[r-t] Pick and mix rules

[Mark Davies]

So here's the pick-and-mix ruleset. Remember it's only talking about what
makes a true peal, not other conditions unrelated to truth!

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First some definitions:

A touch is a block of changes beginning and ending in rounds.

A touch is true if every change is unique.

A touch is an extent at the stage being discussed if it contains every
change in the extent.

A touch is a true extent if it is true and if it is an extent.

Stage is the number of bells considered to be ringing in the methods of the
peal, and hence involved in determination of proof. (Bells covering or
leading for the entire peal have no effect on proof or stage).

The stage of a method is the number of changing bells in a lead of the
method.

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Now the rules for single-stage peals (you can have one of these, and
optionally some of the other rules from the other two sections).

A) It is rung on one stage, and forms a true touch.

B) It is rung on one stage, and either forms a single true touch, or
consists of one or more true extents. **

C) It is rung on one stage, and it consists of one or more true touches, of
which at most one is not an extent. **

D) It is rung on one stage, and each change in the extent at this stage is
rung exactly N or N+1 times, for N>=0.

E) It is rung on one stage, and any change can be rung any number of times.

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For the (optional!) multi-stage rules, X can be "two" or "multiple". The
stages can be further qualified to be "consecutive":

F) It is rung on X stages, but consists of a true touch when considered at
the highest stage in its entirety.

G) It is rung on X stages, and consists of one or more true extents at
either stage. **

H) It is rung on X stages, and consists of one or more true touches at
either stage, of which at most one is not an extent. (May be further
qualified by H1 or H2) **

H1) The non-extent touch, if it exists, must be at the highest stage.

H2) The non-extent touch, if it exists, must be at the lowest stage.

I-A, I-B, I-C, I-D, I-E) It is rung on X stages, and for the set of changes
at each stage, one of A, B, C, D or E applies. (May be further qualified by
I1-3) **

I1) The stage at which a given change is rung is determined by the stage of
the method within which lead it is being rung.

I2) The stage at which a given change is rung is determined by the structure
of the composition.

I3) A given change can be considered to be rung at any stage.

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Finally some rules about how methods at various stages can be incorporated
into peals for the purposes of discovery of proof:

J) No method can be rung at a different stage to the stage or stages of the
peal as a whole.

K) Methods may be rung at lower stages to that of the peal as a whole. They
are considered at the higher stages by including at most one covering bell.

L) Methods may be rung at lower stages to that of the peal as a whole. They
are considered at the higher stages by including one or more covering or
leading bells.

M) Methods may be rung at lower stages to that of the peal as a whole. They
are considered at the higher stages by including one or more covering or
leading bells, and/or ringing one or more lower-stage methods in parallel.

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Sorted! Now we just have to pick the best combination. :-)

MBD