diff --git a/src/math/polysat/interval.h b/src/math/polysat/interval.h
index 90a5d44fe..ea76f6b11 100644
--- a/src/math/polysat/interval.h
+++ b/src/math/polysat/interval.h
@@ -97,11 +97,19 @@ namespace polysat {
         bool contains(eval_interval const& other) const {
             if (is_full())
                 return true;
-            if (lo_val() <= other.lo_val() && other.hi_val() <= hi_val())
+            // lo <= lo' <= hi' <= hi'
+            if (lo_val() <= other.lo_val() && other.lo_val() <= other.hi_val() && other.hi_val() <= hi_val())
                 return true;
-            if (hi_val() < lo_val() && lo_val() <= other.lo_val() && other.lo_val() <= other.hi_val())
+            if (lo_val() <= hi_val())
+                return false;
+            // hi < lo <= lo' <= hi'
+            if (lo_val() <= other.lo_val() && other.lo_val() <= other.hi_val())
                 return true;
-            if (hi_val() < lo_val() && other.lo_val() < hi_val() && other.hi_val() <= hi_val())
+            // lo' <= hi' <= hi < lo 
+            if (other.lo_val() <= other.hi_val() && other.hi_val() <= hi_val())
+                return true;
+            // hi' <= hi < lo <= lo'
+            if (other.hi_val() <= hi_val() && lo_val() <= other.lo_val())
                 return true;
             return false;
         }
diff --git a/src/math/polysat/solver.h b/src/math/polysat/solver.h
index 7d44ef708..74a39e5ed 100644
--- a/src/math/polysat/solver.h
+++ b/src/math/polysat/solver.h
@@ -270,6 +270,8 @@ namespace polysat {
         signed_constraint ule(pdd const& p, pdd const& q) { return m_constraints.ule(p, q); }
         signed_constraint ule(pdd const& p, rational const& q) { return ule(p, p.manager().mk_val(q)); }
         signed_constraint ule(rational const& p, pdd const& q) { return ule(q.manager().mk_val(p), q); }
+        signed_constraint ule(pdd const& p, int n) { return ule(p, rational(n)); }
+        signed_constraint ule(int n, pdd const& p) { return ule(rational(n), p); }
         signed_constraint ult(pdd const& p, pdd const& q) { return m_constraints.ult(p, q); }
         signed_constraint ult(pdd const& p, rational const& q) { return ult(p, p.manager().mk_val(q)); }
         signed_constraint ult(rational const& p, pdd const& q) { return ult(q.manager().mk_val(p), q); }
diff --git a/src/math/polysat/viable2.cpp b/src/math/polysat/viable2.cpp
index 213d010b8..011a9b068 100644
--- a/src/math/polysat/viable2.cpp
+++ b/src/math/polysat/viable2.cpp
@@ -32,6 +32,7 @@ namespace polysat {
         if (m_alloc.empty())
             return alloc(entry);
         auto* e = m_alloc.back();
+        e->side_cond.reset();
         m_alloc.pop_back();
         return e;
     }
@@ -56,21 +57,25 @@ namespace polysat {
     }
 
     void viable2::intersect(pvar v, signed_constraint const& c) {
+        auto& fi = s.m_forbidden_intervals;
+        entry* ne = alloc_entry();
+        if (!fi.get_interval(c, v, ne->interval, ne->side_cond) || ne->interval.is_currently_empty())
+            m_alloc.push_back(ne);
+        else {
+            ne->src = c;
+            intersect(v, ne);
+        }
+    }
+
+    void viable2::intersect(pvar v, entry* ne) {
         entry* e = m_viable[v];
         if (e && e->interval.is_full())
             return;
 
-        auto& fi = s.m_forbidden_intervals;
-        entry* ne = alloc_entry();
-        if (!fi.get_interval(c, v, ne->interval, ne->side_cond)) {
-            m_alloc.push_back(ne);
-            return;
-        }
-        ne->init(ne);
-
         auto create_entry = [&]() {
             m_trail.push_back({ v, ne });
             s.m_trail.push_back(trail_instr_t::viable_add_i);
+            ne->init(ne);            
             return ne;
         };
 
@@ -89,18 +94,19 @@ namespace polysat {
                     m_alloc.push_back(ne);
                     return;
                 }
-                if (ne->interval.contains(e->interval)) {
+                while (ne->interval.contains(e->interval)) {
                     entry* n = e->next();
                     remove_entry(e);
-                    if (e == n) {
+                    if (!m_viable[v]) {
                         m_viable[v] = create_entry();
-                        break;
+                        return;
                     }
+                    if (e == first) 
+                        first = n;                    
                     e = n;
-                    continue;
                 }             
                 SASSERT(e->interval.lo_val() != ne->interval.lo_val());
-                if (e->interval.lo_val() >= ne->interval.lo_val()) {
+                if (e->interval.lo_val() > ne->interval.lo_val()) {
                     e->insert_before(create_entry());
                     if (e == first)
                         m_viable[v] = e->prev();
@@ -121,6 +127,7 @@ namespace polysat {
         if (!e)
             return true;
         entry* first = e;
+        auto const& max_value = s.m_pdd[v]->max_value();
         do {
             if (e->interval.is_full())
                 return false;
@@ -128,8 +135,7 @@ namespace polysat {
             if (n == e)
                 return true;
             if (n == first)
-                return e->interval.hi_val() != e->interval.hi().manager().max_value();
-
+                return e->interval.hi_val() != max_value;
             if (e->interval.hi_val() < n->interval.lo_val())
                 return true;
             e = n;
@@ -143,19 +149,27 @@ namespace polysat {
         if (!e)
             return true;
         entry* first = e;
-        do {
+        entry* last = first->prev();
+        if (last->interval.currently_contains(val))
+            return false;
+        for (; e != last; e = e->next()) {        
             if (e->interval.currently_contains(val))
                 return false;
             if (e->interval.lo_val() < val)
-                return !first->prev()->interval.currently_contains(val);
-            e = e->next();
+                return true;
         }         
-        while (e != first);
         return true; 
     }
 
-    void viable2::add_non_viable(pvar v, rational const& val) { 
-        NOT_IMPLEMENTED_YET();
+    void viable2::add_non_viable(pvar v, rational const& lo_val, signed_constraint const& c) { 
+        entry* ne = alloc_entry();
+        rational const& max_value = s.m_pdd[v]->max_value();
+        rational hi_val = (lo_val == max_value) ? rational::zero() : lo_val + 1;
+        pdd lo = s.m_pdd[v]->mk_val(lo_val);
+        pdd hi = s.m_pdd[v]->mk_val(hi_val);
+        ne->interval = eval_interval::proper(lo, lo_val, hi, hi_val); 
+        ne->src = c;     
+        intersect(v, ne);
     }
 
     rational viable2::min_viable(pvar v) { 
@@ -164,62 +178,74 @@ namespace polysat {
         if (!e)
             return lo;
         entry* first = e;
-        if (first->prev()->interval.currently_contains(lo))
-            lo = first->prev()->interval.hi_val();
-        do {
+        entry* last = first->prev();
+        if (last->interval.currently_contains(lo))
+            lo = last->interval.hi_val();
+        do {        
             if (!e->interval.currently_contains(lo))
-                return lo;
+                break;
             lo = e->interval.hi_val();
             e = e->next();
         }         
         while (e != first);
+        SASSERT(is_viable(v, lo));        
         return lo;
     }
 
     rational viable2::max_viable(pvar v) { 
-        return rational::zero(); 
+        rational hi = s.m_pdd[s.size(v)]->max_value();
+        auto* e = m_viable[v];
+        if (!e)
+            return hi;
+        entry* last = e->prev();
+        e = last;
+        do {
+            if (!e->interval.currently_contains(hi))
+                break;
+            hi = e->interval.lo_val() - 1;
+            e = e->prev();
+        }           
+        while (e != last);
+        SASSERT(is_viable(v, hi));
+        return hi;
     }
 
-    dd::find_t viable2::find_viable(pvar v, rational& val) { 
+    dd::find_t viable2::find_viable(pvar v, rational& lo) { 
+        lo = 0;
         auto* e = m_viable[v];
-        val = 0;
-        if (!e) 
+        if (!e)
             return dd::find_t::multiple;
-
+        if (e->interval.is_full())
+            return dd::find_t::empty;
 
         entry* first = e;
+        entry* last = first->prev();
+        if (last->interval.currently_contains(lo))
+            lo = last->interval.hi_val();
         do {
-            if (e->interval.is_full())
-                return dd::find_t::empty;
-            entry* n = e->next();
-            if (n == e && e->interval.lo_val() != 0) {
-                val = 0;
-                if (e->interval.lo_val() > 1 || e->interval.hi_val() < e->interval.hi().manager().max_value())
-                    return dd::find_t::multiple;
-                return dd::find_t::singleton;
-            }
-            if (n == first) {
-                if (e->interval.hi_val() == e->interval.hi().manager().max_value())
-                    ;
-            }
-            e = n;
+            if (!e->interval.currently_contains(lo))
+                break;
+            lo = e->interval.hi_val();
+            e = e->next();
         }         
         while (e != first);
-        
-#if 0
-        // TODO
-        entry* first = e;
-        do {
-            if (e->interval.is_full())
-                return dd::find_t::empty;
-            if (e->interval.currently_contains(val)) {
-                val = e->interval.hi_val();
-            }
-        }         
-        while (e != first);
-#endif
 
-        return dd::find_t::multiple;
+        if (e->interval.currently_contains(lo))
+            return dd::find_t::empty;
+
+        rational hi = s.m_pdd[s.size(v)]->max_value();
+        e = last;
+        do {
+            if (!e->interval.currently_contains(hi))
+                break;
+            hi = e->interval.lo_val() - 1;
+            e = e->prev();
+        }         
+        while (e != last);
+        if (lo == hi)
+            return dd::find_t::singleton;
+        else
+            return dd::find_t::multiple;
     }
 
     void viable2::log(pvar v) {
@@ -239,6 +265,25 @@ namespace polysat {
             log(v);
     }
 
+    std::ostream& viable2::display(std::ostream& out, pvar v) const {
+        auto* e = m_viable[v];
+        if (!e)
+            return out;
+        entry* first = e;
+        do {
+            out << "v" << v << ": " << e->interval << " " << e->side_cond << " " << e->src << "\n";
+            e = e->next();
+        }         
+        while (e != first);
+        return out;
+    }
+
+    std::ostream& viable2::display(std::ostream& out) const {
+        for (pvar v = 0; v < m_viable.size(); ++v)
+            display(out, v);
+        return out;
+    }
+
     /*
     * Lower bounds are strictly ascending.
     * intervals don't contain each-other (since lower bounds are ascending, 
@@ -249,6 +294,8 @@ namespace polysat {
         while (true) {
             if (e->interval.is_full())
                 return e->next() == e;
+            if (e->interval.is_currently_empty())
+                return false;
             auto* n = e->next();
             if (n != e && e->interval.contains(n->interval))
                 return false;
diff --git a/src/math/polysat/viable2.h b/src/math/polysat/viable2.h
index 4a3662b4a..86c4f3973 100644
--- a/src/math/polysat/viable2.h
+++ b/src/math/polysat/viable2.h
@@ -46,6 +46,10 @@ namespace polysat {
 
         entry* alloc_entry();
 
+        void intersect(pvar v, entry* e);
+
+        std::ostream& display(std::ostream& out, pvar v) const;
+
     public:
         viable2(solver& s);
 
@@ -82,7 +86,7 @@ namespace polysat {
         /**
          * register that val is non-viable for var.
          */
-        void add_non_viable(pvar v, rational const& val);
+        void add_non_viable(pvar v, rational const& val, signed_constraint const& c);
 
         /*
         * Extract min and max viable values for v
@@ -104,7 +108,12 @@ namespace polysat {
         /** Like log(v) but for all variables */
         void log();
 
+        std::ostream& display(std::ostream& out) const;
     };
+
+    inline std::ostream& operator<<(std::ostream& out, viable2 const& v) {
+        return v.display(out);
+    }
 }
 
 
diff --git a/src/test/CMakeLists.txt b/src/test/CMakeLists.txt
index 64d658f6d..2a23ac4ca 100644
--- a/src/test/CMakeLists.txt
+++ b/src/test/CMakeLists.txt
@@ -129,6 +129,7 @@ add_executable(test-z3
   value_generator.cpp
   value_sweep.cpp
   var_subst.cpp
+  viable.cpp	
   vector.cpp
   lp/lp.cpp
   lp/nla_solver_test.cpp
diff --git a/src/test/main.cpp b/src/test/main.cpp
index 3cb287f63..c95eae815 100644
--- a/src/test/main.cpp
+++ b/src/test/main.cpp
@@ -266,4 +266,5 @@ int main(int argc, char ** argv) {
     TST_ARGV(polysat_argv);
     TST(fixplex);
     TST(mod_interval);
+    TST(viable);
 }
diff --git a/src/test/viable.cpp b/src/test/viable.cpp
new file mode 100644
index 000000000..c3368b3dd
--- /dev/null
+++ b/src/test/viable.cpp
@@ -0,0 +1,50 @@
+#include "math/polysat/log.h"
+#include "math/polysat/solver.h"
+#include "math/polysat/viable2.h"
+
+namespace polysat {
+
+    struct solver_scopev {
+        reslimit lim;
+    };
+
+    struct scoped_solverv : public solver_scopev, public solver {
+        viable2 v;
+        scoped_solverv(): solver(lim), v(*this) {}
+    };
+
+    static void test1() {
+        scoped_solverv s;
+        auto xv = s.add_var(3);
+        auto x = s.var(xv);
+        s.v.push(3);
+        rational val;
+        auto c = s.ule(x + 3, x + 5);
+        s.v.intersect(xv, c);
+        std::cout << s.v << "\n";
+        std::cout << "min-max " << s.v.min_viable(xv) << " " << s.v.max_viable(xv) << "\n";
+        s.v.intersect(xv, s.ule(x, 2));
+        std::cout << s.v << "\n";
+        s.v.intersect(xv, s.ule(1, x));
+        std::cout << s.v << "\n";
+        std::cout << "min-max " << s.v.min_viable(xv) << " " << s.v.max_viable(xv) << "\n";
+        s.v.intersect(xv, s.ule(x, 3));
+        std::cout << s.v << "\n";
+        std::cout << s.v.find_viable(xv, val) << " " << val << "\n";        
+        std::cout << "min-max " << s.v.min_viable(xv) << " " << s.v.max_viable(xv) << "\n";
+        s.v.intersect(xv, s.ule(3, x));
+        std::cout << s.v << "\n";
+        std::cout << s.v.find_viable(xv, val) << " " << val << "\n";      
+    }
+
+    static void test2() {
+
+    }
+}
+
+
+
+void tst_viable() {
+    polysat::test1();
+    polysat::test2();
+}
\ No newline at end of file