// special adaptation of the one-max problem for tree representations
// must find maximal number of 1-terminals (maximum for a limited tree height h is 2 ^ (h - 1) )

// the actual grammar:
// E -> 0 | 1 | E E 
//
// leading to example tree:
//   E
//  / \
// 0   E
//    / \
//   1   0
// with a value of 1
//
// optimal tree for height = 3 has the value 4
//       E
//     /   \
//    E     E
//   / \   / \
//  1   1 1   1


// because of constraints of the implemented solvers we have to express the grammar differently
//
// E -> T | N
// N -> E E
// T -> A | B     // A has value 0, B has value 1

PROBLEM OneMaxBinary

NONTERMINALS
  E<<out int n>>.
  T<<out int n>>.
  N<<out int n>>.

TERMINALS
  A.
  B.

RULES
  E<<out int n>> = 
    T<<out n>>
    | N<<out n>>
  .

  N<<out int n>> =                                LOCAL << int n1, n2; >>
    E<<out n1>> E<<out n2>>                       SEM << n = n1 + n2; >>
  .
  
  T<<out int n>> = 
    A                                             SEM << n = 0; >>
    | B                                           SEM << n = 1; >>
  .

MAXIMIZE
  << 
    int n;
    E(out n);
    return (double) n;
  >>
END OneMaxBinary.