/*
 Given the alphabet {A,B}, the function Prefix(e.x1, e.x2) checks whether e.x1 is a prefix of e.x2.
 The function Concat is concatenation.

 The supercompiler is to check when e.x is a prefix of Concat('A'e.x, e.y).
*/

/***********************************************/
/*           the input program                 */
/***********************************************/
$ENTRY Go {
	 (e.x) e.y = <Prefix (e.x) <Concat ('A' e.x) e.y>>;
}

Prefix {
	() e.x = 'T';
	(t.x e.z1) t.x e.z2 = <Prefix (e.z1) e.z2>;
	('A' e.x1) 'B' e.x2 = 'F';
	('B' e.x1) 'A' e.x2 = 'F';
	(t.y e.x) = 'F';
}

Concat {
	(e.x1) e.x2 = e.x1 e.x2;
}

/***********************************************/
/*          the residual program               */
/***********************************************/
/*
$ENTRY Go {
 (e.x1) e.x2 =  <Prefix_124_0 (e.x1) (e.x2)>;
}


Prefix_124_0 {
 () (e.x1) =  'T';
 ('A' e.x1) (e.x2) =  <Prefix_124_0 (e.x1) (e.x2)>;
 ('B' e.x1) (e.x2) =  'F';
}
*/

/*
 The loop Prefix_124_0 of the residual programm answers to the question given by the task:
 a word e.x is a prefix of word 'A' e.x e.y if and only if the word e.x consists only of letters 'A' and is not empty.
*/