diff --git a/src/math/lp/cross_nested.h b/src/math/lp/cross_nested.h
index c5694955c..b7e897eac 100644
--- a/src/math/lp/cross_nested.h
+++ b/src/math/lp/cross_nested.h
@@ -34,8 +34,8 @@ class cross_nested {
     ptr_vector<nex>                                   m_b_split_vec;
     int                                               m_reported;
     bool                                              m_random_bit;
-    nex_creator                                       m_nex_creator;
     std::function<nex_scalar*()>                      m_mk_scalar;
+    nex_creator&                                      m_nex_creator;
 #ifdef Z3DEBUG
     nex* m_e_clone;
 #endif
@@ -45,13 +45,15 @@ public:
     
     cross_nested(std::function<bool (const nex*)> call_on_result,
                  std::function<bool (unsigned)> var_is_fixed,
-                 std::function<unsigned ()> random) :
+                 std::function<unsigned ()> random,
+                 nex_creator& nex_cr) :
         m_call_on_result(call_on_result),
         m_var_is_fixed(var_is_fixed),
         m_random(random),
         m_done(false),
         m_reported(0),
-        m_mk_scalar([this]{return m_nex_creator.mk_scalar(rational(1));})
+        m_mk_scalar([this]{return m_nex_creator.mk_scalar(rational(1));}),
+        m_nex_creator(nex_cr)
     {}
 
     
@@ -369,15 +371,15 @@ public:
     // all factors of j go to a, the rest to b
     void pre_split(nex_sum * e, lpvar j, nex_sum*& a, nex*& b) {
         TRACE("nla_cn_details", tout << "e = " << * e << ", j = " << m_nex_creator.ch(j) << std::endl;);
+        SASSERT(m_nex_creator.is_simplified(e));
         a = m_nex_creator.mk_sum();
         m_b_split_vec.clear();
         for (nex * ce: *e) {
+            TRACE("nla_cn_details", tout << "ce = " << *ce << "\n";);
             if (is_divisible_by_var(ce, j)) {
                 a->add_child(m_nex_creator.mk_div(ce , j));
             } else {
                 m_b_split_vec.push_back(ce);
-                TRACE("nla_cn_details", tout << "ce = " << *ce << "\n";);
-                
             }        
         }
         TRACE("nla_cn_details", tout << "a = " << *a << "\n";);
diff --git a/src/math/lp/horner.cpp b/src/math/lp/horner.cpp
index bab09e9b2..06019990e 100644
--- a/src/math/lp/horner.cpp
+++ b/src/math/lp/horner.cpp
@@ -45,7 +45,7 @@ bool horner::row_is_interesting(const T& row) const {
         return false;
     }
     SASSERT(row_has_monomial_to_refine(row));
-    c().clear_row_var_set();
+    c().clear_active_var_set();
     for (const auto& p : row) {
         lpvar j = p.var();
         if (!c().is_monic_var(j))
@@ -53,19 +53,19 @@ bool horner::row_is_interesting(const T& row) const {
         auto & m = c().emons()[j];
         
         for (lpvar k : m.vars()) {
-            if (c().row_var_set_contains(k))
+            if (c().active_var_set_contains(k))
                 return true;
         }
         for (lpvar k : m.vars()) {
-            c().insert_to_row_var_set(k);
+            c().insert_to_active_var_set(k);
         }
     }
     return false;
 }
 
-bool horner::lemmas_on_expr(cross_nested& cn) {
-    TRACE("nla_horner", tout << "m_row_sum = " << m_row_sum << "\n";);
-    cn.run(&m_row_sum);
+bool horner::lemmas_on_expr(cross_nested& cn, nex_sum* e) {
+    TRACE("nla_horner", tout << "e = " << *e << "\n";);
+    cn.run(e);
     return cn.done();
 }
 
@@ -92,11 +92,15 @@ bool horner::lemmas_on_row(const T& row) {
     cross_nested cn(
         [this](const nex* n) { return check_cross_nested_expr(n); },
         [this](unsigned j)   { return c().var_is_fixed(j); },
-        [this]() { return c().random(); });
+        [this]() { return c().random(); }, m_nex_creator);
 
     SASSERT (row_is_interesting(row));
     create_sum_from_row(row, cn.get_nex_creator(), m_row_sum);
-    return lemmas_on_expr(cn);
+    nex* e =  m_nex_creator.simplify(&m_row_sum);
+    if (!e->is_sum())
+        return false;
+    
+    return lemmas_on_expr(cn, to_sum(e));
 }
 
 void horner::horner_lemmas() {
@@ -112,7 +116,7 @@ void horner::horner_lemmas() {
         for (auto & s : matrix.m_columns[j])
             rows_to_check.insert(s.var());
     }
-    c().prepare_row_var_set();
+    c().prepare_active_var_set();
     svector<unsigned> rows;
     for (unsigned i : rows_to_check) {
         if (row_is_interesting(matrix.m_rows[i]))
diff --git a/src/math/lp/horner.h b/src/math/lp/horner.h
index d35e252a5..d636cdfaa 100644
--- a/src/math/lp/horner.h
+++ b/src/math/lp/horner.h
@@ -53,7 +53,7 @@ public:
     intervals::interval interval_of_sum_no_term_with_deps(const nex_sum*);
     intervals::interval interval_of_mul_with_deps(const nex_mul*);
     void set_var_interval_with_deps(lpvar j, intervals::interval&) const;
-    bool lemmas_on_expr(cross_nested&);
+    bool lemmas_on_expr(cross_nested&, nex_sum*);
     
     template <typename T> // T has an iterator of (coeff(), var())
     bool row_has_monomial_to_refine(const T&) const;
diff --git a/src/math/lp/nex.h b/src/math/lp/nex.h
index f7979e6a8..e09a1eeff 100644
--- a/src/math/lp/nex.h
+++ b/src/math/lp/nex.h
@@ -97,7 +97,8 @@ public:
     lpvar var() const {  return m_j; }
     lpvar& var() {  return m_j; } // the setter
     std::ostream & print(std::ostream& out) const {
-        out <<  (char)('a' + m_j);
+        //        out <<  (char)('a' + m_j);
+        out << "v" << m_j;
         return out;
     }    
 
diff --git a/src/math/lp/nex_creator.cpp b/src/math/lp/nex_creator.cpp
index 688af2d53..e409c8087 100644
--- a/src/math/lp/nex_creator.cpp
+++ b/src/math/lp/nex_creator.cpp
@@ -288,8 +288,12 @@ bool nex_creator::lt(const nex* a, const nex* b) const {
 
 bool nex_creator::is_sorted(const nex_mul* e) const {
     for (unsigned j = 0; j < e->size() - 1; j++) {
-        if (!(less_than_on_nex_pow((*e)[j], (*e)[j+1])))
+        if (!(less_than_on_nex_pow((*e)[j], (*e)[j+1]))) {
+            TRACE("nla_cn_details", tout << "not sorted e " << * e << "\norder is incorrect " <<
+                  (*e)[j] << " >= " << (*e)[j + 1]<< "\n";);
+
             return false;
+        }
     }
     return true;
 }
@@ -298,22 +302,29 @@ bool nex_creator::is_sorted(const nex_mul* e) const {
 
 
 bool nex_creator::mul_is_simplified(const nex_mul* e) const {
+    TRACE("nla_cn_details", tout <<  "e = " << *e << "\n";);
     if (e->size() == 1 && e->begin()->pow() == 1)
         return false;
     std::set<const nex*, nex_lt> s([this](const nex* a, const nex* b) {return lt(a, b); });
     for (const auto &p : *e) {
         const nex* ee = p.e();
-        if (p.pow() == 0)
+        if (p.pow() == 0) {
+            TRACE("nla_cn_details", tout << "not simplified " << *ee << "\n";);
             return false;
-        if (ee->is_mul()) 
+        }
+        if (ee->is_mul()) {
+            TRACE("nla_cn_details", tout << "not simplified " << *ee << "\n";);
             return false;
-        if (ee->is_scalar() && to_scalar(ee)->value().is_one())
+        }
+        if (ee->is_scalar() && to_scalar(ee)->value().is_one()) {
+            TRACE("nla_cn_details", tout << "not simplified " << *ee << "\n";);
             return false;
+        }
 
         auto it = s.find(ee);
         if (it == s.end()) {
             s.insert(ee);
-        } else {
+        } else {            
             TRACE("nla_cn_details", tout << "not simplified " << *ee << "\n";);
             return false;
         }
@@ -340,20 +351,29 @@ nex* nex_creator::simplify_sum(nex_sum *e) {
 }
 
 bool nex_creator::sum_is_simplified(const nex_sum* e) const {
-    
     if (e->size() < 2) return false;
     bool scalar = false;
     for (nex * ee : *e) {
-        if (ee->is_sum())
+        if (ee->is_sum()) {
+            TRACE("nla_cn", tout << "not simplified e = " << *e << "\n"
+                  << " has a child which is a sum " << *ee << "\n";);
             return false;
+        }
         if (ee->is_scalar()) {
             if (scalar) {
+                TRACE("nla_cn", tout <<  "not simplified e = " << *e << "\n"
+                      << " have more than one scalar " << *ee << "\n";);
+                
                 return false;
             }
             if (to_scalar(ee)->value().is_zero()) {
-                return false;
+                if (scalar) {
+                    TRACE("nla_cn", tout << "have a zero scalar " << *ee << "\n";);
+                    
+                    return false;
+                }
+                scalar = true;
             }
-            scalar = true;
         }
         if (!is_simplified(ee))
             return false;
diff --git a/src/math/lp/nex_creator.h b/src/math/lp/nex_creator.h
index d09fd2f86..9dbce32f5 100644
--- a/src/math/lp/nex_creator.h
+++ b/src/math/lp/nex_creator.h
@@ -57,11 +57,11 @@ class nex_creator {
     svector<unsigned>                            m_active_vars_weights;
 
 public:
-    static char ch(unsigned j) {
-        // std::stringstream s;
-        // s << "v" << j;        
-        //    return s.str();
-        return (char)('a'+j);
+    static std::string ch(unsigned j) {
+        std::stringstream s;
+        s << "v" << j;        
+        return s.str();
+          // return (char)('a'+j);
     }
 
     // assuming that every lpvar is less than this number
diff --git a/src/math/lp/nla_common.cpp b/src/math/lp/nla_common.cpp
index 09ec84e27..270cea2b8 100644
--- a/src/math/lp/nla_common.cpp
+++ b/src/math/lp/nla_common.cpp
@@ -122,26 +122,32 @@ unsigned common::random() {
     return c().random();
 }
 
-nex * common::nexvar(lpvar j, nex_creator& cn) const {
+nex * common::nexvar(lpvar j, nex_creator& cn) {
     // todo: consider deepen the recursion
-    if (!c().is_monic_var(j))
+    if (!c().is_monic_var(j)) {
+        c().insert_to_active_var_set(j);
         return cn.mk_var(j);
+    }
     const monic& m = c().emons()[j];
     nex_mul * e = cn.mk_mul();
     for (lpvar k : m.vars()) {
+        c().insert_to_active_var_set(k);
         e->add_child(cn.mk_var(k));
         CTRACE("nla_horner", c().is_monic_var(k), c().print_var(k, tout) << "\n";);
     }
     return e;
 }
 
-nex * common::nexvar(const rational & coeff, lpvar j, nex_creator& cn) const {
+nex * common::nexvar(const rational & coeff, lpvar j, nex_creator& cn) {
     // todo: consider deepen the recursion
-    if (!c().is_monic_var(j))
+    if (!c().is_monic_var(j)) {
+        c().insert_to_active_var_set(j);
         return cn.mk_mul(cn.mk_scalar(coeff), cn.mk_var(j));
+    }
     const monic& m = c().emons()[j];
     nex_mul * e = cn.mk_mul(cn.mk_scalar(coeff));
     for (lpvar k : m.vars()) {
+        c().insert_to_active_var_set(j);
         e->add_child(cn.mk_var(k));
         CTRACE("nla_horner", c().is_monic_var(k), c().print_var(k, tout) << "\n";);
     }
@@ -151,6 +157,7 @@ nex * common::nexvar(const rational & coeff, lpvar j, nex_creator& cn) const {
 
 template <typename T> void common::create_sum_from_row(const T& row, nex_creator& cn, nex_sum& sum) {
     TRACE("nla_horner", tout << "row="; m_core->print_term(row, tout) << "\n";);
+    c().prepare_active_var_set();
     SASSERT(row.size() > 1);
     sum.children().clear();
     for (const auto &p : row) {
@@ -160,7 +167,43 @@ template <typename T> void common::create_sum_from_row(const T& row, nex_creator
             sum.add_child(nexvar(p.coeff(), p.var(), cn));
         }
     }
+    set_active_vars_weights();
 }
+
+void common::set_active_vars_weights() {
+    m_nex_creator.set_number_of_vars(c().m_lar_solver.column_count());
+    for (lpvar j : c().active_var_set()) {
+        m_nex_creator.set_var_weight(j, static_cast<unsigned>(get_var_weight(j)));
+    }
+}
+
+var_weight common::get_var_weight(lpvar j) const {
+    var_weight k;
+    switch (c().m_lar_solver.get_column_type(j)) {
+        
+    case lp::column_type::fixed:
+        k = var_weight::FIXED;
+        break;
+    case lp::column_type::boxed:
+        k = var_weight::BOUNDED;
+        break;
+    case lp::column_type::lower_bound:
+    case lp::column_type::upper_bound:
+        k = var_weight::NOT_FREE;
+    case lp::column_type::free_column:
+        k = var_weight::FREE;
+        break;
+    default:
+        UNREACHABLE();
+        break;
+    }
+    if (c().is_monic_var(j)) {
+        return (var_weight)((int)k + 1);
+    }
+    return k;
+}
+
+
 }
 template void nla::common::create_sum_from_row<old_vector<lp::row_cell<rational>, true, unsigned int> >(old_vector<lp::row_cell<rational>, true, unsigned int> const&, nla::nex_creator&, nla::nex_sum&);
 
diff --git a/src/math/lp/nla_common.h b/src/math/lp/nla_common.h
index 0465ab3c6..b96c15ad4 100644
--- a/src/math/lp/nla_common.h
+++ b/src/math/lp/nla_common.h
@@ -45,7 +45,9 @@ inline llc negate(llc cmp) {
 
 class core;
 struct common {
-    core* m_core;
+    core*                                        m_core;
+    nex_creator                                  m_nex_creator;
+    
     common(core* c): m_core(c) {}
     core& c() { return *m_core; }
     const core& c() const { return *m_core; }
@@ -115,10 +117,11 @@ struct common {
     typedef dependency_manager<ci_dependency_config> ci_dependency_manager;
 
     typedef ci_dependency_manager::dependency ci_dependency;
-    nex* nexvar(lpvar j, nex_creator& ) const;
-    nex* nexvar(const rational& coeff, lpvar j, nex_creator&) const;
+    nex* nexvar(lpvar j, nex_creator& );
+    nex* nexvar(const rational& coeff, lpvar j, nex_creator&);
     template <typename T>
     void create_sum_from_row(const T&, nex_creator&, nex_sum&);
-
+    void set_active_vars_weights();
+    var_weight get_var_weight(lpvar) const;
 };
 }
diff --git a/src/math/lp/nla_core.h b/src/math/lp/nla_core.h
index 8c514a30d..ebddfaebf 100644
--- a/src/math/lp/nla_core.h
+++ b/src/math/lp/nla_core.h
@@ -79,7 +79,7 @@ public:
 
 class core {
 public:
-    var_eqs<emonics>      m_evars;
+    var_eqs<emonics>         m_evars;
     lp::lar_solver&          m_lar_solver;
     vector<lemma> *          m_lemma_vec;
     lp::int_set              m_to_refine;
@@ -91,25 +91,25 @@ public:
     nla_settings             m_nla_settings;
     nla_grobner              m_grobner;
 private:
-    emonics               m_emons;
+    emonics                  m_emons;
     svector<lpvar>           m_add_buffer;
-    mutable lp::int_set      m_row_var_set;
+    mutable lp::int_set      m_active_var_set;
 public:
     reslimit                 m_reslim;
 
     
-    const lp::int_set&  row_var_set () const { return m_row_var_set;}
-    bool row_var_set_contains(unsigned j) const { return m_row_var_set.contains(j); }
+    const lp::int_set&  active_var_set () const { return m_active_var_set;}
+    bool active_var_set_contains(unsigned j) const { return m_active_var_set.contains(j); }
 
-    void insert_to_row_var_set(unsigned j) const { m_row_var_set.insert(j); }    
+    void insert_to_active_var_set(unsigned j) const { m_active_var_set.insert(j); }    
 
-    void clear_row_var_set() const {
-        m_row_var_set.clear();
+    void clear_active_var_set() const {
+        m_active_var_set.clear();
     }
 
-    void prepare_row_var_set() const {
-        m_row_var_set.clear();
-        m_row_var_set.resize(m_lar_solver.number_of_vars());
+    void prepare_active_var_set() const {
+        m_active_var_set.clear();
+        m_active_var_set.resize(m_lar_solver.number_of_vars());
     }
     
     reslimit &               reslim() { return m_reslim; }  
diff --git a/src/math/lp/nla_grobner.cpp b/src/math/lp/nla_grobner.cpp
index d2df9c66c..ab3be29d1 100644
--- a/src/math/lp/nla_grobner.cpp
+++ b/src/math/lp/nla_grobner.cpp
@@ -75,39 +75,6 @@ void nla_grobner::add_var_and_its_factors_to_q_and_collect_new_rows(lpvar j, std
     }            
 }
 
-var_weight nla_grobner::get_var_weight(lpvar j) const {
-    var_weight k;
-    switch (c().m_lar_solver.get_column_type(j)) {
-        
-    case lp::column_type::fixed:
-        k = var_weight::FIXED;
-        break;
-    case lp::column_type::boxed:
-        k = var_weight::BOUNDED;
-        break;
-    case lp::column_type::lower_bound:
-    case lp::column_type::upper_bound:
-        k = var_weight::NOT_FREE;
-    case lp::column_type::free_column:
-        k = var_weight::FREE;
-        break;
-    default:
-        UNREACHABLE();
-        break;
-    }
-    if (c().is_monic_var(j)) {
-        return (var_weight)((int)k + 1);
-    }
-    return k;
-}
-
-void nla_grobner::set_active_vars_weights() {
-    m_nex_creator.set_number_of_vars(c().m_lar_solver.column_count());
-    for (lpvar j : m_active_vars) {
-        m_nex_creator.set_var_weight(j, static_cast<unsigned>(get_var_weight(j)));
-    }
-}
-
 void nla_grobner::find_nl_cluster() {
     prepare_rows_and_active_vars();
     std::queue<lpvar> q;
diff --git a/src/math/lp/nla_grobner.h b/src/math/lp/nla_grobner.h
index af0d63a77..6d0441150 100644
--- a/src/math/lp/nla_grobner.h
+++ b/src/math/lp/nla_grobner.h
@@ -89,7 +89,6 @@ class nla_grobner : common {
     region                                       m_alloc;
     ci_value_manager                             m_val_manager;
     ci_dependency_manager                        m_dep_manager;
-    nex_creator                                  m_nex_creator;
     nex_lt                                       m_lt;
 public:
     nla_grobner(core *core);
@@ -100,9 +99,7 @@ private:
     void prepare_rows_and_active_vars();
     void add_var_and_its_factors_to_q_and_collect_new_rows(lpvar j,  std::queue<lpvar>& q);
     void display(std::ostream&);
-    void set_active_vars_weights();
     void init();
-    var_weight get_var_weight(lpvar) const;
     void compute_basis();
     void update_statistics();
     bool find_conflict(ptr_vector<equation>& eqs);
diff --git a/src/test/lp/lp.cpp b/src/test/lp/lp.cpp
index 21e837818..56eebaa61 100644
--- a/src/test/lp/lp.cpp
+++ b/src/test/lp/lp.cpp
@@ -76,20 +76,20 @@ void test_cn_on_expr(nex_sum *t, cross_nested& cn) {
 
 void test_simplify() {
 #ifdef Z3DEBUG
+    nex_creator r;
     cross_nested cn(
         [](const nex* n) {
                            TRACE("nla_cn_test", tout << *n << "\n";);
                            return false;
                        } ,
         [](unsigned) { return false; },
-        []() { return 1; } // for random
-                    );
+        []() { return 1; }, // for random
+                    r);
     // enable_trace("nla_cn");
     // enable_trace("nla_cn_details");
     //    enable_trace("nla_cn_details_");
     enable_trace("nla_test");
     
-    nex_creator & r = cn.get_nex_creator();
     r.set_number_of_vars(3);
     for (unsigned j = 0; j < r.get_number_of_vars(); j++)
         r.set_var_weight(j, j);
@@ -147,6 +147,7 @@ void test_simplify() {
 
 void test_cn_shorter() {
     nex_sum *clone;
+    nex_creator cr;
     cross_nested cn(
         [](const nex* n) {
             TRACE("nla_test", tout <<"cn form = " <<  *n << "\n";
@@ -155,13 +156,12 @@ void test_cn_shorter() {
             return false;
         } ,
         [](unsigned) { return false; },
-        []{ return 1; });
+        []{ return 1; }, cr);
     enable_trace("nla_test");
     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.set_number_of_vars(20);
     for (unsigned j = 0; j < cr.get_number_of_vars(); j++)
         cr.set_var_weight(j,j);
@@ -191,18 +191,18 @@ void test_cn_shorter() {
 void test_cn() {
 #ifdef Z3DEBUG
     test_cn_shorter();
+    nex_creator cr;
     cross_nested cn(
         [](const nex* n) {
             TRACE("nla_test", tout <<"cn form = " <<  *n << "\n";);
             return false;
         } ,
         [](unsigned) { return false; },
-        []{ return 1; });
+        []{ return 1; }, cr);
     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.set_number_of_vars(20);
     for (unsigned j = 0; j < cr.get_number_of_vars(); j++)
         cr.set_var_weight(j, j);