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) → l2(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: 1 ≤ X₂
t₅: l1(X₀, X₁, X₂, X₃) → l7(X₁, X₁, X₂, X₃) :|: X₂ ≤ 0
t₂: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 2 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1
t₃: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₀, X₀-1, X₃)
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃
t₇: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂
t₈: l5(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃-X₂)
t₉: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁-X₂, X₂-1, X₃) :|: X₃ ≤ 0 ∧ 0 ≤ X₃
t₁₀: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂-1, X₃) :|: X₃+1 ≤ 0
t₁₁: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂-1, X₃) :|: 1 ≤ X₃
t₁₂: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ 0
t₁₃: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀
t₁₄: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₅: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)

Preprocessing

Found invariant 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l6

Found invariant X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l7

Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l5

Found invariant 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l1

Found invariant X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l4

Found invariant 2 ≤ X₀ for location l3

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) → l2(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: 1 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀
t₅: l1(X₀, X₁, X₂, X₃) → l7(X₁, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀
t₂: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 2 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1
t₃: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₀, X₀-1, X₃) :|: 2 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀
t₇: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀
t₈: l5(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃-X₂) :|: X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀
t₉: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁-X₂, X₂-1, X₃) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀
t₁₀: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂-1, X₃) :|: X₃+1 ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀
t₁₁: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂-1, X₃) :|: 1 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀
t₁₂: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀+1 ≤ 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₁₃: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₁₄: l7(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₁₅: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃)

MPRF for transition t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₀) :|: 1 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l5 [X₂ ]
l4 [X₂ ]
l6 [X₂ ]
l1 [X₂+1 ]

MPRF for transition t₇: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₀+2 {O(n)}

MPRF:

l5 [X₀+X₂-2 ]
l4 [X₀+X₂-2 ]
l6 [X₀+X₂-3 ]
l1 [X₀+X₂-2 ]

MPRF for transition t₉: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁-X₂, X₂-1, X₃) :|: X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l5 [X₂ ]
l4 [X₂ ]
l6 [X₂ ]
l1 [X₂ ]

MPRF for transition t₁₀: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂-1, X₃) :|: X₃+1 ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l5 [X₂ ]
l4 [X₂ ]
l6 [X₂ ]
l1 [X₂ ]

MPRF for transition t₁₁: l6(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂-1, X₃) :|: 1 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l5 [X₂ ]
l4 [X₂ ]
l6 [X₂ ]
l1 [X₂ ]

MPRF for transition t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

6⋅X₀⋅X₀+2⋅X₀ {O(n^2)}

MPRF:

l1 [X₀+X₂ ]
l6 [X₂+X₃ ]
l5 [X₂+X₃-1 ]
l4 [X₂+X₃ ]

MPRF for transition t₈: l5(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃-X₂) :|: X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

3⋅X₀⋅X₀+X₀ {O(n^2)}

MPRF:

l1 [X₀ ]
l6 [X₃ ]
l5 [X₃ ]
l4 [X₃ ]

Analysing control-flow refined program

Cut unsatisfiable transition t₇: l4→l6

Found invariant 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ for location n_l5___1

Found invariant 1+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l6

Found invariant 1+X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ for location n_l4___2

Found invariant X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l7

Found invariant 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l1

Found invariant X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ for location l4

Found invariant 2 ≤ X₀ for location l3

Found invariant X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ for location n_l5___3

knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₀₇: l4(X₀, X₁, X₂, X₃) → n_l5___3(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀

knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₁₀₉: n_l5___3(X₀, X₁, X₂, X₃) → n_l4___2(X₀, X₁, X₂, X₃-X₂) :|: X₁ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀

MPRF for transition t₁₀₆: n_l4___2(X₀, X₁, X₂, X₃) → n_l5___1(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₃ ∧ X₂+X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

5⋅X₀⋅X₀+5⋅X₀ {O(n^2)}

MPRF:

l4 [0 ]
n_l5___3 [0 ]
l1 [0 ]
l6 [0 ]
n_l5___1 [X₂+X₃-1 ]
n_l4___2 [X₂+X₃ ]

MPRF for transition t₁₁₃: n_l4___2(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

l4 [X₂ ]
l1 [X₂ ]
l6 [X₂-1 ]
n_l5___1 [X₂ ]
n_l5___3 [X₂ ]
n_l4___2 [X₂ ]

MPRF for transition t₁₀₈: n_l5___1(X₀, X₁, X₂, X₃) → n_l4___2(X₀, X₁, X₂, X₃-X₂) :|: X₁ ≤ X₀ ∧ X₂+X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₀ of depth 1:

new bound:

5⋅X₀⋅X₀+6⋅X₀+1 {O(n^2)}

MPRF:

l4 [0 ]
n_l5___3 [0 ]
l1 [0 ]
l6 [0 ]
n_l5___1 [X₃ ]
n_l4___2 [X₂+X₃-1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:9⋅X₀⋅X₀+9⋅X₀+12 {O(n^2)}
t₀: 1 {O(1)}
t₄: X₀+1 {O(n)}
t₅: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 6⋅X₀⋅X₀+2⋅X₀ {O(n^2)}
t₇: 2⋅X₀+2 {O(n)}
t₈: 3⋅X₀⋅X₀+X₀ {O(n^2)}
t₉: X₀ {O(n)}
t₁₀: X₀ {O(n)}
t₁₁: X₀ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}

Costbounds

Overall costbound: 9⋅X₀⋅X₀+9⋅X₀+12 {O(n^2)}
t₀: 1 {O(1)}
t₄: X₀+1 {O(n)}
t₅: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₆: 6⋅X₀⋅X₀+2⋅X₀ {O(n^2)}
t₇: 2⋅X₀+2 {O(n)}
t₈: 3⋅X₀⋅X₀+X₀ {O(n^2)}
t₉: X₀ {O(n)}
t₁₀: X₀ {O(n)}
t₁₁: X₀ {O(n)}
t₁₂: 1 {O(1)}
t₁₃: 1 {O(1)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₀⋅X₀+2⋅X₀ {O(n^2)}
t₄, X₂: X₀ {O(n)}
t₄, X₃: 4⋅X₀ {O(n)}
t₅, X₀: X₀⋅X₀+2⋅X₀ {O(n^2)}
t₅, X₁: X₀⋅X₀+2⋅X₀ {O(n^2)}
t₅, X₂: 0 {O(1)}
t₅, X₃: 0 {O(1)}
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)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₀ {O(n)}
t₃, X₂: X₀ {O(n)}
t₃, X₃: X₃ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₀⋅X₀+2⋅X₀ {O(n^2)}
t₆, X₂: X₀ {O(n)}
t₆, X₃: 4⋅X₀ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₀⋅X₀+2⋅X₀ {O(n^2)}
t₇, X₂: X₀ {O(n)}
t₇, X₃: 4⋅X₀ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₀⋅X₀+2⋅X₀ {O(n^2)}
t₈, X₂: X₀ {O(n)}
t₈, X₃: 4⋅X₀ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₀⋅X₀+2⋅X₀ {O(n^2)}
t₉, X₂: X₀ {O(n)}
t₉, X₃: 0 {O(1)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₀⋅X₀+2⋅X₀ {O(n^2)}
t₁₀, X₂: X₀ {O(n)}
t₁₀, X₃: 4⋅X₀ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₀⋅X₀+2⋅X₀ {O(n^2)}
t₁₁, X₂: X₀ {O(n)}
t₁₁, X₃: 4⋅X₀ {O(n)}
t₁₂, X₀: X₀⋅X₀+2⋅X₀ {O(n^2)}
t₁₂, X₁: X₀⋅X₀+2⋅X₀ {O(n^2)}
t₁₂, X₂: 0 {O(1)}
t₁₂, X₃: 0 {O(1)}
t₁₃, X₀: X₀⋅X₀+2⋅X₀ {O(n^2)}
t₁₃, X₁: X₀⋅X₀+2⋅X₀ {O(n^2)}
t₁₃, X₂: 0 {O(1)}
t₁₃, X₃: 0 {O(1)}
t₁₄, X₀: 0 {O(1)}
t₁₄, X₁: 0 {O(1)}
t₁₄, X₂: 0 {O(1)}
t₁₄, X₃: 0 {O(1)}
t₁₅, X₀: 2⋅X₀⋅X₀+5⋅X₀ {O(n^2)}
t₁₅, X₁: 2⋅X₀⋅X₀+4⋅X₀+X₁ {O(n^2)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₃ {O(n)}