Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₄, X₅, X₆, X₃, X₄, X₅, X₆)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀+X₁, X₁+X₂, X₂-1, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆) :|: X₀ ≤ 0
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₄, X₅, X₆, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0

Preprocessing

Found invariant X₂ ≤ X₆ ∧ X₀ ≤ 0 for location l2

Found invariant X₂ ≤ X₆ for location l1

Found invariant X₂ ≤ X₆ ∧ X₃ ≤ 0 ∧ X₀+X₃ ≤ 0 ∧ X₀ ≤ 0 for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₄, X₅, X₆, X₃, X₄, X₅, X₆)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀+X₁, X₁+X₂, X₂-1, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ X₂ ≤ X₆
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆) :|: X₀ ≤ 0 ∧ X₂ ≤ X₆
t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₄, X₅, X₆, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₀ ≤ 0
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0 ∧ X₂ ≤ X₆ ∧ X₀ ≤ 0

MPRF for transition t₃: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₄, X₅, X₆, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ X₂ ≤ X₆ ∧ X₀ ≤ 0 of depth 1:

new bound:

X₃+1 {O(n)}

MPRF:

l2 [X₃ ]
l1 [X₃-1 ]

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆) :|: X₀ ≤ 0 ∧ X₂ ≤ X₆ of depth 1:

new bound:

X₃+2 {O(n)}

MPRF:

l1 [1 ]
l2 [0 ]

MPRF for transition t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀+X₁, X₁+X₂, X₂-1, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ X₂ ≤ X₆ of depth 3:

new bound:

54⋅X₃⋅X₄+54⋅X₃⋅X₅+54⋅X₃⋅X₆+55⋅X₃+81⋅X₄+81⋅X₅+81⋅X₆+110 {O(n^2)}

MPRF:

l1 [X₂+1 ; X₁+1 ; X₀ ]
l2 [X₂ ; X₁ ; X₀ ]

Analysing control-flow refined program

Found invariant X₂ ≤ X₆ ∧ X₀ ≤ X₄ ∧ X₀ ≤ 0 for location l2

Found invariant X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₄ for location l1

Found invariant X₂ ≤ X₆ ∧ X₀ ≤ X₄ ∧ X₃ ≤ 0 ∧ X₀+X₃ ≤ 0 ∧ X₀ ≤ 0 for location l3

Found invariant 1+X₂ ≤ X₆ ∧ 1 ≤ X₄ for location n_l1___1

knowledge_propagation leads to new time bound X₃+2 {O(n)} for transition t₄₀: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l1___1(X₀+X₁, X₁+X₂, X₂-1, X₃, X₄, X₅, X₆) :|: X₂ ≤ X₆ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₂ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₀ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₂ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₀ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₄

knowledge_propagation leads to new time bound X₃+2 {O(n)} for transition t₄₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l1___1(X₀+X₁, X₁+X₂, X₂-1, X₃, X₄, X₅, X₆) :|: X₂ ≤ X₆ ∧ X₁ ≤ X₅ ∧ X₅ ≤ X₁ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₂ ∧ X₀ ≤ X₄ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₆ ∧ X₆ ≤ X₂ ∧ X₂ ≤ X₆ ∧ X₅ ≤ X₁ ∧ X₁ ≤ X₅ ∧ X₄ ≤ X₀ ∧ X₀ ≤ X₄

MPRF for transition t₄₄: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆) :|: X₀ ≤ 0 ∧ X₂ ≤ X₆ ∧ 1+X₂ ≤ X₆ ∧ 1 ≤ X₄ of depth 1:

new bound:

9⋅X₃⋅X₄+11⋅X₄+X₃+2 {O(n^2)}

MPRF:

l1 [X₄+1-X₀ ]
n_l1___1 [1 ]
l2 [2⋅X₂+1-2⋅X₆ ]

MPRF for transition t₃₉: n_l1___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → n_l1___1(X₀+X₁, X₁+X₂, X₂-1, X₃, X₄, X₅, X₆) :|: X₂ ≤ X₆ ∧ X₁ ≤ X₀+X₂ ∧ 1+X₂ ≤ X₆ ∧ 1 ≤ X₀ ∧ X₂ ≤ X₆ ∧ 1+X₂ ≤ X₆ ∧ 1 ≤ X₄ of depth 3:

new bound:

1458⋅X₃⋅X₄⋅X₅+1458⋅X₃⋅X₄⋅X₆+729⋅X₃⋅X₄⋅X₄+162⋅X₃⋅X₅+162⋅X₃⋅X₆+1782⋅X₄⋅X₅+1782⋅X₄⋅X₆+333⋅X₃⋅X₄+891⋅X₄⋅X₄+28⋅X₃+378⋅X₅+378⋅X₆+497⋅X₄+84 {O(n^3)}

MPRF:

l2 [X₆ ; X₅+X₆+1 ; X₄+X₅ ]
l1 [X₆ ; X₂+X₅+1 ; X₀+X₁ ]
n_l1___1 [X₂+1 ; X₁+1 ; X₀ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:54⋅X₃⋅X₄+54⋅X₃⋅X₅+54⋅X₃⋅X₆+57⋅X₃+81⋅X₄+81⋅X₅+81⋅X₆+115 {O(n^2)}
t₀: 1 {O(1)}
t₁: 54⋅X₃⋅X₄+54⋅X₃⋅X₅+54⋅X₃⋅X₆+55⋅X₃+81⋅X₄+81⋅X₅+81⋅X₆+110 {O(n^2)}
t₂: X₃+2 {O(n)}
t₃: X₃+1 {O(n)}
t₄: 1 {O(1)}

Costbounds

Overall costbound: 54⋅X₃⋅X₄+54⋅X₃⋅X₅+54⋅X₃⋅X₆+57⋅X₃+81⋅X₄+81⋅X₅+81⋅X₆+115 {O(n^2)}
t₀: 1 {O(1)}
t₁: 54⋅X₃⋅X₄+54⋅X₃⋅X₅+54⋅X₃⋅X₆+55⋅X₃+81⋅X₄+81⋅X₅+81⋅X₆+110 {O(n^2)}
t₂: X₃+2 {O(n)}
t₃: X₃+1 {O(n)}
t₄: 1 {O(1)}

Sizebounds

t₀, X₀: X₄ {O(n)}
t₀, X₁: X₅ {O(n)}
t₀, X₂: X₆ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₆ {O(n)}
t₁, X₀: 157464⋅X₃⋅X₃⋅X₃⋅X₄⋅X₄⋅X₄+157464⋅X₃⋅X₃⋅X₃⋅X₅⋅X₅⋅X₅+157464⋅X₃⋅X₃⋅X₃⋅X₆⋅X₆⋅X₆+472392⋅X₃⋅X₃⋅X₃⋅X₄⋅X₄⋅X₅+472392⋅X₃⋅X₃⋅X₃⋅X₄⋅X₄⋅X₆+472392⋅X₃⋅X₃⋅X₃⋅X₄⋅X₅⋅X₅+472392⋅X₃⋅X₃⋅X₃⋅X₄⋅X₆⋅X₆+472392⋅X₃⋅X₃⋅X₃⋅X₅⋅X₅⋅X₆+472392⋅X₃⋅X₃⋅X₃⋅X₅⋅X₆⋅X₆+944784⋅X₃⋅X₃⋅X₃⋅X₄⋅X₅⋅X₆+2125764⋅X₃⋅X₃⋅X₄⋅X₄⋅X₅+2125764⋅X₃⋅X₃⋅X₄⋅X₅⋅X₅+2143260⋅X₃⋅X₃⋅X₄⋅X₄⋅X₆+2143260⋅X₃⋅X₃⋅X₅⋅X₅⋅X₆+2160756⋅X₃⋅X₃⋅X₄⋅X₆⋅X₆+2160756⋅X₃⋅X₃⋅X₅⋅X₆⋅X₆+4286520⋅X₃⋅X₃⋅X₄⋅X₅⋅X₆+481140⋅X₃⋅X₃⋅X₃⋅X₄⋅X₄+481140⋅X₃⋅X₃⋅X₃⋅X₅⋅X₅+481140⋅X₃⋅X₃⋅X₃⋅X₆⋅X₆+708588⋅X₃⋅X₃⋅X₄⋅X₄⋅X₄+708588⋅X₃⋅X₃⋅X₅⋅X₅⋅X₅+726084⋅X₃⋅X₃⋅X₆⋅X₆⋅X₆+962280⋅X₃⋅X₃⋅X₃⋅X₄⋅X₅+962280⋅X₃⋅X₃⋅X₃⋅X₄⋅X₆+962280⋅X₃⋅X₃⋅X₃⋅X₅⋅X₆+1062882⋅X₃⋅X₄⋅X₄⋅X₄+1062882⋅X₃⋅X₅⋅X₅⋅X₅+1115370⋅X₃⋅X₆⋅X₆⋅X₆+2411532⋅X₃⋅X₃⋅X₄⋅X₄+2411532⋅X₃⋅X₃⋅X₅⋅X₅+2447172⋅X₃⋅X₃⋅X₆⋅X₆+3188646⋅X₃⋅X₄⋅X₄⋅X₅+3188646⋅X₃⋅X₄⋅X₅⋅X₅+3241134⋅X₃⋅X₄⋅X₄⋅X₆+3241134⋅X₃⋅X₅⋅X₅⋅X₆+3293622⋅X₃⋅X₄⋅X₆⋅X₆+3293622⋅X₃⋅X₅⋅X₆⋅X₆+4823064⋅X₃⋅X₃⋅X₄⋅X₅+4858704⋅X₃⋅X₃⋅X₄⋅X₆+4858704⋅X₃⋅X₃⋅X₅⋅X₆+490050⋅X₃⋅X₃⋅X₃⋅X₄+490050⋅X₃⋅X₃⋅X₃⋅X₅+490050⋅X₃⋅X₃⋅X₃⋅X₆+6482268⋅X₃⋅X₄⋅X₅⋅X₆+1594323⋅X₄⋅X₄⋅X₅+1594323⋅X₄⋅X₅⋅X₅+1633689⋅X₄⋅X₄⋅X₆+1633689⋅X₅⋅X₅⋅X₆+166375⋅X₃⋅X₃⋅X₃+1673055⋅X₄⋅X₆⋅X₆+1673055⋅X₅⋅X₆⋅X₆+2707155⋅X₃⋅X₃⋅X₄+2707155⋅X₃⋅X₃⋅X₅+2725305⋅X₃⋅X₃⋅X₆+3267378⋅X₄⋅X₅⋅X₆+3986901⋅X₃⋅X₄⋅X₄+3987225⋅X₃⋅X₅⋅X₅+4112289⋅X₃⋅X₆⋅X₆+531441⋅X₄⋅X₄⋅X₄+531441⋅X₅⋅X₅⋅X₅+570807⋅X₆⋅X₆⋅X₆+7974126⋅X₃⋅X₄⋅X₅+8099190⋅X₃⋅X₄⋅X₆+8099514⋅X₃⋅X₅⋅X₆+1004300⋅X₃⋅X₃+2178252⋅X₄⋅X₄+2178738⋅X₅⋅X₅+2286144⋅X₆⋅X₆+4356990⋅X₄⋅X₅+4464396⋅X₄⋅X₆+4464882⋅X₅⋅X₆+4942134⋅X₃⋅X₄+4942464⋅X₃⋅X₅+5015394⋅X₃⋅X₆+2020755⋅X₃+2976024⋅X₄+2976687⋅X₅+3049947⋅X₆+1355310 {O(n^6)}
t₁, X₁: 2916⋅X₃⋅X₃⋅X₄⋅X₄+2916⋅X₃⋅X₃⋅X₅⋅X₅+2916⋅X₃⋅X₃⋅X₆⋅X₆+5832⋅X₃⋅X₃⋅X₄⋅X₅+5832⋅X₃⋅X₃⋅X₄⋅X₆+5832⋅X₃⋅X₃⋅X₅⋅X₆+17496⋅X₃⋅X₄⋅X₅+17820⋅X₃⋅X₄⋅X₆+17820⋅X₃⋅X₅⋅X₆+5940⋅X₃⋅X₃⋅X₄+5940⋅X₃⋅X₃⋅X₅+5940⋅X₃⋅X₃⋅X₆+8748⋅X₃⋅X₄⋅X₄+8748⋅X₃⋅X₅⋅X₅+9072⋅X₃⋅X₆⋅X₆+13122⋅X₄⋅X₅+13608⋅X₄⋅X₆+13608⋅X₅⋅X₆+20844⋅X₃⋅X₄+20844⋅X₃⋅X₅+21174⋅X₃⋅X₆+3025⋅X₃⋅X₃+6561⋅X₄⋅X₄+6561⋅X₅⋅X₅+7047⋅X₆⋅X₆+12155⋅X₃+17901⋅X₄+17904⋅X₅+18567⋅X₆+12210 {O(n^4)}
t₁, X₂: 54⋅X₃⋅X₄+54⋅X₃⋅X₅+54⋅X₃⋅X₆+55⋅X₃+81⋅X₄+81⋅X₅+84⋅X₆+110 {O(n^2)}
t₁, X₃: 3⋅X₃+2 {O(n)}
t₁, X₄: 2⋅X₄ {O(n)}
t₁, X₅: 2⋅X₅ {O(n)}
t₁, X₆: 2⋅X₆ {O(n)}
t₂, X₀: 157464⋅X₃⋅X₃⋅X₃⋅X₄⋅X₄⋅X₄+157464⋅X₃⋅X₃⋅X₃⋅X₅⋅X₅⋅X₅+157464⋅X₃⋅X₃⋅X₃⋅X₆⋅X₆⋅X₆+472392⋅X₃⋅X₃⋅X₃⋅X₄⋅X₄⋅X₅+472392⋅X₃⋅X₃⋅X₃⋅X₄⋅X₄⋅X₆+472392⋅X₃⋅X₃⋅X₃⋅X₄⋅X₅⋅X₅+472392⋅X₃⋅X₃⋅X₃⋅X₄⋅X₆⋅X₆+472392⋅X₃⋅X₃⋅X₃⋅X₅⋅X₅⋅X₆+472392⋅X₃⋅X₃⋅X₃⋅X₅⋅X₆⋅X₆+944784⋅X₃⋅X₃⋅X₃⋅X₄⋅X₅⋅X₆+2125764⋅X₃⋅X₃⋅X₄⋅X₄⋅X₅+2125764⋅X₃⋅X₃⋅X₄⋅X₅⋅X₅+2143260⋅X₃⋅X₃⋅X₄⋅X₄⋅X₆+2143260⋅X₃⋅X₃⋅X₅⋅X₅⋅X₆+2160756⋅X₃⋅X₃⋅X₄⋅X₆⋅X₆+2160756⋅X₃⋅X₃⋅X₅⋅X₆⋅X₆+4286520⋅X₃⋅X₃⋅X₄⋅X₅⋅X₆+481140⋅X₃⋅X₃⋅X₃⋅X₄⋅X₄+481140⋅X₃⋅X₃⋅X₃⋅X₅⋅X₅+481140⋅X₃⋅X₃⋅X₃⋅X₆⋅X₆+708588⋅X₃⋅X₃⋅X₄⋅X₄⋅X₄+708588⋅X₃⋅X₃⋅X₅⋅X₅⋅X₅+726084⋅X₃⋅X₃⋅X₆⋅X₆⋅X₆+962280⋅X₃⋅X₃⋅X₃⋅X₄⋅X₅+962280⋅X₃⋅X₃⋅X₃⋅X₄⋅X₆+962280⋅X₃⋅X₃⋅X₃⋅X₅⋅X₆+1062882⋅X₃⋅X₄⋅X₄⋅X₄+1062882⋅X₃⋅X₅⋅X₅⋅X₅+1115370⋅X₃⋅X₆⋅X₆⋅X₆+2411532⋅X₃⋅X₃⋅X₄⋅X₄+2411532⋅X₃⋅X₃⋅X₅⋅X₅+2447172⋅X₃⋅X₃⋅X₆⋅X₆+3188646⋅X₃⋅X₄⋅X₄⋅X₅+3188646⋅X₃⋅X₄⋅X₅⋅X₅+3241134⋅X₃⋅X₄⋅X₄⋅X₆+3241134⋅X₃⋅X₅⋅X₅⋅X₆+3293622⋅X₃⋅X₄⋅X₆⋅X₆+3293622⋅X₃⋅X₅⋅X₆⋅X₆+4823064⋅X₃⋅X₃⋅X₄⋅X₅+4858704⋅X₃⋅X₃⋅X₄⋅X₆+4858704⋅X₃⋅X₃⋅X₅⋅X₆+490050⋅X₃⋅X₃⋅X₃⋅X₄+490050⋅X₃⋅X₃⋅X₃⋅X₅+490050⋅X₃⋅X₃⋅X₃⋅X₆+6482268⋅X₃⋅X₄⋅X₅⋅X₆+1594323⋅X₄⋅X₄⋅X₅+1594323⋅X₄⋅X₅⋅X₅+1633689⋅X₄⋅X₄⋅X₆+1633689⋅X₅⋅X₅⋅X₆+166375⋅X₃⋅X₃⋅X₃+1673055⋅X₄⋅X₆⋅X₆+1673055⋅X₅⋅X₆⋅X₆+2707155⋅X₃⋅X₃⋅X₄+2707155⋅X₃⋅X₃⋅X₅+2725305⋅X₃⋅X₃⋅X₆+3267378⋅X₄⋅X₅⋅X₆+3986901⋅X₃⋅X₄⋅X₄+3987225⋅X₃⋅X₅⋅X₅+4112289⋅X₃⋅X₆⋅X₆+531441⋅X₄⋅X₄⋅X₄+531441⋅X₅⋅X₅⋅X₅+570807⋅X₆⋅X₆⋅X₆+7974126⋅X₃⋅X₄⋅X₅+8099190⋅X₃⋅X₄⋅X₆+8099514⋅X₃⋅X₅⋅X₆+1004300⋅X₃⋅X₃+2178252⋅X₄⋅X₄+2178738⋅X₅⋅X₅+2286144⋅X₆⋅X₆+4356990⋅X₄⋅X₅+4464396⋅X₄⋅X₆+4464882⋅X₅⋅X₆+4942134⋅X₃⋅X₄+4942464⋅X₃⋅X₅+5015394⋅X₃⋅X₆+2020755⋅X₃+2976027⋅X₄+2976687⋅X₅+3049947⋅X₆+1355310 {O(n^6)}
t₂, X₁: 2916⋅X₃⋅X₃⋅X₄⋅X₄+2916⋅X₃⋅X₃⋅X₅⋅X₅+2916⋅X₃⋅X₃⋅X₆⋅X₆+5832⋅X₃⋅X₃⋅X₄⋅X₅+5832⋅X₃⋅X₃⋅X₄⋅X₆+5832⋅X₃⋅X₃⋅X₅⋅X₆+17496⋅X₃⋅X₄⋅X₅+17820⋅X₃⋅X₄⋅X₆+17820⋅X₃⋅X₅⋅X₆+5940⋅X₃⋅X₃⋅X₄+5940⋅X₃⋅X₃⋅X₅+5940⋅X₃⋅X₃⋅X₆+8748⋅X₃⋅X₄⋅X₄+8748⋅X₃⋅X₅⋅X₅+9072⋅X₃⋅X₆⋅X₆+13122⋅X₄⋅X₅+13608⋅X₄⋅X₆+13608⋅X₅⋅X₆+20844⋅X₃⋅X₄+20844⋅X₃⋅X₅+21174⋅X₃⋅X₆+3025⋅X₃⋅X₃+6561⋅X₄⋅X₄+6561⋅X₅⋅X₅+7047⋅X₆⋅X₆+12155⋅X₃+17901⋅X₄+17907⋅X₅+18567⋅X₆+12210 {O(n^4)}
t₂, X₂: 54⋅X₃⋅X₄+54⋅X₃⋅X₅+54⋅X₃⋅X₆+55⋅X₃+81⋅X₄+81⋅X₅+87⋅X₆+110 {O(n^2)}
t₂, X₃: 3⋅X₃+2 {O(n)}
t₂, X₄: 2⋅X₄ {O(n)}
t₂, X₅: 2⋅X₅ {O(n)}
t₂, X₆: 2⋅X₆ {O(n)}
t₃, X₀: 2⋅X₄ {O(n)}
t₃, X₁: 2⋅X₅ {O(n)}
t₃, X₂: 2⋅X₆ {O(n)}
t₃, X₃: 3⋅X₃+2 {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 2⋅X₅ {O(n)}
t₃, X₆: 2⋅X₆ {O(n)}
t₄, X₀: 157464⋅X₃⋅X₃⋅X₃⋅X₄⋅X₄⋅X₄+157464⋅X₃⋅X₃⋅X₃⋅X₅⋅X₅⋅X₅+157464⋅X₃⋅X₃⋅X₃⋅X₆⋅X₆⋅X₆+472392⋅X₃⋅X₃⋅X₃⋅X₄⋅X₄⋅X₅+472392⋅X₃⋅X₃⋅X₃⋅X₄⋅X₄⋅X₆+472392⋅X₃⋅X₃⋅X₃⋅X₄⋅X₅⋅X₅+472392⋅X₃⋅X₃⋅X₃⋅X₄⋅X₆⋅X₆+472392⋅X₃⋅X₃⋅X₃⋅X₅⋅X₅⋅X₆+472392⋅X₃⋅X₃⋅X₃⋅X₅⋅X₆⋅X₆+944784⋅X₃⋅X₃⋅X₃⋅X₄⋅X₅⋅X₆+2125764⋅X₃⋅X₃⋅X₄⋅X₄⋅X₅+2125764⋅X₃⋅X₃⋅X₄⋅X₅⋅X₅+2143260⋅X₃⋅X₃⋅X₄⋅X₄⋅X₆+2143260⋅X₃⋅X₃⋅X₅⋅X₅⋅X₆+2160756⋅X₃⋅X₃⋅X₄⋅X₆⋅X₆+2160756⋅X₃⋅X₃⋅X₅⋅X₆⋅X₆+4286520⋅X₃⋅X₃⋅X₄⋅X₅⋅X₆+481140⋅X₃⋅X₃⋅X₃⋅X₄⋅X₄+481140⋅X₃⋅X₃⋅X₃⋅X₅⋅X₅+481140⋅X₃⋅X₃⋅X₃⋅X₆⋅X₆+708588⋅X₃⋅X₃⋅X₄⋅X₄⋅X₄+708588⋅X₃⋅X₃⋅X₅⋅X₅⋅X₅+726084⋅X₃⋅X₃⋅X₆⋅X₆⋅X₆+962280⋅X₃⋅X₃⋅X₃⋅X₄⋅X₅+962280⋅X₃⋅X₃⋅X₃⋅X₄⋅X₆+962280⋅X₃⋅X₃⋅X₃⋅X₅⋅X₆+1062882⋅X₃⋅X₄⋅X₄⋅X₄+1062882⋅X₃⋅X₅⋅X₅⋅X₅+1115370⋅X₃⋅X₆⋅X₆⋅X₆+2411532⋅X₃⋅X₃⋅X₄⋅X₄+2411532⋅X₃⋅X₃⋅X₅⋅X₅+2447172⋅X₃⋅X₃⋅X₆⋅X₆+3188646⋅X₃⋅X₄⋅X₄⋅X₅+3188646⋅X₃⋅X₄⋅X₅⋅X₅+3241134⋅X₃⋅X₄⋅X₄⋅X₆+3241134⋅X₃⋅X₅⋅X₅⋅X₆+3293622⋅X₃⋅X₄⋅X₆⋅X₆+3293622⋅X₃⋅X₅⋅X₆⋅X₆+4823064⋅X₃⋅X₃⋅X₄⋅X₅+4858704⋅X₃⋅X₃⋅X₄⋅X₆+4858704⋅X₃⋅X₃⋅X₅⋅X₆+490050⋅X₃⋅X₃⋅X₃⋅X₄+490050⋅X₃⋅X₃⋅X₃⋅X₅+490050⋅X₃⋅X₃⋅X₃⋅X₆+6482268⋅X₃⋅X₄⋅X₅⋅X₆+1594323⋅X₄⋅X₄⋅X₅+1594323⋅X₄⋅X₅⋅X₅+1633689⋅X₄⋅X₄⋅X₆+1633689⋅X₅⋅X₅⋅X₆+166375⋅X₃⋅X₃⋅X₃+1673055⋅X₄⋅X₆⋅X₆+1673055⋅X₅⋅X₆⋅X₆+2707155⋅X₃⋅X₃⋅X₄+2707155⋅X₃⋅X₃⋅X₅+2725305⋅X₃⋅X₃⋅X₆+3267378⋅X₄⋅X₅⋅X₆+3986901⋅X₃⋅X₄⋅X₄+3987225⋅X₃⋅X₅⋅X₅+4112289⋅X₃⋅X₆⋅X₆+531441⋅X₄⋅X₄⋅X₄+531441⋅X₅⋅X₅⋅X₅+570807⋅X₆⋅X₆⋅X₆+7974126⋅X₃⋅X₄⋅X₅+8099190⋅X₃⋅X₄⋅X₆+8099514⋅X₃⋅X₅⋅X₆+1004300⋅X₃⋅X₃+2178252⋅X₄⋅X₄+2178738⋅X₅⋅X₅+2286144⋅X₆⋅X₆+4356990⋅X₄⋅X₅+4464396⋅X₄⋅X₆+4464882⋅X₅⋅X₆+4942134⋅X₃⋅X₄+4942464⋅X₃⋅X₅+5015394⋅X₃⋅X₆+2020755⋅X₃+2976027⋅X₄+2976687⋅X₅+3049947⋅X₆+1355310 {O(n^6)}
t₄, X₁: 2916⋅X₃⋅X₃⋅X₄⋅X₄+2916⋅X₃⋅X₃⋅X₅⋅X₅+2916⋅X₃⋅X₃⋅X₆⋅X₆+5832⋅X₃⋅X₃⋅X₄⋅X₅+5832⋅X₃⋅X₃⋅X₄⋅X₆+5832⋅X₃⋅X₃⋅X₅⋅X₆+17496⋅X₃⋅X₄⋅X₅+17820⋅X₃⋅X₄⋅X₆+17820⋅X₃⋅X₅⋅X₆+5940⋅X₃⋅X₃⋅X₄+5940⋅X₃⋅X₃⋅X₅+5940⋅X₃⋅X₃⋅X₆+8748⋅X₃⋅X₄⋅X₄+8748⋅X₃⋅X₅⋅X₅+9072⋅X₃⋅X₆⋅X₆+13122⋅X₄⋅X₅+13608⋅X₄⋅X₆+13608⋅X₅⋅X₆+20844⋅X₃⋅X₄+20844⋅X₃⋅X₅+21174⋅X₃⋅X₆+3025⋅X₃⋅X₃+6561⋅X₄⋅X₄+6561⋅X₅⋅X₅+7047⋅X₆⋅X₆+12155⋅X₃+17901⋅X₄+17907⋅X₅+18567⋅X₆+12210 {O(n^4)}
t₄, X₂: 54⋅X₃⋅X₄+54⋅X₃⋅X₅+54⋅X₃⋅X₆+55⋅X₃+81⋅X₄+81⋅X₅+87⋅X₆+110 {O(n^2)}
t₄, X₃: 3⋅X₃+2 {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₄, X₅: 2⋅X₅ {O(n)}
t₄, X₆: 2⋅X₆ {O(n)}