Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₀-1, X₂, X₀)
t₁₅: l2(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 1 < X₀
t₁: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₀, X₃) :|: 0 < X₁
t₅: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0
t₇: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₂ < X₁
t₆: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂
t₁₂: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ < 0
t₁₃: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 < X₃
t₁₄: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 0 ≤ X₃
t₉: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃-X₁) :|: X₂ ≤ 0 ∧ 0 ≤ X₂
t₁₀: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃) :|: X₂ < 0
t₁₁: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃) :|: 0 < X₂
t₈: l8(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂-X₁, X₃)
Preprocessing
Found invariant X₃ ≤ X₀ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ for location l6
Found invariant X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l7
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l5
Found invariant X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l8
Found invariant 2 ≤ X₀ for location l1
Found invariant X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l4
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₀-1, X₂, X₀) :|: 2 ≤ X₀
t₁₅: l2(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: 1 < X₀
t₁: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₀, X₃) :|: 0 < X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₅: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ ≤ 0 ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₇: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₂ < X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₆: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₁₂: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ < 0 ∧ X₃ ≤ X₀ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀
t₁₃: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 0 < X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀
t₁₄: l6(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀
t₉: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃-X₁) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₁₀: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃) :|: X₂ < 0 ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₁₁: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃) :|: 0 < X₂ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₈: l8(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂-X₁, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
MPRF for transition t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₀, X₃) :|: 0 < X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l7 [X₁-1 ]
l4 [X₁ ]
l8 [X₁-1 ]
l5 [X₁-1 ]
MPRF for transition t₇: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₂ < X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l7 [X₁-1 ]
l4 [X₁ ]
l8 [X₁ ]
l5 [X₁ ]
MPRF for transition t₉: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃-X₁) :|: X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l7 [X₁ ]
l4 [X₁ ]
l8 [X₁ ]
l5 [X₁ ]
MPRF for transition t₁₁: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃) :|: 0 < X₂ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l7 [X₁ ]
l4 [X₁ ]
l8 [X₁ ]
l5 [X₁ ]
knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₁₀: l7(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃) :|: X₂ < 0 ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀
MPRF for transition t₆: l5(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
3⋅X₀⋅X₀+X₀ {O(n^2)}
MPRF:
l4 [X₀ ]
l7 [X₂ ]
l8 [X₂-X₁ ]
l5 [X₂ ]
MPRF for transition t₈: l8(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂-X₁, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
3⋅X₀⋅X₀+X₀ {O(n^2)}
MPRF:
l4 [X₀ ]
l7 [X₂ ]
l8 [X₂ ]
l5 [X₂ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₇: l5→l7
Found invariant X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l8___1
Found invariant X₃ ≤ X₀ ∧ X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l6
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l8___3
Found invariant X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l5___2
Found invariant X₃ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l7
Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l5
Found invariant 2 ≤ X₀ for location l1
Found invariant X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l4
knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₁₀₅: l5(X₀, X₁, X₂, X₃) → n_l8___3(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₁₀₇: n_l8___3(X₀, X₁, X₂, X₃) → n_l5___2(X₀, X₁, X₂-X₁, X₃) :|: X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀
MPRF for transition t₁₀₄: n_l5___2(X₀, X₁, X₂, X₃) → n_l8___1(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ X₁+X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
6⋅X₀⋅X₀ {O(n^2)}
MPRF:
l5 [0 ]
n_l8___3 [0 ]
l4 [0 ]
l7 [0 ]
n_l8___1 [X₁+X₂-1 ]
n_l5___2 [X₁+X₂ ]
MPRF for transition t₁₁₁: n_l5___2(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₂ < X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
X₀ {O(n)}
MPRF:
l5 [X₁ ]
l4 [X₁ ]
l7 [X₁-1 ]
n_l8___1 [X₁ ]
n_l8___3 [X₁ ]
n_l5___2 [X₁ ]
MPRF for transition t₁₀₆: n_l8___1(X₀, X₁, X₂, X₃) → n_l5___2(X₀, X₁, X₂-X₁, X₃) :|: X₃ ≤ X₀ ∧ X₁+X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:
new bound:
6⋅X₀⋅X₀+X₀ {O(n^2)}
MPRF:
l5 [0 ]
n_l8___3 [0 ]
l4 [0 ]
l7 [0 ]
n_l8___1 [X₂ ]
n_l5___2 [X₁+X₂-1 ]
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:6⋅X₀⋅X₀+7⋅X₀+9 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: X₀ {O(n)}
t₅: 1 {O(1)}
t₆: 3⋅X₀⋅X₀+X₀ {O(n^2)}
t₇: X₀ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₉: X₀ {O(n)}
t₁₀: X₀ {O(n)}
t₁₁: X₀ {O(n)}
t₈: 3⋅X₀⋅X₀+X₀ {O(n^2)}
Costbounds
Overall costbound: 6⋅X₀⋅X₀+7⋅X₀+9 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: X₀ {O(n)}
t₅: 1 {O(1)}
t₆: 3⋅X₀⋅X₀+X₀ {O(n^2)}
t₇: X₀ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₉: X₀ {O(n)}
t₁₀: X₀ {O(n)}
t₁₁: X₀ {O(n)}
t₈: 3⋅X₀⋅X₀+X₀ {O(n^2)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₀ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₀ {O(n)}
t₁₅, X₀: 7⋅X₀ {O(n)}
t₁₅, X₁: 12⋅X₀+X₁ {O(n)}
t₁₅, X₂: 12⋅X₀+X₂ {O(n)}
t₁₅, X₃: 8⋅X₀⋅X₀+12⋅X₀+X₃ {O(n^2)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: 2⋅X₀ {O(n)}
t₄, X₂: 4⋅X₀ {O(n)}
t₄, X₃: 2⋅X₀⋅X₀+3⋅X₀ {O(n^2)}
t₅, X₀: 2⋅X₀ {O(n)}
t₅, X₁: 4⋅X₀ {O(n)}
t₅, X₂: 4⋅X₀ {O(n)}
t₅, X₃: 4⋅X₀⋅X₀+6⋅X₀ {O(n^2)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: 2⋅X₀ {O(n)}
t₆, X₂: 4⋅X₀ {O(n)}
t₆, X₃: 2⋅X₀⋅X₀+3⋅X₀ {O(n^2)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: 2⋅X₀ {O(n)}
t₇, X₂: 4⋅X₀ {O(n)}
t₇, X₃: 2⋅X₀⋅X₀+3⋅X₀ {O(n^2)}
t₁₂, X₀: 2⋅X₀ {O(n)}
t₁₂, X₁: 4⋅X₀ {O(n)}
t₁₂, X₂: 4⋅X₀ {O(n)}
t₁₂, X₃: 4⋅X₀⋅X₀+6⋅X₀ {O(n^2)}
t₁₃, X₀: 2⋅X₀ {O(n)}
t₁₃, X₁: 4⋅X₀ {O(n)}
t₁₃, X₂: 4⋅X₀ {O(n)}
t₁₃, X₃: 4⋅X₀⋅X₀+6⋅X₀ {O(n^2)}
t₁₄, X₀: 2⋅X₀ {O(n)}
t₁₄, X₁: 4⋅X₀ {O(n)}
t₁₄, X₂: 4⋅X₀ {O(n)}
t₁₄, X₃: 0 {O(1)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: 2⋅X₀ {O(n)}
t₉, X₂: 0 {O(1)}
t₉, X₃: 2⋅X₀⋅X₀+3⋅X₀ {O(n^2)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: 2⋅X₀ {O(n)}
t₁₀, X₂: 4⋅X₀ {O(n)}
t₁₀, X₃: 2⋅X₀⋅X₀+3⋅X₀ {O(n^2)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: 2⋅X₀ {O(n)}
t₁₁, X₂: 4⋅X₀ {O(n)}
t₁₁, X₃: 2⋅X₀⋅X₀+3⋅X₀ {O(n^2)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: 2⋅X₀ {O(n)}
t₈, X₂: 4⋅X₀ {O(n)}
t₈, X₃: 2⋅X₀⋅X₀+3⋅X₀ {O(n^2)}