Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 0 < X₁₁
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₃) :|: X₁₁ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l1(X₈, X₉, X₁₀, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₇, X₁₂, 0, X₁₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l5(X₀, X₁, X₂, X₀, X₁, X₁₁-1, X₁₃+(X₁₁)²+1-2⋅X₁₁, X₇, X₈, X₉, X₁₀, X₁₁, X₀+X₁, X₁₃, X₁₄)
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 0 < X₁₄
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₁₄ ≤ 0
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l1(X₃, X₄, X₃, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₅, X₁₂, X₆, X₁₄) :|: X₁₂ ≤ 0
t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 0 < X₁₂
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l5(X₀, X₁, X₂, X₂, X₇, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂-1, X₁₃, X₁₄)
t₁₀: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄-1)
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄)

Preprocessing

Found invariant 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₁₂+X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₂+X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ for location l6

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ 1 ≤ X₁₄ ∧ 2 ≤ X₁₃+X₁₄ ∧ 1+X₁₁ ≤ X₁₄ ∧ 1 ≤ X₁₃ ∧ 1+X₁₁ ≤ X₁₃ ∧ X₁₁ ≤ 0 for location l7

Found invariant 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₁ for location l5

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₁ ≤ 0 for location l8

Found invariant X₁₁ ≤ X₇ for location l1

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ X₁₁ ≤ 0 for location l4

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₁ ≤ 0 for location l9

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1 ≤ X₁₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 0 < X₁₁ ∧ X₁₁ ≤ X₇
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₃) :|: X₁₁ ≤ 0 ∧ X₁₁ ≤ X₇
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l1(X₈, X₉, X₁₀, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₇, X₁₂, 0, X₁₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l5(X₀, X₁, X₂, X₀, X₁, X₁₁-1, X₁₃+(X₁₁)²+1-2⋅X₁₁, X₇, X₈, X₉, X₁₀, X₁₁, X₀+X₁, X₁₃, X₁₄) :|: 1 ≤ X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1 ≤ X₁₁
t₈: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 0 < X₁₄ ∧ X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ X₁₁ ≤ 0
t₉: l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₁₄ ≤ 0 ∧ X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ X₁₁ ≤ 0
t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l1(X₃, X₄, X₃, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₅, X₁₂, X₆, X₁₄) :|: X₁₂ ≤ 0 ∧ 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₁
t₅: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 0 < X₁₂ ∧ 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₁
t₇: l6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l5(X₀, X₁, X₂, X₂, X₇, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂-1, X₁₃, X₁₄) :|: 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₁₂+X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₂+X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁
t₁₀: l7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄-1) :|: X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ 1 ≤ X₁₄ ∧ 2 ≤ X₁₃+X₁₄ ∧ 1+X₁₁ ≤ X₁₄ ∧ 1 ≤ X₁₃ ∧ 1+X₁₁ ≤ X₁₃ ∧ X₁₁ ≤ 0
t₁₁: l8(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l9(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: X₁₁ ≤ X₇ ∧ X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₁ ≤ 0

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) :|: 0 < X₁₁ ∧ X₁₁ ≤ X₇ of depth 1:

new bound:

X₇ {O(n)}

MPRF for transition t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l5(X₀, X₁, X₂, X₀, X₁, X₁₁-1, X₁₃+Temp_Int₇₂₁+Temp_Int₇₂₂-2⋅X₁₁, X₇, X₈, X₉, X₁₀, X₁₁, X₀+X₁, X₁₃, X₁₄) :|: 0 < Temp_Int₇₂₁ ∧ X₁₁ ≤ Temp_Int₇₂₁ ∧ 1 ≤ X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1 ≤ X₁₁ of depth 1:

new bound:

X₇ {O(n)}

MPRF for transition t₆: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l1(X₃, X₄, X₃, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₅, X₁₂, X₆, X₁₄) :|: X₁₂ ≤ 0 ∧ 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₁ of depth 1:

new bound:

X₇ {O(n)}

TWN: t₅: l5→l6

cycle: [t₅: l5→l6; t₇: l6→l5]
loop: (0 < X₁₂,(X₁₂) -> (X₁₂-1)
order: [X₁₂]
closed-form:
X₁₂: X₁₂ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

1 < 0
∨ 0 < X₁₂ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: 0 < X₁₂
alphas_abs: X₁₂
M: 0
N: 1
Bound: 2⋅X₁₂+2 {O(n)}

TWN - Lifting for t₅: l5→l6 of 2⋅X₁₂+4 {O(n)}

relevant size-bounds w.r.t. t₄:
X₁₂: X₁₀+X₇+X₈+X₉ {O(n)}
Runtime-bound of t₄: X₇ {O(n)}
Results in: 2⋅X₁₀⋅X₇+2⋅X₇⋅X₇+2⋅X₇⋅X₈+2⋅X₇⋅X₉+4⋅X₇ {O(n^2)}

TWN: t₇: l6→l5

TWN - Lifting for t₇: l6→l5 of 2⋅X₁₂+4 {O(n)}

relevant size-bounds w.r.t. t₄:
X₁₂: X₁₀+X₇+X₈+X₉ {O(n)}
Runtime-bound of t₄: X₇ {O(n)}
Results in: 2⋅X₁₀⋅X₇+2⋅X₇⋅X₇+2⋅X₇⋅X₈+2⋅X₇⋅X₉+4⋅X₇ {O(n^2)}

Chain transitions t₆: l5→l1 and t₃: l1→l4 to t₇₂: l5→l4

Chain transitions t₁: l2→l1 and t₃: l1→l4 to t₇₃: l2→l4

Chain transitions t₁: l2→l1 and t₂: l1→l3 to t₇₄: l2→l3

Chain transitions t₆: l5→l1 and t₂: l1→l3 to t₇₅: l5→l3

Chain transitions t₇₅: l5→l3 and t₄: l3→l5 to t₇₆: l5→l5

Chain transitions t₇₄: l2→l3 and t₄: l3→l5 to t₇₇: l2→l5

Chain transitions t₅: l5→l6 and t₇: l6→l5 to t₇₈: l5→l5

Analysing control-flow refined program

Eliminate variables {X₀,X₁} that do not contribute to the problem

Found invariant X₉ ≤ X₅ ∧ X₉ ≤ 1+X₃ ∧ 1 ≤ X₉ ∧ 2 ≤ X₅+X₉ ∧ 1 ≤ X₃+X₉ ∧ 1+X₃ ≤ X₉ ∧ 2 ≤ X₁₀+X₉ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 2 ≤ X₁₀+X₅ ∧ 0 ≤ X₃ ∧ 1 ≤ X₁₀+X₃ ∧ 1 ≤ X₁₀ for location l6

Found invariant X₉ ≤ 0 ∧ X₉ ≤ X₅ ∧ 1+X₉ ≤ X₁₂ ∧ 1+X₉ ≤ X₁₁ ∧ X₁₂ ≤ X₁₁ ∧ 1 ≤ X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ for location l7

Found invariant X₉ ≤ X₅ ∧ X₉ ≤ 1+X₃ ∧ 1 ≤ X₉ ∧ 2 ≤ X₅+X₉ ∧ 1 ≤ X₃+X₉ ∧ 1+X₃ ≤ X₉ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 0 ≤ X₃ for location l5

Found invariant X₉ ≤ 0 ∧ X₉ ≤ X₅ ∧ X₁₂+X₉ ≤ 0 ∧ X₁₂ ≤ 0 ∧ X₁₂ ≤ X₁₁ for location l8

Found invariant X₉ ≤ X₅ for location l1

Found invariant X₉ ≤ 0 ∧ X₉ ≤ X₅ ∧ X₁₂ ≤ X₁₁ for location l4

Found invariant X₉ ≤ 0 ∧ X₉ ≤ X₅ ∧ X₁₂+X₉ ≤ 0 ∧ X₁₂ ≤ 0 ∧ X₁₂ ≤ X₁₁ for location l9

Found invariant X₉ ≤ X₅ ∧ 1 ≤ X₉ ∧ 2 ≤ X₅+X₉ ∧ 1 ≤ X₅ for location l3

MPRF for transition t₁₀₄: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂) -{3}> l5(X₁, X₁, X₂, X₃-1, X₄+Temp_Int₁₈₃₀+Temp_Int₁₈₃₁-2⋅X₃, X₅, X₆, X₇, X₈, X₃, X₁+X₂, X₄, X₁₂) :|: X₁₀ ≤ 0 ∧ 0 < X₃ ∧ 0 < Temp_Int₁₈₃₀ ∧ X₃ ≤ Temp_Int₁₈₃₀ ∧ X₉ ≤ X₅ ∧ X₉ ≤ 1+X₃ ∧ 1 ≤ X₉ ∧ 2 ≤ X₅+X₉ ∧ 1 ≤ X₃+X₉ ∧ 1+X₃ ≤ X₉ ∧ 1 ≤ X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₃ ≤ X₅ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₅+1 {O(n)}

TWN: t₁₀₅: l5→l5

cycle: [t₁₀₅: l5→l5]
loop: (0 < X₁₀,(X₁₀) -> (X₁₀-1)
order: [X₁₀]
closed-form:
X₁₀: X₁₀ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

1 < 0
∨ 0 < X₁₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: 0 < X₁₀
alphas_abs: X₁₀
M: 0
N: 1
Bound: 2⋅X₁₀+2 {O(n)}
loop: (0 < X₁₀,(X₁₀) -> (X₁₀-1)
order: [X₁₀]
closed-form:
X₁₀: X₁₀ + [[n != 0]] * -1 * n^1

Termination: true
Formula:

1 < 0
∨ 0 < X₁₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1

Stabilization-Threshold for: 0 < X₁₀
alphas_abs: X₁₀
M: 0
N: 1
Bound: 2⋅X₁₀+2 {O(n)}

TWN - Lifting for t₁₀₅: l5→l5 of 2⋅X₁₀+4 {O(n)}

relevant size-bounds w.r.t. t₁₀₄:
X₁₀: 2⋅X₇+2⋅X₈+3⋅X₆+6⋅X₅ {O(n)}
Runtime-bound of t₁₀₄: X₅+1 {O(n)}
Results in: 12⋅X₅⋅X₅+4⋅X₅⋅X₇+4⋅X₅⋅X₈+6⋅X₅⋅X₆+16⋅X₅+4⋅X₇+4⋅X₈+6⋅X₆+4 {O(n^2)}

TWN - Lifting for t₁₀₅: l5→l5 of 2⋅X₁₀+4 {O(n)}

relevant size-bounds w.r.t. t₉₈:
X₁₀: X₆+X₇ {O(n)}
Runtime-bound of t₉₈: 1 {O(1)}
Results in: 2⋅X₆+2⋅X₇+4 {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₁₂+X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₂+X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ for location n_l6___3

Found invariant X₇ ≤ X₄ ∧ 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₄+X₇ ∧ X₄ ≤ X₇ ∧ 2 ≤ X₁₂+X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₁₂+X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁₂+X₄ ∧ 2 ≤ X₁₁+X₄ ∧ X₁₁ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₀+X₁ for location n_l6___1

Found invariant X₇ ≤ X₄ ∧ 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₄+X₇ ∧ X₄ ≤ X₇ ∧ 1 ≤ X₁₂+X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 0 ≤ X₁₂+X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁₂+X₄ ∧ 2 ≤ X₁₁+X₄ ∧ X₁₁ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁₂ ∧ 1 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₀+X₁ for location n_l5___2

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ 1 ≤ X₁₄ ∧ 2 ≤ X₁₃+X₁₄ ∧ 1+X₁₁ ≤ X₁₄ ∧ 1 ≤ X₁₃ ∧ 1+X₁₁ ≤ X₁₃ ∧ X₁₁ ≤ 0 for location l7

Found invariant 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁₁ for location l5

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₁ ≤ 0 for location l8

Found invariant X₁₁ ≤ X₇ for location l1

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ X₁₁ ≤ 0 for location l4

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₁ ≤ 0 for location l9

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1 ≤ X₁₁ for location l3

knowledge_propagation leads to new time bound X₇ {O(n)} for transition t₁₉₄: l5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → n_l6___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₅+1, X₁₂, X₁₃, X₁₄) :|: X₁₁ ≤ X₇ ∧ X₅+1 ≤ X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ 1+X₅ ≤ X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ X₀+X₁ ≤ X₁₂ ∧ X₁₂ ≤ X₀+X₁ ∧ X₁₁ ≤ X₇ ∧ 0 < X₁₂ ∧ X₅+1 ≤ X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1+X₅ ≤ X₇ ∧ 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁₁

knowledge_propagation leads to new time bound X₇ {O(n)} for transition t₁₉₆: n_l6___3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → n_l5___2(X₀, X₁, X₂, X₂, X₇, X₅, X₆, X₇, X₈, X₉, X₁₀, X₅+1, X₁₂-1, X₁₃, X₁₄) :|: X₁₁ ≤ X₇ ∧ 0 < X₀+X₁ ∧ X₀+X₁ ≤ X₁₂ ∧ X₁₂ ≤ X₀+X₁ ∧ X₁ ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₅+1 ≤ X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₅+1 ≤ X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₂ ∧ 1+X₅ ≤ X₇ ∧ 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₁₂+X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₂+X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁

MPRF for transition t₁₉₃: n_l5___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → n_l6___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₅+1, X₁₂, X₁₃, X₁₄) :|: X₁₁ ≤ X₇ ∧ X₅+1 ≤ X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1+X₅ ≤ X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₄ ∧ X₁₁ ≤ X₇ ∧ 0 ≤ X₁₂ ∧ 0 < X₁₂ ∧ X₅+1 ≤ X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1+X₅ ≤ X₇ ∧ X₇ ≤ X₄ ∧ 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₄+X₇ ∧ X₄ ≤ X₇ ∧ 1 ≤ X₁₂+X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 0 ≤ X₁₂+X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁₂+X₄ ∧ 2 ≤ X₁₁+X₄ ∧ X₁₁ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁₂ ∧ 1 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₀+X₁ of depth 1:

new bound:

3⋅X₁₀⋅X₇+3⋅X₇⋅X₈+X₇⋅X₇+X₇⋅X₉+X₇ {O(n^2)}

MPRF for transition t₁₉₅: n_l6___1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → n_l5___2(X₀, X₁, X₂, X₂, X₇, X₅, X₆, X₇, X₈, X₉, X₁₀, X₅+1, X₁₂-1, X₁₃, X₁₄) :|: 0 < X₁₂ ∧ X₅+1 ≤ X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ X₄ ≤ X₇ ∧ X₇ ≤ X₄ ∧ X₅+1 ≤ X₁₁ ∧ X₁₁ ≤ 1+X₅ ∧ 1+X₅ ≤ X₇ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₂ ∧ 1+X₅ ≤ X₇ ∧ X₇ ≤ X₄ ∧ 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₄+X₇ ∧ X₄ ≤ X₇ ∧ 2 ≤ X₁₂+X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₁₂+X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁₂+X₄ ∧ 2 ≤ X₁₁+X₄ ∧ X₁₁ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₀+X₁ of depth 1:

new bound:

X₁₀⋅X₇+X₇⋅X₇+X₇⋅X₈+X₇⋅X₉ {O(n^2)}

MPRF for transition t₂₀₀: n_l5___2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄) → l1(X₃, X₄, X₃, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₅, X₁₂, X₆, X₁₄) :|: X₁₂ ≤ 0 ∧ 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₁ ∧ X₇ ≤ X₄ ∧ 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₄+X₇ ∧ X₄ ≤ X₇ ∧ 1 ≤ X₁₂+X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 0 ≤ X₁₂+X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₁₂+X₄ ∧ 2 ≤ X₁₁+X₄ ∧ X₁₁ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₁₂ ∧ 1 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ ∧ 1 ≤ X₀+X₁ of depth 1:

new bound:

X₇ {O(n)}

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Chain transitions t₁₀: l7→l4 and t₉: l4→l8 to t₂₇₇: l7→l8

Chain transitions t₃: l1→l4 and t₉: l4→l8 to t₂₇₈: l1→l8

Chain transitions t₃: l1→l4 and t₈: l4→l7 to t₂₇₉: l1→l7

Chain transitions t₁₀: l7→l4 and t₈: l4→l7 to t₂₈₀: l7→l7

Analysing control-flow refined program

Found invariant 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₁₂+X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₂+X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ for location l6

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ 1 ≤ X₁₄ ∧ 2 ≤ X₁₃+X₁₄ ∧ 1+X₁₁ ≤ X₁₄ ∧ 1 ≤ X₁₃ ∧ 1+X₁₁ ≤ X₁₃ ∧ X₁₁ ≤ 0 for location l7

Found invariant 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₁ for location l5

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₁ ≤ 0 for location l8

Found invariant X₁₁ ≤ X₇ for location l1

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ X₁₁ ≤ 0 for location l4

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₁ ≤ 0 for location l9

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1 ≤ X₁₁ for location l3

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

Analysing control-flow refined program

Found invariant 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₁₂+X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₂+X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₂ ∧ 2 ≤ X₁₁+X₁₂ ∧ 1 ≤ X₁₁ for location l6

Found invariant X₁₁ ≤ X₇ ∧ 1+X₁₄ ≤ X₁₃ ∧ 0 ≤ X₁₄ ∧ 1 ≤ X₁₃+X₁₄ ∧ X₁₁ ≤ X₁₄ ∧ 1 ≤ X₁₃ ∧ 1+X₁₁ ≤ X₁₃ ∧ X₁₁ ≤ 0 for location n_l4___2

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ 1 ≤ X₁₄ ∧ 2 ≤ X₁₃+X₁₄ ∧ X₁₃ ≤ X₁₄ ∧ 1+X₁₁ ≤ X₁₄ ∧ 1 ≤ X₁₃ ∧ 1+X₁₁ ≤ X₁₃ ∧ X₁₁ ≤ 0 for location n_l7___3

Found invariant 1 ≤ X₇ ∧ 1 ≤ X₅+X₇ ∧ 1+X₅ ≤ X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1+X₅ ≤ X₁₁ ∧ 0 ≤ X₅ ∧ 1 ≤ X₁₁+X₅ ∧ X₁₁ ≤ 1+X₅ ∧ 1 ≤ X₁₁ for location l5

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₁ ≤ 0 for location l8

Found invariant X₁₁ ≤ X₇ for location l1

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ X₁₃ ∧ X₁₃ ≤ X₁₄ ∧ X₁₁ ≤ 0 for location l4

Found invariant X₁₁ ≤ X₇ ∧ X₁₄ ≤ 0 ∧ X₁₄ ≤ X₁₃ ∧ X₁₁+X₁₄ ≤ 0 ∧ X₁₁ ≤ 0 for location l9

Found invariant X₁₁ ≤ X₇ ∧ 1+X₁₄ ≤ X₁₃ ∧ 1 ≤ X₁₄ ∧ 3 ≤ X₁₃+X₁₄ ∧ 1+X₁₁ ≤ X₁₄ ∧ 2 ≤ X₁₃ ∧ 2+X₁₁ ≤ X₁₃ ∧ X₁₁ ≤ 0 for location n_l7___1

Found invariant 1 ≤ X₇ ∧ 2 ≤ X₁₁+X₇ ∧ X₁₁ ≤ X₇ ∧ 1 ≤ X₁₁ for location l3

CFR did not improve the program. Rolling back

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₇ {O(n)}
t₃: 1 {O(1)}
t₄: X₇ {O(n)}
t₅: 2⋅X₁₀⋅X₇+2⋅X₇⋅X₇+2⋅X₇⋅X₈+2⋅X₇⋅X₉+4⋅X₇ {O(n^2)}
t₆: X₇ {O(n)}
t₇: 2⋅X₁₀⋅X₇+2⋅X₇⋅X₇+2⋅X₇⋅X₈+2⋅X₇⋅X₉+4⋅X₇ {O(n^2)}
t₈: inf {Infinity}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₇ {O(n)}
t₃: 1 {O(1)}
t₄: X₇ {O(n)}
t₅: 2⋅X₁₀⋅X₇+2⋅X₇⋅X₇+2⋅X₇⋅X₈+2⋅X₇⋅X₉+4⋅X₇ {O(n^2)}
t₆: X₇ {O(n)}
t₇: 2⋅X₁₀⋅X₇+2⋅X₇⋅X₇+2⋅X₇⋅X₈+2⋅X₇⋅X₉+4⋅X₇ {O(n^2)}
t₈: inf {Infinity}
t₉: 1 {O(1)}
t₁₀: inf {Infinity}
t₁₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₆ {O(n)}
t₀, X₇: X₇ {O(n)}
t₀, X₈: X₈ {O(n)}
t₀, X₉: X₉ {O(n)}
t₀, X₁₀: X₁₀ {O(n)}
t₀, X₁₁: X₁₁ {O(n)}
t₀, X₁₂: X₁₂ {O(n)}
t₀, X₁₃: X₁₃ {O(n)}
t₀, X₁₄: X₁₄ {O(n)}
t₁, X₀: X₈ {O(n)}
t₁, X₁: X₉ {O(n)}
t₁, X₂: X₁₀ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₁, X₇: X₇ {O(n)}
t₁, X₈: X₈ {O(n)}
t₁, X₉: X₉ {O(n)}
t₁, X₁₀: X₁₀ {O(n)}
t₁, X₁₁: X₇ {O(n)}
t₁, X₁₂: X₁₂ {O(n)}
t₁, X₁₃: 0 {O(1)}
t₁, X₁₄: X₁₄ {O(n)}
t₂, X₀: X₁₀+X₈ {O(n)}
t₂, X₁: X₇+X₉ {O(n)}
t₂, X₂: X₁₀+X₈ {O(n)}
t₂, X₃: 2⋅X₁₀+2⋅X₈+X₃ {O(n)}
t₂, X₄: 2⋅X₇+X₄+X₉ {O(n)}
t₂, X₅: 2⋅X₇+X₅ {O(n)}
t₂, X₇: X₇ {O(n)}
t₂, X₈: X₈ {O(n)}
t₂, X₉: X₉ {O(n)}
t₂, X₁₀: X₁₀ {O(n)}
t₂, X₁₁: X₇ {O(n)}
t₂, X₁₂: 2⋅X₁₀+2⋅X₇+2⋅X₈+2⋅X₉+X₁₂ {O(n)}
t₂, X₁₄: X₁₄ {O(n)}
t₃, X₀: 2⋅X₈+X₁₀ {O(n)}
t₃, X₁: 2⋅X₉+X₇ {O(n)}
t₃, X₂: 2⋅X₁₀+X₈ {O(n)}
t₃, X₃: 2⋅X₁₀+2⋅X₈+X₃ {O(n)}
t₃, X₄: 2⋅X₇+X₄+X₉ {O(n)}
t₃, X₅: 2⋅X₇+X₅ {O(n)}
t₃, X₇: 2⋅X₇ {O(n)}
t₃, X₈: 2⋅X₈ {O(n)}
t₃, X₉: 2⋅X₉ {O(n)}
t₃, X₁₀: 2⋅X₁₀ {O(n)}
t₃, X₁₁: 2⋅X₇ {O(n)}
t₃, X₁₂: 2⋅X₁₀+2⋅X₇+2⋅X₈+2⋅X₉+X₁₂ {O(n)}
t₄, X₀: X₁₀+X₈ {O(n)}
t₄, X₁: X₇+X₉ {O(n)}
t₄, X₂: X₁₀+X₈ {O(n)}
t₄, X₃: X₁₀+X₈ {O(n)}
t₄, X₄: X₇+X₉ {O(n)}
t₄, X₅: X₇ {O(n)}
t₄, X₇: X₇ {O(n)}
t₄, X₈: X₈ {O(n)}
t₄, X₉: X₉ {O(n)}
t₄, X₁₀: X₁₀ {O(n)}
t₄, X₁₁: X₇ {O(n)}
t₄, X₁₂: X₁₀+X₇+X₈+X₉ {O(n)}
t₄, X₁₄: X₁₄ {O(n)}
t₅, X₀: X₁₀+X₈ {O(n)}
t₅, X₁: X₇+X₉ {O(n)}
t₅, X₂: X₁₀+X₈ {O(n)}
t₅, X₃: 2⋅X₁₀+2⋅X₈ {O(n)}
t₅, X₄: 2⋅X₇+X₉ {O(n)}
t₅, X₅: X₇ {O(n)}
t₅, X₇: X₇ {O(n)}
t₅, X₈: X₈ {O(n)}
t₅, X₉: X₉ {O(n)}
t₅, X₁₀: X₁₀ {O(n)}
t₅, X₁₁: X₇ {O(n)}
t₅, X₁₂: X₁₀+X₇+X₈+X₉ {O(n)}
t₅, X₁₄: X₁₄ {O(n)}
t₆, X₀: X₁₀+X₈ {O(n)}
t₆, X₁: X₇+X₉ {O(n)}
t₆, X₂: X₁₀+X₈ {O(n)}
t₆, X₃: 2⋅X₁₀+2⋅X₈ {O(n)}
t₆, X₄: 2⋅X₇+X₉ {O(n)}
t₆, X₅: 2⋅X₇ {O(n)}
t₆, X₇: X₇ {O(n)}
t₆, X₈: X₈ {O(n)}
t₆, X₉: X₉ {O(n)}
t₆, X₁₀: X₁₀ {O(n)}
t₆, X₁₁: X₇ {O(n)}
t₆, X₁₂: 2⋅X₁₀+2⋅X₇+2⋅X₈+2⋅X₉ {O(n)}
t₆, X₁₄: X₁₄ {O(n)}
t₇, X₀: X₁₀+X₈ {O(n)}
t₇, X₁: X₇+X₉ {O(n)}
t₇, X₂: X₁₀+X₈ {O(n)}
t₇, X₃: X₁₀+X₈ {O(n)}
t₇, X₄: X₇ {O(n)}
t₇, X₅: X₇ {O(n)}
t₇, X₇: X₇ {O(n)}
t₇, X₈: X₈ {O(n)}
t₇, X₉: X₉ {O(n)}
t₇, X₁₀: X₁₀ {O(n)}
t₇, X₁₁: X₇ {O(n)}
t₇, X₁₂: X₁₀+X₇+X₈+X₉ {O(n)}
t₇, X₁₄: X₁₄ {O(n)}
t₈, X₀: 2⋅X₈+X₁₀ {O(n)}
t₈, X₁: 2⋅X₉+X₇ {O(n)}
t₈, X₂: 2⋅X₁₀+X₈ {O(n)}
t₈, X₃: 2⋅X₁₀+2⋅X₈+X₃ {O(n)}
t₈, X₄: 2⋅X₇+X₄+X₉ {O(n)}
t₈, X₅: 2⋅X₇+X₅ {O(n)}
t₈, X₇: 2⋅X₇ {O(n)}
t₈, X₈: 2⋅X₈ {O(n)}
t₈, X₉: 2⋅X₉ {O(n)}
t₈, X₁₀: 2⋅X₁₀ {O(n)}
t₈, X₁₁: 2⋅X₇ {O(n)}
t₈, X₁₂: 2⋅X₁₀+2⋅X₇+2⋅X₈+2⋅X₉+X₁₂ {O(n)}
t₉, X₀: 2⋅X₁₀+4⋅X₈ {O(n)}
t₉, X₁: 2⋅X₇+4⋅X₉ {O(n)}
t₉, X₂: 2⋅X₈+4⋅X₁₀ {O(n)}
t₉, X₃: 2⋅X₃+4⋅X₁₀+4⋅X₈ {O(n)}
t₉, X₄: 2⋅X₄+2⋅X₉+4⋅X₇ {O(n)}
t₉, X₅: 2⋅X₅+4⋅X₇ {O(n)}
t₉, X₇: 4⋅X₇ {O(n)}
t₉, X₈: 4⋅X₈ {O(n)}
t₉, X₉: 4⋅X₉ {O(n)}
t₉, X₁₀: 4⋅X₁₀ {O(n)}
t₉, X₁₁: 4⋅X₇ {O(n)}
t₉, X₁₂: 2⋅X₁₂+4⋅X₁₀+4⋅X₇+4⋅X₈+4⋅X₉ {O(n)}
t₁₀, X₀: 2⋅X₈+X₁₀ {O(n)}
t₁₀, X₁: 2⋅X₉+X₇ {O(n)}
t₁₀, X₂: 2⋅X₁₀+X₈ {O(n)}
t₁₀, X₃: 2⋅X₁₀+2⋅X₈+X₃ {O(n)}
t₁₀, X₄: 2⋅X₇+X₄+X₉ {O(n)}
t₁₀, X₅: 2⋅X₇+X₅ {O(n)}
t₁₀, X₇: 2⋅X₇ {O(n)}
t₁₀, X₈: 2⋅X₈ {O(n)}
t₁₀, X₉: 2⋅X₉ {O(n)}
t₁₀, X₁₀: 2⋅X₁₀ {O(n)}
t₁₀, X₁₁: 2⋅X₇ {O(n)}
t₁₀, X₁₂: 2⋅X₁₀+2⋅X₇+2⋅X₈+2⋅X₉+X₁₂ {O(n)}
t₁₁, X₀: 2⋅X₁₀+4⋅X₈ {O(n)}
t₁₁, X₁: 2⋅X₇+4⋅X₉ {O(n)}
t₁₁, X₂: 2⋅X₈+4⋅X₁₀ {O(n)}
t₁₁, X₃: 2⋅X₃+4⋅X₁₀+4⋅X₈ {O(n)}
t₁₁, X₄: 2⋅X₄+2⋅X₉+4⋅X₇ {O(n)}
t₁₁, X₅: 2⋅X₅+4⋅X₇ {O(n)}
t₁₁, X₇: 4⋅X₇ {O(n)}
t₁₁, X₈: 4⋅X₈ {O(n)}
t₁₁, X₉: 4⋅X₉ {O(n)}
t₁₁, X₁₀: 4⋅X₁₀ {O(n)}
t₁₁, X₁₁: 4⋅X₇ {O(n)}
t₁₁, X₁₂: 2⋅X₁₂+4⋅X₁₀+4⋅X₇+4⋅X₈+4⋅X₉ {O(n)}