Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₂, X₃, X₄, X₅) :|: 0 < X₅
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅) :|: 0 < X₂
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₂, X₄, X₅) :|: X₂ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 0 < X₅
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(5⋅X₀+(X₂)², 2⋅X₁, X₂, X₃, X₄, X₅) :|: X₀ < (X₁)² ∧ 0 < X₀

Preprocessing

Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location l2

Found invariant 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l1

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₂, X₃, X₄, X₅) :|: 0 < X₅
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₄, X₅) :|: 0 < X₂ ∧ 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₂, X₄, X₅) :|: X₂ ≤ 0 ∧ 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 0 < X₅ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l2(5⋅X₀+(X₂)², 2⋅X₁, X₂, X₃, X₄, X₅) :|: X₀ < (X₁)² ∧ 0 < X₀ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₂, X₄, X₅) :|: X₂ ≤ 0 ∧ 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

l2 [X₅ ]
l1 [X₅+1 ]

MPRF for transition t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 0 < X₅ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

l2 [X₅+1 ]
l1 [X₅+1 ]

Found invariant 1 ≤ 0 for location l2

Found invariant 1 ≤ 0 for location l1

Found invariant 1 ≤ X₅ ∧ 1+X₃ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location l2

Found invariant 1 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₁ 8⋅X₅⋅X₅+12⋅X₅+2⋅X₂+8 {O(n^2)}

TWN-Loops:

entry: t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 0 < X₅ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0
results in twn-loop: twn:Inv: [0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀] , (X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀+X₂,X₁,X₂-1,X₃,X₄,X₅) :|: 0 < X₂
entry: t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₂, X₃, X₄, X₅) :|: 0 < X₅
results in twn-loop: twn:Inv: [0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀] , (X₀,X₁,X₂,X₃,X₄,X₅) -> (X₀+X₂,X₁,X₂-1,X₃,X₄,X₅) :|: 0 < X₂
order: [X₂; X₀; X₁; X₃; X₄; X₅]
closed-form:
X₂: X₂ + [[n != 0]] * -1 * n^1
X₀: X₀ + [[n != 0]] * X₂ * n^1 + [[n != 0, n != 1]] * -1/2 * n^2 + [[n != 0, n != 1]] * 1/2 * n^1
X₁: X₁
X₃: X₃
X₄: X₄
X₅: X₅

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃
∨ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 0 < X₂ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₂ ∧ 2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃

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

relevant size-bounds w.r.t. t₄:
X₂: 4⋅X₅ {O(n)}
Runtime-bound of t₄: X₅+1 {O(n)}
Results in: 8⋅X₅⋅X₅+12⋅X₅+4 {O(n^2)}

order: [X₂; X₀; X₁; X₃; X₄; X₅]
closed-form:
X₂: X₂ + [[n != 0]] * -1 * n^1
X₀: X₀ + [[n != 0]] * X₂ * n^1 + [[n != 0, n != 1]] * -1/2 * n^2 + [[n != 0, n != 1]] * 1/2 * n^1
X₁: X₁
X₃: X₃
X₄: X₄
X₅: X₅

Termination: true
Formula:

1 < 0
∨ 1 < 0 ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃
∨ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ 0 < X₂ ∧ 0 < 2⋅X₂+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < X₂ ∧ 2⋅X₃ < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0
∨ 0 < X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 2⋅X₂+1 ∧ 2⋅X₂+1 ≤ 0 ∧ 2⋅X₃ ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 2⋅X₃

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

relevant size-bounds w.r.t. t₀:
X₂: X₂ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 2⋅X₂+4 {O(n)}

8⋅X₅⋅X₅+12⋅X₅+2⋅X₂+8 {O(n^2)}

Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location l2

Found invariant 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l1

Time-Bound by TWN-Loops:

TWN-Loops: t₃ 16⋅X₂⋅X₂⋅X₅+288⋅X₄⋅X₄⋅X₅+64⋅X₂⋅X₅⋅X₅+64⋅X₅⋅X₅⋅X₅+16⋅X₂⋅X₂+288⋅X₄⋅X₄+64⋅X₂⋅X₅+64⋅X₅⋅X₅+16⋅X₅+16 {O(n^3)}

TWN-Loops:

entry: t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₂, X₄, X₅) :|: X₂ ≤ 0 ∧ 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀
results in twn-loop: twn:Inv: [0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0] , (X₀,X₁,X₂,X₃,X₄,X₅) -> (5⋅X₀+(X₂)²,2⋅X₁,X₂,X₃,X₄,X₅) :|: X₀ < (X₁)² ∧ 0 < X₀
order: [X₂; X₀; X₁; X₃; X₅]
closed-form:
X₂: X₂
X₀: X₀ * 5^n + [[n != 0]] * 1/4⋅(X₂)² * 5^n + [[n != 0]] * -1/4⋅(X₂)²
X₁: X₁ * 2^n
X₃: X₃
X₅: X₅

Termination: true
Formula:

0 < 4⋅X₀+(X₂)² ∧ 4⋅X₀+(X₂)² < 0
∨ 0 < 4⋅X₀+(X₂)² ∧ 0 < 4⋅(X₁)² ∧ 4⋅X₀+(X₂)² ≤ 0 ∧ 0 ≤ 4⋅X₀+(X₂)²
∨ 0 < 4⋅X₀+(X₂)² ∧ 0 < (X₂)² ∧ 4⋅X₀+(X₂)² ≤ 0 ∧ 0 ≤ 4⋅X₀+(X₂)² ∧ 0 ≤ 4⋅(X₁)² ∧ 4⋅(X₁)² ≤ 0
∨ (X₂)² < 0 ∧ 0 ≤ 4⋅X₀+(X₂)² ∧ 4⋅X₀+(X₂)² ≤ 0 ∧ 4⋅X₀+(X₂)² < 0
∨ (X₂)² < 0 ∧ 0 < 4⋅(X₁)² ∧ 4⋅X₀+(X₂)² ≤ 0 ∧ 0 ≤ 4⋅X₀+(X₂)²
∨ (X₂)² < 0 ∧ 0 < (X₂)² ∧ 4⋅X₀+(X₂)² ≤ 0 ∧ 0 ≤ 4⋅X₀+(X₂)² ∧ 0 ≤ 4⋅(X₁)² ∧ 4⋅(X₁)² ≤ 0

Stabilization-Threshold for: 0 < X₀
alphas_abs: (X₂)²
M: 0
N: 1
Bound: 2⋅X₂⋅X₂+2 {O(n^2)}
Stabilization-Threshold for: X₀ < (X₁)²
alphas_abs: 4⋅(X₁)²+(X₂)²
M: 11
N: 1
Bound: 2⋅X₂⋅X₂+8⋅X₁⋅X₁+12 {O(n^2)}

relevant size-bounds w.r.t. t₂:
X₁: 6⋅X₄ {O(n)}
X₂: 2⋅X₂+4⋅X₅ {O(n)}
Runtime-bound of t₂: X₅+1 {O(n)}
Results in: 16⋅X₂⋅X₂⋅X₅+288⋅X₄⋅X₄⋅X₅+64⋅X₂⋅X₅⋅X₅+64⋅X₅⋅X₅⋅X₅+16⋅X₂⋅X₂+288⋅X₄⋅X₄+64⋅X₂⋅X₅+64⋅X₅⋅X₅+16⋅X₅+16 {O(n^3)}

16⋅X₂⋅X₂⋅X₅+288⋅X₄⋅X₄⋅X₅+64⋅X₂⋅X₅⋅X₅+64⋅X₅⋅X₅⋅X₅+16⋅X₂⋅X₂+288⋅X₄⋅X₄+64⋅X₂⋅X₅+64⋅X₅⋅X₅+16⋅X₅+16 {O(n^3)}

Analysing control-flow refined program

Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location l2

Found invariant 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 for location n_l2___1

Found invariant 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ for location l1

knowledge_propagation leads to new time bound X₅+1 {O(n)} for transition t₇₆: l2(X₀, X₁, X₂, X₃, X₄, X₅) → n_l2___1(NoDet0, 2⋅X₁, X₂, X₂, X₄, Arg5_P) :|: X₂ ≤ 0 ∧ 0 ≤ X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₅ ∧ X₂ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₅ ∧ X₃ ≤ 0 ∧ X₂ ≤ 0 ∧ 0 ≤ Arg5_P ∧ 0 < X₀ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₅ ≤ Arg5_P ∧ Arg5_P ≤ X₅ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0

MPRF for transition t₆₆: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₁, X₅) :|: 0 < X₂ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 0 < X₂ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

6⋅X₅⋅X₅+6⋅X₅+X₂ {O(n^2)}

MPRF:

l2 [X₃ ]
n_l2___1 [X₅ ]
l1 [X₂ ]

MPRF for transition t₆₇: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+X₂, X₁, X₂-1, X₃, X₁, X₅) :|: X₃ ≤ X₀ ∧ 0 ≤ X₅ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 0 < X₂ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ 0 ≤ X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ of depth 1:

new bound:

6⋅X₅⋅X₅+6⋅X₅+X₂ {O(n^2)}

MPRF:

l2 [X₂ ]
n_l2___1 [X₅ ]
l1 [X₂ ]

MPRF for transition t₇₉: n_l2___1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₅, X₃, X₄, X₅-1) :|: 0 < X₅ ∧ 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 0 ≤ X₅ ∧ X₃ ≤ X₅ ∧ X₂ ≤ X₅ ∧ X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₂+X₃ ≤ 0 ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 of depth 1:

new bound:

X₅+1 {O(n)}

MPRF:

l2 [X₅+1 ]
n_l2___1 [X₅+1 ]
l1 [X₅+1 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:16⋅X₂⋅X₂⋅X₅+288⋅X₄⋅X₄⋅X₅+64⋅X₂⋅X₅⋅X₅+64⋅X₅⋅X₅⋅X₅+16⋅X₂⋅X₂+288⋅X₄⋅X₄+64⋅X₂⋅X₅+72⋅X₅⋅X₅+2⋅X₂+30⋅X₅+27 {O(n^3)}
t₀: 1 {O(1)}
t₁: 8⋅X₅⋅X₅+12⋅X₅+2⋅X₂+8 {O(n^2)}
t₂: X₅+1 {O(n)}
t₃: 16⋅X₂⋅X₂⋅X₅+288⋅X₄⋅X₄⋅X₅+64⋅X₂⋅X₅⋅X₅+64⋅X₅⋅X₅⋅X₅+16⋅X₂⋅X₂+288⋅X₄⋅X₄+64⋅X₂⋅X₅+64⋅X₅⋅X₅+16⋅X₅+16 {O(n^3)}
t₄: X₅+1 {O(n)}

Costbounds

Overall costbound: 16⋅X₂⋅X₂⋅X₅+288⋅X₄⋅X₄⋅X₅+64⋅X₂⋅X₅⋅X₅+64⋅X₅⋅X₅⋅X₅+16⋅X₂⋅X₂+288⋅X₄⋅X₄+64⋅X₂⋅X₅+72⋅X₅⋅X₅+2⋅X₂+30⋅X₅+27 {O(n^3)}
t₀: 1 {O(1)}
t₁: 8⋅X₅⋅X₅+12⋅X₅+2⋅X₂+8 {O(n^2)}
t₂: X₅+1 {O(n)}
t₃: 16⋅X₂⋅X₂⋅X₅+288⋅X₄⋅X₄⋅X₅+64⋅X₂⋅X₅⋅X₅+64⋅X₅⋅X₅⋅X₅+16⋅X₂⋅X₂+288⋅X₄⋅X₄+64⋅X₂⋅X₅+64⋅X₅⋅X₅+16⋅X₅+16 {O(n^3)}
t₄: X₅+1 {O(n)}

Sizebounds

t₀, X₀: X₃ {O(n)}
t₀, X₁: X₄ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₁, X₀: 16⋅X₂⋅X₅⋅X₅+64⋅X₅⋅X₅⋅X₅+4⋅X₂⋅X₂+40⋅X₂⋅X₅+96⋅X₅⋅X₅+22⋅X₂+80⋅X₅+X₃ {O(n^3)}
t₁, X₁: 5⋅X₄ {O(n)}
t₁, X₂: 4⋅X₅+X₂ {O(n)}
t₁, X₃: 4⋅X₂+8⋅X₅+X₃ {O(n)}
t₁, X₄: 2⋅X₄ {O(n)}
t₁, X₅: 2⋅X₅ {O(n)}
t₂, X₀: 16⋅X₂⋅X₅⋅X₅+64⋅X₅⋅X₅⋅X₅+4⋅X₂⋅X₂+40⋅X₂⋅X₅+96⋅X₅⋅X₅+2⋅X₃+22⋅X₂+80⋅X₅ {O(n^3)}
t₂, X₁: 6⋅X₄ {O(n)}
t₂, X₂: 2⋅X₂+4⋅X₅ {O(n)}
t₂, X₃: 2⋅X₂+4⋅X₅ {O(n)}
t₂, X₄: 2⋅X₄ {O(n)}
t₂, X₅: 2⋅X₅ {O(n)}
t₃, X₁: 2^(16⋅X₂⋅X₂⋅X₅+288⋅X₄⋅X₄⋅X₅+64⋅X₂⋅X₅⋅X₅+64⋅X₅⋅X₅⋅X₅+16⋅X₂⋅X₂+288⋅X₄⋅X₄+64⋅X₂⋅X₅+64⋅X₅⋅X₅+16⋅X₅+16)⋅6⋅X₄ {O(EXP)}
t₃, X₂: 2⋅X₂+4⋅X₅ {O(n)}
t₃, X₃: 2⋅X₂+4⋅X₅ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₄, X₀: 4⋅X₂+8⋅X₅ {O(n)}
t₄, X₁: 4⋅X₄ {O(n)}
t₄, X₂: 4⋅X₅ {O(n)}
t₄, X₃: 4⋅X₂+8⋅X₅ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}