VI. A. Does the variable index depending upon the chosen func-

 tion index decouple the function type from the unassigned

 functions? Tag the function indices which fail for all

 functions. If no decoupling, go to V.B.

 B. Assign the chosen variable type to the chosen function

 type. Give the function type a position in the function

 ordering immediately after all of the presently

 unassigned functions.

 C. Make the index output set assignments which produced

 the decoupling. Flag the function index as a decoupling

 index. Go to II.C.

 The decoupling algorithm performs an exhaustive search over all

combinations of directions of index incrementing. Additionally, when-

ever an output assignment is made, all remaining function and variable

types are untagged and the algorithm restarted on the remaining

unassigned function and variable types. Generally, an exhaustive search

of this type would be extremely long. In the case of the decoupling

algorithm, the search will be relatively short since the FVIM will

usually have only a few function and variable types and there are

usually only one or two function indices.

 For some of the function index directions it may be possible to

reject certain variable types at the outset. Remember that the aim of

decoupling is to manipulate the choice of solution procedure so that

variables which would otherwise have to be torn do not have to be torn.

Suppose that the function index ii is incremented in ascending order.

Suppose, also, that the variable type x is being examined to determine

if it can be used to decouple a function type from the others. If x has