Initial Problem

Start: l0
Program_Vars: X₀
Temp_Vars: B
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀) → l1(B)
t₁: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 3 ∧ 1 ≤ X₀
t₂: l1(X₀) → l1(1) :|: X₀ ≤ 0 ∧ X₀ ≤ 3
t₃: l1(X₀) → l2(X₀) :|: 4 ≤ X₀

Preprocessing

Found invariant 4 ≤ X₀ for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars: B
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀) → l1(B)
t₁: l1(X₀) → l1(X₀+1) :|: X₀ ≤ 3 ∧ 1 ≤ X₀
t₂: l1(X₀) → l1(1) :|: X₀ ≤ 0 ∧ X₀ ≤ 3
t₃: l1(X₀) → l2(X₀) :|: 4 ≤ X₀

knowledge_propagation leads to new time bound 1 {O(1)} for transition t₂: l1(X₀) → l1(1) :|: X₀ ≤ 0 ∧ X₀ ≤ 3

Found invariant 1 ≤ 0 for location l2

Found invariant 1 ≤ 0 for location l1

Found invariant 4 ≤ X₀ for location l2

Analysing control-flow refined program

Cut unsatisfiable transition t₆₃: n_l1___1→l2

Cut unsatisfiable transition t₆₄: n_l1___2→l2

Found invariant 4 ≤ X₀ for location l2

Found invariant X₀ ≤ 1 ∧ 1 ≤ X₀ for location n_l1___2

Found invariant X₀ ≤ 4 ∧ 2 ≤ X₀ for location n_l1___3

Found invariant X₀ ≤ 2 ∧ 2 ≤ X₀ for location n_l1___1

MPRF for transition t₅₄: n_l1___3(X₀) → n_l1___3(X₀+1) :|: 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3 ∧ X₀ ≤ 4 ∧ 2 ≤ X₀ of depth 1:

new bound:

17 {O(1)}

MPRF:

n_l1___3 [5-X₀ ]

CFR: Improvement to new bound with the following program:

new bound:

17 {O(1)}

cfr-program:

Start: l0
Program_Vars: X₀
Temp_Vars: B
Locations: l0, l1, l2, n_l1___1, n_l1___2, n_l1___3
Transitions:
t₀: l0(X₀) → l1(B)
t₃: l1(X₀) → l2(X₀) :|: 4 ≤ X₀
t₅₅: l1(X₀) → n_l1___2(1) :|: X₀ ≤ 0
t₅₆: l1(X₀) → n_l1___3(X₀+1) :|: 1 ≤ X₀ ∧ X₀ ≤ 3
t₅₂: n_l1___1(X₀) → n_l1___3(X₀+1) :|: X₀ ≤ 3 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 3 ∧ 2 ≤ X₀ ∧ X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3 ∧ X₀ ≤ 2 ∧ 2 ≤ X₀
t₅₃: n_l1___2(X₀) → n_l1___1(X₀+1) :|: X₀ ≤ 3 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 3 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 3 ∧ X₀ ≤ 1 ∧ 1 ≤ X₀
t₆₅: n_l1___3(X₀) → l2(X₀) :|: 4 ≤ X₀ ∧ X₀ ≤ 4 ∧ 2 ≤ X₀
t₅₄: n_l1___3(X₀) → n_l1___3(X₀+1) :|: 1 ≤ X₀ ∧ 2 ≤ X₀ ∧ X₀ ≤ 4 ∧ 1 ≤ X₀ ∧ X₀ ≤ 3 ∧ X₀ ≤ 4 ∧ 2 ≤ X₀

All Bounds

Timebounds

Overall timebound:24 {O(1)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: 1 {O(1)}
t₅₄: 17 {O(1)}
t₆₅: 1 {O(1)}

Costbounds

Overall costbound: 24 {O(1)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₅₅: 1 {O(1)}
t₅₆: 1 {O(1)}
t₅₂: 1 {O(1)}
t₅₃: 1 {O(1)}
t₅₄: 17 {O(1)}
t₆₅: 1 {O(1)}

Sizebounds

t₅₅, X₀: 1 {O(1)}
t₅₆, X₀: 4 {O(1)}
t₅₂, X₀: 3 {O(1)}
t₅₃, X₀: 2 {O(1)}
t₅₄, X₀: 4 {O(1)}
t₆₅, X₀: 4 {O(1)}