diff --git a/src/storm/modelchecker/rpatl/SparseSmgRpatlModelChecker.cpp b/src/storm/modelchecker/rpatl/SparseSmgRpatlModelChecker.cpp
index cb110be26..30001ce75 100644
--- a/src/storm/modelchecker/rpatl/SparseSmgRpatlModelChecker.cpp
+++ b/src/storm/modelchecker/rpatl/SparseSmgRpatlModelChecker.cpp
@@ -142,6 +142,7 @@ namespace storm {
             ExplicitQualitativeCheckResult const& rightResult = rightResultPointer->asExplicitQualitativeCheckResult();
 
             auto ret = storm::modelchecker::helper::SparseSmgRpatlHelper<ValueType>::computeUntilProbabilitiesSound(env, storm::solver::SolveGoal<ValueType>(this->getModel(), checkTask), this->getModel().getTransitionMatrix(), this->getModel().getBackwardTransitions(), leftResult.getTruthValuesVector(), rightResult.getTruthValuesVector(), checkTask.isQualitativeSet(), statesOfCoalition, checkTask.isProduceSchedulersSet(), checkTask.getHint());
+            STORM_LOG_DEBUG(ret.values);
             std::unique_ptr<CheckResult> result(new ExplicitQuantitativeCheckResult<ValueType>(std::move(ret.values)));
             if(checkTask.isShieldingTask()) {
                 storm::storage::BitVector allStatesBv = storm::storage::BitVector(this->getModel().getTransitionMatrix().getRowGroupCount(), true);
@@ -151,6 +152,7 @@ namespace storm {
             if (checkTask.isProduceSchedulersSet() && ret.scheduler) {
                 result->asExplicitQuantitativeCheckResult<ValueType>().setScheduler(std::move(ret.scheduler));
             }
+            //STORM_LOG_DEBUG(result);
             return result;
         }
 
diff --git a/src/storm/modelchecker/rpatl/helper/SparseSmgRpatlHelper.cpp b/src/storm/modelchecker/rpatl/helper/SparseSmgRpatlHelper.cpp
index 566120827..e3dc2d8ee 100644
--- a/src/storm/modelchecker/rpatl/helper/SparseSmgRpatlHelper.cpp
+++ b/src/storm/modelchecker/rpatl/helper/SparseSmgRpatlHelper.cpp
@@ -83,11 +83,13 @@ namespace storm {
                 storm::storage::BitVector probGreater0 = storm::utility::graph::performProbGreater0(backwardTransitions, phiStates, psiStates);
                 // assigning 1s to the xU vector for all states except the states s where Prob(sEf) = 0 for all goal states f
                 assert(xU.size() == probGreater0.size());
-                for (size_t i = 0; i < xL.size(); i++) // TODO Fabian: do this more efficient
-                {
-                    if (probGreater0[i])
-                        xU[i] = 1;
-                }
+                auto xU_begin = xU.begin();
+                std::for_each(xU.begin(), xU.end(), [&probGreater0, &xU_begin](ValueType &it)
+                              {
+                                  if (probGreater0[&it - &(*xU_begin)])
+                                      it = 1;
+                              });
+
                 STORM_LOG_DEBUG("xU " << xU);
 
                 std::vector<ValueType> result = std::vector<ValueType>(transitionMatrix.getRowGroupCount(), storm::utility::zero<ValueType>());
@@ -95,9 +97,9 @@ namespace storm {
                 std::vector<ValueType> constrainedChoiceValues;
 
                 viHelper.performValueIteration(env, xL, xU, goal.direction(), constrainedChoiceValues);
-                return SMGSparseModelCheckingHelperReturnType<ValueType>(std::move(xU), std::move(relevantStates), std::move(scheduler), std::move(constrainedChoiceValues));
 
-                assert(false);
+                STORM_LOG_DEBUG(xU);
+                return SMGSparseModelCheckingHelperReturnType<ValueType>(std::move(xU), std::move(relevantStates), std::move(scheduler), std::move(constrainedChoiceValues));
             }
 
             template<typename ValueType>
diff --git a/src/storm/modelchecker/rpatl/helper/internal/SoundGameViHelper.cpp b/src/storm/modelchecker/rpatl/helper/internal/SoundGameViHelper.cpp
index 5a7109cac..732127ce9 100644
--- a/src/storm/modelchecker/rpatl/helper/internal/SoundGameViHelper.cpp
+++ b/src/storm/modelchecker/rpatl/helper/internal/SoundGameViHelper.cpp
@@ -84,62 +84,82 @@ namespace storm {
                         prepareSolversAndMultipliers(env);
                     }
                     _x1IsCurrent = !_x1IsCurrent;
+                    std::vector<ValueType> choiceValuesL = std::vector<ValueType>(this->_transitionMatrix.getRowCount(), storm::utility::zero<ValueType>());
 
-                    std::vector<ValueType> choiceValues = xNewL();
-                    choiceValues.resize(this->_transitionMatrix.getRowCount());
-
-                    _multiplier->multiply(env, xOldL(), nullptr, choiceValues);
-                    reduceChoiceValues(choiceValues, &reducedMinimizerActions);
-                    xNewL() = choiceValues;
+                    _multiplier->multiply(env, xOldL(), nullptr, choiceValuesL);
+                    reduceChoiceValues(choiceValuesL, &reducedMinimizerActions, xNewL());
 
                     // over_approximation
 
-                    _multiplier->multiplyAndReduce(env, dir, xOldU(), nullptr, xNewU(), nullptr, &_statesOfCoalition);
+                    std::vector<ValueType> choiceValuesU = std::vector<ValueType>(this->_transitionMatrix.getRowCount(), storm::utility::zero<ValueType>());
+
+                    _multiplier->multiply(env, xOldU(), nullptr, choiceValuesU);
+                    reduceChoiceValues(choiceValuesU, nullptr, xNewU());
+
+                    //_multiplier->multiplyAndReduce(env, dir, xOldU(), nullptr, xNewU(), nullptr, &_statesOfCoalition);
 
                     // restricting the none optimal minimizer choices
                     storage::SparseMatrix<ValueType> restrictedTransMatrix = this->_transitionMatrix.restrictRows(reducedMinimizerActions);
-                    _multiplierRestricted = storm::solver::MultiplierFactory<ValueType>().create(env, restrictedTransMatrix);
 
                     // STORM_LOG_DEBUG("restricted Transition: \n" << restrictedTransMatrix);
 
-                    // find_MSECs() & deflate()
+                    // find_MSECs()
                     storm::storage::MaximalEndComponentDecomposition<ValueType> MSEC = storm::storage::MaximalEndComponentDecomposition<ValueType>(restrictedTransMatrix, _backwardTransitions);
 
-                    // STORM_LOG_DEBUG("MECD: \n" << MECD);
-                    deflate(MSEC,restrictedTransMatrix, xNewU());
+                    // STORM_LOG_DEBUG("MECD: \n" << MSEC);
+
+                    // reducing the choiceValuesU
+                    size_t i = 0;
+                    auto new_end = std::remove_if(choiceValuesU.begin(), choiceValuesU.end(), [&reducedMinimizerActions, &i](const auto& item) {
+                        bool ret = !(reducedMinimizerActions[i]);
+                        i++;
+                        return ret;
+                    });
+                    choiceValuesU.erase(new_end, choiceValuesU.end());
+
+                    // deflating the MSECs
+                    deflate(MSEC, restrictedTransMatrix, xNewU(), choiceValuesU);
                 }
 
                 template <typename ValueType>
-                void SoundGameViHelper<ValueType>::deflate(storm::storage::MaximalEndComponentDecomposition<ValueType> const MSEC, storage::SparseMatrix<ValueType> const restrictedMatrix,  std::vector<ValueType>& xU) {
+                void SoundGameViHelper<ValueType>::deflate(storm::storage::MaximalEndComponentDecomposition<ValueType> const MSEC, storage::SparseMatrix<ValueType> const restrictedMatrix,  std::vector<ValueType>& xU, std::vector<ValueType> choiceValues) {
                     auto rowGroupIndices = restrictedMatrix.getRowGroupIndices();
 
+                    auto choice_begin = choiceValues.begin();
                     // iterating over all MSECs
                     for (auto smec_it : MSEC) {
                         ValueType bestExit = 0;
+                        if (smec_it.isErgodic(restrictedMatrix)) continue; // TODO Fabian: ?? isErgodic undefined ref
                         auto stateSet = smec_it.getStateSet();
                         for (uint state : stateSet) {
-                            uint rowGroupSize = rowGroupIndices[state + 1] - rowGroupIndices[state];
-                            if (!_minimizerStates[state]) {                                           // check if current state is maximizer state
-                                for (uint choice = 0; choice < rowGroupSize; choice++) {
-                                    if (!smec_it.containsChoice(state, choice + rowGroupIndices[state])) {
-                                        ValueType choiceValue = 0;
-                                        _multiplierRestricted->multiplyRow(choice + rowGroupIndices[state], xU, choiceValue);
-                                        if (choiceValue > bestExit)
-                                            bestExit = choiceValue;
-                                    }
-                                }
-                            }
+                            if (_minimizerStates[state]) continue;
+                            uint rowGroupIndex = rowGroupIndices[state];
+                            auto exitingCompare = [&state, &smec_it, &choice_begin](const ValueType &lhs, const ValueType &rhs)
+                            {
+                                bool lhsExiting = !smec_it.containsChoice(state, (&lhs - &(*choice_begin)));
+                                bool rhsExiting = !smec_it.containsChoice(state, (&rhs - &(*choice_begin)));
+                                if( lhsExiting && !rhsExiting) return false;
+                                if(!lhsExiting &&  rhsExiting) return true;
+                                if(!lhsExiting && !rhsExiting) return false;
+                                return lhs < rhs;
+                            };
+                            uint rowGroupSize = rowGroupIndices[state + 1] - rowGroupIndex;
+
+                            auto choice_it = choice_begin + rowGroupIndex;
+                            ValueType newBestExit = *std::max_element(choice_it, choice_it + rowGroupSize, exitingCompare);
+                            if (newBestExit > bestExit)
+                                bestExit = newBestExit;
                         }
                         // deflating the states of the current MSEC
                         for (uint state : stateSet) {
-                            if (!_psiStates[state])
-                                xU[state] = std::min(xU[state], bestExit);
+                            if (_psiStates[state]) continue;
+                            xU[state] = std::min(xU[state], bestExit);
                         }
                     }
                 }
 
                 template <typename ValueType>
-                void SoundGameViHelper<ValueType>::reduceChoiceValues(std::vector<ValueType>& choiceValues, storm::storage::BitVector* result)
+                void SoundGameViHelper<ValueType>::reduceChoiceValues(std::vector<ValueType>& choiceValues, storm::storage::BitVector* result, std::vector<ValueType>& x)
                 {
                     // result BitVec should be initialized with 1s outside the method
 
@@ -153,23 +173,26 @@ namespace storm {
                             // getting the optimal minimizer choice for the given state
                             optChoice = *std::min_element(choice_it, choice_it + rowGroupSize);
 
-                            for (uint choice = 0; choice < rowGroupSize; choice++, choice_it++) {
-                                if (*choice_it > optChoice) {
-                                    result->set(rowGroupIndices[state] + choice, 0);
+                            if (result != nullptr) {
+                                for (uint choice = 0; choice < rowGroupSize; choice++, choice_it++) {
+                                    if (*choice_it > optChoice) {
+                                        result->set(rowGroupIndices[state] + choice, 0);
+                                    }
                                 }
                             }
-                            // reducing the xNew() (choiceValues) vector for minimizer states
-                            choiceValues[state] = optChoice;
+                            else
+                                choice_it += rowGroupSize;
+                            // reducing the xNew() vector for minimizer states
+                            x[state] = optChoice;
                         }
                         else
                         {
                             optChoice = *std::max_element(choice_it, choice_it + rowGroupSize);
-                            // reducing the xNew() (choiceValues) vector for maximizer states
-                            choiceValues[state] = optChoice;
+                            // reducing the xNew() vector for maximizer states
+                            x[state] = optChoice;
                             choice_it += rowGroupSize;
                         }
                     }
-                    choiceValues.resize(this->_transitionMatrix.getRowGroupCount());
                 }
 
 
diff --git a/src/storm/modelchecker/rpatl/helper/internal/SoundGameViHelper.h b/src/storm/modelchecker/rpatl/helper/internal/SoundGameViHelper.h
index 5fecd8d87..f738958ca 100644
--- a/src/storm/modelchecker/rpatl/helper/internal/SoundGameViHelper.h
+++ b/src/storm/modelchecker/rpatl/helper/internal/SoundGameViHelper.h
@@ -74,9 +74,9 @@ namespace storm {
                      */
                     void performIterationStep(Environment const& env, storm::solver::OptimizationDirection const dir, std::vector<uint64_t>* choices = nullptr);
 
-                    void deflate(storm::storage::MaximalEndComponentDecomposition<ValueType> const MECD, storage::SparseMatrix<ValueType> const restrictedMatrix, std::vector<ValueType>& xU);
+                    void deflate(storm::storage::MaximalEndComponentDecomposition<ValueType> const MECD, storage::SparseMatrix<ValueType> const restrictedMatrix, std::vector<ValueType>& xU, std::vector<ValueType> choiceValues);
 
-                    void reduceChoiceValues(std::vector<ValueType>& choiceValues, storm::storage::BitVector* result);
+                    void reduceChoiceValues(std::vector<ValueType>& choiceValues, storm::storage::BitVector* result, std::vector<ValueType>& x);
 
                     /*!
                      * Checks whether the curently computed value achieves the desired precision
@@ -117,7 +117,6 @@ namespace storm {
                     storm::storage::BitVector _psiStates;
                     std::vector<ValueType> _x, _x1L, _x2L, _x1U, _x2U;
                     std::unique_ptr<storm::solver::Multiplier<ValueType>> _multiplier;
-                    std::unique_ptr<storm::solver::Multiplier<ValueType>> _multiplierRestricted;
                     OptimizationDirection _optimizationDirection;
 
                     bool _produceScheduler = false;
diff --git a/src/storm/storage/MaximalEndComponent.cpp b/src/storm/storage/MaximalEndComponent.cpp
index aa7453277..d4f51e089 100644
--- a/src/storm/storage/MaximalEndComponent.cpp
+++ b/src/storm/storage/MaximalEndComponent.cpp
@@ -4,7 +4,6 @@
 
 namespace storm {
     namespace storage {
-
         std::ostream& operator<<(std::ostream& out, storm::storage::FlatSet<uint_fast64_t> const& block);
 
         MaximalEndComponent::MaximalEndComponent() : stateToChoicesMapping() {
@@ -100,6 +99,18 @@ namespace storm {
             return stateChoicePair->second.find(choice) != stateChoicePair->second.end();
         }
 
+        template<typename ValueType>
+        bool MaximalEndComponent::isErgodic(storm::storage::SparseMatrix<ValueType> transitionMatrix) const {
+            auto rowGroupIndices = transitionMatrix.getRowGroupIndices();
+            for (auto state : this->getStateSet())
+            {
+                if (getChoicesForState(state).size() == (rowGroupIndices[state + 1] - rowGroupIndices[state])) continue;
+                return false;
+            }
+            return true;
+        }
+
+
         MaximalEndComponent::set_type MaximalEndComponent::getStateSet() const {
             set_type states;
             states.reserve(stateToChoicesMapping.size());
@@ -136,5 +147,8 @@ namespace storm {
         MaximalEndComponent::const_iterator MaximalEndComponent::end() const {
             return stateToChoicesMapping.end();
         }
+
+        template bool MaximalEndComponent::isErgodic<double>(storm::storage::SparseMatrix<double> transitionMatrix) const;
+        template bool MaximalEndComponent::isErgodic<storm::RationalNumber>(storm::storage::SparseMatrix<storm::RationalNumber> transitionMatrix) const;
     }
 }
diff --git a/src/storm/storage/MaximalEndComponent.h b/src/storm/storage/MaximalEndComponent.h
index a1d5b37c2..66c1d1c4a 100644
--- a/src/storm/storage/MaximalEndComponent.h
+++ b/src/storm/storage/MaximalEndComponent.h
@@ -5,6 +5,7 @@
 
 #include "storm/storage/sparse/StateType.h"
 #include "storm/storage/BoostTypes.h"
+#include "storm/storage/SparseMatrix.h"
 
 namespace storm {
     namespace storage {
@@ -20,6 +21,7 @@ namespace storm {
             typedef std::unordered_map<uint_fast64_t, set_type> map_type;
             typedef map_type::iterator iterator;
             typedef map_type::const_iterator const_iterator;
+
             
             /*!
              * Creates an empty MEC.
@@ -124,6 +126,15 @@ namespace storm {
              * @return True if the given choice is contained in the MEC.
              */
             bool containsChoice(uint_fast64_t state, uint_fast64_t choice) const;
+
+            /*!
+             * Retrieves wether the MEC is ergodic or not i.e. wether the MEC is exitable or not
+             *
+             * @param transitionMatrix the given transition matrix
+             * @return True if the MEC is ergodic
+             */
+            template<typename ValueType>
+            bool isErgodic(storm::storage::SparseMatrix<ValueType> transitionMatrix) const;
             
             /*!
              * Retrieves the set of states contained in the MEC.