First let us introduce a few necessary notations.

An inequality of the form *x′* ≤ *x″* between two 4-dimensional vectors *x′*, *x″* ∈ *X* will mean the validity of four inequalities *x′*_{i} ≤ *x″ _{i}*,

We denote *D*^{−}(x′) {*x* ∈ *X*| *x* ≥ *X*}, *D*^{+}(*x*′) {*x* ∈ *X*| *x* ≥ *x*′}, *D*^{−} (*X*′) ∪_{x∈X}, *D*^{−}(*x*), *D*^{+}(*X*′) ∪_{x∈X′} *D*^{+}(*x*); *X*(*I*) (*T*, Δ_{V}, Δ_{V,C}, Δ_{C,V}).

Letter *I* will denote the set of all inputs of the CLC problem.

In the previous section eight CLC(*x*) problems for eight different values of the constraining vector *x* were analyzed. Yet we recall that in Section 12.4 an infinite family CLC(*X*) of CLC(*x*) problems over all possible vectors *x* ∈ *X* was defined. Does this mean that, once we have committed ourselves to obtaining the whole picture of complexity over all problems in CLC(*X*), we have to perform a similar complexity analysis for **every** CLC(*x*) problem from CLC(*X*)?

If this were so, it would be very unfortunate, ...

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