As a rule of thumb, if a Turing machine executes many steps before halting, it does perform many simple iterations of this type. Longer tapes indicate nearly always non-termination or inappropriate K. Practical experience indicates that K should be chosen seperately and carefully for each Turing machine. Other techniques to accellerate especially counting machines are currently studied by the authors. Because both of the above techniques involve tape representation, they also influence other aspects, especially some non-termination decisions. Explication of iteration can be generalized, but it is not yet clear which generalization does pay off.
Further research is necessary here.
Nontermination Decisions Deciding that a Turing machine will never halt is always done by predicting the behaviour of the machine exactly enough, that it is sure that no not yet defined transition will ever be used, i.e. those that are already defined will be reused infinitely. This can be achieved by quite different arguments. Thus, during normal simulation all defined transitions do not halt. Let D and U be the set of currently defined and not yet defined transitions. In order to halt, one transition u in U has to be needed and defined.