diff --git a/src/math/lp/cross_nested.h b/src/math/lp/cross_nested.h
index e82de1683..c5694955c 100644
--- a/src/math/lp/cross_nested.h
+++ b/src/math/lp/cross_nested.h
@@ -60,8 +60,7 @@ public:
         SASSERT(m_nex_creator.is_simplified(e));
         m_e = e;
 #ifdef Z3DEBUG
-        //        m_e_clone = clone(m_e);
-        //        m_e_clone = normalize(m_e_clone);
+        m_e_clone = m_nex_creator.clone(m_e);
 #endif
         vector<nex**> front;
         explore_expr_on_front_elem(&m_e, front);
@@ -255,13 +254,9 @@ public:
             if(front.empty()) {
                 TRACE("nla_cn", tout << "got the cn form: =" << *m_e << "\n";);
                 m_done = m_call_on_result(m_e) || ++m_reported > 100;
-// #ifdef Z3DEBUG
-//                 nex *ce = clone(m_e);
-//                 TRACE("nla_cn", tout << "ce = " << *ce <<  "\n";);
-//                 nex *n = normalize(ce);
-//                 TRACE("nla_cn", tout << "n = " << *n << "\nm_e_clone=" << * m_e_clone << "\n";);
-//                 SASSERT(*n == *m_e_clone);
-// #endif
+ #ifdef Z3DEBUG
+                SASSERT(nex_creator::equal(m_e, m_e_clone));
+ #endif
             } else {
                 nex** f = pop_front(front);
                 explore_expr_on_front_elem(f, front);     
diff --git a/src/math/lp/nex.h b/src/math/lp/nex.h
index 397242a62..f7979e6a8 100644
--- a/src/math/lp/nex.h
+++ b/src/math/lp/nex.h
@@ -410,6 +410,7 @@ inline std::unordered_set<lpvar> get_vars_of_expr(const nex *e ) {
                     for ( lpvar j : get_vars_of_expr(c))
                         r.insert(j);
             }
+            return r;
         case expr_type::MUL:
             {
                 for (auto &c: *to_mul(e))
diff --git a/src/math/lp/nex_creator.cpp b/src/math/lp/nex_creator.cpp
index 1570cbde9..5e1fefe8f 100644
--- a/src/math/lp/nex_creator.cpp
+++ b/src/math/lp/nex_creator.cpp
@@ -65,6 +65,8 @@ bool nex_creator::eat_scalar_pow(nex_scalar *& r, nex_pow& p, unsigned pow) {
     if (!p.e()->is_scalar())
         return false;
     nex_scalar *pe = to_scalar(p.e());
+    if (pe->value().is_one())
+        return true; // but do not change r here
     if (r == nullptr) {
         r = pe;
         r->value() = r->value().expt(p.pow()*pow);                
@@ -207,9 +209,7 @@ bool nex_creator::less_than_on_var_nex(const nex_var* a, const nex* b) const {
             
     case expr_type::SUM:
         {
-            nex_sum m;
-            m.add_child(const_cast<nex_var*>(a));
-            return lt(&m, to_sum(b));
+            return !lt((*to_sum(b))[0], a);
         }
     default:
         UNREACHABLE();
@@ -243,7 +243,20 @@ bool nex_creator::less_than_on_mul_nex(const nex_mul* a, const nex* b) const {
     }    
 }
 
+bool nex_creator::less_than_on_sum_sum(const nex_sum* a, const nex_sum* b) const {
+    unsigned size = std::min(a->size(), b->size());
+    for (unsigned j = 0; j < size; j++) {
+        if (lt((*a)[j], (*b)[j]))
+            return true;
+        if (lt((*b)[j], (*a)[j]))
+            return false;
+    }
+    return size < b->size();
+            
+}
+
 bool nex_creator::lt(const nex* a, const nex* b) const {
+    TRACE("nla_cn_details", tout << *a << " ^ " << *b << "\n";);
     bool ret;
     switch (a->type()) {
     case expr_type::VAR: 
@@ -261,8 +274,9 @@ bool nex_creator::lt(const nex* a, const nex* b) const {
         break;
     }
     case expr_type::SUM: {
-        UNREACHABLE();
-        return false;
+        if (b->is_sum())
+            return less_than_on_sum_sum(to_sum(a), to_sum(b));
+        return lt((*to_sum(a))[0], b);
     }
     default:
         UNREACHABLE();
@@ -479,9 +493,7 @@ void nex_creator::sort_join_sum(ptr_vector<nex> & children) {
                                        { return lt(a, b); });
     std::unordered_set<nex*> existing_nex; // handling (nex*) as numbers
     nex_scalar * common_scalar;
-    bool simplified = fill_join_map_for_sum(children, map, existing_nex, common_scalar);
-    if (!simplified)
-        return;
+    fill_join_map_for_sum(children, map, existing_nex, common_scalar);
 
     TRACE("nla_cn_details", for (auto & p : map ) { tout << "(" << *p.first << ", " << p.second << ") ";});
     children.clear();
@@ -676,4 +688,78 @@ bool nex_creator::is_simplified(const nex *e) const
         return sum_is_simplified(to_sum(e));
     return true;
 }
+
+#ifdef Z3DEBUG
+unsigned nex_creator::find_sum_in_mul(const nex_mul* a) const {
+    for (unsigned j = 0; j < a->size(); j++)
+        if ((*a)[j].e()->is_sum())
+            return j;
+
+    return -1;
+}
+nex* nex_creator::canonize_mul(nex_mul *a) {    
+    unsigned j = find_sum_in_mul(a);
+    if (j + 1 == 0)
+        return a;
+    nex_pow& np = (*a)[j];
+    SASSERT(np.pow());
+    unsigned power = np.pow();
+    nex_sum * s = to_sum(np.e()); // s is going to explode        
+    nex_sum * r = mk_sum();
+    nex *sclone = power > 1? clone(s) : nullptr;
+    for (nex *e : *s) {
+        nex_mul *m = mk_mul();
+        if (power > 1)
+            m->add_child_in_power(sclone, power - 1);
+        m->add_child(e);
+        for (unsigned k = 0; k < a->size(); k++) {
+            if (k == j)
+                continue;
+            m->add_child_in_power(clone((*a)[k].e()), (*a)[k].pow());
+        }
+        r->add_child(m);
+    }
+    TRACE("nla_cn_details", tout << *r << "\n";);
+    return canonize(r);
+}
+
+
+nex* nex_creator::canonize(const nex *a) {
+    if (a->is_elementary())
+        return clone(a);
+    
+    nex *t = simplify(clone(a));
+    if (t->is_sum()) {
+        nex_sum * s = to_sum(t);
+        for (unsigned j = 0; j < s->size(); j++) {
+            (*s)[j] = canonize((*s)[j]);
+        }
+        t = simplify(s);
+        TRACE("nla_cn_details", tout << *t << "\n";);
+        return t;
+    }
+    return canonize_mul(to_mul(t));
+}
+
+bool nex_creator::equal(const nex* a, const nex* b) {
+    nex_creator cn;
+    unsigned n = 0;
+    for (lpvar j : get_vars_of_expr(a)) {
+        n = std::max(j + 1, n);
+    }
+    for (lpvar j : get_vars_of_expr(b)) {
+        n = std::max(j + 1, n);
+    }
+    cn.set_number_of_vars(n);
+    for (lpvar j = 0; j < n; j++) {
+        cn.set_var_weight(j, j);
+    }
+    nex * ca = cn.canonize(a);
+    nex * cb = cn.canonize(b);
+    TRACE("nla_cn_test", tout << "a = " << *a << ", canonized a = " << *ca << "\n";);
+    TRACE("nla_cn_test", tout << "b = " << *b << ", canonized b = " << *cb << "\n";);
+    return !(cn.lt(ca, cb) || cn.lt(cb, ca));
+}
+#endif
+
 }
diff --git a/src/math/lp/nex_creator.h b/src/math/lp/nex_creator.h
index 6fbf5e073..598bf5b26 100644
--- a/src/math/lp/nex_creator.h
+++ b/src/math/lp/nex_creator.h
@@ -54,7 +54,7 @@ class nex_creator {
     ptr_vector<nex>                              m_allocated;
     std::unordered_map<lpvar, occ>               m_occurences_map;
     std::unordered_map<lpvar, unsigned>          m_powers;
-    svector<var_weight>                          m_active_vars_weights;
+    svector<unsigned>                            m_active_vars_weights;
 
 public:
     static char ch(unsigned j) {
@@ -64,9 +64,23 @@ public:
         return (char)('a'+j);
     }
 
-    svector<var_weight>& active_vars_weights() { return m_active_vars_weights;}
-    const svector<var_weight>& active_vars_weights() const { return m_active_vars_weights;}
+    // assuming that every lpvar is less than this number
+    void set_number_of_vars(unsigned k) {
+        m_active_vars_weights.resize(k);
+    }
 
+    unsigned get_number_of_vars() const {
+        return m_active_vars_weights.size();
+    }
+
+    
+    void set_var_weight(unsigned j, unsigned weight) {
+        m_active_vars_weights[j] = weight;
+    }
+private:
+    svector<unsigned>& active_vars_weights() { return m_active_vars_weights;}
+    const svector<unsigned>& active_vars_weights() const { return m_active_vars_weights;}
+public:
     nex* simplify(nex* e);
     
     bool less_than(lpvar j, lpvar k) const{
@@ -237,7 +251,15 @@ public:
     bool less_than_on_mul(const nex_mul* a, const nex_mul* b) const;
     bool less_than_on_var_nex(const nex_var* a, const nex* b) const;
     bool less_than_on_mul_nex(const nex_mul* a, const nex* b) const;
+    bool less_than_on_sum_sum(const nex_sum* a, const nex_sum* b) const;
     void fill_map_with_children(std::map<nex*, rational, nex_lt> & m, ptr_vector<nex> & children);
     void process_map_pair(nex *e, const rational& coeff, ptr_vector<nex> & children, std::unordered_set<nex*>&);
+#ifdef Z3DEBUG
+    static
+    bool equal(const nex*, const nex* );
+    nex* canonize(const nex*);
+    nex* canonize_mul(nex_mul*);
+    unsigned find_sum_in_mul(const nex_mul* a) const;
+#endif
 };
 }
diff --git a/src/math/lp/nla_grobner.cpp b/src/math/lp/nla_grobner.cpp
index 3533865bd..d2df9c66c 100644
--- a/src/math/lp/nla_grobner.cpp
+++ b/src/math/lp/nla_grobner.cpp
@@ -102,9 +102,9 @@ var_weight nla_grobner::get_var_weight(lpvar j) const {
 }
 
 void nla_grobner::set_active_vars_weights() {
-    m_nex_creator.active_vars_weights().resize(c().m_lar_solver.column_count());
+    m_nex_creator.set_number_of_vars(c().m_lar_solver.column_count());
     for (lpvar j : m_active_vars) {
-        m_nex_creator.active_vars_weights()[j] = get_var_weight(j);
+        m_nex_creator.set_var_weight(j, static_cast<unsigned>(get_var_weight(j)));
     }
 }
 
diff --git a/src/test/lp/lp.cpp b/src/test/lp/lp.cpp
index aa00adc64..11177e619 100644
--- a/src/test/lp/lp.cpp
+++ b/src/test/lp/lp.cpp
@@ -108,27 +108,6 @@ bool mul_has_var_in_power(lpvar j, unsigned k, const nex_mul* e) {
     return false;
 }
 
-bool has_var_in_power(lpvar j, unsigned k, const nex* e) {
-    TRACE("nla_cn", tout << "j = " << nex_creator::ch(j) << ", e = " << *e << ", k = " << k << "\n";);
-    if (k == 0)
-        return true;
-    if (e->is_scalar())
-        return false;
-    if (e->is_var()) {
-        return k == 1 && to_var(e)->var() == j;
-    }
-    if (e->is_sum()) {
-        for (auto ee : *to_sum(e)) {
-            if (has_var_in_power(j, k, ee))
-                return true;
-        }
-        return false;
-    }
-    if (e->is_mul()) {
-        return mul_has_var_in_power(j, k, to_mul(e));
-    }
-}
-
 void test_simplify() {
     cross_nested cn(
         [](const nex* n) {
@@ -144,9 +123,9 @@ void test_simplify() {
     enable_trace("nla_test");
     
     nex_creator & r = cn.get_nex_creator();
-    r.active_vars_weights().resize(3);
-    for (unsigned j = 0; j < r.active_vars_weights().size(); j++)
-        r.active_vars_weights()[j] = static_cast<var_weight>(5 - j);
+    r.set_number_of_vars(3);
+    for (unsigned j = 0; j < r.get_number_of_vars(); j++)
+        r.set_var_weight(j, j);
     nex_var* a = r.mk_var(0);
     nex_var* b = r.mk_var(1);
     nex_var* c = r.mk_var(2);
@@ -199,24 +178,25 @@ void test_simplify() {
 }
 
 void test_cn_shorter() {
+    nex_sum *clone;
     cross_nested cn(
         [](const nex* n) {
             TRACE("nla_test", tout <<"cn form = " <<  *n << "\n";
-                  SASSERT(has_var_in_power(4, // stands for e
-                                           2, n));
+                  
 );
             return false;
         } ,
         [](unsigned) { return false; },
         []{ return 1; });
     enable_trace("nla_test");
-    // enable_trace("nla_cn");
-    // enable_trace("nla_cn_details");
-    // enable_trace("nla_test_details");
+    enable_trace("nla_cn");
+    enable_trace("nla_cn_test");
+    enable_trace("nla_cn_details");
+    enable_trace("nla_test_details");
     auto & cr = cn.get_nex_creator();
-    cr.active_vars_weights().resize(20);
-    for (unsigned j = 0; j < cr.active_vars_weights().size(); j++)
-        cr.active_vars_weights()[j] = static_cast<var_weight>(1);
+    cr.set_number_of_vars(20);
+    for (unsigned j = 0; j < cr.get_number_of_vars(); j++)
+        cr.set_var_weight(j,j);
         
     nex_var* a = cr.mk_var(0);
     nex_var* b = cr.mk_var(1);
@@ -238,20 +218,11 @@ void test_cn_shorter() {
     nex* eac = cr.mk_mul(e, a, c);
     nex* ed = cr.mk_mul(e, d);
     nex* _6aad = cr.mk_mul(cr.mk_scalar(rational(6)), a, a, d);
-#ifdef Z3DEBUG
-    nex * clone = cr.clone(cr.mk_sum(_6aad, abcd, eae, eac));
-    clone = cr.simplify(clone);
-    SASSERT(cr.is_simplified(clone));
+    clone = to_sum(cr.clone(cr.mk_sum(_6aad, abcd, eae, eac)));
+    clone = to_sum(cr.simplify(clone));
     TRACE("nla_test", tout << "clone = " << *clone << "\n";);
-#endif
     //    test_cn_on_expr(cr.mk_sum(aad,  abcd, aaccd, add, eae, eac, ed), cn);
-    test_cn_on_expr(to_sum(clone), cn);
-    // TRACE("nla_test", tout << "done\n";);
-    // test_cn_on_expr(a*b*d + a*b*c + c*b*d + a*c*d);
-    // TRACE("nla_test", tout << "done\n";);
-    // test_cn_on_expr(a*b*b*d*d + a*b*b*c*d + c*b*b*d);
-    // TRACE("nla_test", tout << "done\n";);
-    // test_cn_on_expr(a*b*d + a*b*c + c*b*d);
+    test_cn_on_expr(clone, cn);
 }
 
 void test_cn() {
@@ -264,12 +235,13 @@ void test_cn() {
         [](unsigned) { return false; },
         []{ return 1; });
     enable_trace("nla_test");
+    enable_trace("nla_cn_test");
     //    enable_trace("nla_cn");
     //   enable_trace("nla_test_details");
     auto & cr = cn.get_nex_creator();
-    cr.active_vars_weights().resize(20);
-    for (unsigned j = 0; j < cr.active_vars_weights().size(); j++)
-        cr.active_vars_weights()[j] = static_cast<var_weight>(1);
+    cr.set_number_of_vars(20);
+    for (unsigned j = 0; j < cr.get_number_of_vars(); j++)
+        cr.set_var_weight(j, j);
         
     nex_var* a = cr.mk_var(0);
     nex_var* b = cr.mk_var(1);