Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃
t₅: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂
t₆: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+1, X₃)
t₇: l3(X₀, X₁, X₂, X₃) → l4(X₀+1, X₁, X₂, X₃)
t₂: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, 1, X₃) :|: X₀ ≤ X₁
t₃: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₀
t₈: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₁: l6(X₀, X₁, X₂, X₃) → l4(1, X₁, X₂, X₃)

Preprocessing

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l7

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l5

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

Found invariant 1 ≤ X₀ for location l4

Found invariant 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ 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
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₅: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+1, X₃) :|: 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₇: l3(X₀, X₁, X₂, X₃) → l4(X₀+1, X₁, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, 1, X₃) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀
t₃: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₁+1 ≤ X₀ ∧ 1 ≤ X₀
t₈: l5(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₀
t₁: l6(X₀, X₁, X₂, X₃) → l4(1, X₁, X₂, X₃)

MPRF for transition t₂: l4(X₀, X₁, X₂, X₃) → l1(X₀, X₁, 1, X₃) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF for transition t₅: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF for transition t₇: l3(X₀, X₁, X₂, X₃) → l4(X₀+1, X₁, X₂, X₃) :|: 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+2 {O(n)}

TWN: t₄: l1→l2

cycle: [t₄: l1→l2; t₆: l2→l1]
loop: (X₂ ≤ X₃,(X₂,X₃) -> (X₂+1,X₃)
order: [X₂; X₃]
closed-form:
X₂: X₂ + [[n != 0]] * n^1
X₃: X₃

Termination: true
Formula:

1 < 0
∨ X₂ < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂

Stabilization-Threshold for: X₂ ≤ X₃
alphas_abs: X₂+X₃
M: 0
N: 1
Bound: 2⋅X₂+2⋅X₃+2 {O(n)}

TWN - Lifting for t₄: l1→l2 of 2⋅X₂+2⋅X₃+4 {O(n)}

relevant size-bounds w.r.t. t₂:
X₂: 1 {O(1)}
X₃: X₃ {O(n)}
Runtime-bound of t₂: X₁+2 {O(n)}
Results in: 2⋅X₁⋅X₃+4⋅X₃+6⋅X₁+12 {O(n^2)}

TWN: t₆: l2→l1

TWN - Lifting for t₆: l2→l1 of 2⋅X₂+2⋅X₃+4 {O(n)}

relevant size-bounds w.r.t. t₂:
X₂: 1 {O(1)}
X₃: X₃ {O(n)}
Runtime-bound of t₂: X₁+2 {O(n)}
Results in: 2⋅X₁⋅X₃+4⋅X₃+6⋅X₁+12 {O(n^2)}

Chain transitions t₂: l4→l1 and t₅: l1→l3 to t₅₃: l4→l3

Chain transitions t₆: l2→l1 and t₅: l1→l3 to t₅₄: l2→l3

Chain transitions t₆: l2→l1 and t₄: l1→l2 to t₅₅: l2→l2

Chain transitions t₂: l4→l1 and t₄: l1→l2 to t₅₆: l4→l2

Chain transitions t₅₃: l4→l3 and t₇: l3→l4 to t₅₇: l4→l4

Chain transitions t₅₄: l2→l3 and t₇: l3→l4 to t₅₈: l2→l4

Analysing control-flow refined program

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l2

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l7

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l5

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

Found invariant 1 ≤ X₀ for location l4

Found invariant 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3

MPRF for transition t₅₆: l4(X₀, X₁, X₂, X₃) -{2}> l2(X₀, X₁, 1, X₃) :|: X₀ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF for transition t₅₇: l4(X₀, X₁, X₂, X₃) -{3}> l4(X₀+1, X₁, 1, X₃) :|: X₀ ≤ X₁ ∧ X₃ ≤ 0 ∧ 1 ≤ X₀ ∧ 0 ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₃ ≤ 0 ∧ 0 ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF for transition t₅₈: l2(X₀, X₁, X₂, X₃) -{3}> l4(X₀+1, X₁, 1+X₂, X₃) :|: X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+2 {O(n)}

TWN: t₅₅: l2→l2

cycle: [t₅₅: l2→l2]
loop: (1+X₂ ≤ X₃,(X₂,X₃) -> (1+X₂,X₃)
order: [X₂; X₃]
closed-form:
X₂: X₂ + [[n != 0]] * n^1
X₃: X₃

Termination: true
Formula:

1 < 0
∨ 1+X₂ < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₂ ≤ X₃ ∧ X₃ ≤ 1+X₂

Stabilization-Threshold for: 1+X₂ ≤ X₃
alphas_abs: 1+X₂+X₃
M: 0
N: 1
Bound: 2⋅X₂+2⋅X₃+4 {O(n)}

TWN - Lifting for t₅₅: l2→l2 of 2⋅X₂+2⋅X₃+6 {O(n)}

relevant size-bounds w.r.t. t₅₆:
X₂: 1 {O(1)}
X₃: X₃ {O(n)}
Runtime-bound of t₅₆: X₁+2 {O(n)}
Results in: 2⋅X₁⋅X₃+4⋅X₃+8⋅X₁+16 {O(n^2)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___2

Found invariant 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l2___1

Found invariant 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l2___3

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l7

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l5

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

Found invariant 1 ≤ X₀ for location l4

Found invariant 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3

knowledge_propagation leads to new time bound X₁+2 {O(n)} for transition t₁₂₁: l1(X₀, X₁, X₂, X₃) → n_l2___3(X₀, X₁, X₂, X₃) :|: X₂ ≤ 1 ∧ X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₁+2 {O(n)} for transition t₁₂₃: n_l2___3(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁, X₂+1, X₃) :|: X₂ ≤ 1 ∧ 1 ≤ X₃ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

MPRF for transition t₁₂₀: n_l1___2(X₀, X₁, X₂, X₃) → n_l2___1(X₀, X₁, X₂, X₃) :|: 2 ≤ X₂ ∧ X₂ ≤ 1+X₃ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁⋅X₃+2⋅X₃+3⋅X₁+6 {O(n^2)}

MPRF for transition t₁₂₂: n_l2___1(X₀, X₁, X₂, X₃) → n_l1___2(X₀, X₁, X₂+1, X₃) :|: 2 ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁⋅X₃+2⋅X₃+3⋅X₁+6 {O(n^2)}

MPRF for transition t₁₂₇: n_l1___2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃+1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ 1+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+2 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:4⋅X₁⋅X₃+15⋅X₁+8⋅X₃+34 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+2 {O(n)}
t₃: 1 {O(1)}
t₄: 2⋅X₁⋅X₃+4⋅X₃+6⋅X₁+12 {O(n^2)}
t₅: X₁+2 {O(n)}
t₆: 2⋅X₁⋅X₃+4⋅X₃+6⋅X₁+12 {O(n^2)}
t₇: X₁+2 {O(n)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₁⋅X₃+15⋅X₁+8⋅X₃+34 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+2 {O(n)}
t₃: 1 {O(1)}
t₄: 2⋅X₁⋅X₃+4⋅X₃+6⋅X₁+12 {O(n^2)}
t₅: X₁+2 {O(n)}
t₆: 2⋅X₁⋅X₃+4⋅X₃+6⋅X₁+12 {O(n^2)}
t₇: X₁+2 {O(n)}
t₈: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: 1 {O(1)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₁+3 {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 1 {O(1)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₁+4 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: 2⋅X₁⋅X₃+4⋅X₃+6⋅X₁+X₂+14 {O(n^2)}
t₃, X₃: 2⋅X₃ {O(n)}
t₄, X₀: X₁+3 {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: 2⋅X₁⋅X₃+4⋅X₃+6⋅X₁+13 {O(n^2)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₁+3 {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: 2⋅X₁⋅X₃+4⋅X₃+6⋅X₁+14 {O(n^2)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: X₁+3 {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: 2⋅X₁⋅X₃+4⋅X₃+6⋅X₁+13 {O(n^2)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₁+3 {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: 2⋅X₁⋅X₃+4⋅X₃+6⋅X₁+14 {O(n^2)}
t₇, X₃: X₃ {O(n)}
t₈, X₀: X₁+4 {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: 2⋅X₁⋅X₃+4⋅X₃+6⋅X₁+X₂+14 {O(n^2)}
t₈, X₃: 2⋅X₃ {O(n)}