Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₀ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, X₀, X₇, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₆
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₆ ≤ 0
t₆: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ < 0
t₇: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: 0 < X₁
t₈: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₁ ≤ 0 ∧ 0 ≤ X₁
t₁₀: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: X₂ ≤ (X₁)²+(X₆)⁵
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) :|: (X₁)²+(X₆)⁵ < X₂
t₁₂: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₀-1, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l1(X₃, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₃: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇)
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇) → l3(X₀, -2⋅X₁, 3⋅X₂-(X₆)³, X₃, X₄, X₅, X₆, X₇)

Preprocessing

Eliminate variables {X₄,X₅} that do not contribute to the problem

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

Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l7

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

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l8

Found invariant X₀ ≤ X₃ for location l1

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l4

Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l9

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₆, X₇
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₂₈: l0(X₀, X₁, X₂, X₃, X₆, X₇) → l6(X₀, X₁, X₂, X₃, X₆, X₇)
t₂₉: l1(X₀, X₁, X₂, X₃, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₆, X₇) :|: 0 < X₀ ∧ X₀ ≤ X₃
t₃₀: l1(X₀, X₁, X₂, X₃, X₆, X₇) → l7(X₀, X₁, X₂, X₃, X₆, X₇) :|: X₀ ≤ 0 ∧ X₀ ≤ X₃
t₃₁: l2(X₀, X₁, X₂, X₃, X₆, X₇) → l3(X₀, X₀, X₇, X₃, X₆, X₇) :|: 0 < X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₂: l2(X₀, X₁, X₂, X₃, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₆, X₇) :|: X₆ ≤ 0 ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₃: l3(X₀, X₁, X₂, X₃, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₆, X₇) :|: X₁ < 0 ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₄: l3(X₀, X₁, X₂, X₃, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₆, X₇) :|: 0 < X₁ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₅: l3(X₀, X₁, X₂, X₃, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₆, X₇) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₇: l4(X₀, X₁, X₂, X₃, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₆, X₇) :|: X₂ ≤ (X₁)²+(X₆)⁵ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₆: l4(X₀, X₁, X₂, X₃, X₆, X₇) → l8(X₀, X₁, X₂, X₃, X₆, X₇) :|: (X₁)²+(X₆)⁵ < X₂ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₈: l5(X₀, X₁, X₂, X₃, X₆, X₇) → l1(X₀-1, X₁, X₂, X₃, X₆, X₇) :|: 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
t₃₉: l6(X₀, X₁, X₂, X₃, X₆, X₇) → l1(X₃, X₁, X₂, X₃, X₆, X₇)
t₄₀: l7(X₀, X₁, X₂, X₃, X₆, X₇) → l9(X₀, X₁, X₂, X₃, X₆, X₇) :|: X₀ ≤ X₃ ∧ X₀ ≤ 0
t₄₁: l8(X₀, X₁, X₂, X₃, X₆, X₇) → l3(X₀, -2⋅X₁, 3⋅X₂-(X₆)³, X₃, X₆, X₇) :|: 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀

MPRF for transition t₂₉: l1(X₀, X₁, X₂, X₃, X₆, X₇) → l2(X₀, X₁, X₂, X₃, X₆, X₇) :|: 0 < X₀ ∧ X₀ ≤ X₃ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

l2 [X₀ ]
l4 [X₀ ]
l5 [X₀ ]
l1 [X₀+1 ]
l8 [X₀ ]
l3 [X₀ ]

MPRF for transition t₃₁: l2(X₀, X₁, X₂, X₃, X₆, X₇) → l3(X₀, X₀, X₇, X₃, X₆, X₇) :|: 0 < X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

l2 [X₀+1 ]
l4 [X₀ ]
l5 [X₀ ]
l1 [X₀+1 ]
l8 [X₀ ]
l3 [X₀ ]

MPRF for transition t₃₂: l2(X₀, X₁, X₂, X₃, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₆, X₇) :|: X₆ ≤ 0 ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l2 [X₀ ]
l4 [X₀ ]
l5 [X₀-1 ]
l1 [X₀ ]
l8 [X₀ ]
l3 [X₀ ]

MPRF for transition t₃₅: l3(X₀, X₁, X₂, X₃, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₆, X₇) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l2 [X₀ ]
l4 [X₀ ]
l5 [X₀-1 ]
l1 [X₀ ]
l8 [X₀ ]
l3 [X₀ ]

MPRF for transition t₃₇: l4(X₀, X₁, X₂, X₃, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₆, X₇) :|: X₂ ≤ (X₁)²+(X₆)⁵ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l2 [X₀ ]
l4 [X₀ ]
l5 [X₀-1 ]
l1 [X₀ ]
l8 [X₀ ]
l3 [X₀ ]

MPRF for transition t₃₈: l5(X₀, X₁, X₂, X₃, X₆, X₇) → l1(X₀-1, X₁, X₂, X₃, X₆, X₇) :|: 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l2 [X₀ ]
l4 [X₀ ]
l5 [X₀ ]
l1 [X₀ ]
l8 [X₀ ]
l3 [X₀ ]

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

Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l7

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

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l8

Found invariant X₀ ≤ X₃ for location l1

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l4

Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l9

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ for location l3

Time-Bound by TWN-Loops:

TWN-Loops: t₃₆ 32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21 {O(n^2)}

TWN-Loops:

entry: t₃₁: l2(X₀, X₁, X₂, X₃, X₆, X₇) → l3(X₀, X₀, X₇, X₃, X₆, X₇) :|: 0 < X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀
results in twn-loop: twn:Inv: [1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₃,X₆,X₇) -> (X₀,-2⋅X₁,3⋅X₂-(X₆)³,X₃,X₆,X₇) :|: X₁ < 0 ∧ (X₁)²+(X₆)⁵ < X₂ ∨ 0 < X₁ ∧ (X₁)²+(X₆)⁵ < X₂
order: [X₀; X₁; X₆; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁ * 4^n
X₆: X₆
X₂: X₂ * 9^n + [[n != 0]] * -1/2⋅(X₆)³ * 9^n + [[n != 0]] * 1/2⋅(X₆)³
X₃: X₃

Termination: true
Formula:

8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ 2⋅(X₁)² < 0 ∧ X₁ < 0
∨ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ (X₆)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ X₁ < 0
∨ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ 2⋅(X₆)⁵ < (X₆)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₆)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₆)³ ∧ X₁ < 0
∨ 3⋅(X₆)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ 2⋅(X₁)² < 0 ∧ X₁ < 0
∨ 3⋅(X₆)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ (X₆)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ X₁ < 0
∨ 3⋅(X₆)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ 2⋅(X₆)⁵ < (X₆)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₆)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₆)³ ∧ X₁ < 0
∨ 2⋅(X₆)⁵ < (X₆)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₆)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₆)³ ∧ 0 < 2⋅X₁ ∧ 2⋅(X₁)² < 0 ∧ X₁ < 0
∨ 2⋅(X₆)⁵ < (X₆)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₆)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₆)³ ∧ 0 < 2⋅X₁ ∧ (X₆)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ X₁ < 0
∨ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₆)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₆)³ ∧ 0 < 2⋅X₁ ∧ 2⋅(X₆)⁵ < (X₆)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₆)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₆)³ ∧ X₁ < 0
∨ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ 2⋅(X₁)² < 0 ∧ X₁ < 0
∨ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ (X₆)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ X₁ < 0
∨ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ 2⋅(X₆)⁵ < (X₆)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₆)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₆)³ ∧ X₁ < 0
∨ 3⋅(X₆)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ 2⋅(X₁)² < 0 ∧ X₁ < 0
∨ 3⋅(X₆)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ (X₆)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ X₁ < 0
∨ 3⋅(X₆)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ 2⋅(X₆)⁵ < (X₆)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₆)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₆)³ ∧ X₁ < 0
∨ 2⋅(X₆)⁵ < (X₆)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₆)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₆)³ ∧ 2⋅X₁ < 0 ∧ 2⋅(X₁)² < 0 ∧ X₁ < 0
∨ 2⋅(X₆)⁵ < (X₆)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₆)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₆)³ ∧ 2⋅X₁ < 0 ∧ (X₆)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ X₁ < 0
∨ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₆)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₆)³ ∧ 2⋅X₁ < 0 ∧ 2⋅(X₆)⁵ < (X₆)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₆)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₆)³ ∧ X₁ < 0
∨ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ 2⋅(X₁)² < 0 ∧ 0 < X₁
∨ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ (X₆)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ 0 < X₁
∨ 8⋅(X₁)² < 0 ∧ 0 < 2⋅X₁ ∧ 2⋅(X₆)⁵ < (X₆)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₆)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₆)³ ∧ 0 < X₁
∨ 3⋅(X₆)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ 2⋅(X₁)² < 0 ∧ 0 < X₁
∨ 3⋅(X₆)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ (X₆)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ 0 < X₁
∨ 3⋅(X₆)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 0 < 2⋅X₁ ∧ 2⋅(X₆)⁵ < (X₆)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₆)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₆)³ ∧ 0 < X₁
∨ 2⋅(X₆)⁵ < (X₆)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₆)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₆)³ ∧ 0 < 2⋅X₁ ∧ 2⋅(X₁)² < 0 ∧ 0 < X₁
∨ 2⋅(X₆)⁵ < (X₆)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₆)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₆)³ ∧ 0 < 2⋅X₁ ∧ (X₆)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ 0 < X₁
∨ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₆)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₆)³ ∧ 0 < 2⋅X₁ ∧ 2⋅(X₆)⁵ < (X₆)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₆)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₆)³ ∧ 0 < X₁
∨ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ 2⋅(X₁)² < 0 ∧ 0 < X₁
∨ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ (X₆)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ 0 < X₁
∨ 8⋅(X₁)² < 0 ∧ 2⋅X₁ < 0 ∧ 2⋅(X₆)⁵ < (X₆)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₆)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₆)³ ∧ 0 < X₁
∨ 3⋅(X₆)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ 2⋅(X₁)² < 0 ∧ 0 < X₁
∨ 3⋅(X₆)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ (X₆)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ 0 < X₁
∨ 3⋅(X₆)³ < 6⋅X₂ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 2⋅X₁ < 0 ∧ 2⋅(X₆)⁵ < (X₆)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₆)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₆)³ ∧ 0 < X₁
∨ 2⋅(X₆)⁵ < (X₆)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₆)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₆)³ ∧ 2⋅X₁ < 0 ∧ 2⋅(X₁)² < 0 ∧ 0 < X₁
∨ 2⋅(X₆)⁵ < (X₆)³ ∧ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₆)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₆)³ ∧ 2⋅X₁ < 0 ∧ (X₆)³ < 2⋅X₂ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ 0 < X₁
∨ 8⋅(X₁)² ≤ 0 ∧ 0 ≤ 8⋅(X₁)² ∧ 3⋅(X₆)³ ≤ 6⋅X₂ ∧ 6⋅X₂ ≤ 3⋅(X₆)³ ∧ 2⋅X₁ < 0 ∧ 2⋅(X₆)⁵ < (X₆)³ ∧ 2⋅(X₁)² ≤ 0 ∧ 0 ≤ 2⋅(X₁)² ∧ (X₆)³ ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ (X₆)³ ∧ 0 < X₁

Stabilization-Threshold for: 4⋅(X₁)²+(X₆)⁵+(X₆)³ < 3⋅X₂
alphas_abs: 6⋅X₂
M: 0
N: 1
Bound: 12⋅X₂+2 {O(n)}
Stabilization-Threshold for: (X₁)²+(X₆)⁵ < X₂
alphas_abs: 2⋅X₂
M: 0
N: 1
Bound: 4⋅X₂+2 {O(n)}

relevant size-bounds w.r.t. t₃₁:
X₂: X₇ {O(n)}
Runtime-bound of t₃₁: X₃+1 {O(n)}
Results in: 32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21 {O(n^2)}

32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₄₁ 32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21 {O(n^2)}

relevant size-bounds w.r.t. t₃₁:
X₂: X₇ {O(n)}
Runtime-bound of t₃₁: X₃+1 {O(n)}
Results in: 32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21 {O(n^2)}

32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21 {O(n^2)}

knowledge_propagation leads to new time bound 32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21 {O(n^2)} for transition t₃₃: l3(X₀, X₁, X₂, X₃, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₆, X₇) :|: X₁ < 0 ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound 32⋅X₃⋅X₇+22⋅X₃+32⋅X₇+22 {O(n^2)} for transition t₃₄: l3(X₀, X₁, X₂, X₃, X₆, X₇) → l4(X₀, X₁, X₂, X₃, X₆, X₇) :|: 0 < X₁ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀

Analysing control-flow refined program

Cut unsatisfiable transition t₃₅: l3→l5

Cut unsatisfiable transition t₂₄₁: n_l3___1→l5

Cut unsatisfiable transition t₂₄₂: n_l3___4→l5

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

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 3+X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location n_l3___4

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 3+X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location n_l8___2

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l4___6

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 3+X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ for location n_l4___3

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l8___5

Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l7

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

Found invariant X₀ ≤ X₃ for location l1

Found invariant X₀ ≤ X₃ ∧ X₀ ≤ 0 for location l9

Found invariant 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 5 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 4 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 3+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l3___1

Found invariant X₇ ≤ X₂ ∧ X₂ ≤ X₇ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3

knowledge_propagation leads to new time bound X₃+1 {O(n)} for transition t₂₂₈: l3(X₀, X₁, X₂, X₃, X₆, X₇) → n_l4___6(X₀, X₁, X₂, X₃, X₆, X₇) :|: X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 0 < X₁ ∧ 0 < X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₆ ∧ X₀ ≤ X₃ ∧ X₇ ≤ X₂ ∧ X₂ ≤ X₇ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

MPRF for transition t₂₄₃: n_l4___3(X₀, X₁, X₂, X₃, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₆, X₇) :|: X₂ ≤ (X₁)²+(X₆)⁵ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 3+X₁ ≤ X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 3+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ 1+X₀+X₁ ≤ 0 ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

l2 [X₀+1 ]
l3 [X₀+1 ]
l1 [X₀+1 ]
n_l4___3 [X₀+1 ]
n_l4___6 [X₀+1 ]
l5 [X₀ ]
n_l8___2 [X₀+1 ]
n_l3___1 [X₀+1 ]
n_l8___5 [X₀+1 ]
n_l3___4 [X₀+1 ]

MPRF for transition t₂₄₄: n_l4___6(X₀, X₁, X₂, X₃, X₆, X₇) → l5(X₀, X₁, X₂, X₃, X₆, X₇) :|: X₂ ≤ (X₁)²+(X₆)⁵ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₁+X₆ ∧ 2 ≤ X₀+X₆ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₃ {O(n)}

MPRF:

l2 [X₀ ]
l3 [X₀ ]
l1 [X₀ ]
n_l4___3 [X₀ ]
n_l4___6 [X₀ ]
l5 [X₀-1 ]
n_l8___2 [X₀ ]
n_l3___1 [X₀ ]
n_l8___5 [X₀ ]
n_l3___4 [X₀ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:128⋅X₃⋅X₇+128⋅X₇+91⋅X₃+91 {O(n^2)}
t₂₈: 1 {O(1)}
t₂₉: X₃+1 {O(n)}
t₃₀: 1 {O(1)}
t₃₁: X₃+1 {O(n)}
t₃₂: X₃ {O(n)}
t₃₃: 32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21 {O(n^2)}
t₃₄: 32⋅X₃⋅X₇+22⋅X₃+32⋅X₇+22 {O(n^2)}
t₃₅: X₃ {O(n)}
t₃₆: 32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21 {O(n^2)}
t₃₇: X₃ {O(n)}
t₃₈: X₃ {O(n)}
t₃₉: 1 {O(1)}
t₄₀: 1 {O(1)}
t₄₁: 32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21 {O(n^2)}

Costbounds

Overall costbound: 128⋅X₃⋅X₇+128⋅X₇+91⋅X₃+91 {O(n^2)}
t₂₈: 1 {O(1)}
t₂₉: X₃+1 {O(n)}
t₃₀: 1 {O(1)}
t₃₁: X₃+1 {O(n)}
t₃₂: X₃ {O(n)}
t₃₃: 32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21 {O(n^2)}
t₃₄: 32⋅X₃⋅X₇+22⋅X₃+32⋅X₇+22 {O(n^2)}
t₃₅: X₃ {O(n)}
t₃₆: 32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21 {O(n^2)}
t₃₇: X₃ {O(n)}
t₃₈: X₃ {O(n)}
t₃₉: 1 {O(1)}
t₄₀: 1 {O(1)}
t₄₁: 32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21 {O(n^2)}

Sizebounds

t₂₈, X₀: X₀ {O(n)}
t₂₈, X₁: X₁ {O(n)}
t₂₈, X₂: X₂ {O(n)}
t₂₈, X₃: X₃ {O(n)}
t₂₈, X₆: X₆ {O(n)}
t₂₈, X₇: X₇ {O(n)}
t₂₉, X₀: X₃ {O(n)}
t₂₉, X₁: 2⋅2^(32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21)⋅X₃+X₁ {O(EXP)}
t₂₉, X₃: X₃ {O(n)}
t₂₉, X₆: X₆ {O(n)}
t₂₉, X₇: X₇ {O(n)}
t₃₀, X₀: 2⋅X₃ {O(n)}
t₃₀, X₁: 2⋅2^(32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21)⋅X₃+2⋅X₁ {O(EXP)}
t₃₀, X₃: 2⋅X₃ {O(n)}
t₃₀, X₆: 2⋅X₆ {O(n)}
t₃₀, X₇: 2⋅X₇ {O(n)}
t₃₁, X₀: X₃ {O(n)}
t₃₁, X₁: X₃ {O(n)}
t₃₁, X₂: X₇ {O(n)}
t₃₁, X₃: X₃ {O(n)}
t₃₁, X₆: X₆ {O(n)}
t₃₁, X₇: X₇ {O(n)}
t₃₂, X₀: X₃ {O(n)}
t₃₂, X₁: 2⋅2^(32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21)⋅X₃+X₁ {O(EXP)}
t₃₂, X₃: X₃ {O(n)}
t₃₂, X₆: X₆ {O(n)}
t₃₂, X₇: X₇ {O(n)}
t₃₃, X₀: X₃ {O(n)}
t₃₃, X₁: 2^(32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21)⋅X₃ {O(EXP)}
t₃₃, X₃: X₃ {O(n)}
t₃₃, X₆: X₆ {O(n)}
t₃₃, X₇: X₇ {O(n)}
t₃₄, X₀: X₃ {O(n)}
t₃₄, X₁: 2^(32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21)⋅X₃ {O(EXP)}
t₃₄, X₃: X₃ {O(n)}
t₃₄, X₆: X₆ {O(n)}
t₃₄, X₇: X₇ {O(n)}
t₃₅, X₀: X₃ {O(n)}
t₃₅, X₁: 0 {O(1)}
t₃₅, X₃: X₃ {O(n)}
t₃₅, X₆: X₆ {O(n)}
t₃₅, X₇: X₇ {O(n)}
t₃₆, X₀: X₃ {O(n)}
t₃₆, X₁: 2^(32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21)⋅X₃ {O(EXP)}
t₃₆, X₃: X₃ {O(n)}
t₃₆, X₆: X₆ {O(n)}
t₃₆, X₇: X₇ {O(n)}
t₃₇, X₀: X₃ {O(n)}
t₃₇, X₁: 2⋅2^(32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21)⋅X₃ {O(EXP)}
t₃₇, X₃: X₃ {O(n)}
t₃₇, X₆: X₆ {O(n)}
t₃₇, X₇: X₇ {O(n)}
t₃₈, X₀: X₃ {O(n)}
t₃₈, X₁: 2⋅2^(32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21)⋅X₃+X₁ {O(EXP)}
t₃₈, X₃: X₃ {O(n)}
t₃₈, X₆: X₆ {O(n)}
t₃₈, X₇: X₇ {O(n)}
t₃₉, X₀: X₃ {O(n)}
t₃₉, X₁: X₁ {O(n)}
t₃₉, X₂: X₂ {O(n)}
t₃₉, X₃: X₃ {O(n)}
t₃₉, X₆: X₆ {O(n)}
t₃₉, X₇: X₇ {O(n)}
t₄₀, X₀: 2⋅X₃ {O(n)}
t₄₀, X₁: 2⋅2^(32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21)⋅X₃+2⋅X₁ {O(EXP)}
t₄₀, X₃: 2⋅X₃ {O(n)}
t₄₀, X₆: 2⋅X₆ {O(n)}
t₄₀, X₇: 2⋅X₇ {O(n)}
t₄₁, X₀: X₃ {O(n)}
t₄₁, X₁: 2^(32⋅X₃⋅X₇+21⋅X₃+32⋅X₇+21)⋅X₃ {O(EXP)}
t₄₁, X₃: X₃ {O(n)}
t₄₁, X₆: X₆ {O(n)}
t₄₁, X₇: X₇ {O(n)}