Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+X₃, X₃-1) :|: 1 ≤ X₃
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ < 1
t₃: l2(X₀, X₁, X₂, X₃) → l3(X₂, X₂, X₂, X₃) :|: 1 ≤ X₂
t₅: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂-1, X₃) :|: X₀ ≤ 0
t₄: l3(X₀, X₁, X₂, X₃) → l3(X₀+X₁, X₁-1, X₂, X₃) :|: 1 ≤ X₀

Preprocessing

Found invariant X₃ ≤ 0 for location l2

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+X₃, X₃-1) :|: 1 ≤ X₃
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ < 1
t₃: l2(X₀, X₁, X₂, X₃) → l3(X₂, X₂, X₂, X₃) :|: 1 ≤ X₂ ∧ X₃ ≤ 0
t₅: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂-1, X₃) :|: X₀ ≤ 0 ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀
t₄: l3(X₀, X₁, X₂, X₃) → l3(X₀+X₁, X₁-1, X₂, X₃) :|: 1 ≤ X₀ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀

MPRF for transition t₁: l1(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂+X₃, X₃-1) :|: 1 ≤ X₃ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l1 [X₃ ]

MPRF for transition t₃: l2(X₀, X₁, X₂, X₃) → l3(X₂, X₂, X₂, X₃) :|: 1 ≤ X₂ ∧ X₃ ≤ 0 of depth 1:

new bound:

2⋅X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}

MPRF:

l3 [X₂-1 ]
l2 [X₂ ]

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂-1, X₃) :|: X₀ ≤ 0 ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ of depth 1:

new bound:

2⋅X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}

MPRF:

l3 [X₂ ]
l2 [X₂ ]

Found invariant X₃ ≤ 0 for location l2

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₄ 64⋅X₃⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃⋅X₃+128⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃+64⋅X₂⋅X₂+78⋅X₃⋅X₃+14⋅X₂+14⋅X₃ {O(n^4)}

TWN-Loops:

entry: t₃: l2(X₀, X₁, X₂, X₃) → l3(X₂, X₂, X₂, X₃) :|: 1 ≤ X₂ ∧ X₃ ≤ 0
results in twn-loop: twn:Inv: [X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀+X₁,X₁-1,X₂,X₃) :|: 1 ≤ X₀
order: [X₁; X₀; X₂; X₃]
closed-form:
X₁: X₁ + [[n != 0]] * -1 * n^1
X₀: X₀ + [[n != 0]] * X₁ * n^1 + [[n != 0, n != 1]] * -1/2 * n^2 + [[n != 0, n != 1]] * 1/2 * n^1
X₂: X₂
X₃: X₃

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ 0 < 2⋅X₁+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 2⋅X₁ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+3 ∧ 2⋅X₁+3 ≤ 0
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+3 ∧ 2⋅X₁+3 ≤ 0 ∧ 2⋅X₁ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₁
∨ 0 < 2⋅X₁+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 0 < 2⋅X₁+1 ∧ 0 < 2⋅X₁+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 2⋅X₁+1 ∧ 2⋅X₁ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+3 ∧ 2⋅X₁+3 ≤ 0
∨ 0 < 2⋅X₁+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+3 ∧ 2⋅X₁+3 ≤ 0 ∧ 2⋅X₁ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₁
∨ 2 < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+1 ∧ 2⋅X₁+1 ≤ 0 ∧ 1 < 0
∨ 2 < 2⋅X₀ ∧ 0 ≤ 2⋅X₁+1 ∧ 2⋅X₁+1 ≤ 0 ∧ 0 < 2⋅X₁+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2 < 2⋅X₀ ∧ 0 ≤ 2⋅X₁+1 ∧ 2⋅X₁+1 ≤ 0 ∧ 2⋅X₁ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+3 ∧ 2⋅X₁+3 ≤ 0
∨ 2 < 2⋅X₀ ∧ 0 ≤ 2⋅X₁+1 ∧ 2⋅X₁+1 ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+3 ∧ 2⋅X₁+3 ≤ 0 ∧ 2⋅X₁ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₁
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+1 ∧ 2⋅X₁+1 ≤ 0 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2 ∧ 1 < 0
∨ 0 ≤ 2⋅X₁+1 ∧ 2⋅X₁+1 ≤ 0 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2 ∧ 0 < 2⋅X₁+3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 ≤ 2⋅X₁+1 ∧ 2⋅X₁+1 ≤ 0 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2 ∧ 2⋅X₁ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+3 ∧ 2⋅X₁+3 ≤ 0
∨ 0 ≤ 2⋅X₁+1 ∧ 2⋅X₁+1 ≤ 0 ∧ 2 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₁+3 ∧ 2⋅X₁+3 ≤ 0 ∧ 2⋅X₁ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₁

Stabilization-Threshold for: 1 ≤ X₀
alphas_abs: 1+2⋅X₀+2⋅X₁
M: 0
N: 2
Bound: 4⋅X₀+4⋅X₁+5 {O(n)}

relevant size-bounds w.r.t. t₃:
X₀: 4⋅X₃⋅X₃+4⋅X₂+4⋅X₃ {O(n^2)}
X₁: 4⋅X₃⋅X₃+4⋅X₂+4⋅X₃ {O(n^2)}
Runtime-bound of t₃: 2⋅X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}
Results in: 64⋅X₃⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃⋅X₃+128⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃+64⋅X₂⋅X₂+78⋅X₃⋅X₃+14⋅X₂+14⋅X₃ {O(n^4)}

64⋅X₃⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃⋅X₃+128⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃+64⋅X₂⋅X₂+78⋅X₃⋅X₃+14⋅X₂+14⋅X₃ {O(n^4)}

Analysing control-flow refined program

Found invariant X₃ ≤ 0 for location l2

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___4

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l3___3

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 2+X₁+X₃ ≤ 0 ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location n_l2___1

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₀ for location n_l3___2

MPRF for transition t₆₁: n_l2___1(X₀, X₁, X₂, X₃) → n_l3___4(X₂, X₂, X₂, X₃) :|: X₃ ≤ 0 ∧ X₃ ≤ 0 ∧ 0 ≤ X₂ ∧ X₃ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ X₂ ∧ X₃ ≤ 0 ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 2+X₁+X₃ ≤ 0 ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 of depth 1:

new bound:

2⋅X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}

MPRF:

n_l2___1 [X₂+1 ]
n_l3___2 [X₂ ]
n_l3___4 [X₂ ]
n_l3___3 [X₂ ]

MPRF for transition t₆₃: n_l3___2(X₀, X₁, X₂, X₃) → n_l2___1(X₀, X₁, X₂-1, X₃) :|: X₁ ≤ X₀ ∧ X₃ ≤ 0 ∧ 1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 0 ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ 2+2⋅X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ X₃ ≤ 0 ∧ X₁ ≤ X₀ ∧ X₀ ≤ 0 ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₀ of depth 1:

new bound:

2⋅X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}

MPRF:

n_l2___1 [X₂ ]
n_l3___2 [X₂ ]
n_l3___4 [X₂ ]
n_l3___3 [X₂ ]

MPRF for transition t₆₅: n_l3___3(X₀, X₁, X₂, X₃) → n_l3___2(X₀+X₁, X₁-1, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₃ ≤ 0 ∧ 1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₃ ≤ 0 ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 0 ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ 2+2⋅X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₃ ≤ 0 ∧ X₁ ≤ X₂ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}

MPRF:

n_l2___1 [X₂ ]
n_l3___2 [X₂-1 ]
n_l3___4 [X₂ ]
n_l3___3 [X₂ ]

MPRF for transition t₆₆: n_l3___4(X₀, X₁, X₂, X₃) → n_l3___3(X₀+X₁, X₁-1, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₃ ≤ 0 ∧ 1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₀ ∧ X₃ ≤ 0 ∧ X₃ ≤ 0 ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₃ ≤ 0 ∧ X₁ ≤ X₂ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}

MPRF:

n_l2___1 [X₂ ]
n_l3___2 [X₂-1 ]
n_l3___4 [X₀ ]
n_l3___3 [X₂-1 ]

Found invariant X₃ ≤ 0 for location l2

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___4

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l3___3

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ 2+X₁+X₃ ≤ 0 ∧ X₀+X₃ ≤ 0 ∧ 0 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 2+X₁ ≤ 0 ∧ 2+X₁ ≤ X₀ ∧ 2+X₀+X₁ ≤ 0 ∧ X₀ ≤ 0 for location n_l2___1

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₀ for location n_l3___2

MPRF for transition t₆₄: n_l3___2(X₀, X₁, X₂, X₃) → n_l3___2(X₀+X₁, X₁-1, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₃ ≤ 0 ∧ 1 ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₃ ≤ 0 ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₀ ∧ 2+2⋅X₁ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₃ ≤ 0 ∧ X₁ ≤ X₂ ∧ X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2+X₁ ≤ X₂ ∧ 2+X₁ ≤ X₀ of depth 2:

new bound:

320⋅X₃⋅X₃⋅X₃⋅X₃+640⋅X₂⋅X₃⋅X₃+640⋅X₃⋅X₃⋅X₃+320⋅X₂⋅X₂+482⋅X₃⋅X₃+640⋅X₂⋅X₃+162⋅X₂+162⋅X₃+1 {O(n^4)}

MPRF:

n_l2___1 [2⋅X₂ ; 8⋅X₂ ]
n_l3___2 [X₁+3 ; X₀+2⋅X₂-2⋅X₁ ]
n_l3___4 [X₁+X₂ ; 4⋅X₀+2⋅X₁+2⋅X₂ ]
n_l3___3 [X₁+2 ; 3⋅X₀+2⋅X₂-X₁ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:64⋅X₃⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃⋅X₃+128⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃+64⋅X₂⋅X₂+82⋅X₃⋅X₃+18⋅X₂+19⋅X₃+2 {O(n^4)}
t₀: 1 {O(1)}
t₁: X₃ {O(n)}
t₂: 1 {O(1)}
t₃: 2⋅X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}
t₄: 64⋅X₃⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃⋅X₃+128⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃+64⋅X₂⋅X₂+78⋅X₃⋅X₃+14⋅X₂+14⋅X₃ {O(n^4)}
t₅: 2⋅X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}

Costbounds

Overall costbound: 64⋅X₃⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃⋅X₃+128⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃+64⋅X₂⋅X₂+82⋅X₃⋅X₃+18⋅X₂+19⋅X₃+2 {O(n^4)}
t₀: 1 {O(1)}
t₁: X₃ {O(n)}
t₂: 1 {O(1)}
t₃: 2⋅X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}
t₄: 64⋅X₃⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃⋅X₃+128⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃+64⋅X₂⋅X₂+78⋅X₃⋅X₃+14⋅X₂+14⋅X₃ {O(n^4)}
t₅: 2⋅X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: 2⋅X₃⋅X₃+2⋅X₃+X₂ {O(n^2)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₁: 2⋅X₁ {O(n)}
t₂, X₂: 2⋅X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}
t₂, X₃: 2⋅X₃ {O(n)}
t₃, X₀: 4⋅X₃⋅X₃+4⋅X₂+4⋅X₃ {O(n^2)}
t₃, X₁: 4⋅X₃⋅X₃+4⋅X₂+4⋅X₃ {O(n^2)}
t₃, X₂: 2⋅X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}
t₃, X₃: 2⋅X₃ {O(n)}
t₄, X₀: 4096⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16384⋅X₂⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16384⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+24576⋅X₂⋅X₂⋅X₃⋅X₃⋅X₃⋅X₃+26880⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+49152⋅X₂⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16384⋅X₂⋅X₂⋅X₂⋅X₃⋅X₃+23296⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+49152⋅X₂⋅X₂⋅X₃⋅X₃⋅X₃+56064⋅X₂⋅X₃⋅X₃⋅X₃⋅X₃+11380⋅X₃⋅X₃⋅X₃⋅X₃+16384⋅X₂⋅X₂⋅X₂⋅X₃+30208⋅X₂⋅X₃⋅X₃⋅X₃+31488⋅X₂⋅X₂⋅X₃⋅X₃+4096⋅X₂⋅X₂⋅X₂⋅X₂+2304⋅X₂⋅X₂⋅X₂+3048⋅X₃⋅X₃⋅X₃+6912⋅X₂⋅X₂⋅X₃+7656⋅X₂⋅X₃⋅X₃+372⋅X₂⋅X₂+398⋅X₃⋅X₃+744⋅X₂⋅X₃+26⋅X₂+26⋅X₃ {O(n^8)}
t₄, X₁: 64⋅X₃⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃⋅X₃+128⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃+64⋅X₂⋅X₂+82⋅X₃⋅X₃+18⋅X₂+18⋅X₃ {O(n^4)}
t₄, X₂: 2⋅X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}
t₄, X₃: 2⋅X₃ {O(n)}
t₅, X₀: 4096⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16384⋅X₂⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16384⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+24576⋅X₂⋅X₂⋅X₃⋅X₃⋅X₃⋅X₃+26880⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+49152⋅X₂⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+16384⋅X₂⋅X₂⋅X₂⋅X₃⋅X₃+23296⋅X₃⋅X₃⋅X₃⋅X₃⋅X₃+49152⋅X₂⋅X₂⋅X₃⋅X₃⋅X₃+56064⋅X₂⋅X₃⋅X₃⋅X₃⋅X₃+11380⋅X₃⋅X₃⋅X₃⋅X₃+16384⋅X₂⋅X₂⋅X₂⋅X₃+30208⋅X₂⋅X₃⋅X₃⋅X₃+31488⋅X₂⋅X₂⋅X₃⋅X₃+4096⋅X₂⋅X₂⋅X₂⋅X₂+2304⋅X₂⋅X₂⋅X₂+3048⋅X₃⋅X₃⋅X₃+6912⋅X₂⋅X₂⋅X₃+7656⋅X₂⋅X₃⋅X₃+372⋅X₂⋅X₂+398⋅X₃⋅X₃+744⋅X₂⋅X₃+26⋅X₂+26⋅X₃ {O(n^8)}
t₅, X₁: 64⋅X₃⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃⋅X₃+128⋅X₃⋅X₃⋅X₃+128⋅X₂⋅X₃+64⋅X₂⋅X₂+82⋅X₃⋅X₃+18⋅X₂+18⋅X₃ {O(n^4)}
t₅, X₂: 2⋅X₃⋅X₃+2⋅X₂+2⋅X₃ {O(n^2)}
t₅, X₃: 2⋅X₃ {O(n)}