
/* 
 * Kodkod -- Copyright (c) 2005-2011, Emina Torlak
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 * THE SOFTWARE.
 */

package kodkod.engine.bool;

import static kodkod.engine.bool.BooleanConstant.FALSE;
import static kodkod.engine.bool.BooleanConstant.TRUE;
import static kodkod.engine.bool.Operator.AND;
import static kodkod.engine.bool.Operator.CONST;
import static kodkod.engine.bool.Operator.ITE;
import static kodkod.engine.bool.Operator.NOT;
import static kodkod.engine.bool.Operator.OR;
import static kodkod.engine.bool.Operator.VAR;

import java.util.Iterator;
import java.util.Set;

import kodkod.ast.operator.ExprOperator;
import kodkod.engine.bool.Operator.Nary;
import kodkod.util.collections.CacheSet;
import kodkod.util.collections.IdentityHashSet;


/**
 * A factory for creating variables, multigates, and if-then-else gates.
 * @specfield values: set (BooleanVariable + MultiGate + ITEGate)
 * @specfield cmpMax: int // the maximum number of comparisons made when comparing circuits for equality
 * @invariant no disj factory, factory' : CircuitFactory | some factory.values & factory'.values
 * @author Emina Torlak
 */
final class CBCFactory {
	
	/**
	 * Sets used as `scrap paper' for gate comparisons.  Its capacity is 2^(depth), where
	 * depth is the depth to which gates should be checked for equality.
	 */
	private final Set<BooleanFormula> scrap0, scrap1;
	/**
	 * Stores input variables.
	 * @invariant all i: [1..iLits.size()] | vars[i-1].positive.label = i
	 */
	private final BooleanVariable[] vars;
	/**
	 * Caches the AND, OR, and ITE gates.  
	 * @invariant all i: [0..2] | c[i].op.ordinal = i
	 */
	private final CacheSet<BooleanFormula>[] cache;
	private int label, cmpMax;
	

	
	/**
	 * Constructs a CircuitFactory using the given max comparison parameter, initialized
	 * to contain the given number of variables. 
	 * @requires cmpMax > 0 && numVars >= 0
	 * @ensures #this.values' = numVars && this.values in BooleanVariable
	 * @ensures this.cmpMax' = cmpMax
	 */
	@SuppressWarnings("unchecked") CBCFactory(int numVars, int cmpMax) {
		assert cmpMax > 0 && numVars >= 0;
		this.cmpMax = cmpMax;
		this.label = numVars + 1;
		vars = new BooleanVariable[numVars];
		for(int i = 0; i < numVars; i++) {
			vars[i]= new BooleanVariable(i+1);                                                                        
		}
		scrap0 = new IdentityHashSet<BooleanFormula>(cmpMax);
		scrap1 = new IdentityHashSet<BooleanFormula>(cmpMax);
		cache = new CacheSet[]{new CacheSet<BooleanFormula>(), new CacheSet<BooleanFormula>(), new CacheSet<BooleanFormula>()};
	}
	
	/**
	 * Returns the cache for gates with the given operator.
	 * @requires op in AND + OR + ITE
	 * @return cache[op.ordinal]
	 */
	private CacheSet<BooleanFormula> opCache(Operator op) {
		return cache[op.ordinal];
	}
	
	/**
	 * Sets this.cmpMax to the given value.
	 * @requires cmpMax > 0
	 * @ensures this.cmpMax' = cmpMax
	 */
	void setCmpMax(int cmpMax) {
		assert cmpMax > 0;
		this.cmpMax = cmpMax;
	}
	
	/**
	 * Returns this.cmpMax.
	 * @return this.cmpMax
	 */
	int cmpMax() { return cmpMax; }
	
	/**
	 * Removes all MultiGates and ITEGates from this.factory.
	 * @ensures this.values' = this.values & BooleanVariable 
	 */
	void clear() {
		label = vars.length+1;
		cache[0].clear();
		cache[1].clear();
		cache[2].clear();
		scrap0.clear(); 
		scrap1.clear();
	}
	
	/**
	 * Returns true if the given value
	 * is a valid argument to one of the <tt>assemble</tt>
	 * methods.  Otherwise returns false.
	 * @return v in this.values + this.values.negation + BooleanConstant
	 */
	boolean canAssemble(BooleanValue v) {
		if (v.op()==CONST) return true;
		if (v.label() < 0) v = v.negation();
		final int absLit = v.label();
		if (absLit <= vars.length) {
			return v == vars[absLit-1];
		} else {
			final BooleanFormula g = (BooleanFormula) v;
			for(Iterator<BooleanFormula> gates = opCache(g.op()).get(g.hashCode()); gates.hasNext(); ) {
			    	if (gates.next()==g) return true;
		    }
			return false;
		}
	}
	
	/**
	 * Returns the number of variables in this factory.
	 * @return #(this.values & BooleanVariable)
	 */
	int numVars() { return vars.length; }
	
	/**
	 * Returns the boolean variable from this.values with the given label.
	 * @requires 0 < label <= #(this.values & BooleanVariable)
	 * @return (this.values & BooleanVariable).label 
	 */
	BooleanVariable variable(int label) {
		return vars[label-1];
	}
	
	/**
	 * Returns a boolean value whose meaning is (if [[i]] then [[t]] else [[e]]).
	 * @requires i + t + e in (this.values + this.values.negation + BooleanConstant)
	 * @return v: BooleanValue | [[v]] = if [[i]] then [[t]] else [[e]] 
	 * @ensures v in BooleanFormula - NotGate => this.values' = this.values + v, this.values' = this.values
	 * @throws NullPointerException  any of the arguments are null
	 */
	BooleanValue assemble(BooleanValue i, BooleanValue t, BooleanValue e) {
		if (i==TRUE || t==e) return t;
		else if (i==FALSE) return e;
		else if (t==TRUE || i==t) return assemble(OR, i, e);
		else if (t==FALSE || i.label()==-t.label()) return assemble(AND, i.negation(), e);
		else if (e==TRUE || i.label()==-e.label()) return assemble(OR, i.negation(), t);
		else if (e==FALSE || i==e) return assemble(AND, i, t);
		else {
			final BooleanFormula f0 = (BooleanFormula) i, f1 = (BooleanFormula) t, f2 = (BooleanFormula) e;
			final int hash = ITE.hash(f0, f1, f2);
			
			for(Iterator<BooleanFormula> gates = opCache(ITE).get(hash); gates.hasNext();) {
				BooleanFormula gate = gates.next();
				if (gate.input(0)==i && gate.input(1)==t && gate.input(2)==e)
					return gate;
			}
			final BooleanFormula ret = new ITEGate(label++, hash, f0, f1, f2);
			opCache(ITE).add(ret);
			return ret;
		}
	}
		
	/**
	 * Returns a boolean value whose meaning is ([[v0]] op [[v1]]).
	 * @requires v0 + v1 in (this.values + this.values.negation + BooleanConstant)
	 * @return  v: BooleanValue | [[v]] = [[v0]] op [[v1]] 
	 * @ensures v in BooleanFormula - NotGate => this.values' = this.values + v, this.values' = this.values
	 * @throws NullPointerException  any of the arguments are null
	 */
	BooleanValue assemble(Operator.Nary op, BooleanValue v0, BooleanValue v1) {
		final BooleanValue l, h;
		if (v0.op().ordinal < v1.op().ordinal) {
			l = v0; h = v1;
		} else {
			l = v1; h = v0;
		}
		if (h.op()==CONST) 
			return h==op.identity() ? l : h;
		else 
			return assembler(l.op(), h.op()).assemble(op, (BooleanFormula)l, (BooleanFormula)h);
		}
	
	/**
	 * Returns a boolean value with the same meaning as the given accumulator.
	 * @requires acc.components in (this.values + this.values.negation + BooleanConstant)
	 * @return v: BooleanValue | [[v]] = [[acc]] 
	 * @ensures v in BooleanFormula - NotGate => this.values' = this.values + v, this.values' = this.values
	 * @throws NullPointerException  any of the arguments are null
	 */
	@SuppressWarnings({ "unchecked", "rawtypes" }) 
	BooleanValue assemble(BooleanAccumulator acc) {
		final int asize = acc.size();
		final Operator.Nary op = acc.op;
		switch(asize) {
		case 0 : return op.identity();
		case 1 : return acc.iterator().next();
		case 2 : 
			final Iterator<BooleanValue> inputs = acc.iterator();
			return assemble(op, inputs.next(), inputs.next());
		default :
			final int hash = op.hash((Iterator)acc.iterator());
			if (asize > cmpMax) {
				for(Iterator<BooleanFormula> gates = opCache(op).get(hash); gates.hasNext(); ) {
					BooleanFormula g = gates.next();
					if (g.size()==asize && ((NaryGate) g).sameInputs(acc.iterator())) { 
						return g;
					} 
				}
			} else {
				LOOKUP: for(Iterator<BooleanFormula> gates = opCache(op).get(hash); gates.hasNext(); ) {
					BooleanFormula g = gates.next();
					if (g.size()==asize && ((NaryGate) g).sameInputs(acc.iterator())) { 
						return g;
					} else if (g.size() < asize) {
						scrap0.clear();
						g.flatten(op, scrap0, cmpMax);
						if (scrap0.size()==asize) {
							for(BooleanValue v : acc) {
								if (!scrap0.contains(v))
									continue LOOKUP;
							}
							return g;
						}
					}
				}
			}
			final BooleanFormula ret = new NaryGate(acc, label++, hash);	
			opCache(acc.op).add(ret);
			return ret;
		}
	}
	
	/**
	 * Given two operators, op0 and op1, returns an Assembler
	 * which contains the creator method for expressions of the form v0 op v1 where 
	 * op in ExprOperator.Nary and v0.op = op0 and v1.op = op1.
	 * @requires op0 <= op1 && no (op0 + op1) & CONST
	 * @requires op0 != null && op1 != null
	 * @return a Assembler which contains the creator method for expressions of the form v0 op v1 where 
	 * op in ExprOperator.Nary and v0.op = op0 and v1.op = op1.
	 */
	private Assembler assembler(Operator op0, Operator op1) { 
		return ASSEMBLERS[(op0.ordinal << 2) + op1.ordinal - ( (op0.ordinal*(op0.ordinal-1) >> 1 ))];
	}
	
	/**
	 * Returns a BooleanFormula f such that [[f]] = f0 op f1.  The method
	 * requires that the formulas f0 and f1 be already reduced with respect to op.
	 * A new formula is created and cached iff the circuit with the meaning
	 * [[f0]] op [[f1]] has not already been created.
	 * @requires f0 and f1 have already been reduced with respect to op; i.e.  
	 * f0 op f1 cannot be reduced to a constant or a simple circuit 
	 * by applying absorption, idempotence, etc. laws to f0 and f1.
	 * @return f : BooleanFormula | [[f]] = [[f0]] op [[f1]]
	 * @ensures f !in this.values => this.values' = this.values + f,
	 * 	        this.values' = this.values
	 */
	private BooleanFormula cache(Operator.Nary op, BooleanFormula f0, BooleanFormula f1) {
		final BooleanFormula l, h;
		if (f0.label()<f1.label()) {
			l = f0; h = f1;
		} else {
			l = f1; h = f0;
		}
		final int hash = op.hash(l,h);
		if (l.op()==op || h.op()==op) {
			scrap0.clear();
			l.flatten(op, scrap0, cmpMax-1);
			h.flatten(op, scrap0, cmpMax-scrap0.size());
			for(Iterator<BooleanFormula> gates = opCache(op).get(hash); gates.hasNext(); ) {
				BooleanFormula gate = gates.next();
				if (gate.size()==2 && gate.input(0)==l && gate.input(1)==h)
					return gate;
				else {
					scrap1.clear();
					gate.flatten(op, scrap1, cmpMax);
					if (scrap0.equals(scrap1))
						return gate;
				}
			}
		} else {
			for(Iterator<BooleanFormula> gates = opCache(op).get(hash); gates.hasNext(); ) {
				BooleanFormula gate = gates.next();
				if (gate.size()==2 && gate.input(0)==l && gate.input(1)==h)
					return gate;
			}
		}
		final BooleanFormula ret = new BinaryGate(op, label++, hash, l, h);
		opCache(op).add(ret);
		return ret;
	}

	/**
	 * Wrapper for a method that generates boolean values
	 * out of existing gates, using AND and OR operators.
	 * @author Emina Torlak
	 */
	private static abstract class Assembler {
		
		/**
		 * Returns a BooleanValue whose meaning is [[f0]] op [[f1]].  A
		 * new circuit is created and cached iff [[f0]] op [[f1]] cannot be reduced
		 * to a simpler value and a circuit with equivalent meaning has not already been created.
		 * @requires f0.op <= f1.op && f0 + f1 in CircuitFactory.this.values + CircuitFactory.this.values.negation
		 * @return { v: BooleanValue | [[v]] = [[f0]] op [[f1]] }
		 * @ensures (no v: CircuitFactory.this.values | [[v]] = [[f0]] op [[f1]]) => 
		 *          CircuitFactory.this.values' = CircuitFactory.this.values + {v: BooleanValue | [[v]] = [[f0]] op [[f1]]} => 
		 *          CircuitFactory.this.values' = CircuitFactory.this.values 
		 */
		abstract BooleanValue assemble(Operator.Nary op, BooleanFormula f0, BooleanFormula f1);	
	}
	
	/**
	 * Performs common simplifications on circuits of the form AND op X or OR op X, 
	 * where X can be any operator other than CONST (J stands for 'junction').
	 */
	private  final Assembler JoX = new Assembler() {
		/**
		 * Performs the following reductions, if possible.  Note that 
		 * these reductions will be possible only if f0 was created after f1 (i.e.  |f0.label| > |f1.label|).
		 * (a & b) & a = a & b	(a & b) & !a = F	  (a & b) | a = a
		 * (a | b) | a = a | b	(a | b) | !a = T	  (a | b) & a = a
		 * @requires f0.op in (AND + OR)
		 */
		BooleanValue assemble(Nary op, BooleanFormula f0, BooleanFormula f1) {
			assert f0.op().ordinal < 2;
			final int label = f1.label();
			if (f0.contains(f0.op(), label, cmpMax) > 0) 
				return op==f0.op() ? f0 : f1;
			else if (op==f0.op() && f0.contains(op, -label, cmpMax)>0) 
				return op.shortCircuit();
			else 
				return cache(op, f0, f1);
		}
	};
	
	/**
	 * Performs common simplifications on circuits of the form AND op OR.
	 */
	private  final Assembler AoO = new Assembler() {
		/**
		 * Performs the following reductions, if possible, along with JoX reductions.
		 * (aj & ... & ak) & (a1 | ... | an) = (aj & ... & ak) where 1 <= j <= k <= n  
		 * (a1 & ... & an) | (aj | ... | ak) = (aj | ... | ak) where 1 <= j <= k <= n
		 * @requires f0.op = AND && f1.op = OR
		 */
		BooleanValue assemble(Nary op, BooleanFormula f0, BooleanFormula f1) {
			assert f0.op() == AND && f1.op() == OR;
			scrap0.clear(); 
			scrap1.clear();
			f0.flatten(f0.op(), scrap0, cmpMax);
			f1.flatten(f1.op(), scrap1, cmpMax);
			for(BooleanFormula formula : scrap1) {
				if (scrap0.contains(formula)) 
					return op==AND ? f0 : f1;
			}
			return (f0.label() < f1.label()) ? JoX.assemble(op, f1, f0) : JoX.assemble(op, f0, f1);
		}
	};
	
	/**
	 * Performs common simplifications on circuits of the form AND op AND or OR op OR.
	 */
	private  final Assembler JoJ = new Assembler() {
		/**
		 * Performs the following reductions, if possible, along with the JoX reductions.
		 * (a1 & ... & an) & (aj & ... & ak) = (a1 & ... & an) where 1 <= j <= k <= n
		 * (a1 & ... & an) | (aj & ... & ak) = (aj & ... & ak) where 1 <= j <= k <= n
		 * (a1 | ... | an) | (aj | ... | ak) = (a1 | ... | an) where 1 <= j <= k <= n
		 * (a1 | ... | an) & (aj | ... | ak) = (aj | ... | ak) where 1 <= j <= k <= n
		 * @requires f0.op = f1.op && (f0+f1).op in (AND + OR)
		 */
		BooleanValue assemble(Nary op, BooleanFormula f0, BooleanFormula f1) {
			assert f0.op() == f1.op();
			if (f0==f1) return f0;
			final Operator fop = f0.op();
			scrap0.clear(); 
			scrap1.clear();
			f0.flatten(fop, scrap0, cmpMax);
			f1.flatten(fop, scrap1, cmpMax);
			if (scrap0.size() < scrap1.size() && scrap1.containsAll(scrap0))
				return op==fop ? f1 : f0;
			else if (scrap0.size() >= scrap1.size() && scrap0.containsAll(scrap1))
				return op==fop ? f0 : f1;
			else if (f0.label()<f1.label()) 
				return JoX.assemble(op, f1, f0); 
			else
				return JoX.assemble(op, f0, f1) ;
		}		
	};
	
	/**
	 * Performs common simplifications on circuits of the form AND op ITE or OR op ITE.
	 */
	private  final Assembler JoI = new Assembler() {
		/**
		 * Combines JoX and IoX reductions.
		 * @requires f0.op in (AND + OR) && f1.op = ITE
		 */
		BooleanValue assemble(Nary op, BooleanFormula f0, BooleanFormula f1) {
			assert f0.op().ordinal < 2 && f1.op() == ITE;
			if (f0.label() < f1.label()) // f0 created before f1
				return cache(op, f1, f0); 
			else
				return JoX.assemble(op, f0, f1);
		}
	};
	
	/**
	 * Performs common simplifications on circuits of the form AND op NOT or OR op NOT.
	 */
	private  final Assembler JoN = new Assembler() {
		/**
		 * Performs the following reductions, if possible, along with the JoX/NoX reductions.
		 * a & !a = F	a | !a = T
		 * @requires f0.op in (AND + OR) && f1.op = NOT
		 */
		BooleanValue assemble(Nary op, BooleanFormula f0, BooleanFormula f1) {
			assert f0.op().ordinal < 2 && f1.op() == NOT;
			if (f0.label()==-f1.label()) return op.shortCircuit();
			else if (f0.label() < StrictMath.abs(f1.label()))  // f0 created before f1
				return NoX.assemble(op, f1, f0);
			else 
				return JoX.assemble(op, f0, f1);
		}
	};
	
	/**
	 * Performs common simplifications on circuits of the form ITE op VAR.
	 */
	private  final Assembler IoV = new Assembler() {
		/**
		 * Returns cache(op, f0, f1)
		 * @requires f0.op = ITE && f1.op = VAR
		 */
		BooleanValue assemble(Nary op, BooleanFormula f0, BooleanFormula f1) {
			assert f0.op() == ITE && f1.op() == VAR;
			return cache(op, f0, f1);
		}
	};
	
	
	/**
	 * Performs common simplifications on circuits of the form ITE op NOT.
	 */
	private  final Assembler IoN =new Assembler() {
		/**
		 * Performs the following reductions, if possible, along with IoX/NoX reductions.
		 * (a ? b : c) & !(a ? b : c) = F		
		 * (a ? b : c) | !(a ? b : c) = T
		 * @requires f0.op = ITE && f1.op = NOT
		 */
		BooleanValue assemble(Nary op, BooleanFormula f0, BooleanFormula f1) {
			assert f0.op() == ITE && f1.op() == NOT;
			if (f0.label()==-f1.label()) return op.shortCircuit();
			else if (f0.label() < StrictMath.abs(f1.label()))  // f0 created before f1
				return NoX.assemble(op, f1, f0);
			else 
				return cache(op, f0, f1);
		}
	};
	
	/**
	 * Performs common simplifications on circuits of the form NOT op X, where X can be any operator other than CONST.
	 */
	private  final Assembler NoX = new Assembler() {
		/**
		 * Performs the following reductions, if possible.  Note that 
		 * these reductions will be possible only if f0 was created after f1 (i.e.  |f0.label| > |f1.label|).
		 * !(a | b) & a = F	!(a | b) & !a = !(a | b)
		 * !(a & b) | a = T	!(a & b) | !a = !(a & b)
		 * @requires f0.op = NOT
		 */
		BooleanValue assemble(Nary op, BooleanFormula f0, BooleanFormula f1) {
			assert f0.op() == NOT ;
			final int label = f1.label();
			if (f0.input(0).contains(op.complement(), label, cmpMax)>0) return op.shortCircuit();
			else if (f0.input(0).contains(op.complement(), -label, cmpMax)>0) return f0;
			else return cache(op, f0, f1);
		}
	};
	
	/**
	 * Performs common simplifications on circuits of the form NOT op NOT.
	 */
	private  final Assembler NoN = new Assembler() {
		/**
		 * Performs the following reductions, if possible, along with NoX reductions.
		 * !a & !a = !a		!a | !a = !a
		 * @requires f1.op + f0.op = NOT
		 */
		BooleanValue assemble(Nary op, BooleanFormula f0, BooleanFormula f1) {
			assert f0.op() == NOT && f1.op() == NOT;
			if (f0==f1) return f0;
			else if (f0.label() < f1.label()) // f0 created after f1
				return NoX.assemble(op, f0, f1);
			else 
				return NoX.assemble(op, f1, f0);
		}
	};
	
	/**
	 * Performs common simplifications on circuits of the form NOT op VAR.
	 */
	private  final Assembler NoV = new Assembler() {
		/**
		 * Performs the following reductions, if possible, along with NoX reductions.
		 * !a & a = F		!a | a = T
		 * @requires f1.op = NOT && f1.op = VAR
		 */
		BooleanValue assemble(Nary op, BooleanFormula f0, BooleanFormula f1) {
			assert f0.op() == NOT && f1.op() == VAR;
			if (f0.label()==-f1.label()) return op.shortCircuit();
			else return NoX.assemble(op, f0, f1);
		}
	};
 
	
	/**
	 * Performs common simplifications on circuits of the form X op X.
	 */
	private final Assembler XoX = new Assembler() {
		/**
		 * Performs the following reductions, if possible.
		 * a & a = a	a | a = a
		 * @requires f0.op = f1.op
		 */
		@Override
		BooleanValue assemble(Nary op, BooleanFormula f0, BooleanFormula f1) {
			assert f0.op()==f1.op();
			return (f0==f1) ? f0 : cache(op, f0, f1); 
		}
	};

	
	/**
	 * 15 Assembler entires representing all possible composition combinations of 
	 * non-constant vertices using the operators AND and OR.  Note that there
	 * are 15 of them rather than 25 because of the v0.op <= v1.op requirement
	 * of the {@link Assembler#assemble(ExprOperator.Nary, BooleanFormula, BooleanFormula)} method.
	 */
	private final Assembler[] ASSEMBLERS = {
		JoJ,		/* AND op AND */
		AoO,		/* AND op OR */
		JoI,		/* AND op ITE */
		JoN,		/* AND op NOT */
		JoX,		/* AND op VAR */
		JoJ,		/* OR op OR */
		JoI,		/* OR op ITE */
		JoN,		/* OR op NOT */
		JoX,		/* OR op VAR */
		XoX,		/* ITE op ITE */
		IoN, 		/* ITE op NOT */
		IoV,		/* ITE op VAR */
		NoN,		/* NOT op NOT */
		NoV,		/* NOT op VAR */
		XoX			/* VAR op VAR */
	};
	
//	/**
//	 * Returns true if for all inputs i1 in f1 there is a corresponding input i0 in 
//	 * f0 such that  i0.label = i1.label 
//	 * @requires #f0.inputs <= f1.inputs
//	 */
//	private static boolean containsAll(BooleanFormula f0, BooleanFormula f1) { 
//		final int s0 = f0.size(), s1 = f1.size();
//		for(int i = 0, j = 0; i<s0 && j<s1;) { 
//			final int l0 = f0.input(i).label(), l1 = f1.input(j).label();
//			if (l0 < l1) { 
//				i++;
//			} else if (l0 == l1) { 
//				i++; j++;
//			} else {
//				return false;
//			}
//		}
//		return true;
//	}
//	
//	/**
//	 * Returns true if for all inputs i1 in f1 there is a corresponding input i0 in 
//	 * f0 such that  i0.label = -i1.label 
//	 * @requires #f0.inputs <= f1.inputs
//	 */
//	private static boolean containsAllNeg(BooleanFormula f0, BooleanFormula f1) { 
//		final int s0 = f0.size(), s1 = f1.size();
//		for(int i = 0, j = s1-1; i<s0 && j>=0;) { 
//			final int l0 = f0.input(i).label(), l1 = -f1.input(j).label();
//			if (l0 < l1) { 
//				i++;
//			} else if (l0 == l1) { 
//				i++; j--;
//			} else {
//				return false;
//			}
//		}
//		return true;
//	}
//
//	/**
//	 * Returns true if there are inputs i0 in f0 and i1 in f1 such that  i0.label = i1.label 
//	 * @requires #f0.inputs <= f1.inputs
//	 */
//	private static boolean containsSome(BooleanFormula f0, BooleanFormula f1) { 
//		final int s0 = f0.size(), s1 = f1.size();
//		for(int i = 0, j = 0; i<s0 && j<s1;) { 
//			final int l0 = f0.input(i).label(), l1 = f1.input(j).label();
//			if (l0 < l1) { 
//				i++;
//			} else if (l0 == l1) { 
//				return true;
//			} else {
//				j++;
//			}
//		}
//		return false;
//	}
//	
//	/**
//	 * Returns true if there are inputs i0 in f0 and i1 in f1 such that  i0.label = -i1.label 
//	 * @requires #f0.inputs <= f1.inputs
//	 */
//	private static boolean containsSomeNeg(BooleanFormula f0, BooleanFormula f1) { 
//		final int s0 = f0.size(), s1 = f1.size();
//		for(int i = 0, j = s1-1; i<s0 && j>=0;) { 
//			final int l0 = f0.input(i).label(), l1 = -f1.input(j).label();
//			if (l0 < l1) { 
//				i++;
//			} else if (l0 == l1) { 
//				return true;
//			} else {
//				j--;
//			}
//		}
//		return false;
//	}
}