → f3(0)
t₃: f3(X₀) → f13(X₀) :|: 42 ≤ X₀ ∧ X₀ ≤ 42 ∧ 0 ≤ X₀
t₁: f3(X₀) → f3(1+X₀) :|: X₀ ≤ 41 ∧ X₀ ≤ 42 ∧ 0 ≤ X₀
t₂: f3(X₀) → f3(1+X₀) :|: X₀ ≤ 41 ∧ 1+B ≤ 0 ∧ X₀ ≤ 42 ∧ 0 ≤ X₀

MPRF for transition t₁: f3(X₀) → f3(1+X₀) :|: X₀ ≤ 41 ∧ X₀ ≤ 42 ∧ 0 ≤ X₀ of depth 1:

new bound:

43 {O(1)}

• f3: [43-X₀]

MPRF for transition t₂: f3(X₀) → f3(1+X₀) :|: X₀ ≤ 41 ∧ 1+B ≤ 0 ∧ X₀ ≤ 42 ∧ 0 ≤ X₀ of depth 1:

new bound:

43 {O(1)}

• f3: [43-X₀]

All Bounds

Timebounds

Overall timebound:88 {O(1)}
t₀: 1 {O(1)}
t₁: 43 {O(1)}
t₂: 43 {O(1)}
t₃: 1 {O(1)}

Costbounds

Overall costbound: 88 {O(1)}
t₀: 1 {O(1)}
t₁: 43 {O(1)}
t₂: 43 {O(1)}
t₃: 1 {O(1)}

Sizebounds

t₀, X₀: 0 {O(1)}
t₁, X₀: 42 {O(1)}
t₂, X₀: 42 {O(1)}
t₃, X₀: 42 {O(1)}