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) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, 0, X₂, X₃) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₁, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁
t₄: l3(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₈: l4(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₇: l5(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l3(X₀, X₁+1, X₂, X₃)

Preprocessing

Eliminate variables {X₃} that do not contribute to the problem

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l7

Found invariant 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 l5

Found invariant X₀ ≤ X₂ for location l1

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l4

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₇: l0(X₀, X₁, X₂) → l2(X₀, X₁, X₂)
t₁₈: l1(X₀, X₁, X₂) → l3(X₀, 0, X₂) :|: 0 < X₀ ∧ X₀ ≤ X₂
t₁₉: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ X₀ ≤ X₂
t₂₀: l2(X₀, X₁, X₂) → l1(X₂, X₁, X₂)
t₂₁: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₂: l3(X₀, X₁, X₂) → l6(X₀, X₁, X₂) :|: X₁ < X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₃: l4(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₀ ≤ X₂ ∧ X₀ ≤ 0
t₂₄: l5(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₂₅: l6(X₀, X₁, X₂) → l3(X₀, X₁+1, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₁₈: l1(X₀, X₁, X₂) → l3(X₀, 0, X₂) :|: 0 < X₀ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₂₁: l3(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₂₄: l5(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: 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:

X₂+1 {O(n)}

TWN: t₂₂: l3→l6

cycle: [t₂₂: l3→l6; t₂₅: l6→l3]
loop: (X₁ < X₀,(X₀,X₁) -> (X₀,X₁+1)
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1

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

TWN - Lifting for t₂₂: l3→l6 of 2⋅X₀+2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₁₈:
X₀: X₂ {O(n)}
X₁: 0 {O(1)}
Runtime-bound of t₁₈: X₂ {O(n)}
Results in: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}

TWN: t₂₅: l6→l3

TWN - Lifting for t₂₅: l6→l3 of 2⋅X₀+2⋅X₁+4 {O(n)}

relevant size-bounds w.r.t. t₁₈:
X₀: X₂ {O(n)}
X₁: 0 {O(1)}
Runtime-bound of t₁₈: X₂ {O(n)}
Results in: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}

Chain transitions t₂₄: l5→l1 and t₁₉: l1→l4 to t₅₃: l5→l4

Chain transitions t₂₀: l2→l1 and t₁₉: l1→l4 to t₅₄: l2→l4

Chain transitions t₂₀: l2→l1 and t₁₈: l1→l3 to t₅₅: l2→l3

Chain transitions t₂₄: l5→l1 and t₁₈: l1→l3 to t₅₆: l5→l3

Chain transitions t₂₅: l6→l3 and t₂₂: l3→l6 to t₅₇: l6→l6

Chain transitions t₅₆: l5→l3 and t₂₂: l3→l6 to t₅₈: l5→l6

Chain transitions t₅₆: l5→l3 and t₂₁: l3→l5 to t₅₉: l5→l5

Chain transitions t₂₅: l6→l3 and t₂₁: l3→l5 to t₆₀: l6→l5

Chain transitions t₅₅: l2→l3 and t₂₁: l3→l5 to t₆₁: l2→l5

Chain transitions t₅₅: l2→l3 and t₂₂: l3→l6 to t₆₂: l2→l6

Analysing control-flow refined program

Cut unsatisfiable transition t₅₉: l5→l5

Cut unsatisfiable transition t₆₁: l2→l5

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l6

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l7

Found invariant 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 l5

Found invariant X₀ ≤ X₂ for location l1

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l4

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

MPRF for transition t₅₈: l5(X₀, X₁, X₂) -{3}> l6(X₀-1, 0, X₂) :|: 1 < X₀ ∧ 1 < X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂ ∧ 0 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 0 ≤ 0 ∧ 2 ≤ X₀ ∧ 2 ≤ 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:

X₂+1 {O(n)}

MPRF for transition t₆₀: l6(X₀, X₁, X₂) -{2}> l5(X₀, 1+X₁, X₂) :|: X₀ ≤ X₁+1 ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁+1 ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

TWN: t₅₇: l6→l6

cycle: [t₅₇: l6→l6]
loop: (1+X₁ < X₀,(X₀,X₁) -> (X₀,1+X₁)
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: 1+X₁ < X₀
alphas_abs: 1+X₁+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+4 {O(n)}
loop: (1+X₁ < X₀,(X₀,X₁) -> (X₀,1+X₁)
order: [X₀; X₁]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * n^1

Termination: true
Formula:

1 < 0
∨ 1+X₁ < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1

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

TWN - Lifting for t₅₇: l6→l6 of 2⋅X₀+2⋅X₁+6 {O(n)}

relevant size-bounds w.r.t. t₅₈:
X₀: X₂ {O(n)}
X₁: 0 {O(1)}
Runtime-bound of t₅₈: X₂+1 {O(n)}
Results in: 2⋅X₂⋅X₂+8⋅X₂+6 {O(n^2)}

TWN - Lifting for t₅₇: l6→l6 of 2⋅X₀+2⋅X₁+6 {O(n)}

relevant size-bounds w.r.t. t₆₂:
X₀: X₂ {O(n)}
X₁: 0 {O(1)}
Runtime-bound of t₆₂: 1 {O(1)}
Results in: 2⋅X₂+6 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Cut unsatisfiable transition t₂₁: l3→l5

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l6___3

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l6___1

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l7

Found invariant 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 l5

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

Found invariant X₀ ≤ X₂ for location l1

Found invariant X₀ ≤ X₂ ∧ X₀ ≤ 0 for location l4

Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₁₃₃: l3(X₀, X₁, X₂) → n_l6___3(X₀, X₁, X₂) :|: X₁ < X₀ ∧ X₁ < X₀ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₁₃₅: n_l6___3(X₀, X₁, X₂) → n_l3___2(X₀, X₁+1, X₂) :|: X₁ < X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₁₃₂: n_l3___2(X₀, X₁, X₂) → n_l6___1(X₀, X₁, X₂) :|: 1 ≤ X₁ ∧ X₁ < X₀ ∧ 1 ≤ X₀ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+4⋅X₂ {O(n^2)}

MPRF for transition t₁₃₄: n_l6___1(X₀, X₁, X₂) → n_l3___2(X₀, X₁+1, X₂) :|: X₁ < X₀ ∧ 1 ≤ X₁ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₁ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₂⋅X₂+X₂ {O(n^2)}

MPRF for transition t₁₃₉: n_l3___2(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+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⋅X₂⋅X₂+11⋅X₂+5 {O(n^2)}
t₁₇: 1 {O(1)}
t₁₈: X₂ {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₂ {O(n)}
t₂₂: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₂₃: 1 {O(1)}
t₂₄: X₂+1 {O(n)}
t₂₅: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}

Costbounds

Overall costbound: 4⋅X₂⋅X₂+11⋅X₂+5 {O(n^2)}
t₁₇: 1 {O(1)}
t₁₈: X₂ {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₂ {O(n)}
t₂₂: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₂₃: 1 {O(1)}
t₂₄: X₂+1 {O(n)}
t₂₅: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}

Sizebounds

t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₈, X₀: X₂ {O(n)}
t₁₈, X₁: 0 {O(1)}
t₁₈, X₂: X₂ {O(n)}
t₁₉, X₀: 2⋅X₂ {O(n)}
t₁₉, X₁: 2⋅X₂⋅X₂+4⋅X₂+X₁ {O(n^2)}
t₁₉, X₂: 2⋅X₂ {O(n)}
t₂₀, X₀: X₂ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₁, X₀: X₂ {O(n)}
t₂₁, X₁: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₂₁, X₂: X₂ {O(n)}
t₂₂, X₀: X₂ {O(n)}
t₂₂, X₁: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₂₂, X₂: X₂ {O(n)}
t₂₃, X₀: 2⋅X₂ {O(n)}
t₂₃, X₁: 2⋅X₂⋅X₂+4⋅X₂+X₁ {O(n^2)}
t₂₃, X₂: 2⋅X₂ {O(n)}
t₂₄, X₀: X₂ {O(n)}
t₂₄, X₁: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₂₄, X₂: X₂ {O(n)}
t₂₅, X₀: X₂ {O(n)}
t₂₅, X₁: 2⋅X₂⋅X₂+4⋅X₂ {O(n^2)}
t₂₅, X₂: X₂ {O(n)}