Added command 'reconcile'.

5 files changed, 463 insertions, 205 deletions

diff --git a/src/aig/llb/llb4Cex.c b/src/aig/llb/llb4Cex.c
index e63b48f3..54b4d965 100644
--- a/src/aig/llb/llb4Cex.c
+++ b/src/aig/llb/llb4Cex.c
@@ -171,17 +171,122 @@ Abc_Cex_t * Llb4_Nonlin4TransformCex( Aig_Man_t * pAig, Vec_Ptr_t * vStates, int
         pCex->iPo = status;
     else
     {
-        printf( "Inter_ManGetCounterExample(): Counter-example verification has FAILED.\n" );
+        printf( "Llb4_Nonlin4TransformCex(): Counter-example verification has FAILED.\n" );
         ABC_FREE( pCex );
         return NULL;
     }
     // report the results
 //    if ( fVerbose )
-//        Abc_PrintTime( 1, "SAT-based cex generation time", clock() - clk );
+//       Abc_PrintTime( 1, "SAT-based cex generation time", clock() - clk );
     return pCex;
 }
 
 
+/**Function*************************************************************
+
+  Synopsis    [Resimulates the counter-example.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Vec_Ptr_t * Llb4_Nonlin4VerifyCex( Aig_Man_t * pAig, Abc_Cex_t * p )
+{
+    Vec_Ptr_t * vStates;
+    Aig_Obj_t * pObj, * pObjRi, * pObjRo;
+    int i, k, iBit = 0;
+    // create storage for states
+    vStates = Vec_PtrAllocSimInfo( p->iFrame+1, Aig_BitWordNum(Aig_ManRegNum(pAig)) );
+    Vec_PtrCleanSimInfo( vStates, 0, Aig_BitWordNum(Aig_ManRegNum(pAig)) );
+    // verify counter-example
+    Aig_ManCleanMarkB(pAig);
+    Aig_ManConst1(pAig)->fMarkB = 1;
+    Saig_ManForEachLo( pAig, pObj, i )
+        pObj->fMarkB = Aig_InfoHasBit(p->pData, iBit++);
+    for ( i = 0; i <= p->iFrame; i++ )
+    {
+        // save current state
+        Saig_ManForEachLo( pAig, pObj, k )
+            if ( pObj->fMarkB )
+                Aig_InfoSetBit( (unsigned *)Vec_PtrEntry(vStates, i), k );
+        // compute new state
+        Saig_ManForEachPi( pAig, pObj, k )
+            pObj->fMarkB = Aig_InfoHasBit(p->pData, iBit++);
+        Aig_ManForEachNode( pAig, pObj, k )
+            pObj->fMarkB = (Aig_ObjFanin0(pObj)->fMarkB ^ Aig_ObjFaninC0(pObj)) & 
+                           (Aig_ObjFanin1(pObj)->fMarkB ^ Aig_ObjFaninC1(pObj));
+        Aig_ManForEachPo( pAig, pObj, k )
+            pObj->fMarkB = Aig_ObjFanin0(pObj)->fMarkB ^ Aig_ObjFaninC0(pObj);
+        if ( i == p->iFrame )
+            break;
+        Saig_ManForEachLiLo( pAig, pObjRi, pObjRo, k )
+            pObjRo->fMarkB = pObjRi->fMarkB;
+    }
+/*
+    {
+        unsigned * pNext;
+        Vec_PtrForEachEntry( unsigned *, vStates, pNext, i )
+        {
+            printf( "%4d : ", i );
+            Extra_PrintBinary( stdout, pNext, Aig_ManRegNum(pAig) );
+            printf( "\n" );
+        }
+    }
+*/
+    assert( iBit == p->nBits );
+    if ( Aig_ManPo(pAig, p->iPo)->fMarkB == 0 )
+        Vec_PtrFreeP( &vStates );
+    Aig_ManCleanMarkB(pAig);
+    return vStates;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Translates a sequence of states into a counter-example.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Abc_Cex_t * Llb4_Nonlin4NormalizeCex( Aig_Man_t * pAigOrg, Aig_Man_t * pAigRpm, Abc_Cex_t * pCexRpm )
+{
+    Abc_Cex_t * pCexOrg;
+    Vec_Ptr_t * vStates;
+    // check parameters of the AIG
+    if ( Saig_ManRegNum(pAigOrg) != Saig_ManRegNum(pAigRpm) )
+    {
+        printf( "Llb4_Nonlin4NormalizeCex(): The number of flops in the original and reparametrized AIGs do not agree.\n" );
+        return NULL;
+    }
+    if ( Saig_ManRegNum(pAigRpm) != pCexRpm->nRegs )
+    {
+        printf( "Llb4_Nonlin4NormalizeCex(): The number of flops in the reparametrized AIG and in the CEX do not agree.\n" );
+        return NULL;
+    }
+    if ( Saig_ManPiNum(pAigRpm) != pCexRpm->nPis )
+    {
+        printf( "Llb4_Nonlin4NormalizeCex(): The number of PIs in the reparametrized AIG and in the CEX do not agree.\n" );
+        return NULL;
+    }
+    // get the sequence of states
+    vStates = Llb4_Nonlin4VerifyCex( pAigRpm, pCexRpm );
+    if ( vStates == NULL )
+    {
+        Abc_Print( 1, "Llb4_Nonlin4NormalizeCex(): The given CEX does not fail outputs of pAigRpm.\n" );
+        return NULL;
+    }
+    // derive updated counter-example
+    pCexOrg = Llb4_Nonlin4TransformCex( pAigOrg, vStates, 0 );
+    Vec_PtrFree( vStates );
+    return pCexOrg;
+}
+
 ////////////////////////////////////////////////////////////////////////
 ///                       END OF FILE                                ///
 ////////////////////////////////////////////////////////////////////////
diff --git a/src/aig/llb/llb4Cluster.c b/src/aig/llb/llb4Cluster.c
index adb03873..8d29eed4 100644
--- a/src/aig/llb/llb4Cluster.c
+++ b/src/aig/llb/llb4Cluster.c
@@ -27,8 +27,6 @@ ABC_NAMESPACE_IMPL_START
 ///                        DECLARATIONS                              ///
 ////////////////////////////////////////////////////////////////////////
 
-static inline int Llb_MnxBddVar( Vec_Int_t * vOrder, Aig_Obj_t * pObj ) { return Vec_IntEntry(vOrder, Aig_ObjId(pObj)); }
-
 ////////////////////////////////////////////////////////////////////////
 ///                     FUNCTION DEFINITIONS                         ///
 ////////////////////////////////////////////////////////////////////////
@@ -50,7 +48,7 @@ void Llb_Nonlin4FindOrder_rec( Aig_Man_t * pAig, Aig_Obj_t * pObj, Vec_Int_t * v
     if ( Aig_ObjIsTravIdCurrent(pAig, pObj) )
         return;
     Aig_ObjSetTravIdCurrent( pAig, pObj );
-    assert( Llb_MnxBddVar(vOrder, pObj) < 0 );
+    assert( Llb_ObjBddVar(vOrder, pObj) < 0 );
     if ( Aig_ObjIsPi(pObj) )
     {
         Vec_IntWriteEntry( vOrder, Aig_ObjId(pObj), (*pCounter)++ );
@@ -110,7 +108,7 @@ Vec_Int_t * Llb_Nonlin4FindOrder( Aig_Man_t * pAig, int * pCounter )
         Llb_Nonlin4FindOrder_rec( pAig, Aig_ObjFanin0(pObj), vOrder, &Counter );
     }
     Aig_ManForEachPi( pAig, pObj, i )
-        if ( Llb_MnxBddVar(vOrder, pObj) < 0 )
+        if ( Llb_ObjBddVar(vOrder, pObj) < 0 )
             Vec_IntWriteEntry( vOrder, Aig_ObjId(pObj), Counter++ );
     Aig_ManCleanMarkA( pAig );
     Vec_IntFreeP( &vNodes );
@@ -118,19 +116,19 @@ Vec_Int_t * Llb_Nonlin4FindOrder( Aig_Man_t * pAig, int * pCounter )
 
 /*
     Saig_ManForEachPi( pAig, pObj, i )
-        printf( "pi%d ", Llb_MnxBddVar(vOrder, pObj) );
+        printf( "pi%d ", Llb_ObjBddVar(vOrder, pObj) );
     printf( "\n" );
     Saig_ManForEachLo( pAig, pObj, i )
-        printf( "lo%d ", Llb_MnxBddVar(vOrder, pObj) );
+        printf( "lo%d ", Llb_ObjBddVar(vOrder, pObj) );
     printf( "\n" );
     Saig_ManForEachPo( pAig, pObj, i )
-        printf( "po%d ", Llb_MnxBddVar(vOrder, pObj) );
+        printf( "po%d ", Llb_ObjBddVar(vOrder, pObj) );
     printf( "\n" );
     Saig_ManForEachLi( pAig, pObj, i )
-        printf( "li%d ", Llb_MnxBddVar(vOrder, pObj) );
+        printf( "li%d ", Llb_ObjBddVar(vOrder, pObj) );
     printf( "\n" );
     Aig_ManForEachNode( pAig, pObj, i )
-        printf( "n%d ", Llb_MnxBddVar(vOrder, pObj) );
+        printf( "n%d ", Llb_ObjBddVar(vOrder, pObj) );
     printf( "\n" );
 */
     if ( pCounter )
@@ -149,77 +147,74 @@ Vec_Int_t * Llb_Nonlin4FindOrder( Aig_Man_t * pAig, int * pCounter )
   SeeAlso     []
 
 ***********************************************************************/
-Vec_Ptr_t * Llb_Nonlin4FindPartitions( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * vOrder )
+DdNode * Llb_Nonlin4FindPartitions_rec( DdManager * dd, Aig_Obj_t * pObj, Vec_Int_t * vOrder, Vec_Ptr_t * vRoots )
+{
+    DdNode * bBdd, * bBdd0, * bBdd1, * bPart, * vVar;
+    if ( Aig_ObjIsConst1(pObj) )
+        return Cudd_ReadOne(dd); 
+    if ( Aig_ObjIsPi(pObj) )
+        return Cudd_bddIthVar( dd, Llb_ObjBddVar(vOrder, pObj) );
+    if ( pObj->pData )
+        return (DdNode *)pObj->pData;
+    if ( Aig_ObjIsPo(pObj) )
+    {
+        bBdd0 = Cudd_NotCond( Llb_Nonlin4FindPartitions_rec(dd, Aig_ObjFanin0(pObj), vOrder, vRoots), Aig_ObjFaninC0(pObj) );
+        bPart = Cudd_bddXnor( dd, Cudd_bddIthVar( dd, Llb_ObjBddVar(vOrder, pObj) ), bBdd0 );  Cudd_Ref( bPart );
+        Vec_PtrPush( vRoots, bPart );
+        return NULL;
+    }
+    bBdd0 = Cudd_NotCond( Llb_Nonlin4FindPartitions_rec(dd, Aig_ObjFanin0(pObj), vOrder, vRoots), Aig_ObjFaninC0(pObj) );
+    bBdd1 = Cudd_NotCond( Llb_Nonlin4FindPartitions_rec(dd, Aig_ObjFanin1(pObj), vOrder, vRoots), Aig_ObjFaninC1(pObj) );
+    bBdd  = Cudd_bddAnd( dd, bBdd0, bBdd1 );   Cudd_Ref( bBdd );
+    if ( Llb_ObjBddVar(vOrder, pObj) >= 0 )
+    {
+        vVar  = Cudd_bddIthVar( dd, Llb_ObjBddVar(vOrder, pObj) );
+        bPart = Cudd_bddXnor( dd, vVar, bBdd );  Cudd_Ref( bPart );
+        Vec_PtrPush( vRoots, bPart );
+        Cudd_RecursiveDeref( dd, bBdd );
+        bBdd = vVar;  Cudd_Ref( vVar );
+    }
+    pObj->pData = bBdd;
+    return bBdd;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Derives BDDs for the partitions.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Vec_Ptr_t * Llb_Nonlin4FindPartitions( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * vOrder, int fOutputs )
 {
     Vec_Ptr_t * vRoots;
     Aig_Obj_t * pObj;
-    DdNode * bBdd, * bBdd0, * bBdd1, * bPart;
     int i;
     Aig_ManCleanData( pAig );
-    // assign elementary variables
-    Aig_ManConst1(pAig)->pData = Cudd_ReadOne(dd); 
-    Aig_ManForEachPi( pAig, pObj, i )
-        pObj->pData = Cudd_bddIthVar( dd, Llb_MnxBddVar(vOrder, pObj) );
-    Aig_ManForEachNode( pAig, pObj, i )
-        if ( Llb_MnxBddVar(vOrder, pObj) >= 0 )
-        {
-            pObj->pData = Cudd_bddIthVar( dd, Llb_MnxBddVar(vOrder, pObj) );
-            Cudd_Ref( (DdNode *)pObj->pData );
-        }
-//    Aig_ManForEachPo( pAig, pObj, i )
-    Saig_ManForEachLi( pAig, pObj, i )
-        pObj->pData = Cudd_bddIthVar( dd, Llb_MnxBddVar(vOrder, pObj) );
-    // compute intermediate BDDs
     vRoots = Vec_PtrAlloc( 100 );
-    Aig_ManForEachNode( pAig, pObj, i )
+    if ( fOutputs )
     {
-        bBdd0 = Cudd_NotCond( (DdNode *)Aig_ObjFanin0(pObj)->pData, Aig_ObjFaninC0(pObj) );
-        bBdd1 = Cudd_NotCond( (DdNode *)Aig_ObjFanin1(pObj)->pData, Aig_ObjFaninC1(pObj) );
-        bBdd  = Cudd_bddAnd( dd, bBdd0, bBdd1 );
-        Cudd_Ref( bBdd );
-        if ( pObj->pData == NULL )
-        {
-            pObj->pData = bBdd;
-            continue;
-        }
-        // create new partition
-        bPart = Cudd_bddXnor( dd, (DdNode *)pObj->pData, bBdd );  
-        if ( bPart == NULL )
-            goto finish;
-        Cudd_Ref( bPart );
-        Cudd_RecursiveDeref( dd, bBdd );
-        Vec_PtrPush( vRoots, bPart );
+        Saig_ManForEachPo( pAig, pObj, i )
+            Llb_Nonlin4FindPartitions_rec( dd, pObj, vOrder, vRoots );
     }
-    // compute register output BDDs
-//    Aig_ManForEachPo( pAig, pObj, i )
-    Saig_ManForEachLi( pAig, pObj, i )
+    else
     {
-        bBdd0 = Cudd_NotCond( (DdNode *)Aig_ObjFanin0(pObj)->pData, Aig_ObjFaninC0(pObj) );
-        bPart = Cudd_bddXnor( dd, (DdNode *)pObj->pData, bBdd0 );  
-        if ( bPart == NULL )
-            goto finish;
-        Cudd_Ref( bPart );
-        Vec_PtrPush( vRoots, bPart );
-//printf( "%d ", Cudd_DagSize(bPart) );
+        Saig_ManForEachLi( pAig, pObj, i )
+            Llb_Nonlin4FindPartitions_rec( dd, pObj, vOrder, vRoots );
     }
-//printf( "\n" );
-    Aig_ManForEachNode( pAig, pObj, i )
-        Cudd_RecursiveDeref( dd, (DdNode *)pObj->pData );
-    return vRoots;
-    // early termination
-finish:
     Aig_ManForEachNode( pAig, pObj, i )
         if ( pObj->pData )
             Cudd_RecursiveDeref( dd, (DdNode *)pObj->pData );
-    Vec_PtrForEachEntry( DdNode *, vRoots, bPart, i )
-        Cudd_RecursiveDeref( dd, bPart );
-    Vec_PtrFree( vRoots );
-    return NULL;
+    return vRoots;
 }
 
 /**Function*************************************************************
 
-  Synopsis    [Creates quantifiable varaibles for both types of traversal.]
+  Synopsis    [Creates quantifiable variables for both types of traversal.]
 
   Description []
                
@@ -236,16 +231,16 @@ Vec_Int_t * Llb_Nonlin4FindVars2Q( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t *
     vVars2Q = Vec_IntAlloc( 0 );
     Vec_IntFill( vVars2Q, Cudd_ReadSize(dd), 1 );
     Saig_ManForEachLo( pAig, pObj, i )
-        Vec_IntWriteEntry( vVars2Q, Llb_MnxBddVar(vOrder, pObj), 0 );
+        Vec_IntWriteEntry( vVars2Q, Llb_ObjBddVar(vOrder, pObj), 0 );
 //    Aig_ManForEachPo( pAig, pObj, i )
     Saig_ManForEachLi( pAig, pObj, i )
-        Vec_IntWriteEntry( vVars2Q, Llb_MnxBddVar(vOrder, pObj), 0 );
+        Vec_IntWriteEntry( vVars2Q, Llb_ObjBddVar(vOrder, pObj), 0 );
     return vVars2Q;
 }
 
 /**Function*************************************************************
 
-  Synopsis    [Creates quantifiable varaibles for both types of traversal.]
+  Synopsis    [Creates quantifiable variables for both types of traversal.]
 
   Description []
                
@@ -263,26 +258,26 @@ int Llb_Nonlin4CountTerms( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * vOrder,
     if ( !fCo && !fFlop )
     {
         Saig_ManForEachPi( pAig, pObj, i )
-            if ( Llb_MnxBddVar(vOrder, pObj) >= 0 )
-                Counter += Cudd_bddLeq( dd, bSupp, Cudd_bddIthVar(dd, Llb_MnxBddVar(vOrder, pObj)) );
+            if ( Llb_ObjBddVar(vOrder, pObj) >= 0 )
+                Counter += Cudd_bddLeq( dd, bSupp, Cudd_bddIthVar(dd, Llb_ObjBddVar(vOrder, pObj)) );
     }
     else if ( fCo && !fFlop )
     {
         Saig_ManForEachPo( pAig, pObj, i )
-            if ( Llb_MnxBddVar(vOrder, pObj) >= 0 )
-                Counter += Cudd_bddLeq( dd, bSupp, Cudd_bddIthVar(dd, Llb_MnxBddVar(vOrder, pObj)) );
+            if ( Llb_ObjBddVar(vOrder, pObj) >= 0 )
+                Counter += Cudd_bddLeq( dd, bSupp, Cudd_bddIthVar(dd, Llb_ObjBddVar(vOrder, pObj)) );
     }
     else if ( !fCo && fFlop )
     {
         Saig_ManForEachLo( pAig, pObj, i )
-            if ( Llb_MnxBddVar(vOrder, pObj) >= 0 )
-                Counter += Cudd_bddLeq( dd, bSupp, Cudd_bddIthVar(dd, Llb_MnxBddVar(vOrder, pObj)) );
+            if ( Llb_ObjBddVar(vOrder, pObj) >= 0 )
+                Counter += Cudd_bddLeq( dd, bSupp, Cudd_bddIthVar(dd, Llb_ObjBddVar(vOrder, pObj)) );
     }
     else if ( fCo && fFlop )
     {
         Saig_ManForEachLi( pAig, pObj, i )
-            if ( Llb_MnxBddVar(vOrder, pObj) >= 0 )
-                Counter += Cudd_bddLeq( dd, bSupp, Cudd_bddIthVar(dd, Llb_MnxBddVar(vOrder, pObj)) );
+            if ( Llb_ObjBddVar(vOrder, pObj) >= 0 )
+                Counter += Cudd_bddLeq( dd, bSupp, Cudd_bddIthVar(dd, Llb_ObjBddVar(vOrder, pObj)) );
     }
     Cudd_RecursiveDeref( dd, bSupp );
     return Counter;
@@ -290,7 +285,7 @@ int Llb_Nonlin4CountTerms( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * vOrder,
 
 /**Function*************************************************************
 
-  Synopsis    [Creates quantifiable varaibles for both types of traversal.]
+  Synopsis    [Creates quantifiable variables for both types of traversal.]
 
   Description []
                
@@ -328,7 +323,7 @@ void Llb_Nonlin4PrintGroups( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * vOrde
 
 /**Function*************************************************************
 
-  Synopsis    [Creates quantifiable varaibles for both types of traversal.]
+  Synopsis    [Creates quantifiable variables for both types of traversal.]
 
   Description []
                
@@ -348,10 +343,10 @@ void Llb_Nonlin4PrintSuppProfile( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t *
 
     Aig_ManForEachObj( pAig, pObj, i )
     {
-        if ( Llb_MnxBddVar(vOrder, pObj) < 0 )
+        if ( Llb_ObjBddVar(vOrder, pObj) < 0 )
             continue;
         // remove variables that do not participate
-        if ( pSupp[Llb_MnxBddVar(vOrder, pObj)] == 0 )
+        if ( pSupp[Llb_ObjBddVar(vOrder, pObj)] == 0 )
         {
             if ( Aig_ObjIsNode(pObj) )
                 Vec_IntWriteEntry( vOrder, Aig_ObjId(pObj), -1 );
@@ -371,7 +366,8 @@ void Llb_Nonlin4PrintSuppProfile( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t *
     }
     ABC_FREE( pSupp );
 
-    printf( "Variable counts: all =%4d ",  nSuppAll );
+    printf( "Groups =%3d  ", Vec_PtrSize(vGroups) );
+    printf( "Variables: all =%4d ",  nSuppAll );
     printf( "pi =%4d ",  nSuppPi );
     printf( "po =%4d ",  nSuppPo );
     printf( "lo =%4d ",  nSuppLo );
@@ -402,10 +398,10 @@ void Llb_Nonlin4Cluster( Aig_Man_t * pAig, DdManager ** pdd, Vec_Int_t ** pvOrde
     // create the BDD manager
     vOrder  = Llb_Nonlin4FindOrder( pAig, &nVarNum );
     dd      = Cudd_Init( nVarNum, 0, CUDD_UNIQUE_SLOTS, CUDD_CACHE_SLOTS, 0 );
-    Cudd_AutodynEnable( dd,  CUDD_REORDER_SYMM_SIFT );
+//    Cudd_AutodynEnable( dd,  CUDD_REORDER_SYMM_SIFT );
 
     vVars2Q = Llb_Nonlin4FindVars2Q( dd, pAig, vOrder );
-    vParts  = Llb_Nonlin4FindPartitions( dd, pAig, vOrder );
+    vParts  = Llb_Nonlin4FindPartitions( dd, pAig, vOrder, 0 );
 
     vGroups = Llb_Nonlin4Group( dd, vParts, vVars2Q, nBddMax );
     Vec_IntFree( vVars2Q );
diff --git a/src/aig/llb/llb4Nonlin.c b/src/aig/llb/llb4Nonlin.c
index 868745c4..5659f25a 100644
--- a/src/aig/llb/llb4Nonlin.c
+++ b/src/aig/llb/llb4Nonlin.c
@@ -54,8 +54,6 @@ struct Llb_Mnx_t_
     int             timeTotal;
 };
 
-static inline int Llb_MnxBddVar( Vec_Int_t * vOrder, Aig_Obj_t * pObj ) { return Vec_IntEntry(vOrder, Aig_ObjId(pObj)); }
-
 //extern int timeBuild, timeAndEx, timeOther;
 //extern int nSuppMax;
 
@@ -77,14 +75,14 @@ static inline int Llb_MnxBddVar( Vec_Int_t * vOrder, Aig_Obj_t * pObj ) { return
 DdNode * Llb_Nonlin4ComputeBad( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * vOrder )
 {
     Vec_Ptr_t * vNodes;
-    DdNode * bBdd, * bBdd0, * bBdd1, * bTemp, * bResult;
+    DdNode * bBdd, * bBdd0, * bBdd1, * bTemp, * bResult, * bCube;
     Aig_Obj_t * pObj;
     int i;
     Aig_ManCleanData( pAig );
     // assign elementary variables
     Aig_ManConst1(pAig)->pData = Cudd_ReadOne(dd); 
     Aig_ManForEachPi( pAig, pObj, i )
-        pObj->pData = Cudd_bddIthVar( dd, Llb_MnxBddVar(vOrder, pObj) );
+        pObj->pData = Cudd_bddIthVar( dd, Llb_ObjBddVar(vOrder, pObj) );
     // compute internal nodes
     vNodes = Aig_ManDfsNodes( pAig, (Aig_Obj_t **)Vec_PtrArray(pAig->vPos), Saig_ManPoNum(pAig) );
     Vec_PtrForEachEntry( Aig_Obj_t *, vNodes, pObj, i )
@@ -125,7 +123,18 @@ DdNode * Llb_Nonlin4ComputeBad( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * vO
             Cudd_RecursiveDeref( dd, (DdNode *)pObj->pData );
     Vec_PtrFree( vNodes );
     if ( bResult )
+    {
+        bCube = Cudd_ReadOne(dd);  Cudd_Ref( bCube );
+        Saig_ManForEachPi( pAig, pObj, i )
+        {
+            bCube = Cudd_bddAnd( dd, bTemp = bCube, (DdNode *)pObj->pData );  Cudd_Ref( bCube );
+            Cudd_RecursiveDeref( dd, bTemp );
+        }
+        bResult = Cudd_bddExistAbstract( dd, bTemp = bResult, bCube );  Cudd_Ref( bResult );
+        Cudd_RecursiveDeref( dd, bTemp );
+        Cudd_RecursiveDeref( dd, bCube );
         Cudd_Deref( bResult );
+    }
 //if ( bResult )
 //printf( "Bad state = %d.\n", Cudd_DagSize(bResult) );
     return bResult;
@@ -152,15 +161,15 @@ Vec_Ptr_t * Llb_Nonlin4DerivePartitions( DdManager * dd, Aig_Man_t * pAig, Vec_I
     // assign elementary variables
     Aig_ManConst1(pAig)->pData = Cudd_ReadOne(dd); 
     Aig_ManForEachPi( pAig, pObj, i )
-        pObj->pData = Cudd_bddIthVar( dd, Llb_MnxBddVar(vOrder, pObj) );
+        pObj->pData = Cudd_bddIthVar( dd, Llb_ObjBddVar(vOrder, pObj) );
     Aig_ManForEachNode( pAig, pObj, i )
-        if ( Llb_MnxBddVar(vOrder, pObj) >= 0 )
+        if ( Llb_ObjBddVar(vOrder, pObj) >= 0 )
         {
-            pObj->pData = Cudd_bddIthVar( dd, Llb_MnxBddVar(vOrder, pObj) );
+            pObj->pData = Cudd_bddIthVar( dd, Llb_ObjBddVar(vOrder, pObj) );
             Cudd_Ref( (DdNode *)pObj->pData );
         }
     Saig_ManForEachLi( pAig, pObj, i )
-        pObj->pData = Cudd_bddIthVar( dd, Llb_MnxBddVar(vOrder, pObj) );
+        pObj->pData = Cudd_bddIthVar( dd, Llb_ObjBddVar(vOrder, pObj) );
     // compute intermediate BDDs
     vRoots = Vec_PtrAlloc( 100 );
     Aig_ManForEachNode( pAig, pObj, i )
@@ -252,7 +261,7 @@ void Llb_Nonlin4CreateOrder_rec( Aig_Man_t * pAig, Aig_Obj_t * pObj, Vec_Int_t *
     if ( Aig_ObjIsTravIdCurrent(pAig, pObj) )
         return;
     Aig_ObjSetTravIdCurrent( pAig, pObj );
-    assert( Llb_MnxBddVar(vOrder, pObj) < 0 );
+    assert( Llb_ObjBddVar(vOrder, pObj) < 0 );
     if ( Aig_ObjIsPi(pObj) )
     {
 //        if ( Saig_ObjIsLo(pAig, pObj) )
@@ -345,7 +354,7 @@ printf( "Techmapping added %d pivots.\n", Vec_IntSize(vNodes) );
         Llb_Nonlin4CreateOrder_rec( pAig, Aig_ObjFanin0(pObj), vOrder, &Counter );
     }
     Aig_ManForEachPi( pAig, pObj, i )
-        if ( Llb_MnxBddVar(vOrder, pObj) < 0 )
+        if ( Llb_ObjBddVar(vOrder, pObj) < 0 )
         {
 //            if ( Saig_ObjIsLo(pAig, pObj) )
 //                Vec_IntWriteEntry( vOrder, Aig_ObjId(Saig_ObjLoToLi(pAig, pObj)), Counter++ );
@@ -369,24 +378,15 @@ printf( "Techmapping added %d pivots.\n", Vec_IntSize(vNodes) );
   SeeAlso     []
 
 ***********************************************************************/
-Vec_Int_t * Llb_Nonlin4CreateVars2Q( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * vOrder, int fForward )
+Vec_Int_t * Llb_Nonlin4CreateVars2Q( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * vOrder, int fBackward )
 {
     Vec_Int_t * vVars2Q;
-    Aig_Obj_t * pObj;
+    Aig_Obj_t * pObjLi, * pObjLo;
     int i;
     vVars2Q = Vec_IntAlloc( 0 );
     Vec_IntFill( vVars2Q, Cudd_ReadSize(dd), 1 );
-    if ( fForward )
-    {
-        Saig_ManForEachLi( pAig, pObj, i )
-            Vec_IntWriteEntry( vVars2Q, Llb_MnxBddVar(vOrder, pObj), 0 );
-    }
-    else
-    {
-        Aig_ManForEachPi( pAig, pObj, i )
-//        Saig_ManForEachLo( pAig, pObj, i )
-            Vec_IntWriteEntry( vVars2Q, Llb_MnxBddVar(vOrder, pObj), 0 );
-    }
+    Saig_ManForEachLiLo( pAig, pObjLi, pObjLo, i )
+        Vec_IntWriteEntry( vVars2Q, Llb_ObjBddVar(vOrder, fBackward ? pObjLo : pObjLi), 0 );
     return vVars2Q;
 }
 
@@ -410,10 +410,10 @@ void Llb_Nonlin4SetupVarMap( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * vOrde
     pVarsY = ABC_ALLOC( DdNode *, Cudd_ReadSize(dd) );
     Saig_ManForEachLiLo( pAig, pObjLo, pObjLi, i )
     {
-        assert( Llb_MnxBddVar(vOrder, pObjLo) >= 0 );
-        assert( Llb_MnxBddVar(vOrder, pObjLi) >= 0 );
-        pVarsX[i] = Cudd_bddIthVar( dd, Llb_MnxBddVar(vOrder, pObjLo) );
-        pVarsY[i] = Cudd_bddIthVar( dd, Llb_MnxBddVar(vOrder, pObjLi) );
+        assert( Llb_ObjBddVar(vOrder, pObjLo) >= 0 );
+        assert( Llb_ObjBddVar(vOrder, pObjLi) >= 0 );
+        pVarsX[i] = Cudd_bddIthVar( dd, Llb_ObjBddVar(vOrder, pObjLo) );
+        pVarsY[i] = Cudd_bddIthVar( dd, Llb_ObjBddVar(vOrder, pObjLi) );
     }
     Cudd_SetVarMap( dd, pVarsX, pVarsY, Aig_ManRegNum(pAig) );
     ABC_FREE( pVarsX );
@@ -431,16 +431,16 @@ void Llb_Nonlin4SetupVarMap( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * vOrde
   SeeAlso     []
 
 ***********************************************************************/
-DdNode * Llb_Nonlin4ComputeInitState( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * vOrder )
+DdNode * Llb_Nonlin4ComputeInitState( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * vOrder, int fBackward )
 {
-    Aig_Obj_t * pObj;
+    Aig_Obj_t * pObjLi, * pObjLo;
     DdNode * bRes, * bVar, * bTemp;
     int i, TimeStop;
     TimeStop = dd->TimeStop;  dd->TimeStop = 0;
     bRes = Cudd_ReadOne( dd );   Cudd_Ref( bRes );
-    Saig_ManForEachLo( pAig, pObj, i )
+    Saig_ManForEachLiLo( pAig, pObjLi, pObjLo, i )
     {
-        bVar = Cudd_bddIthVar( dd, Llb_MnxBddVar(vOrder, pObj) );
+        bVar = Cudd_bddIthVar( dd, Llb_ObjBddVar(vOrder, fBackward? pObjLi : pObjLo) );
         bRes = Cudd_bddAnd( dd, bTemp = bRes, Cudd_Not(bVar) );  Cudd_Ref( bRes );
         Cudd_RecursiveDeref( dd, bTemp );
     }
@@ -460,19 +460,20 @@ DdNode * Llb_Nonlin4ComputeInitState( DdManager * dd, Aig_Man_t * pAig, Vec_Int_
   SeeAlso     []
 
 ***********************************************************************/
-DdNode * Llb_Nonlin4ComputeCube( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * vOrder, char * pValues )
+DdNode * Llb_Nonlin4ComputeCube( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * vOrder, char * pValues, int Flag )
 {
-    Aig_Obj_t * pObj, * pObjLi;
+    Aig_Obj_t * pObjLo, * pObjLi, * pObjTemp;
     DdNode * bRes, * bVar, * bTemp;
     int i, TimeStop;
     TimeStop = dd->TimeStop;  dd->TimeStop = 0;
     bRes = Cudd_ReadOne( dd );   Cudd_Ref( bRes );
-    Saig_ManForEachLo( pAig, pObj, i )
+    Saig_ManForEachLiLo( pAig, pObjLi, pObjLo, i )
     {
+        if ( Flag )
+            pObjTemp = pObjLo, pObjLo = pObjLi, pObjLi = pObjTemp;
         // get the correspoding flop input variable
-        pObjLi = Saig_ObjLoToLi(pAig, pObj);
-        bVar = Cudd_bddIthVar( dd, Llb_MnxBddVar(vOrder, pObjLi) );
-        if ( pValues[Llb_MnxBddVar(vOrder, pObj)] != 1 )
+        bVar = Cudd_bddIthVar( dd, Llb_ObjBddVar(vOrder, pObjLi) );
+        if ( pValues[Llb_ObjBddVar(vOrder, pObjLo)] != 1 )
             bVar = Cudd_Not(bVar);
         // create cube
         bRes = Cudd_bddAnd( dd, bTemp = bRes, bVar );  Cudd_Ref( bRes );
@@ -483,6 +484,70 @@ DdNode * Llb_Nonlin4ComputeCube( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * v
     return bRes;
 }
 
+/**Function*************************************************************
+
+  Synopsis    [Compute initial state in terms of current state variables.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Llb_Nonlin4RecordState( Aig_Man_t * pAig, Vec_Int_t * vOrder, unsigned * pState, char * pValues, int fBackward )
+{
+    Aig_Obj_t * pObjLo, * pObjLi;
+    int i;
+    Saig_ManForEachLiLo( pAig, pObjLi, pObjLo, i )
+        if ( pValues[Llb_ObjBddVar(vOrder, fBackward? pObjLi : pObjLo)] == 1 )
+            Aig_InfoSetBit( pState, i );
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Multiply every partition by the cube.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+Vec_Ptr_t * Llb_Nonlin4Multiply( DdManager * dd, DdNode * bCube, Vec_Ptr_t * vParts )
+{
+    Vec_Ptr_t * vNew;
+    DdNode * bTemp, * bFunc;
+    int i;
+    vNew = Vec_PtrAlloc( Vec_PtrSize(vParts) );
+    Vec_PtrForEachEntry( DdNode *, vParts, bFunc, i )
+    {
+        bTemp = Cudd_bddAnd( dd, bFunc, bCube );  Cudd_Ref( bTemp );
+        Vec_PtrPush( vNew, bTemp );
+    }
+    return vNew;
+}
+
+/**Function*************************************************************
+
+  Synopsis    [Multiply every partition by the cube.]
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
+void Llb_Nonlin4Deref( DdManager * dd, Vec_Ptr_t * vParts )
+{
+    DdNode * bFunc;
+    int i;
+    Vec_PtrForEachEntry( DdNode *, vParts, bFunc, i )
+        Cudd_RecursiveDeref( dd, bFunc );
+    Vec_PtrFree( vParts );
+}
 
 /**Function*************************************************************
 
@@ -495,17 +560,24 @@ DdNode * Llb_Nonlin4ComputeCube( DdManager * dd, Aig_Man_t * pAig, Vec_Int_t * v
   SeeAlso     []
 
 ***********************************************************************/
-Abc_Cex_t * Llb_Nonlin4DeriveCex( Llb_Mnx_t * p, int fBackward, Vec_Ptr_t * vStates, int fVerbose )
+Vec_Ptr_t * Llb_Nonlin4DeriveCex( Llb_Mnx_t * p, int fBackward, int fVerbose )
 {
-    Abc_Cex_t * pCex = NULL;
+    Vec_Int_t * vVars2Q;
+    Vec_Ptr_t * vStates, * vRootsNew;
     Aig_Obj_t * pObj;
     DdNode * bState, * bImage, * bOneCube, * bRing;
-    int i, v, RetValue, nPiOffset = -1, clk = clock();
+    int i, v, RetValue, clk = clock();
     char * pValues;
     assert( Vec_PtrSize(p->vRings) > 0 );
     // disable the timeout
     p->dd->TimeStop  = 0;
 
+    // start the state set
+    vStates = Vec_PtrAllocSimInfo( Vec_PtrSize(p->vRings), Aig_BitWordNum(Aig_ManRegNum(p->pAig)) );
+    Vec_PtrCleanSimInfo( vStates, 0, Aig_BitWordNum(Aig_ManRegNum(p->pAig)) );
+    if ( fBackward )
+        Vec_PtrReverseOrder( vStates );
+
     // get the last cube
     pValues = ABC_ALLOC( char, Cudd_ReadSize(p->dd) );
     bOneCube = Cudd_bddIntersect( p->dd, (DdNode *)Vec_PtrEntryLast(p->vRings), p->bBad );  Cudd_Ref( bOneCube );
@@ -514,45 +586,28 @@ Abc_Cex_t * Llb_Nonlin4DeriveCex( Llb_Mnx_t * p, int fBackward, Vec_Ptr_t * vSta
     assert( RetValue );
 
     // record the cube
-    if ( vStates == NULL )
-    {
-        // allocate room for the counter-example
-        pCex = Abc_CexAlloc( Saig_ManRegNum(p->pAig), Saig_ManPiNum(p->pAig), Vec_PtrSize(p->vRings) );
-        pCex->iFrame = Vec_PtrSize(p->vRings) - 1;
-        pCex->iPo = -1;
-        // write PIs of the counter-example
-        nPiOffset = Saig_ManRegNum(p->pAig) + Saig_ManPiNum(p->pAig) * (Vec_PtrSize(p->vRings) - 1);
-        Saig_ManForEachPi( p->pAig, pObj, i )
-            if ( pValues[Llb_MnxBddVar(p->vOrder, pObj)] == 1 )
-                Aig_InfoSetBit( pCex->pData, nPiOffset + i );
-    }
-    else
-    {
-        Saig_ManForEachLo( p->pAig, pObj, i )
-            if ( pValues[Llb_MnxBddVar(p->vOrder, pObj)] == 1 )
-                Aig_InfoSetBit( (unsigned *)Vec_PtrEntryLast(vStates), i );
-    }
-
-    // update quantifiable vars
-    Vec_IntFreeP( &p->vVars2Q );
-    p->vVars2Q = Llb_Nonlin4CreateVars2Q( p->dd, p->pAig, p->vOrder, 0 );
+    Llb_Nonlin4RecordState( p->pAig, p->vOrder, (unsigned *)Vec_PtrEntryLast(vStates), pValues, fBackward );
 
     // write state in terms of NS variables
     if ( Vec_PtrSize(p->vRings) > 1 )
     {
-        bState = Llb_Nonlin4ComputeCube( p->dd, p->pAig, p->vOrder, pValues );   Cudd_Ref( bState );
+        bState = Llb_Nonlin4ComputeCube( p->dd, p->pAig, p->vOrder, pValues, fBackward );   Cudd_Ref( bState );
     }
     // perform backward analysis
+    vVars2Q = Llb_Nonlin4CreateVars2Q( p->dd, p->pAig, p->vOrder, !fBackward );
     Vec_PtrForEachEntryReverse( DdNode *, p->vRings, bRing, v )
     { 
         if ( v == Vec_PtrSize(p->vRings) - 1 )
             continue;
-        // compute the next states
-        bImage = Llb_Nonlin4Image( p->dd, p->vRoots, bState, p->vVars2Q );
-        assert( bImage != NULL );
-        Cudd_Ref( bImage );
+
+        // preprocess partitions
+        vRootsNew = Llb_Nonlin4Multiply( p->dd, bState, p->vRoots );
         Cudd_RecursiveDeref( p->dd, bState );
 
+        // compute the next states
+        bImage = Llb_Nonlin4Image( p->dd, vRootsNew, NULL, vVars2Q ); Cudd_Ref( bImage );
+        Llb_Nonlin4Deref( p->dd, vRootsNew );
+
         // intersect with the previous set
         bOneCube = Cudd_bddIntersect( p->dd, bImage, bRing );  Cudd_Ref( bOneCube );
         Cudd_RecursiveDeref( p->dd, bImage );
@@ -563,46 +618,26 @@ Abc_Cex_t * Llb_Nonlin4DeriveCex( Llb_Mnx_t * p, int fBackward, Vec_Ptr_t * vSta
         assert( RetValue );
 
         // record the cube
-        if ( vStates == NULL )
-        {
-            // write PIs of counter-example
-            nPiOffset -= Saig_ManPiNum(p->pAig);
-            Saig_ManForEachPi( p->pAig, pObj, i )
-                if ( pValues[Llb_MnxBddVar(p->vOrder, pObj)] == 1 )
-                    Aig_InfoSetBit( pCex->pData, nPiOffset + i );
-        }
-        else
-        {
-            Saig_ManForEachLo( p->pAig, pObj, i )
-                if ( pValues[Llb_MnxBddVar(p->vOrder, pObj)] == 1 )
-                    Aig_InfoSetBit( (unsigned *)Vec_PtrEntry(vStates, v), i );
-        }
+        Llb_Nonlin4RecordState( p->pAig, p->vOrder, (unsigned *)Vec_PtrEntry(vStates, v), pValues, fBackward );
 
         // check that we get the init state
         if ( v == 0 )
         {
             Saig_ManForEachLo( p->pAig, pObj, i )
-                assert( pValues[Llb_MnxBddVar(p->vOrder, pObj)] == 0 );
+                assert( fBackward || pValues[Llb_ObjBddVar(p->vOrder, pObj)] == 0 );
             break;
         } 
 
         // write state in terms of NS variables
-        bState = Llb_Nonlin4ComputeCube( p->dd, p->pAig, p->vOrder, pValues );   Cudd_Ref( bState );
-    }
-    assert( vStates != NULL || nPiOffset == Saig_ManRegNum(p->pAig) );
-    // update the output number
-    if ( pCex )
-    {
-    //Abc_CexPrint( pCex );
-        RetValue = Saig_ManFindFailedPoCex( p->pAig, pCex );
-        assert( RetValue >= 0 && RetValue < Saig_ManPoNum(p->pAig) ); // invalid CEX!!!
-        pCex->iPo = RetValue;
+        bState = Llb_Nonlin4ComputeCube( p->dd, p->pAig, p->vOrder, pValues, fBackward );   Cudd_Ref( bState );
     }
-    // cleanup
+    Vec_IntFree( vVars2Q );
     ABC_FREE( pValues );
+    if ( fBackward )
+        Vec_PtrReverseOrder( vStates );
 //    if ( fVerbose )
 //        Abc_PrintTime( 1, "BDD-based cex generation time", clock() - clk );
-    return pCex;
+    return vStates;
 }
 
 
@@ -632,23 +667,56 @@ int Llb_Nonlin4Reachability( Llb_Mnx_t * p )
     // set the stop time parameter
     p->dd->TimeStop  = p->pPars->TimeTarget;
 
-    // create bad state in the ring manager
-    if ( !p->pPars->fSkipOutCheck )
+    if ( p->pPars->fBackward )
     {
-        p->bBad = Llb_Nonlin4ComputeBad( p->dd, p->pAig, p->vOrder );          
-        if ( p->bBad == NULL )
+        // create bad state in the ring manager
+        if ( !p->pPars->fSkipOutCheck )
+        {
+            p->bBad = Llb_Nonlin4ComputeInitState( p->dd, p->pAig, p->vOrder, p->pPars->fBackward );  Cudd_Ref( p->bBad );
+        }
+        // create init state
+        p->bCurrent = Llb_Nonlin4ComputeBad( p->dd, p->pAig, p->vOrder );          
+        if ( p->bCurrent == NULL )
         {
             if ( !p->pPars->fSilent )
                 printf( "Reached timeout (%d seconds) during constructing the bad states.\n", p->pPars->TimeLimit );
             p->pPars->iFrame = -1;
             return -1;
         }
-        Cudd_Ref( p->bBad );
+        Cudd_Ref( p->bCurrent );
+        // remap into the next states
+        p->bCurrent = Cudd_bddVarMap( p->dd, bAux = p->bCurrent );
+        if ( p->bCurrent == NULL )
+        {
+            if ( !p->pPars->fSilent )
+                printf( "Reached timeout (%d seconds) during remapping bad states.\n",  p->pPars->TimeLimit );
+            Cudd_RecursiveDeref( p->dd, bAux );
+            p->pPars->iFrame = -1;
+            return -1;
+        }
+        Cudd_Ref( p->bCurrent );
+        Cudd_RecursiveDeref( p->dd, bAux );
+    }
+    else
+    {
+        // create bad state in the ring manager
+        if ( !p->pPars->fSkipOutCheck )
+        {
+            p->bBad = Llb_Nonlin4ComputeBad( p->dd, p->pAig, p->vOrder );          
+            if ( p->bBad == NULL )
+            {
+                if ( !p->pPars->fSilent )
+                    printf( "Reached timeout (%d seconds) during constructing the bad states.\n", p->pPars->TimeLimit );
+                p->pPars->iFrame = -1;
+                return -1;
+            }
+            Cudd_Ref( p->bBad );
+        }
+        // compute the starting set of states
+        p->bCurrent = Llb_Nonlin4ComputeInitState( p->dd, p->pAig, p->vOrder, p->pPars->fBackward );  Cudd_Ref( p->bCurrent );
     }
-
-    // compute the starting set of states
-    p->bCurrent = Llb_Nonlin4ComputeInitState( p->dd, p->pAig, p->vOrder );  Cudd_Ref( p->bCurrent );
-    p->bReached = p->bCurrent;                                               Cudd_Ref( p->bCurrent );
+    // perform iterations
+    p->bReached = p->bCurrent; Cudd_Ref( p->bReached );
     for ( nIters = 0; nIters < p->pPars->nIterMax; nIters++ )
     { 
         clkIter = clock();
@@ -667,24 +735,14 @@ int Llb_Nonlin4Reachability( Llb_Mnx_t * p )
         // check it for bad states
         if ( !p->pPars->fSkipOutCheck && !Cudd_bddLeq( p->dd, p->bCurrent, Cudd_Not(p->bBad) ) ) 
         {
+            Vec_Ptr_t * vStates;
             assert( p->pAig->pSeqModel == NULL );
-            if ( p->pPars->fCluster )
-            {
-                Vec_Ptr_t * vStates = Vec_PtrAllocSimInfo( Vec_PtrSize(p->vRings), Aig_BitWordNum(Aig_ManRegNum(p->pAig)) );
-                Vec_PtrCleanSimInfo( vStates, 0, Aig_BitWordNum(Aig_ManRegNum(p->pAig)) );
-                p->pAig->pSeqModel = Llb_Nonlin4DeriveCex( p, p->pPars->fBackward, vStates, p->pPars->fVerbose ); 
-                ABC_FREE( p->pAig->pSeqModel );
-                p->pAig->pSeqModel = Llb4_Nonlin4TransformCex( p->pAig, vStates, p->pPars->fVerbose );
-                Vec_PtrFreeP( &vStates );
-            }
-            else
-                p->pAig->pSeqModel = Llb_Nonlin4DeriveCex( p, p->pPars->fBackward, NULL, p->pPars->fVerbose ); 
-            if ( !p->pPars->fSilent && p->pAig->pSeqModel )
+            vStates = Llb_Nonlin4DeriveCex( p, p->pPars->fBackward, p->pPars->fVerbose ); 
+            p->pAig->pSeqModel = Llb4_Nonlin4TransformCex( p->pAig, vStates, p->pPars->fVerbose );
+            Vec_PtrFreeP( &vStates );
+            if ( !p->pPars->fSilent )
             {
-                if ( !p->pPars->fBackward )
-                    printf( "Output %d was asserted in frame %d (use \"write_counter\" to dump a witness).  ", p->pAig->pSeqModel->iPo, nIters );
-                else
-                    printf( "Output ??? was asserted in frame %d (counter-example is not produced).  ", nIters );
+                printf( "Output %d was asserted in frame %d (use \"write_counter\" to dump a witness).  ", p->pAig->pSeqModel->iPo, nIters );
                 Abc_PrintTime( 1, "Time", clock() - clk );
             }
             p->pPars->iFrame = nIters - 1;
@@ -880,7 +938,7 @@ Llb_Mnx_t * Llb_MnxStart( Aig_Man_t * pAig, Gia_ParLlb_t * pPars )
     }
 
     Llb_Nonlin4SetupVarMap( p->dd, pAig, p->vOrder );
-    p->vVars2Q = Llb_Nonlin4CreateVars2Q( p->dd, pAig, p->vOrder, 1 );
+    p->vVars2Q = Llb_Nonlin4CreateVars2Q( p->dd, pAig, p->vOrder, p->pPars->fBackward );
     p->vRings  = Vec_PtrAlloc( 100 );
 
     if ( pPars->fReorder )
diff --git a/src/aig/llb/llbInt.h b/src/aig/llb/llbInt.h
index 9e930ca3..23eb455e 100644
--- a/src/aig/llb/llbInt.h
+++ b/src/aig/llb/llbInt.h
@@ -107,6 +107,8 @@ struct Llb_Grp_t_
 ///                      MACRO DEFINITIONS                           ///
 ////////////////////////////////////////////////////////////////////////
 
+static inline int Llb_ObjBddVar( Vec_Int_t * vOrder, Aig_Obj_t * pObj ) { return Vec_IntEntry(vOrder, Aig_ObjId(pObj)); }
+
 ////////////////////////////////////////////////////////////////////////
 ///                    FUNCTION DECLARATIONS                         ///
 ////////////////////////////////////////////////////////////////////////
diff --git a/src/base/abci/abc.c b/src/base/abci/abc.c
index 4a741a1b..60d66ca8 100644
--- a/src/base/abci/abc.c
+++ b/src/base/abci/abc.c
@@ -276,6 +276,7 @@ static int Abc_CommandFold                   ( Abc_Frame_t * pAbc, int argc, cha
 static int Abc_CommandBm                     ( Abc_Frame_t * pAbc, int argc, char ** argv );
 static int Abc_CommandTestCex                ( Abc_Frame_t * pAbc, int argc, char ** argv );
 static int Abc_CommandPdr                    ( Abc_Frame_t * pAbc, int argc, char ** argv );
+static int Abc_CommandReconcile              ( Abc_Frame_t * pAbc, int argc, char ** argv );
 
 static int Abc_CommandTraceStart             ( Abc_Frame_t * pAbc, int argc, char ** argv );
 static int Abc_CommandTraceCheck             ( Abc_Frame_t * pAbc, int argc, char ** argv );
@@ -693,6 +694,7 @@ void Abc_Init( Abc_Frame_t * pAbc )
     Cmd_CommandAdd( pAbc, "Verification", "bm",            Abc_CommandBm,               1 );
     Cmd_CommandAdd( pAbc, "Verification", "testcex",       Abc_CommandTestCex,          0 );
     Cmd_CommandAdd( pAbc, "Verification", "pdr",           Abc_CommandPdr,              0 );
+    Cmd_CommandAdd( pAbc, "Verification", "reconcile",     Abc_CommandReconcile,        1 );
 
 
     Cmd_CommandAdd( pAbc, "ABC8",         "*r",            Abc_CommandAbc8Read,         0 );
@@ -8527,13 +8529,16 @@ int Abc_CommandTest( Abc_Frame_t * pAbc, int argc, char ** argv )
     {
 //        extern void Llb_Nonlin4Cluster( Aig_Man_t * pAig );
 //        extern void Aig_ManTerSimulate( Aig_Man_t * pAig );
+        extern void Llb4_Nonlin4Sweep( Aig_Man_t * pAig, int nBddLimit );
         extern Aig_Man_t * Abc_NtkToDar( Abc_Ntk_t * pNtk, int fExors, int fRegisters );
         Aig_Man_t * pAig = Abc_NtkToDar( pNtk, 0, 0 );
 //        Aig_ManTerSimulate( pAig );
 //        Llb_Nonlin4Cluster( pAig );
+        Llb4_Nonlin4Sweep( pAig, 100 );
         Aig_ManStop( pAig );
     }
 */
+
 /*
 {
     extern void Ssm_ManExperiment( char * pFileIn, char * pFileOut );
@@ -20009,6 +20014,94 @@ usage:
   SeeAlso     []
 
 ***********************************************************************/
+int Abc_CommandReconcile( Abc_Frame_t * pAbc, int argc, char ** argv )
+{    
+    extern Aig_Man_t * Abc_NtkToDar( Abc_Ntk_t * pNtk, int fExors, int fRegisters );
+    extern Abc_Cex_t * Llb4_Nonlin4NormalizeCex( Aig_Man_t * pAigOrg, Aig_Man_t * pAigRpm, Abc_Cex_t * pCexRpm );
+    Abc_Cex_t * pCex;
+    Abc_Ntk_t * pNtk1, * pNtk2;
+    Aig_Man_t * pAig1, * pAig2;
+    int c;
+    Extra_UtilGetoptReset();
+    while ( ( c = Extra_UtilGetopt( argc, argv, "h" ) ) != EOF )
+    {
+        switch ( c )
+        {
+        case 'h':
+            goto usage;
+        default:
+            Abc_Print( -2, "Unknown switch.\n");
+            goto usage;
+        }
+    }
+    if ( argc != globalUtilOptind + 2 ) 
+    {
+        printf( "Does not seen to have two files names as arguments.\n" );
+        return 1;
+    }
+    if ( pAbc->pCex == NULL )
+    {
+        printf( "There is no current counter-example.\n" );
+        return 1;
+    }
+
+    // derive networks
+    pNtk1 = Io_Read( argv[globalUtilOptind], Io_ReadFileType(argv[globalUtilOptind]), 1 );
+    if ( pNtk1 == NULL )
+        return 1;
+    pNtk2 = Io_Read( argv[globalUtilOptind+1], Io_ReadFileType(argv[globalUtilOptind+1]), 1 );
+    if ( pNtk2 == NULL )
+    {
+        Abc_NtkDelete( pNtk1 );
+        return 1;
+    }
+    // create counter-examples
+    pAig1 = Abc_NtkToDar( pNtk1, 0, 0 );
+    pAig2 = Abc_NtkToDar( pNtk2, 0, 0 );
+    pCex = Llb4_Nonlin4NormalizeCex( pAig1, pAig2, pAbc->pCex );
+    Aig_ManStop( pAig1 );
+    Aig_ManStop( pAig2 );
+    Abc_NtkDelete( pNtk2 );
+    if ( pCex == NULL )
+    {
+        printf( "Counter-example computation has failed.\n" );
+        Abc_NtkDelete( pNtk1 );
+        return 1;
+    }
+
+    // replace the current network
+    Abc_FrameReplaceCurrentNetwork( pAbc, pNtk1 );
+    // update the counter-example
+    pAbc->nFrames = pCex->iFrame;
+    Abc_FrameReplaceCex( pAbc, &pCex );
+    return 0;
+
+usage:
+    Abc_Print( -2, "usage: reconcile [-h] <fileOrigin> <fileReparam>\n" );
+    Abc_Print( -2, "\t        reconciles current CEX with <fileOrigin>\n" );
+    Abc_Print( -2, "\t        More specifically:\n" );
+    Abc_Print( -2, "\t        (i) assumes that <fileReparam> is an AIG derived by input\n" );
+    Abc_Print( -2, "\t        reparametrization of <fileOrigin> without seq synthesis;\n" );
+    Abc_Print( -2, "\t        (ii) assumes that current CEX is valid for <fileReparam>;\n" );
+    Abc_Print( -2, "\t        (iii) derives new CEX for <fileOrigin> and sets this CEX\n" );
+    Abc_Print( -2, "\t        and <fileOrigin> to be current CEX and current network\n" );
+    Abc_Print( -2, "\t<fileOrigin>   : file name with the original AIG\n");
+    Abc_Print( -2, "\t<fileReparam>  : file name with the reparametrized AIG\n");
+    Abc_Print( -2, "\t-h    : print the command usage\n");
+    return 1;
+}
+
+/**Function*************************************************************
+
+  Synopsis    []
+
+  Description []
+               
+  SideEffects []
+
+  SeeAlso     []
+
+***********************************************************************/
 int Abc_CommandTraceStart( Abc_Frame_t * pAbc, int argc, char ** argv )
 {
     Abc_Ntk_t * pNtk = Abc_FrameReadNtk(pAbc);
@@ -27995,7 +28088,7 @@ int Abc_CommandAbc9ReachY( Abc_Frame_t * pAbc, int argc, char ** argv )
     pPars->fReorder = 0;
     pPars->nBddMax  = 1000;
     Extra_UtilGetoptReset();
-    while ( ( c = Extra_UtilGetopt( argc, argv, "BFTLcryzvwh" ) ) != EOF )
+    while ( ( c = Extra_UtilGetopt( argc, argv, "BFTLbcryzvwh" ) ) != EOF )
     {
         switch ( c )
         {
@@ -28041,6 +28134,9 @@ int Abc_CommandAbc9ReachY( Abc_Frame_t * pAbc, int argc, char ** argv )
             pLogFileName = argv[globalUtilOptind];
             globalUtilOptind++;
             break;
+        case 'b':
+            pPars->fBackward ^= 1;
+            break;
         case 'c':
             pPars->fCluster ^= 1;
             break;
@@ -28090,12 +28186,13 @@ int Abc_CommandAbc9ReachY( Abc_Frame_t * pAbc, int argc, char ** argv )
     return 0;
 
 usage:
-    Abc_Print( -2, "usage: &reachy [-BFT num] [-L file] [-cryzvh]\n" );
+    Abc_Print( -2, "usage: &reachy [-BFT num] [-L file] [-bcryzvh]\n" );
     Abc_Print( -2, "\t         model checking via BDD-based reachability (non-linear-QS-based)\n" );
     Abc_Print( -2, "\t-B num : the BDD node threshold for clustering [default = %d]\n", pPars->nBddMax );
     Abc_Print( -2, "\t-F num : max number of reachability iterations [default = %d]\n", pPars->nIterMax );
     Abc_Print( -2, "\t-T num : approximate time limit in seconds (0=infinite) [default = %d]\n", pPars->TimeLimit );
     Abc_Print( -2, "\t-L file: the log file name [default = %s]\n", pLogFileName ? pLogFileName : "no logging" );
+    Abc_Print( -2, "\t-b     : enable using backward enumeration [default = %s]\n", pPars->fBackward? "yes": "no" );  
     Abc_Print( -2, "\t-c     : enable reparametrization clustering [default = %s]\n", pPars->fCluster? "yes": "no" );  
     Abc_Print( -2, "\t-r     : enable additional BDD var reordering before image [default = %s]\n", pPars->fReorder? "yes": "no" );  
     Abc_Print( -2, "\t-y     : skip checking property outputs [default = %s]\n", pPars->fSkipOutCheck? "yes": "no" );