// L = number of levels in the tree.
// By default, use a tree tall enough to contain all three types of processes.
constant L := 3;

variable x[(2^L-1)] < 3;

process Root[i < 1]
{
  read:  x[1];
  read:  x[2];
  write: x[0];

  (future & silent)
    (x[0] != x[1] && x[0] != x[2])
    ;
}

process P[j < (2^(L-1)-2)]
{
  let i := j + 1;
  let parent_idx := (i-1)/2;
  let left_idx := 2*(i+1)-1;
  let right_idx := 2*(i+1);
  read:  x[parent_idx];
  read:  x[left_idx];
  read:  x[right_idx];
  write: x[i];

  (future & silent)
    (x[parent_idx] != x[i] && x[i] != x[left_idx] && x[i] != x[right_idx])
    ;

  puppet action:
    ( x[i]==x[parent_idx] --> x[i]:=x[i]+1; )
    ;
}

process Leaf[j < (2^(L-1))]
{
  let i := j + (2^(L-1)-1);
  let parent_idx := (i-1)/2;
  read:  x[parent_idx];
  write: x[i];

  puppet action:
    ( x[i]==x[parent_idx] --> x[i]:=x[i]+1; )
    ;
}