R1:	SearchSpace(expr; prop; index; logOp; phyOp; lExpr;
	lProp; rExpr; rProp) :-
	Expr(expr; prop), Fn_isleaf(expr; false),
	Fn_split(expr; prop; index; logOp; phyOp; lExpr,
	lProp; rExpr; rProp);
R2:	SearchSpace(expr; prop; index; logOp; phyOp;
	lExpr; lProp; rExpr; rProp) :-
	SearchSpace(–;–;–;–;–; expr; prop;–___________;–),
	Fn_isleaf(expr; false),
	Fn_split(expr; prop; index; logOp; phyOp;
	lExpr; lProp; rExpr; rProp);
R3:	SearchSpace(expr; prop; index; logOp; phyOp;
	lExpr; lProp; rExpr; rProp) :-
	SearchSpace(–;–;–;–;–;–;–; expr; prop),
	Fn_isleaf(expr; false)),
	Fn_split(expr; prop; index; logOp; phyOp;
	lExpr; lProp; rExpr; rProp);
R4:	SearchSpace(expr; prop;–;′ scan′; phyOp;–;–;–;–)) :-
	SearchSpace(–;–;–;–;–; expr; prop;–;–),
	Fn_isleaf(expr; true), Fn_phyOp(prop; phyOp);
R5:	SearchSpace(expr; prop;–;′ scan′; phyOp;–;–;–;–) :-
	SearchSpace(–;–;–;–;–;–;–; expr; prop),
	Fn_isleaf(expr; true), Fn_phyOp(prop; phyOp);
R6:	PlanCost(expr; prop; index; logOp; phyOp;–;–;–;–;
	md; cost) :-
	SearchSpace(expr; prop; index; logOp; phyOp;–;–;–;–),
	Fn_scansummary(expr; prop;md),
	Fn_scancost(expr; prop;md; cost);
R7:	PlanCost(expr; prop; index; logOp; phyOp;
	lExpr; lProp;–;–;md; cost) :-
	SearchSpace(expr; prop; index; logOp; phyOp;
	lExpr; lProp;–;–, Fn_isleaf(lExpr; false),
	PlanCost(lExpr; lProp;–;–;–;–;–;–;–; lMd; lCost),
	Fn_nonscansummary(expr; prop; index; logOp; lMd;–;md),
	Fn_nonscancost(expr; prop; index; logOp; phyOp;
	lExpr; lProp;–;–;md; localCost),
	Fn_sum(lCost; null ; localCost; cost);
R8:	PlanCost(expr; prop; index; logOp; phyOp;
	lExpr; lProp; rExpr; rProp;md; cost) :-
	SearchSpace(expr; prop; index; logOp; phyOp;
	lExpr; lProp; rExpr; rProp),
	Fn_isleaf(lExpr; false); Fn_isleaf (rExpr; false),
	PlanCost(lExpr; lProp;–;–;–;–;–;–;–; lMd; lCost),
	PlanCost(rExpr; rProp;–;–;–;–;–;–;–; rMd; rCost),
	Fn_nonscansummary(expr; prop; index; logOp; lMd; rMd;md),
	Fn_nonscancost(expr; prop; index; logOp; phyOp;
	lExpr; lProp; rExpr; rProp;md; localCost),
	Fn_sum(lCost; rCost; localCost; cost);
R9:	BestCost(expr; prop; min < cost >) :-
	PlanCost(expr; prop; index; logOp; phyOp;
	lExpr; lProp; rExpr; rProp;md; cost);
R10:	BestPlan(expr; prop; index; logOp; phyOp;
	lExpr; lProp; rExpr; rProp;md; cost) :-
	BestCost(expr; prop; cost),
	PlanCost(expr; prop; index; logOp; phyOp;
	lExpr; lProp; rExpr; rProp;md; cost);