Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₂) :|: X₄ ≤ X₁
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₄
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₀, X₅)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₅
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄+1, X₅)
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅+1)

Preprocessing

Found invariant X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location l6

Found invariant 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄ for location l7

Found invariant 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location l5

Found invariant X₀ ≤ X₄ for location l1

Found invariant 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄ for location l4

Found invariant X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₂) :|: X₄ ≤ X₁ ∧ X₀ ≤ X₄
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₄ ∧ X₀ ≤ X₄
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₀, X₅)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄+1, X₅) :|: 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁
t₆: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅+1) :|: X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₂) :|: X₄ ≤ X₁ ∧ X₀ ≤ X₄ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

MPRF for transition t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄+1, X₅) :|: 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

TWN: t₄: l3→l6

cycle: [t₄: l3→l6; t₆: l6→l3]
loop: (X₅ ≤ X₃,(X₃,X₅) -> (X₃,X₅+1)
order: [X₃; X₅]
closed-form:
X₃: X₃
X₅: X₅ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₅ < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ X₅ ≤ X₃ ∧ X₃ ≤ X₅

Stabilization-Threshold for: X₅ ≤ X₃
alphas_abs: X₅+X₃
M: 0
N: 1
Bound: 2⋅X₃+2⋅X₅+2 {O(n)}

TWN - Lifting for t₄: l3→l6 of 2⋅X₃+2⋅X₅+4 {O(n)}

relevant size-bounds w.r.t. t₂:
X₃: X₃ {O(n)}
X₅: 2⋅X₂ {O(n)}
Runtime-bound of t₂: X₀+X₁+1 {O(n)}
Results in: 2⋅X₀⋅X₃+2⋅X₁⋅X₃+4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+4⋅X₂+4 {O(n^2)}

TWN: t₆: l6→l3

TWN - Lifting for t₆: l6→l3 of 2⋅X₃+2⋅X₅+4 {O(n)}

relevant size-bounds w.r.t. t₂:
X₃: X₃ {O(n)}
X₅: 2⋅X₂ {O(n)}
Runtime-bound of t₂: X₀+X₁+1 {O(n)}
Results in: 2⋅X₀⋅X₃+2⋅X₁⋅X₃+4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+4⋅X₂+4 {O(n^2)}

Chain transitions t₇: l5→l1 and t₃: l1→l4 to t₅₃: l5→l4

Chain transitions t₁: l2→l1 and t₃: l1→l4 to t₅₄: l2→l4

Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₅₅: l2→l3

Chain transitions t₇: l5→l1 and t₂: l1→l3 to t₅₆: l5→l3

Chain transitions t₆: l6→l3 and t₄: l3→l6 to t₅₇: l6→l6

Chain transitions t₅₆: l5→l3 and t₄: l3→l6 to t₅₈: l5→l6

Chain transitions t₅₆: l5→l3 and t₅: l3→l5 to t₅₉: l5→l5

Chain transitions t₆: l6→l3 and t₅: l3→l5 to t₆₀: l6→l5

Chain transitions t₅₅: l2→l3 and t₅: l3→l5 to t₆₁: l2→l5

Chain transitions t₅₅: l2→l3 and t₄: l3→l6 to t₆₂: l2→l6

Analysing control-flow refined program

Found invariant X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location l6

Found invariant 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄ for location l7

Found invariant 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location l5

Found invariant X₀ ≤ X₄ for location l1

Found invariant 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄ for location l4

Found invariant X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location l3

MPRF for transition t₅₈: l5(X₀, X₁, X₂, X₃, X₄, X₅) -{3}> l6(X₀, X₁, X₂, X₃, 1+X₄, X₂) :|: 1+X₄ ≤ X₁ ∧ X₂ ≤ X₃ ∧ 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄+1 ∧ 0 ≤ 0 ∧ 1+X₄ ≤ X₁ ∧ X₀ ≤ 1+X₄ ∧ X₀ ≤ X₁ ∧ 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₀+2⋅X₁+2 {O(n)}

MPRF for transition t₅₉: l5(X₀, X₁, X₂, X₃, X₄, X₅) -{3}> l5(X₀, X₁, X₂, X₃, 1+X₄, X₂) :|: 1+X₄ ≤ X₁ ∧ X₃ < X₂ ∧ 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₄+1 ∧ 0 ≤ 0 ∧ 1+X₄ ≤ X₁ ∧ X₀ ≤ 1+X₄ ∧ X₀ ≤ X₁ ∧ 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₀+2⋅X₁+2 {O(n)}

MPRF for transition t₆₀: l6(X₀, X₁, X₂, X₃, X₄, X₅) -{2}> l5(X₀, X₁, X₂, X₃, X₄, 1+X₅) :|: X₃ < X₅+1 ∧ X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₅+1 ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ ∧ X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₀+2⋅X₁+1 {O(n)}

TWN: t₅₇: l6→l6

cycle: [t₅₇: l6→l6]
loop: (1+X₅ ≤ X₃,(X₃,X₅) -> (X₃,1+X₅)
order: [X₃; X₅]
closed-form:
X₃: X₃
X₅: X₅ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ 1+X₅ < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₅ ≤ X₃ ∧ X₃ ≤ 1+X₅

Stabilization-Threshold for: 1+X₅ ≤ X₃
alphas_abs: 1+X₅+X₃
M: 0
N: 1
Bound: 2⋅X₃+2⋅X₅+4 {O(n)}
loop: (1+X₅ ≤ X₃,(X₃,X₅) -> (X₃,1+X₅)
order: [X₃; X₅]
closed-form:
X₃: X₃
X₅: X₅ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ 1+X₅ < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1+X₅ ≤ X₃ ∧ X₃ ≤ 1+X₅

Stabilization-Threshold for: 1+X₅ ≤ X₃
alphas_abs: 1+X₅+X₃
M: 0
N: 1
Bound: 2⋅X₃+2⋅X₅+4 {O(n)}

TWN - Lifting for t₅₇: l6→l6 of 2⋅X₃+2⋅X₅+6 {O(n)}

relevant size-bounds w.r.t. t₅₈:
X₃: X₃ {O(n)}
X₅: X₂ {O(n)}
Runtime-bound of t₅₈: 2⋅X₀+2⋅X₁+2 {O(n)}
Results in: 4⋅X₀⋅X₂+4⋅X₀⋅X₃+4⋅X₁⋅X₂+4⋅X₁⋅X₃+12⋅X₀+12⋅X₁+4⋅X₂+4⋅X₃+12 {O(n^2)}

TWN - Lifting for t₅₇: l6→l6 of 2⋅X₃+2⋅X₅+6 {O(n)}

relevant size-bounds w.r.t. t₆₂:
X₃: X₃ {O(n)}
X₅: X₂ {O(n)}
Runtime-bound of t₆₂: 1 {O(1)}
Results in: 2⋅X₂+2⋅X₃+6 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant X₅ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location n_l6___3

Found invariant X₅ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location n_l6___1

Found invariant 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄ for location l7

Found invariant 1+X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location l5

Found invariant X₅ ≤ 1+X₃ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ for location n_l3___2

Found invariant X₀ ≤ X₄ for location l1

Found invariant 1+X₁ ≤ X₄ ∧ X₀ ≤ X₄ for location l4

Found invariant X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ for location l3

knowledge_propagation leads to new time bound X₀+X₁+1 {O(n)} for transition t₁₄₉: l3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l6___3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₅ ≤ X₂ ∧ X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁

knowledge_propagation leads to new time bound X₀+X₁+1 {O(n)} for transition t₁₅₁: n_l6___3(X₀, X₁, X₂, X₃, X₄, X₅) → n_l3___2(X₀, X₁, X₂, X₃, X₄, X₅+1) :|: X₅ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₅ ∧ X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₅ ≤ X₂ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁

MPRF for transition t₁₄₈: n_l3___2(X₀, X₁, X₂, X₃, X₄, X₅) → n_l6___1(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₂ ≤ X₅ ∧ X₅ ≤ 1+X₃ ∧ X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₅ ≤ 1+X₃ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₀+2⋅X₁+2⋅X₂+X₃+2 {O(n^2)}

MPRF for transition t₁₅₀: n_l6___1(X₀, X₁, X₂, X₃, X₄, X₅) → n_l3___2(X₀, X₁, X₂, X₃, X₄, X₅+1) :|: 1+X₂ ≤ X₅ ∧ X₅ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₅ ≤ X₃ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₅ ≤ X₃ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₀⋅X₂+2⋅X₁⋅X₂+X₀⋅X₃+X₁⋅X₃+2⋅X₀+2⋅X₁+2⋅X₂+X₃+2 {O(n^2)}

MPRF for transition t₁₅₅: n_l3___2(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ < X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₀ ≤ X₁ ∧ X₅ ≤ 1+X₃ ∧ 1+X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₀+X₁+1 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:4⋅X₀⋅X₃+4⋅X₁⋅X₃+8⋅X₀⋅X₂+8⋅X₁⋅X₂+11⋅X₀+11⋅X₁+4⋅X₃+8⋅X₂+15 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: 2⋅X₀⋅X₃+2⋅X₁⋅X₃+4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+4⋅X₂+4 {O(n^2)}
t₅: X₀+X₁+1 {O(n)}
t₆: 2⋅X₀⋅X₃+2⋅X₁⋅X₃+4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+4⋅X₂+4 {O(n^2)}
t₇: X₀+X₁+1 {O(n)}
t₈: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₀⋅X₃+4⋅X₁⋅X₃+8⋅X₀⋅X₂+8⋅X₁⋅X₂+11⋅X₀+11⋅X₁+4⋅X₃+8⋅X₂+15 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀+X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: 2⋅X₀⋅X₃+2⋅X₁⋅X₃+4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+4⋅X₂+4 {O(n^2)}
t₅: X₀+X₁+1 {O(n)}
t₆: 2⋅X₀⋅X₃+2⋅X₁⋅X₃+4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+4⋅X₂+4 {O(n^2)}
t₇: X₀+X₁+1 {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)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₀ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: 2⋅X₀+X₁+1 {O(n)}
t₂, X₅: 2⋅X₂ {O(n)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 3⋅X₀+X₁+1 {O(n)}
t₃, X₅: 2⋅X₀⋅X₃+2⋅X₁⋅X₃+4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+8⋅X₂+X₅+4 {O(n^2)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: 2⋅X₀+X₁+1 {O(n)}
t₄, X₅: 2⋅X₀⋅X₃+2⋅X₁⋅X₃+4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+6⋅X₂+4 {O(n^2)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: 2⋅X₀+X₁+1 {O(n)}
t₅, X₅: 2⋅X₀⋅X₃+2⋅X₁⋅X₃+4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+8⋅X₂+4 {O(n^2)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: 2⋅X₀+X₁+1 {O(n)}
t₆, X₅: 2⋅X₀⋅X₃+2⋅X₁⋅X₃+4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+6⋅X₂+4 {O(n^2)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: 2⋅X₀+X₁+1 {O(n)}
t₇, X₅: 2⋅X₀⋅X₃+2⋅X₁⋅X₃+4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+8⋅X₂+4 {O(n^2)}
t₈, X₀: 2⋅X₀ {O(n)}
t₈, X₁: 2⋅X₁ {O(n)}
t₈, X₂: 2⋅X₂ {O(n)}
t₈, X₃: 2⋅X₃ {O(n)}
t₈, X₄: 3⋅X₀+X₁+1 {O(n)}
t₈, X₅: 2⋅X₀⋅X₃+2⋅X₁⋅X₃+4⋅X₀⋅X₂+4⋅X₁⋅X₂+2⋅X₃+4⋅X₀+4⋅X₁+8⋅X₂+X₅+4 {O(n^2)}