Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < X₁
t₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₁ < X₀ ∧ X₁ < X₀
t₆: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+1, X₂, X₃) :|: X₁ < X₀ ∧ X₀ ≤ X₁
t₇: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ < X₀
t₈: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₁
t₉: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)

Preprocessing

Cut unsatisfiable transition t₆: l3→l1

Cut unsatisfiable transition t₇: l3→l1

Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l1

Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4

Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ < X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₁ < X₀ ∧ X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀
t₈: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀
t₉: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁

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

new bound:

X₂+X₃ {O(n)}

MPRF:

l3 [X₁-X₀-1 ]
l1 [X₁-X₀ ]

MPRF for transition t₈: l3(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ of depth 1:

new bound:

X₂+X₃+1 {O(n)}

MPRF:

l3 [X₁+1-X₀ ]
l1 [X₁+1-X₀ ]

MPRF for transition t₃: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ of depth 1:

new bound:

2⋅X₂⋅X₂+2⋅X₃⋅X₃+4⋅X₂⋅X₃+6⋅X₂+6⋅X₃+5 {O(n^2)}

MPRF:

l3 [X₀+1-X₁ ]
l1 [X₀+2-X₁ ]

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₁ < X₀ ∧ X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ of depth 1:

new bound:

2⋅X₂⋅X₂+2⋅X₃⋅X₃+4⋅X₂⋅X₃+5⋅X₂+5⋅X₃+3 {O(n^2)}

MPRF:

l3 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]

Analysing control-flow refined program

Cut unsatisfiable transition t₈₁: n_l1___3→n_l3___2

Cut unsatisfiable transition t₈₂: n_l1___6→n_l3___4

Cut unreachable locations [n_l3___2; n_l3___4] from the program graph

Found invariant X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___6

Found invariant X₃ ≤ X₁ ∧ 2+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location n_l3___5

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ for location n_l1___3

Found invariant X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁ for location n_l3___8

Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5

Found invariant X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ for location l1

Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4

Found invariant 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___1

Found invariant 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ for location n_l3___7

MPRF for transition t₈₀: n_l1___3(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ < X₀ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀ of depth 1:

new bound:

X₂+X₃+2 {O(n)}

MPRF:

n_l3___1 [X₀-X₁ ]
n_l1___3 [X₀+1-X₁ ]

MPRF for transition t₈₆: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___3(X₀, X₁+1, X₂, X₃) :|: X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ < X₀ ∧ X₃ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₂+X₃+1 {O(n)}

MPRF:

n_l3___1 [X₂-X₁ ]
n_l1___3 [X₂-X₁ ]

MPRF for transition t₈₃: n_l1___6(X₀, X₁, X₂, X₃) → n_l3___5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ < X₁ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₂+X₃+2 {O(n)}

MPRF:

n_l3___5 [X₃-X₀ ]
n_l1___6 [X₁+1-X₀ ]

MPRF for transition t₈₉: n_l3___5(X₀, X₁, X₂, X₃) → n_l1___6(X₀+1, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₀ < X₁ ∧ 1+X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁ of depth 1:

new bound:

X₂+X₃+2 {O(n)}

MPRF:

n_l3___5 [X₁+1-X₀ ]
n_l1___6 [X₁+1-X₀ ]

CFR: Improvement to new bound with the following program:

new bound:

4⋅X₂+4⋅X₃+7 {O(n)}

cfr-program:

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l4, l5, n_l1___3, n_l1___6, n_l3___1, n_l3___5, n_l3___7, n_l3___8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₈₄: l1(X₀, X₁, X₂, X₃) → n_l3___7(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₈₅: l1(X₀, X₁, X₂, X₃) → n_l3___8(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ < X₁ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₉: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₁₀₂: n_l1___3(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀
t₈₀: n_l1___3(X₀, X₁, X₂, X₃) → n_l3___1(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ < X₀ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₀
t₁₀₃: n_l1___6(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁
t₈₃: n_l1___6(X₀, X₁, X₂, X₃) → n_l3___5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ < X₁ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ X₀ ≤ X₁
t₈₆: n_l3___1(X₀, X₁, X₂, X₃) → n_l1___3(X₀, X₁+1, X₂, X₃) :|: X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ < X₀ ∧ X₃ ≤ X₁ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₈₉: n_l3___5(X₀, X₁, X₂, X₃) → n_l1___6(X₀+1, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₀ < X₁ ∧ 1+X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 2+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1+X₀ ≤ X₁
t₉₀: n_l3___7(X₀, X₁, X₂, X₃) → n_l1___3(X₀, X₁+1, X₂, X₃) :|: X₁ < X₀ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ < X₀ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀
t₉₁: n_l3___8(X₀, X₁, X₂, X₃) → n_l1___6(X₀+1, X₁, X₂, X₃) :|: X₀ < X₃ ∧ X₁ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 1+X₀ ≤ X₁

All Bounds

Timebounds

Overall timebound:4⋅X₂+4⋅X₃+17 {O(n)}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₈₄: 1 {O(1)}
t₈₅: 1 {O(1)}
t₁: 1 {O(1)}
t₉: 1 {O(1)}
t₈₀: X₂+X₃+2 {O(n)}
t₁₀₂: 1 {O(1)}
t₈₃: X₂+X₃+2 {O(n)}
t₁₀₃: 1 {O(1)}
t₈₆: X₂+X₃+1 {O(n)}
t₈₉: X₂+X₃+2 {O(n)}
t₉₀: 1 {O(1)}
t₉₁: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₂+4⋅X₃+17 {O(n)}
t₀: 1 {O(1)}
t₄: 1 {O(1)}
t₈₄: 1 {O(1)}
t₈₅: 1 {O(1)}
t₁: 1 {O(1)}
t₉: 1 {O(1)}
t₈₀: X₂+X₃+2 {O(n)}
t₁₀₂: 1 {O(1)}
t₈₃: X₂+X₃+2 {O(n)}
t₁₀₃: 1 {O(1)}
t₈₆: X₂+X₃+1 {O(n)}
t₈₉: X₂+X₃+2 {O(n)}
t₉₀: 1 {O(1)}
t₉₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: X₃ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₈₄, X₀: X₂ {O(n)}
t₈₄, X₁: X₃ {O(n)}
t₈₄, X₂: X₂ {O(n)}
t₈₄, X₃: X₃ {O(n)}
t₈₅, X₀: X₂ {O(n)}
t₈₅, X₁: X₃ {O(n)}
t₈₅, X₂: X₂ {O(n)}
t₈₅, X₃: X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₉, X₀: 6⋅X₂+X₃+4 {O(n)}
t₉, X₁: 6⋅X₃+X₂+3 {O(n)}
t₉, X₂: 5⋅X₂ {O(n)}
t₉, X₃: 5⋅X₃ {O(n)}
t₈₀, X₀: X₂ {O(n)}
t₈₀, X₁: 2⋅X₃+X₂+2 {O(n)}
t₈₀, X₂: X₂ {O(n)}
t₈₀, X₃: X₃ {O(n)}
t₁₀₂, X₀: 2⋅X₂ {O(n)}
t₁₀₂, X₁: 3⋅X₃+X₂+3 {O(n)}
t₁₀₂, X₂: 2⋅X₂ {O(n)}
t₁₀₂, X₃: 2⋅X₃ {O(n)}
t₈₃, X₀: 2⋅X₂+X₃+3 {O(n)}
t₈₃, X₁: X₃ {O(n)}
t₈₃, X₂: X₂ {O(n)}
t₈₃, X₃: X₃ {O(n)}
t₁₀₃, X₀: 3⋅X₂+X₃+4 {O(n)}
t₁₀₃, X₁: 2⋅X₃ {O(n)}
t₁₀₃, X₂: 2⋅X₂ {O(n)}
t₁₀₃, X₃: 2⋅X₃ {O(n)}
t₈₆, X₀: X₂ {O(n)}
t₈₆, X₁: 2⋅X₃+X₂+2 {O(n)}
t₈₆, X₂: X₂ {O(n)}
t₈₆, X₃: X₃ {O(n)}
t₈₉, X₀: 2⋅X₂+X₃+3 {O(n)}
t₈₉, X₁: X₃ {O(n)}
t₈₉, X₂: X₂ {O(n)}
t₈₉, X₃: X₃ {O(n)}
t₉₀, X₀: X₂ {O(n)}
t₉₀, X₁: X₃+1 {O(n)}
t₉₀, X₂: X₂ {O(n)}
t₉₀, X₃: X₃ {O(n)}
t₉₁, X₀: X₂+1 {O(n)}
t₉₁, X₁: X₃ {O(n)}
t₉₁, X₂: X₂ {O(n)}
t₉₁, X₃: X₃ {O(n)}