The name is absent

21

Example 9. We are given

Now let us give a proof of Theorem 2.2. We are given a polytope which has the
standard form. Since P contains no integral point, the algorithm terminates with
a completely labeled simplex of type 77, say, σ₁(⅛¹,π), within a finite number of
steps. Suppose to the contrary that there is another completely labeled simplex of
tpye 77, say, σ₂(y¹, p). Without loss of generality we may assume that π is equal to
(1,..., n), l(x^t^) = i for any i ∈ .V. and х^г = y^l for all i ∈ ʌ except for some index k,
1 < к < n -∖- 1. It implies that l(x^t^) = l(y^t) = i for all i ∈ N. We have to consider
the following cases:

(1). If к = 1, then /∕^l = xⁿ⁺¹ ⅛ ¢(1). Since l(xⁿ⁺¹~) = n ⅛ 1, we have

<P₊∖^x" ⁺ ' - ^n+ι > ^al^χn+1 - b_t,l = 1, ■ ■ ■ ,n.

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