diff --git a/src/ast/euf/euf_ac_plugin.cpp b/src/ast/euf/euf_ac_plugin.cpp
index 99c9a2fd8..8558eb925 100644
--- a/src/ast/euf/euf_ac_plugin.cpp
+++ b/src/ast/euf/euf_ac_plugin.cpp
@@ -93,7 +93,7 @@ namespace euf {
             return;
         for (auto arg : enode_args(n))
             if (is_op(arg))
-                register_shared(arg); // TODO optimization to avoid registering shared terms twice
+                register_shared(arg); 
     }
 
     void ac_plugin::register_shared(enode* n) {
@@ -180,7 +180,7 @@ namespace euf {
     std::ostream& ac_plugin::display_monomial(std::ostream& out, ptr_vector<node> const& m) const {
         for (auto n : m) {
             if (n->n->num_args() == 0)
-                out << mk_pp(n->n->get_expr(), g.get_manager()) << " ";
+                out << n->n->get_expr_id() << ": " << mk_pp(n->n->get_expr(), g.get_manager()) << " ";
             else
                 out << g.bpp(n->n) << " ";
         }
@@ -244,6 +244,7 @@ namespace euf {
         if (l == r)
             return;
         auto j = justification::equality(l, r);
+        TRACE(plugin, tout << g.bpp(l) << " == " << g.bpp(r) << " " << is_op(l) << " " << is_op(r) << "\n");
         if (!is_op(l) && !is_op(r))
             merge(mk_node(l), mk_node(r), j);
         else
@@ -263,6 +264,7 @@ namespace euf {
     void ac_plugin::init_equation(eq const& e) {
         m_eqs.push_back(e);
         auto& eq = m_eqs.back();
+        TRACE(plugin, display_equation(tout, e) << "\n");
         if (orient_equation(eq)) {
             
             unsigned eq_id = m_eqs.size() - 1;
@@ -273,6 +275,8 @@ namespace euf {
                     n->root->n->mark1();
                     push_undo(is_add_eq_index);
                     m_node_trail.push_back(n->root);
+                    for (auto s : n->root->shared)
+                        m_shared_todo.insert(s);
                 }
             }
 
@@ -282,6 +286,8 @@ namespace euf {
                     n->root->n->mark1();
                     push_undo(is_add_eq_index);
                     m_node_trail.push_back(n->root);
+                    for (auto s : n->root->shared)
+                        m_shared_todo.insert(s);
                 }
             }
 
@@ -291,6 +297,7 @@ namespace euf {
             for (auto n : monomial(eq.r))
                 n->root->n->unmark1();
 
+            TRACE(plugin, display_equation(tout, e) << "\n");
             m_to_simplify_todo.insert(eq_id);
         }
         else
@@ -368,6 +375,7 @@ namespace euf {
     }
 
     void ac_plugin::merge(node* root, node* other, justification j) {
+        TRACE(plugin, tout << root << " == " << other << " num shared " << other->shared.size() << "\n");
         for (auto n : equiv(other))
             n->root = root;
         m_merge_trail.push_back({ other, root->shared.size(), root->eqs.size() });
@@ -394,22 +402,34 @@ namespace euf {
         ptr_vector<node> m;
         ns.push_back(n);
         for (unsigned i = 0; i < ns.size(); ++i) {
-            n = ns[i];
-            if (is_op(n)) 
-                ns.append(n->num_args(), n->args());            
+            auto k = ns[i];
+            if (is_op(k)) 
+                ns.append(k->num_args(), k->args());            
             else 
-                m.push_back(mk_node(n));            
+                m.push_back(mk_node(k));            
         }
         return to_monomial(n, m);
     }
 
     unsigned ac_plugin::to_monomial(enode* e, ptr_vector<node> const& ms) {
         unsigned id = m_monomials.size();
-        m_monomials.push_back({ ms, bloom() });
+        m_monomials.push_back({ ms, bloom(), e });
         push_undo(is_add_monomial);
         return id;
     }
 
+    enode* ac_plugin::from_monomial(ptr_vector<node> const& mon) {
+        auto& m = g.get_manager();
+        ptr_buffer<expr> args;
+        enode_vector nodes;
+        for (auto arg : mon) {
+            nodes.push_back(arg->root->n);
+            args.push_back(arg->root->n->get_expr());
+        }
+        auto n = m.mk_app(m_fid, m_op, args.size(), args.data());
+        return g.mk(n, 0, nodes.size(), nodes.data());
+    }
+
     ac_plugin::node* ac_plugin::node::mk(region& r, enode* n) {
         auto* mem = r.allocate(sizeof(node));
         node* res = new (mem) node();
@@ -427,6 +447,9 @@ namespace euf {
         push_undo(is_add_node);
         m_nodes.setx(id, r, nullptr);
         m_node_trail.push_back(r);
+        if (is_op(n)) {
+            // extract shared sub-expressions
+        }
         return r;
     }
 
@@ -983,6 +1006,7 @@ namespace euf {
     // 
 
     void ac_plugin::propagate_shared() {
+        TRACE(plugin, tout << "num shared todo " << m_shared_todo.size() << "\n");
         if (m_shared_todo.empty())
             return;
         while (!m_shared_todo.empty()) {
@@ -1007,12 +1031,15 @@ namespace euf {
     void ac_plugin::simplify_shared(unsigned idx, shared s) {
         auto j = s.j;
         auto old_m = s.m;
+        auto old_n = monomial(old_m).m_src;
         ptr_vector<node> m1(monomial(old_m).m_nodes);
-        TRACE(plugin, tout << "simplify " << m_pp(*this, monomial(old_m)) << "\n");
+        TRACE(plugin, tout << "simplify " << g.bpp(old_n) << ": " << m_pp(*this, monomial(old_m)) << "\n");
         if (!reduce(m1, j))
             return;
 
-        auto new_m = to_monomial(m1);
+
+        auto new_n = from_monomial(m1);
+        auto new_m = to_monomial(new_n, m1);
         // update shared occurrences for members of the new monomial that are not already in the old monomial.
         for (auto n : monomial(old_m))
             n->root->n->mark1();
@@ -1029,6 +1056,10 @@ namespace euf {
         push_undo(is_update_shared);
         m_shared[idx].m = new_m;
         m_shared[idx].j = j;
+
+        TRACE(plugin, tout << "shared simplified to " << m_pp(*this, monomial(new_m)) << "\n");
+        
+        push_merge(old_n, new_n, j);
     }
 
     justification ac_plugin::justify_rewrite(unsigned eq1, unsigned eq2) {
diff --git a/src/ast/euf/euf_ac_plugin.h b/src/ast/euf/euf_ac_plugin.h
index 809ac55cf..290ddb561 100644
--- a/src/ast/euf/euf_ac_plugin.h
+++ b/src/ast/euf/euf_ac_plugin.h
@@ -97,6 +97,7 @@ namespace euf {
         struct monomial_t {
             ptr_vector<node> m_nodes;
             bloom m_bloom;
+            enode* m_src = nullptr;
             node* operator[](unsigned i) const { return m_nodes[i]; }
             unsigned size() const { return m_nodes.size(); }
             void set(ptr_vector<node> const& ns) { m_nodes.reset(); m_nodes.append(ns); m_bloom.m_tick = 0; }
@@ -187,6 +188,7 @@ namespace euf {
         unsigned to_monomial(enode* n);
         unsigned to_monomial(enode* n, ptr_vector<node> const& ms);
         unsigned to_monomial(ptr_vector<node> const& ms) { return to_monomial(nullptr, ms); }
+        enode* from_monomial(ptr_vector<node> const& m);
         monomial_t const& monomial(unsigned i) const { return m_monomials[i]; }
         monomial_t& monomial(unsigned i) { return m_monomials[i]; }
         void sort(monomial_t& monomial);
diff --git a/src/ast/euf/euf_arith_plugin.cpp b/src/ast/euf/euf_arith_plugin.cpp
index 268eff38d..317b192c6 100644
--- a/src/ast/euf/euf_arith_plugin.cpp
+++ b/src/ast/euf/euf_arith_plugin.cpp
@@ -33,10 +33,13 @@ namespace euf {
     }    
 
     void arith_plugin::register_node(enode* n) {
-        // no-op
+        TRACE(plugin, tout << g.bpp(n) << "\n");
+        m_add.register_node(n);
+        m_mul.register_node(n);
     }
 
     void arith_plugin::merge_eh(enode* n1, enode* n2) {
+        TRACE(plugin, tout << g.bpp(n1) << " == " << g.bpp(n2) << "\n");
         m_add.merge_eh(n1, n2);
         m_mul.merge_eh(n1, n2);
     }
diff --git a/src/ast/euf/euf_egraph.cpp b/src/ast/euf/euf_egraph.cpp
index a3f07e9cb..10ed000c6 100644
--- a/src/ast/euf/euf_egraph.cpp
+++ b/src/ast/euf/euf_egraph.cpp
@@ -310,6 +310,13 @@ namespace euf {
         }
     }
 
+    void egraph::register_shared(enode* n, theory_id id) {
+        force_push();
+        auto* p = get_plugin(id);
+        if (p)
+            p->register_node(n);
+    }
+
     void egraph::undo_add_th_var(enode* n, theory_id tid) {
         theory_var v = n->get_th_var(tid);
         SASSERT(v != null_theory_var);
diff --git a/src/ast/euf/euf_egraph.h b/src/ast/euf/euf_egraph.h
index 4280b4780..53a0b7da2 100644
--- a/src/ast/euf/euf_egraph.h
+++ b/src/ast/euf/euf_egraph.h
@@ -318,6 +318,7 @@ namespace euf {
 
 
         void add_th_var(enode* n, theory_var v, theory_id id);
+        void register_shared(enode* n, theory_id id);
         void set_th_propagates_diseqs(theory_id id);
         void set_cgc_enabled(enode* n, bool enable_cgc);
         void set_merge_tf_enabled(enode* n, bool enable_merge_tf);
diff --git a/src/ast/euf/euf_mam.cpp b/src/ast/euf/euf_mam.cpp
index c87cd4197..ea928415c 100644
--- a/src/ast/euf/euf_mam.cpp
+++ b/src/ast/euf/euf_mam.cpp
@@ -649,7 +649,7 @@ namespace euf {
         }
     
         bool is_ac(func_decl* f) const {
-            return false && f->is_associative() && f->is_commutative();
+            return f->is_associative() && f->is_commutative();
         }
         
         instruction * mk_init(func_decl* f, unsigned n) {
@@ -1777,6 +1777,10 @@ namespace euf {
             m_use_filters(use_filters) {
         }
 
+        bool is_ac(func_decl* f) const {
+            return f->is_associative() && f->is_commutative();
+        }
+
         /**
            \brief Create a new code tree for the given quantifier.
 
@@ -1791,6 +1795,8 @@ namespace euf {
             code_tree * r     = m_ct_manager.mk_code_tree(p->get_decl(), num_args, filter_candidates);
             init(r, qa, mp, first_idx);
             linearise(r->m_root, first_idx);
+            if (is_ac(p->get_decl()))
+                ++m_num_choices;
             r->m_num_choices  = m_num_choices;
             TRACE(mam_compiler, tout << "new tree for:\n" << mk_pp(mp, m) << "\n" << *r;);
             return r;
@@ -1861,9 +1867,6 @@ namespace euf {
         unsigned             m_old_max_generation;
         union {
             enode *  m_curr;
-            struct {
-                unsigned m_next_pattern;
-            };
             struct {
                 enode_vector *  m_to_recycle;
                 enode * const * m_it;
@@ -2009,7 +2012,7 @@ namespace euf {
 
         void display_pc_info(std::ostream & out);
 
-        bool match_ac(initn const* pc);
+        bool next_ac_match(initn const* pc);
 
 #define INIT_ARGS_SIZE 16
 
@@ -2291,9 +2294,53 @@ namespace euf {
     // Established: use Diophantine equations to capture matchability.
     //
 
-    bool interpreter::match_ac(initn const* pc) {
+    bool interpreter::next_ac_match(initn const* pc) {
         unsigned f_args = pc->m_num_args;
         SASSERT(f_args <= m_acargs.size());        
+        for (unsigned i = f_args; i-- > 0;) {
+            unsigned j = m_acpatarg[i];
+            m_acbitset[j] = false;
+        next_j:
+            ++j;
+            for (; j < m_acargs.size(); ++j) {
+                if (m_acbitset[j])
+                    continue;
+                m_registers[i + 1] = m_acargs[j];
+                m_acbitset[j] = true;
+                m_acpatarg[i] = j;
+                break;
+            }
+            if (j == m_acargs.size())
+                continue;
+            
+            for (unsigned ii = i + 1; ii < f_args; ++ii) {
+                unsigned k = 0;
+                // populate arguments after i
+                for (; k < m_acargs.size(); ++k) {
+                    if (!m_acbitset[k]) {
+                        m_registers[ii + 1] = m_acargs[k];
+                        m_acbitset[k] = true;
+                        m_acpatarg[ii] = k;
+                        break;
+                    }
+                }
+                if (k == m_acargs.size()) {
+                    --ii;
+                    // clean up 
+                    for (; ii >= i; --ii) {
+                        k = m_acpatarg[ii];
+                        m_acbitset[k] = false;
+                    }
+                    goto next_j;
+                }
+            }
+            IF_VERBOSE(2,
+                verbose_stream() << "next ac: ";
+            for (unsigned j = 0; j < f_args; ++j)
+                verbose_stream() << m_acpatarg[j] << " ";
+            verbose_stream() << "\n";);
+            return true;
+        }
         return false;
     }
 
@@ -2412,6 +2459,7 @@ namespace euf {
             m_acargs.reset();
             m_acargs.push_back(m_app);
             auto* f = m_app->get_decl();
+            auto num_pat_args = static_cast<const initn*>(m_pc)->m_num_args;
             for (unsigned i = 0; i < m_acargs.size(); ++i) {
                 auto* arg = m_acargs[i];
                 if (is_app(arg->get_expr()) && f == arg->get_decl()) {
@@ -2421,7 +2469,7 @@ namespace euf {
                     --i;
                 }
             }
-            if (static_cast<const initn*>(m_pc)->m_num_args > m_acargs.size())
+            if (num_pat_args > m_acargs.size())
                 goto backtrack;
             m_acbitset.reset();
             m_acbitset.reserve(m_acargs.size(), false);
@@ -2429,11 +2477,12 @@ namespace euf {
             m_acpatarg.reserve(m_acargs.size(), 0);
             m_backtrack_stack[m_top].m_instr = m_pc;                                                  
             m_backtrack_stack[m_top].m_old_max_generation = m_curr_max_generation;      
-            m_backtrack_stack[m_top].m_next_pattern = 0;
-            ++m_top;
-            // perform the match relative index
-            if (!match_ac(static_cast<initn const*>(m_pc)))
-                goto backtrack;
+            ++m_top;            
+            for (unsigned i = 0; i < num_pat_args; ++i) {
+                m_acpatarg[i] = i;
+                m_acbitset[i] = true;
+                m_registers[i + 1] = m_acargs[i];
+            }
             m_pc = m_pc->m_next;
             goto main_loop;
         }
@@ -2499,7 +2548,7 @@ namespace euf {
                  m_app  = get_first_f_app(static_cast<const bind *>(m_pc)->m_label, static_cast<const bind *>(m_pc)->m_num_args, m_n1); \
                  if (!m_app)                                                                                            \
                      goto backtrack;                                                                                    \
-                 TRACE(mam_int, tout << "bind candidate: " << mk_pp(m_app->get_expr(), m) << "\n";);     \
+                 TRACE(mam_int, tout << "bind candidate: " << mk_pp(m_app->get_expr(), m) << " " << m_top << " " << m_backtrack_stack.size() << "\n";);     \
                  m_backtrack_stack[m_top].m_instr              = m_pc;                                                  \
                  m_backtrack_stack[m_top].m_old_max_generation = m_curr_max_generation;                                 \
                  m_backtrack_stack[m_top].m_curr               = m_app;                                                 \
@@ -2832,7 +2881,11 @@ namespace euf {
 
         case INITAC:
             // this is a backtracking point.
-            NOT_IMPLEMENTED_YET();
+            if (!next_ac_match(static_cast<initn const*>(bp.m_instr))) {
+                --m_top;
+                goto backtrack;
+            }            
+            m_pc = bp.m_instr->m_next;
             goto main_loop;
 
         case CONTINUE:
diff --git a/src/ast/simplifiers/euf_completion.cpp b/src/ast/simplifiers/euf_completion.cpp
index d4eee6832..0d685e903 100644
--- a/src/ast/simplifiers/euf_completion.cpp
+++ b/src/ast/simplifiers/euf_completion.cpp
@@ -51,6 +51,8 @@ Mam optimization?
 #include "ast/ast_pp.h"
 #include "ast/ast_util.h"
 #include "ast/euf/euf_egraph.h"
+#include "ast/euf/euf_arith_plugin.h"
+#include "ast/euf/euf_bv_plugin.h"
 #include "ast/rewriter/var_subst.h"
 #include "ast/simplifiers/euf_completion.h"
 #include "ast/shared_occs.h"
@@ -87,6 +89,9 @@ namespace euf {
 
         m_egraph.set_on_merge(_on_merge);
         m_egraph.set_on_make(_on_make);
+
+        m_egraph.add_plugin(alloc(arith_plugin, m_egraph));
+        m_egraph.add_plugin(alloc(bv_plugin, m_egraph));
     }
 
     completion::~completion() {
@@ -203,6 +208,7 @@ namespace euf {
             if (!m_should_propagate && !should_stop())
                 propagate_all_rules();
         }
+        TRACE(euf, m_egraph.display(tout));
     }
 
     unsigned completion::push_pr_dep(proof* pr, expr_dependency* d) {
@@ -520,7 +526,7 @@ namespace euf {
             if (g != f) {
                 m_fmls.update(i, dependent_expr(m, g, pr, dep));
                 m_stats.m_num_rewrites++;
-                IF_VERBOSE(0, verbose_stream() << mk_bounded_pp(f, m, 3) << " -> " << mk_bounded_pp(g, m, 3) << "\n");
+                IF_VERBOSE(2, verbose_stream() << mk_bounded_pp(f, m, 3) << " -> " << mk_bounded_pp(g, m, 3) << "\n");
                 update_has_new_eq(g);
             }
             CTRACE(euf_completion, g != f, tout << mk_bounded_pp(f, m) << " -> " << mk_bounded_pp(g, m) << "\n");
@@ -579,7 +585,16 @@ namespace euf {
                     m_todo.push_back(arg);
             }
             if (sz == m_todo.size()) {
-                m_nodes_to_canonize.push_back(m_egraph.mk(e, m_generation, m_args.size(), m_args.data()));
+                n = m_egraph.mk(e, m_generation, m_args.size(), m_args.data());
+                if (m_egraph.get_plugin(e->get_sort()->get_family_id()))
+                    m_egraph.add_th_var(n, m_th_var++, e->get_sort()->get_family_id());
+                if (!m.is_eq(e)) {
+                    for (auto ch : m_args)
+                        for (auto idv : euf::enode_th_vars(*ch))
+                            m_egraph.register_shared(n, idv.get_id());
+                }
+                                    
+                m_nodes_to_canonize.push_back(n);
                 m_todo.pop_back();
             }
         }
diff --git a/src/ast/simplifiers/euf_completion.h b/src/ast/simplifiers/euf_completion.h
index 5bfecb86c..d6a02ddd1 100644
--- a/src/ast/simplifiers/euf_completion.h
+++ b/src/ast/simplifiers/euf_completion.h
@@ -122,6 +122,7 @@ namespace euf {
 
         smt_params             m_smt_params;
         egraph                 m_egraph;
+        unsigned               m_th_var = 0;
         scoped_ptr<mam>        m_mam;
         enode*                 m_tt, *m_ff;
         ptr_vector<expr>       m_todo;