diff --git a/src/smt/theory_seq.cpp b/src/smt/theory_seq.cpp
index 70f7baecd..dc9cdf083 100644
--- a/src/smt/theory_seq.cpp
+++ b/src/smt/theory_seq.cpp
@@ -562,55 +562,66 @@ void theory_seq::mk_decompose(expr* e, expr_ref& head, expr_ref& tail) {
 /*
    \brief Check extensionality (for sequences).
  */
+
+bool theory_seq::check_extensionality(expr* e1, enode* n1, enode* n2) {
+    dependency* dep = nullptr;
+    expr* o1 = n1->get_expr();
+    expr* o2 = n2->get_expr();
+    if (o1->get_sort() != o2->get_sort()) 
+        return true;
+    if (ctx.is_diseq(n1, n2) || m_exclude.contains(o1, o2)) 
+        return true;
+    expr_ref e2(m);
+    if (!canonize(n2->get_expr(), dep, e2)) 
+        return false;
+    m_new_eqs.reset();
+    bool change = false;
+    if (!m_seq_rewrite.reduce_eq(e1, e2, m_new_eqs, change)) {
+        TRACE("seq", tout << "exclude " << mk_pp(o1, m) << " " << mk_pp(o2, m) << "\n";);
+        m_exclude.update(o1, o2);
+        return true;
+    }
+    for (auto const& p : m_new_eqs) {
+        if (m_exclude.contains(p.first, p.second)) {
+            TRACE("seq", tout << "excluded " << mk_pp(p.first, m) << " " << mk_pp(p.second, m) << "\n";);
+            return true;
+        }
+    }
+    ctx.assume_eq(n1, n2);
+    return false;
+}
+
 bool theory_seq::check_extensionality() {
     unsigned sz = get_num_vars();
     unsigned_vector seqs;
+    dependency* dep = nullptr;
+    expr_ref e1(m);
     for (unsigned v = 0; v < sz; ++v) {
         enode* n1 = get_enode(v);
         expr* o1 = n1->get_expr();
-        if (n1 != n1->get_root()) {
-            continue;
-        }
-        if (!seqs.empty() && ctx.is_relevant(n1) && m_util.is_seq(o1) && ctx.is_shared(n1)) {
-            dependency* dep = nullptr;
-            expr_ref e1(m);
-            if (!canonize(o1, dep, e1)) {
+        // check extensionality for sequence arguments of nth_u
+        // two occurrences of nth_u(a,x), nth_u(b,y) must induce comparing sequences a, b
+        // whenever x = y
+        if (m_util.str.is_nth_u(o1) && n1->is_cgr()) {
+            auto* r0 = n1->get_arg(0)->get_root();
+            auto* r1 = n1->get_arg(1)->get_root();
+            if (!canonize(r0->get_expr(), dep, e1)) 
                 return false;
-            }
-            for (theory_var v : seqs) {
-                enode* n2 = get_enode(v);
-                expr* o2 = n2->get_expr();
-                if (o1->get_sort() != o2->get_sort()) {
-                    continue;
-                }
-                if (ctx.is_diseq(n1, n2) || m_exclude.contains(o1, o2)) {
-                    continue;
-                }
-                expr_ref e2(m);
-                if (!canonize(n2->get_expr(), dep, e2)) {
+            for (auto* p : r1->get_parents()) 
+                if (p != n1 && p->is_cgr() && m_util.str.is_nth_u(p->get_expr()) && 
+                    !check_extensionality(e1, r0, p->get_arg(0)->get_root())) 
                     return false;
-                }
-                m_new_eqs.reset();
-                bool change = false;
-                if (!m_seq_rewrite.reduce_eq(e1, e2, m_new_eqs, change)) {
-                    TRACE("seq", tout << "exclude " << mk_pp(o1, m) << " " << mk_pp(o2, m) << "\n";);
-                    m_exclude.update(o1, o2);
-                    continue;
-                }
-                bool excluded = false;
-                for (auto const& p : m_new_eqs) {
-                    if (m_exclude.contains(p.first, p.second)) {
-                        TRACE("seq", tout << "excluded " << mk_pp(p.first, m) << " " << mk_pp(p.second, m) << "\n";);
-                        excluded = true;
-                        break;
-                    }
-                }
-                if (excluded) {
-                    continue;
-                }
-                ctx.assume_eq(n1, n2);
+        }
+        if (!n1->is_root())
+            continue;
+        if (!m_util.is_seq(o1))
+            continue;        
+        if (!seqs.empty() && ctx.is_relevant(n1) && ctx.is_shared(n1)) {
+            if (!canonize(o1, dep, e1)) 
                 return false;
-            }
+            for (theory_var v : seqs) 
+                if (!check_extensionality(e1, n1, get_enode(v))) 
+                    return false;
         }
         seqs.push_back(v);
     }
@@ -2368,7 +2379,7 @@ void theory_seq::validate_fmls(enode_pair_vector const& eqs, literal_vector cons
 theory_var theory_seq::mk_var(enode* n) {
     expr* o = n->get_expr();
 
-    if (!m_util.is_seq(o) && !m_util.is_re(o))
+    if (!m_util.is_seq(o) && !m_util.is_re(o) && !m_util.str.is_nth_u(o))
         return null_theory_var;
 
     if (is_attached_to_var(n)) 
diff --git a/src/smt/theory_seq.h b/src/smt/theory_seq.h
index ad6ef0695..68e9f3762 100644
--- a/src/smt/theory_seq.h
+++ b/src/smt/theory_seq.h
@@ -458,6 +458,7 @@ namespace smt {
         void add_unhandled_expr(expr* e);
 
         bool check_extensionality();
+        bool check_extensionality(expr* e1, enode* n1, enode* n2);
         bool check_contains();
         bool check_lts();
         dependency* m_eq_deps { nullptr };