Initial Problem

Start: l0
Program_Vars: X₀
Temp_Vars: B
Locations: l0, l1, l2
Transitions:
t₂: l0(X₀) → l1(B) :|: B ≤ 0
t₀: l0(X₀) → l2(B) :|: 1 ≤ B
t₃: l2(X₀) → l1(X₀) :|: 20 ≤ X₀
t₁: l2(X₀) → l2(X₀+1) :|: X₀ ≤ 19

Preprocessing

Found invariant 1 ≤ X₀ for location l2

Problem after Preprocessing

Start: l0
Program_Vars: X₀
Temp_Vars: B
Locations: l0, l1, l2
Transitions:
t₂: l0(X₀) → l1(B) :|: B ≤ 0
t₀: l0(X₀) → l2(B) :|: 1 ≤ B
t₃: l2(X₀) → l1(X₀) :|: 20 ≤ X₀ ∧ 1 ≤ X₀
t₁: l2(X₀) → l2(X₀+1) :|: X₀ ≤ 19 ∧ 1 ≤ X₀

Analysing control-flow refined program

Found invariant 1 ≤ X₀ for location l2

Found invariant X₀ ≤ 20 ∧ 2 ≤ X₀ for location n_l2___1

MPRF for transition t₂₈: n_l2___1(X₀) → n_l2___1(X₀+1) :|: 2 ≤ X₀ ∧ X₀ ≤ 20 ∧ X₀ ≤ 19 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 20 ∧ 2 ≤ X₀ of depth 1:

new bound:

41 {O(1)}

CFR: Improvement to new bound with the following program:

new bound:

Infinite

cfr-program:

Start: l0
Program_Vars: X₀
Temp_Vars: B
Locations: l0, l1, l2, n_l2___1
Transitions:
t₂: l0(X₀) → l1(B) :|: B ≤ 0
t₀: l0(X₀) → l2(B) :|: 1 ≤ B
t₃: l2(X₀) → l1(X₀) :|: 20 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀
t₂₉: l2(X₀) → n_l2___1(X₀+1) :|: X₀ ≤ 19 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀
t₃₂: n_l2___1(X₀) → l1(X₀) :|: 20 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 20 ∧ 2 ≤ X₀
t₂₈: n_l2___1(X₀) → n_l2___1(X₀+1) :|: 2 ≤ X₀ ∧ X₀ ≤ 20 ∧ X₀ ≤ 19 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 20 ∧ 2 ≤ X₀

CFR: Improvement to new bound with the following program:

new bound:

41 {O(1)}

cfr-program:

Start: l0
Program_Vars: X₀
Temp_Vars: B
Locations: l0, l1, l2, n_l2___1
Transitions:
t₂: l0(X₀) → l1(B) :|: B ≤ 0
t₀: l0(X₀) → l2(B) :|: 1 ≤ B
t₃: l2(X₀) → l1(X₀) :|: 20 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀
t₂₉: l2(X₀) → n_l2___1(X₀+1) :|: X₀ ≤ 19 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀
t₃₂: n_l2___1(X₀) → l1(X₀) :|: 20 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 20 ∧ 2 ≤ X₀
t₂₈: n_l2___1(X₀) → n_l2___1(X₀+1) :|: 2 ≤ X₀ ∧ X₀ ≤ 20 ∧ X₀ ≤ 19 ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ 20 ∧ 2 ≤ X₀

All Bounds

Timebounds

Overall timebound:46 {O(1)}
t₀: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₂₈: 41 {O(1)}
t₂₉: 1 {O(1)}
t₃₂: 1 {O(1)}

Costbounds

Overall costbound: 46 {O(1)}
t₀: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₂₈: 41 {O(1)}
t₂₉: 1 {O(1)}
t₃₂: 1 {O(1)}

Sizebounds

t₂₈, X₀: 20 {O(1)}
t₂₉, X₀: 20 {O(1)}
t₃₂, X₀: 20 {O(1)}