diff --git a/src/library/equations_compiler/elim_match.cpp b/src/library/equations_compiler/elim_match.cpp
index 4eb608d49c..6e354a2d29 100644
--- a/src/library/equations_compiler/elim_match.cpp
+++ b/src/library/equations_compiler/elim_match.cpp
@@ -98,7 +98,7 @@ struct elim_match_fn {
         buffer<expr> patterns;
         get_app_args(equation_lhs(it), patterns);
         for (expr & p : patterns) {
-            p = instantiate_rev(p, locals);
+            p = eqns_env_interface(m_env).whnf_upto_constructor(ctx, instantiate_rev(p, locals));
         }
         E.m_patterns = to_list(patterns);
         E.m_ref  = eqn;
@@ -165,6 +165,49 @@ struct elim_match_fn {
         return r;
     }
 
+    bool is_constructor(expr const & e) const {
+        return static_cast<bool>(eqns_env_interface(m_env).is_constructor(get_app_fn(e)));
+    }
+
+    template<typename Pred>
+    bool all_next_pattern(program const & P, Pred && p) const {
+        for (equation const & eqn : P.m_equations) {
+            lean_assert(eqn.m_patterns);
+            if (!p(head(eqn.m_patterns)))
+                return false;
+        }
+        return true;
+    }
+
+    /* Return true iff the next pattern in all equations is a variable. */
+    bool is_variable_transition(program const & P) const {
+        return all_next_pattern(P, is_local);
+    }
+
+    /* Return true iff the next pattern in all equations is an inaccessible term. */
+    bool is_inaccessible_transition(program const & P) const {
+        return all_next_pattern(P, is_inaccessible);
+    }
+
+    /* Return true iff the next pattern in all equations is a constructor. */
+    bool is_constructor_transition(program const & P) const {
+        return all_next_pattern(P, [&](expr const & p) { return is_constructor(p); });
+    }
+
+    /* Return true iff the next pattern of every equation is a constructor or variable,
+       and there are at least one equation where it is a variable and another where it is a
+       constructor. */
+    bool is_complete_transition(program const & P) const {
+        bool has_variable    = false;
+        bool has_constructor = false;
+        bool r = all_next_pattern(P, [&](expr const & p) {
+                if (is_local(p)) { has_variable = true; return true; }
+                else if (is_constructor(p)) { has_constructor = true; return true; }
+                else { return false; }
+            });
+        return r && has_variable && has_constructor;
+    }
+
     expr operator()(local_context const & lctx, expr const & eqns) {
         lean_assert(equations_num_fns(eqns) == 1);
         DEBUG_CODE({
diff --git a/src/library/equations_compiler/util.cpp b/src/library/equations_compiler/util.cpp
index 49cfde8bde..7e7577c9e5 100644
--- a/src/library/equations_compiler/util.cpp
+++ b/src/library/equations_compiler/util.cpp
@@ -165,6 +165,10 @@ unsigned eqns_env_interface::get_inductive_num_indices(name const & n) const {
     return *inductive::get_num_indices(m_env, n);
 }
 
+expr eqns_env_interface::whnf_upto_constructor(type_context & ctx, expr const & e) {
+    return ctx.relaxed_whnf(e);
+}
+
 bool is_recursive_eqns(type_context & ctx, expr const & e) {
     unpack_eqns ues(ctx, e);
     for (unsigned fidx = 0; fidx < ues.get_num_fns(); fidx++) {
diff --git a/src/library/equations_compiler/util.h b/src/library/equations_compiler/util.h
index 9debbb777f..73cd609ca2 100644
--- a/src/library/equations_compiler/util.h
+++ b/src/library/equations_compiler/util.h
@@ -84,6 +84,7 @@ public:
     optional<name> is_constructor(expr const & e) const;
     unsigned get_inductive_num_params(name const & n) const;
     unsigned get_inductive_num_indices(name const & n) const;
+    expr whnf_upto_constructor(type_context & ctx, expr const & e);
 };
 
 /** \brief Return true iff \c e is recursive. That is, some equation