Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₁
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₁ < X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁+1, X₂, X₃, X₄) :|: X₁ < X₀ ∧ X₁ < X₀
t₆: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁+1, X₂, X₃, X₄) :|: X₁ < X₀ ∧ X₀ ≤ X₁
t₇: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁ ∧ X₁ < X₀
t₈: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₁
t₉: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
Preprocessing
Cut unsatisfiable transition t₆: l3→l1
Cut unsatisfiable transition t₇: l3→l1
Eliminate variables {X₂} that do not contribute to the problem
Found invariant X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ for location l1
Found invariant X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₂₃: l0(X₀, X₁, X₃, X₄) → l2(X₀, X₁, X₃, X₄)
t₂₄: l1(X₀, X₁, X₃, X₄) → l3(X₀, X₁, X₃, X₄) :|: X₀ < X₁ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀
t₂₅: l1(X₀, X₁, X₃, X₄) → l3(X₀, X₁, X₃, X₄) :|: X₁ < X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀
t₂₆: l1(X₀, X₁, X₃, X₄) → l4(X₀, X₁, X₃, X₄) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀
t₂₇: l2(X₀, X₁, X₃, X₄) → l1(X₃, X₄, X₃, X₄)
t₂₈: l3(X₀, X₁, X₃, X₄) → l1(X₀, X₁+1, X₃, X₄) :|: X₁ < X₀ ∧ X₁ < X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀
t₂₉: l3(X₀, X₁, X₃, X₄) → l1(X₀+1, X₁, X₃, X₄) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀
t₃₀: l4(X₀, X₁, X₃, X₄) → l5(X₀, X₁, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
MPRF for transition t₂₄: l1(X₀, X₁, X₃, X₄) → l3(X₀, X₁, X₃, X₄) :|: X₀ < X₁ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀ of depth 1:
new bound:
X₃+X₄ {O(n)}
MPRF:
l3 [X₁-X₀-1 ]
l1 [X₁-X₀ ]
MPRF for transition t₂₉: l3(X₀, X₁, X₃, X₄) → l1(X₀+1, X₁, X₃, X₄) :|: X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀ of depth 1:
new bound:
X₃+X₄+1 {O(n)}
MPRF:
l3 [X₁+1-X₀ ]
l1 [X₁+1-X₀ ]
Found invariant 1 ≤ 0 for location l5
Found invariant 1 ≤ 0 for location l1
Found invariant 1 ≤ 0 for location l4
Found invariant 1 ≤ 0 for location l3
Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location l1
Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4
Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location l3
MPRF for transition t₂₅: l1(X₀, X₁, X₃, X₄) → l3(X₀, X₁, X₃, X₄) :|: X₁ < X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀ of depth 1:
new bound:
2⋅X₃⋅X₃+2⋅X₄⋅X₄+4⋅X₃⋅X₄+6⋅X₃+6⋅X₄+5 {O(n^2)}
MPRF:
l3 [X₀+1-X₁ ]
l1 [X₀+2-X₁ ]
MPRF for transition t₂₈: l3(X₀, X₁, X₃, X₄) → l1(X₀, X₁+1, X₃, X₄) :|: X₁ < X₀ ∧ X₁ < X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀ of depth 1:
new bound:
2⋅X₃⋅X₃+2⋅X₄⋅X₄+4⋅X₃⋅X₄+5⋅X₃+5⋅X₄+3 {O(n^2)}
MPRF:
l3 [X₀+1-X₁ ]
l1 [X₀+1-X₁ ]
Analysing control-flow refined program
Cut unsatisfiable transition t₉₉: n_l1___3→n_l3___2
Cut unsatisfiable transition t₁₀₀: n_l1___6→n_l3___4
Cut unreachable locations [n_l3___2; n_l3___4] from the program graph
Found invariant X₄ ≤ X₁ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₁ for location n_l1___6
Found invariant X₄ ≤ X₁ ∧ 2+X₃ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ for location n_l3___5
Found invariant 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ for location n_l1___3
Found invariant X₄ ≤ X₁ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁ for location n_l3___8
Found invariant X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l5
Found invariant X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ for location l1
Found invariant X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l4
Found invariant 2+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ 2+X₄ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l3___1
Found invariant 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ for location n_l3___7
MPRF for transition t₉₈: n_l1___3(X₀, X₁, X₃, X₄) → n_l3___1(X₀, X₁, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₁ < X₀ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀ of depth 1:
new bound:
X₃+X₄+2 {O(n)}
MPRF:
n_l3___1 [X₀-X₁ ]
n_l1___3 [X₀+1-X₁ ]
MPRF for transition t₁₀₄: n_l3___1(X₀, X₁, X₃, X₄) → n_l1___3(X₀, X₁+1, X₃, X₄) :|: X₁ < X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₁ < X₀ ∧ X₄ ≤ X₁ ∧ 2+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ 2+X₄ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀ of depth 1:
new bound:
X₃+X₄+1 {O(n)}
MPRF:
n_l3___1 [X₃-X₁ ]
n_l1___3 [X₃-X₁ ]
MPRF for transition t₁₀₁: n_l1___6(X₀, X₁, X₃, X₄) → n_l3___5(X₀, X₁, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₀ < X₁ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:
new bound:
X₃+X₄+2 {O(n)}
MPRF:
n_l3___5 [X₄-X₀ ]
n_l1___6 [X₁+1-X₀ ]
MPRF for transition t₁₀₇: n_l3___5(X₀, X₁, X₃, X₄) → n_l1___6(X₀+1, X₁, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₀ < X₁ ∧ 1+X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ of depth 1:
new bound:
X₃+X₄+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⋅X₃+4⋅X₄+7 {O(n)}
cfr-program:
Start: l0
Program_Vars: X₀, X₁, X₃, X₄
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:
t₂₃: l0(X₀, X₁, X₃, X₄) → l2(X₀, X₁, X₃, X₄)
t₂₆: l1(X₀, X₁, X₃, X₄) → l4(X₀, X₁, X₃, X₄) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁₀₂: l1(X₀, X₁, X₃, X₄) → n_l3___7(X₀, X₁, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₁ < X₀ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₁₀₃: l1(X₀, X₁, X₃, X₄) → n_l3___8(X₀, X₁, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₀ < X₁ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₂₇: l2(X₀, X₁, X₃, X₄) → l1(X₃, X₄, X₃, X₄)
t₃₀: l4(X₀, X₁, X₃, X₄) → l5(X₀, X₁, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₁₂₀: n_l1___3(X₀, X₁, X₃, X₄) → l4(X₀, X₁, X₃, X₄) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀
t₉₈: n_l1___3(X₀, X₁, X₃, X₄) → n_l3___1(X₀, X₁, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₁ < X₀ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ X₁ ≤ X₀
t₁₂₁: n_l1___6(X₀, X₁, X₃, X₄) → l4(X₀, X₁, X₃, X₄) :|: X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₁
t₁₀₁: n_l1___6(X₀, X₁, X₃, X₄) → n_l3___5(X₀, X₁, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ 1+X₁ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₀ < X₁ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ X₁
t₁₀₄: n_l3___1(X₀, X₁, X₃, X₄) → n_l1___3(X₀, X₁+1, X₃, X₄) :|: X₁ < X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₁ < X₀ ∧ X₄ ≤ X₁ ∧ 2+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₁ ∧ 2+X₄ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀
t₁₀₇: n_l3___5(X₀, X₁, X₃, X₄) → n_l1___6(X₀+1, X₁, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₀ < X₁ ∧ 1+X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 2+X₃ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁
t₁₀₈: n_l3___7(X₀, X₁, X₃, X₄) → n_l1___3(X₀, X₁+1, X₃, X₄) :|: X₁ < X₀ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₁ < X₀ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₀ ≤ X₃ ∧ 1+X₁ ≤ X₀
t₁₀₉: n_l3___8(X₀, X₁, X₃, X₄) → n_l1___6(X₀+1, X₁, X₃, X₄) :|: X₀ < X₄ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₄ ∧ X₁ ≤ X₄ ∧ 1+X₀ ≤ X₄ ∧ 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1+X₀ ≤ X₁
All Bounds
Timebounds
Overall timebound:4⋅X₃+4⋅X₄+17 {O(n)}
t₂₃: 1 {O(1)}
t₂₆: 1 {O(1)}
t₁₀₂: 1 {O(1)}
t₁₀₃: 1 {O(1)}
t₂₇: 1 {O(1)}
t₃₀: 1 {O(1)}
t₉₈: X₃+X₄+2 {O(n)}
t₁₂₀: 1 {O(1)}
t₁₀₁: X₃+X₄+2 {O(n)}
t₁₂₁: 1 {O(1)}
t₁₀₄: X₃+X₄+1 {O(n)}
t₁₀₇: X₃+X₄+2 {O(n)}
t₁₀₈: 1 {O(1)}
t₁₀₉: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₃+4⋅X₄+17 {O(n)}
t₂₃: 1 {O(1)}
t₂₆: 1 {O(1)}
t₁₀₂: 1 {O(1)}
t₁₀₃: 1 {O(1)}
t₂₇: 1 {O(1)}
t₃₀: 1 {O(1)}
t₉₈: X₃+X₄+2 {O(n)}
t₁₂₀: 1 {O(1)}
t₁₀₁: X₃+X₄+2 {O(n)}
t₁₂₁: 1 {O(1)}
t₁₀₄: X₃+X₄+1 {O(n)}
t₁₀₇: X₃+X₄+2 {O(n)}
t₁₀₈: 1 {O(1)}
t₁₀₉: 1 {O(1)}
Sizebounds
t₂₃, X₀: X₀ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₃, X₃: X₃ {O(n)}
t₂₃, X₄: X₄ {O(n)}
t₂₆, X₀: X₃ {O(n)}
t₂₆, X₁: X₄ {O(n)}
t₂₆, X₃: X₃ {O(n)}
t₂₆, X₄: X₄ {O(n)}
t₁₀₂, X₀: X₃ {O(n)}
t₁₀₂, X₁: X₄ {O(n)}
t₁₀₂, X₃: X₃ {O(n)}
t₁₀₂, X₄: X₄ {O(n)}
t₁₀₃, X₀: X₃ {O(n)}
t₁₀₃, X₁: X₄ {O(n)}
t₁₀₃, X₃: X₃ {O(n)}
t₁₀₃, X₄: X₄ {O(n)}
t₂₇, X₀: X₃ {O(n)}
t₂₇, X₁: X₄ {O(n)}
t₂₇, X₃: X₃ {O(n)}
t₂₇, X₄: X₄ {O(n)}
t₃₀, X₀: 6⋅X₃+X₄+4 {O(n)}
t₃₀, X₁: 6⋅X₄+X₃+3 {O(n)}
t₃₀, X₃: 5⋅X₃ {O(n)}
t₃₀, X₄: 5⋅X₄ {O(n)}
t₉₈, X₀: X₃ {O(n)}
t₉₈, X₁: 2⋅X₄+X₃+2 {O(n)}
t₉₈, X₃: X₃ {O(n)}
t₉₈, X₄: X₄ {O(n)}
t₁₂₀, X₀: 2⋅X₃ {O(n)}
t₁₂₀, X₁: 3⋅X₄+X₃+3 {O(n)}
t₁₂₀, X₃: 2⋅X₃ {O(n)}
t₁₂₀, X₄: 2⋅X₄ {O(n)}
t₁₀₁, X₀: 2⋅X₃+X₄+3 {O(n)}
t₁₀₁, X₁: X₄ {O(n)}
t₁₀₁, X₃: X₃ {O(n)}
t₁₀₁, X₄: X₄ {O(n)}
t₁₂₁, X₀: 3⋅X₃+X₄+4 {O(n)}
t₁₂₁, X₁: 2⋅X₄ {O(n)}
t₁₂₁, X₃: 2⋅X₃ {O(n)}
t₁₂₁, X₄: 2⋅X₄ {O(n)}
t₁₀₄, X₀: X₃ {O(n)}
t₁₀₄, X₁: 2⋅X₄+X₃+2 {O(n)}
t₁₀₄, X₃: X₃ {O(n)}
t₁₀₄, X₄: X₄ {O(n)}
t₁₀₇, X₀: 2⋅X₃+X₄+3 {O(n)}
t₁₀₇, X₁: X₄ {O(n)}
t₁₀₇, X₃: X₃ {O(n)}
t₁₀₇, X₄: X₄ {O(n)}
t₁₀₈, X₀: X₃ {O(n)}
t₁₀₈, X₁: X₄+1 {O(n)}
t₁₀₈, X₃: X₃ {O(n)}
t₁₀₈, X₄: X₄ {O(n)}
t₁₀₉, X₀: X₃+1 {O(n)}
t₁₀₉, X₁: X₄ {O(n)}
t₁₀₉, X₃: X₃ {O(n)}
t₁₀₉, X₄: X₄ {O(n)}