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language Essence 1.3
given n : int(1..) $ The size of the wheels
letting V be domain int(0..2*n) $ The vertices
letting E be domain int(0..4*n-1) $ The edges
letting Colours be domain int(0..4*n) $ The colours
letting C be 2*n $ The centre vertex
letting C1 be domain int(0..n-1) $ The inner circle
letting C2 be domain int(n..2*n-1) $ The outer circle
find colouring : function(total,injective) V --> Colours
find edgeID : function(total,injective) E --> Colours
such that
$ The inner circle is graceful
forAll v : C1 .
edgeID(v) = |colouring(v)-colouring((v+1)%n)|,
$ The outer circle is graceful
forAll v : C2 .
edgeID(v) = |colouring(v) - colouring((v+1)%n+n)|,
$ connections to the centre are graceful
forAll v : C1 .
edgeID(2*n+v) = |colouring(C) - colouring(v)|,
forAll v : C2 .
edgeID(2*n+v) = |colouring(C) - colouring(v)|