Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₁+1) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂+1 ≤ X₁
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁+1 ≤ X₂
t₃: l2(X₀, X₁, X₂) → l1(X₀, X₁, 0) :|: 0 ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₀+1 ≤ X₂
t₄: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: X₂ ≤ X₀ ∧ 0 ≤ 1+X₂
Preprocessing
Found invariant X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l2
Found invariant X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₁+1) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂+1 ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₃: l2(X₀, X₁, X₂) → l1(X₀, X₁, 0) :|: 0 ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₄: l2(X₀, X₁, X₂) → l1(X₀, X₁, X₂+1) :|: X₂ ≤ X₀ ∧ 0 ≤ 1+X₂ ∧ X₂ ≤ 1+X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
Analysing control-flow refined program
Cut unsatisfiable transition t₁₇₉: n_l1___4→n_l2___2
Cut unreachable locations [n_l2___2] from the program graph
Found invariant X₂ ≤ 1+X₀ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l1___6
Found invariant X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___4
Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___5
Found invariant X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l1___7
Found invariant X₂ ≤ 1+X₀ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l2___1
Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l2___3
Found invariant X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l1
Found invariant X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l2___8
MPRF for transition t₁₈₁: n_l1___6(X₀, X₁, X₂) → n_l2___1(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+X₁+4 {O(n)}
MPRF:
n_l2___1 [X₀+1-X₂ ]
n_l1___6 [X₀+2-X₂ ]
MPRF for transition t₁₈₄: n_l2___1(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂+1) :|: X₂ ≤ 1+X₀ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀+X₁+3 {O(n)}
MPRF:
n_l2___1 [X₀+1-X₂ ]
n_l1___6 [X₀+1-X₂ ]
MPRF for transition t₁₈₀: n_l1___4(X₀, X₁, X₂) → n_l2___3(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:
new bound:
2⋅X₀+2 {O(n)}
MPRF:
n_l2___3 [X₀-X₂ ]
n_l1___4 [X₀+1-X₂ ]
MPRF for transition t₁₈₇: n_l2___3(X₀, X₁, X₂) → n_l1___4(X₀, X₁, X₂+1) :|: X₁ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
2⋅X₀+2 {O(n)}
MPRF:
n_l2___3 [X₀+1-X₂ ]
n_l1___4 [X₀+1-X₂ ]
CFR: Improvement to new bound with the following program:
new bound:
2⋅X₁+6⋅X₀+11 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, n_l1___4, n_l1___6, n_l1___7, n_l2___1, n_l2___3, n_l2___5, n_l2___8
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₁+1) :|: X₁ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁
t₁₈₃: l1(X₀, X₁, X₂) → n_l2___8(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₈₀: n_l1___4(X₀, X₁, X₂) → n_l2___3(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₁ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₈₁: n_l1___6(X₀, X₁, X₂) → n_l2___1(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 1+X₁ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₈₂: n_l1___7(X₀, X₁, X₂) → n_l2___5(X₀, X₁, X₂) :|: X₁ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₈₄: n_l2___1(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂+1) :|: X₂ ≤ 1+X₀ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₈₅: n_l2___1(X₀, X₁, X₂) → n_l1___7(X₀, X₁, 0) :|: X₂ ≤ 1+X₀ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₀ ∧ 3 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₈₇: n_l2___3(X₀, X₁, X₂) → n_l1___4(X₀, X₁, X₂+1) :|: X₁ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₈₈: n_l2___5(X₀, X₁, X₂) → n_l1___4(X₀, X₁, X₂+1) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₈₉: n_l2___8(X₀, X₁, X₂) → n_l1___6(X₀, X₁, X₂+1) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₉₀: n_l2___8(X₀, X₁, X₂) → n_l1___7(X₀, X₁, 0) :|: X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁+1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
All Bounds
Timebounds
Overall timebound:2⋅X₁+6⋅X₀+18 {O(n)}
t₀: 1 {O(1)}
t₁₈₃: 1 {O(1)}
t₁₈₀: 2⋅X₀+2 {O(n)}
t₁₈₁: X₀+X₁+4 {O(n)}
t₁₈₂: 1 {O(1)}
t₁₈₄: X₀+X₁+3 {O(n)}
t₁₈₅: 1 {O(1)}
t₁₈₇: 2⋅X₀+2 {O(n)}
t₁₈₈: 1 {O(1)}
t₁₈₉: 1 {O(1)}
t₁₉₀: 1 {O(1)}
Costbounds
Overall costbound: 2⋅X₁+6⋅X₀+18 {O(n)}
t₀: 1 {O(1)}
t₁₈₃: 1 {O(1)}
t₁₈₀: 2⋅X₀+2 {O(n)}
t₁₈₁: X₀+X₁+4 {O(n)}
t₁₈₂: 1 {O(1)}
t₁₈₄: X₀+X₁+3 {O(n)}
t₁₈₅: 1 {O(1)}
t₁₈₇: 2⋅X₀+2 {O(n)}
t₁₈₈: 1 {O(1)}
t₁₈₉: 1 {O(1)}
t₁₉₀: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₁+1 {O(n)}
t₁₈₃, X₀: X₀ {O(n)}
t₁₈₃, X₁: X₁ {O(n)}
t₁₈₃, X₂: X₁+1 {O(n)}
t₁₈₀, X₀: 2⋅X₀ {O(n)}
t₁₈₀, X₁: 2⋅X₁ {O(n)}
t₁₈₀, X₂: 2⋅X₀+3 {O(n)}
t₁₈₁, X₀: X₀ {O(n)}
t₁₈₁, X₁: X₁ {O(n)}
t₁₈₁, X₂: 2⋅X₁+X₀+5 {O(n)}
t₁₈₂, X₀: 2⋅X₀ {O(n)}
t₁₈₂, X₁: 2⋅X₁ {O(n)}
t₁₈₂, X₂: 0 {O(1)}
t₁₈₄, X₀: X₀ {O(n)}
t₁₈₄, X₁: X₁ {O(n)}
t₁₈₄, X₂: 2⋅X₁+X₀+5 {O(n)}
t₁₈₅, X₀: X₀ {O(n)}
t₁₈₅, X₁: X₁ {O(n)}
t₁₈₅, X₂: 0 {O(1)}
t₁₈₇, X₀: 2⋅X₀ {O(n)}
t₁₈₇, X₁: 2⋅X₁ {O(n)}
t₁₈₇, X₂: 2⋅X₀+3 {O(n)}
t₁₈₈, X₀: 2⋅X₀ {O(n)}
t₁₈₈, X₁: 2⋅X₁ {O(n)}
t₁₈₈, X₂: 1 {O(1)}
t₁₈₉, X₀: X₀ {O(n)}
t₁₈₉, X₁: X₁ {O(n)}
t₁₈₉, X₂: X₁+2 {O(n)}
t₁₉₀, X₀: X₀ {O(n)}
t₁₉₀, X₁: X₁ {O(n)}
t₁₉₀, X₂: 0 {O(1)}