diff --git a/src/ast/euf/euf_seq_plugin.cpp b/src/ast/euf/euf_seq_plugin.cpp
index 618b1699a..0a025c5c7 100644
--- a/src/ast/euf/euf_seq_plugin.cpp
+++ b/src/ast/euf/euf_seq_plugin.cpp
@@ -212,11 +212,16 @@ namespace euf {
         if (same_star_body(a, b))
             push_merge(n, a);
 
-        // Rule 1 extended: concat(v*, concat(v*, c)) = concat(v*, c)
+        // Rule 1 extended (right): concat(v*, concat(v*, c)) = concat(v*, c)
         enode* b1, *b2;
         if (is_concat(b, b1, b2) && same_star_body(a, b1))
             push_merge(n, b);
 
+        // Rule 1 extended (left): concat(concat(c, v*), v*) = concat(c, v*)
+        enode* a1, *a2;
+        if (is_concat(a, a1, a2) && same_star_body(a2, b))
+            push_merge(n, a);
+
         // Rule 2: Nullable absorption by .*
         // concat(.*, v) = .* when v is nullable
         if (is_full_seq(a) && is_nullable(b))
diff --git a/src/ast/euf/euf_sgraph.cpp b/src/ast/euf/euf_sgraph.cpp
index eff926004..b332cd2a4 100644
--- a/src/ast/euf/euf_sgraph.cpp
+++ b/src/ast/euf/euf_sgraph.cpp
@@ -200,13 +200,18 @@ namespace euf {
             n->m_length = 1;
             break;
 
-        case snode_kind::s_loop:
+        case snode_kind::s_loop: {
+            bool body_nullable = n->num_args() > 0 && n->arg(0)->is_nullable();
+            unsigned lo = 0, hi = 0;
+            expr* body = nullptr;
+            bool lo_zero = n->get_expr() && m_seq.re.is_loop(n->get_expr(), body, lo, hi) && lo == 0;
             n->m_ground = n->num_args() > 0 ? n->arg(0)->is_ground() : true;
             n->m_regex_free = false;
-            n->m_nullable = false; // depends on lower bound
+            n->m_nullable = lo_zero || body_nullable;
             n->m_level = 1;
             n->m_length = 1;
             break;
+        }
 
         case snode_kind::s_union:
             SASSERT(n->num_args() == 2);
@@ -461,13 +466,17 @@ namespace euf {
     }
 
     snode* sgraph::drop_left(snode* n, unsigned count) {
-        for (unsigned i = 0; i < count && !n->is_empty(); ++i)
+        if (count == 0 || n->is_empty()) return n;
+        if (count >= n->length()) return mk_empty();
+        for (unsigned i = 0; i < count; ++i)
             n = drop_first(n);
         return n;
     }
 
     snode* sgraph::drop_right(snode* n, unsigned count) {
-        for (unsigned i = 0; i < count && !n->is_empty(); ++i)
+        if (count == 0 || n->is_empty()) return n;
+        if (count >= n->length()) return mk_empty();
+        for (unsigned i = 0; i < count; ++i)
             n = drop_last(n);
         return n;
     }