diff --git a/resources/3rdparty/cudd-3.0.0/cplusplus/cuddObj.cc b/resources/3rdparty/cudd-3.0.0/cplusplus/cuddObj.cc
index 800ebe26a..2f91c20a7 100644
--- a/resources/3rdparty/cudd-3.0.0/cplusplus/cuddObj.cc
+++ b/resources/3rdparty/cudd-3.0.0/cplusplus/cuddObj.cc
@@ -3503,6 +3503,15 @@ BDD::ExistAbstract(
 
 } // BDD::ExistAbstract
 
+BDD
+ExistAbstractRepresentative(const BDD& cube) const {
+    DdManager *mgr = checkSameManager(cube);
+    DdNode *result;
+    result = Cudd_bddExistAbstractRepresentative(mgr, node, cube.node);
+    checkReturnValue(result);
+    return BDD(p, result);
+} // BDD::ExistAbstractRepresentative
+    
 BDD
 BDD::ExistAbstractRepresentative(
   const BDD& cube) const
diff --git a/src/modelchecker/abstraction/GameBasedMdpModelChecker.cpp b/src/modelchecker/abstraction/GameBasedMdpModelChecker.cpp
index 71e39cf67..d5a4928c0 100644
--- a/src/modelchecker/abstraction/GameBasedMdpModelChecker.cpp
+++ b/src/modelchecker/abstraction/GameBasedMdpModelChecker.cpp
@@ -2,6 +2,8 @@
 
 #include "src/storage/expressions/ExpressionManager.h"
 
+#include "src/logic/FragmentSpecification.h"
+
 #include "src/utility/macros.h"
 
 #include "src/exceptions/NotSupportedException.h"
@@ -31,22 +33,8 @@ namespace storm {
         template<storm::dd::DdType Type, typename ValueType>
         bool GameBasedMdpModelChecker<Type, ValueType>::canHandle(CheckTask<storm::logic::Formula> const& checkTask) const {
             storm::logic::Formula const& formula = checkTask.getFormula();
-            if (formula.isProbabilityOperatorFormula()) {
-                return this->canHandle(checkTask.replaceFormula(formula.asProbabilityOperatorFormula().getSubformula()));
-            } else if (formula.isUntilFormula() || formula.isEventuallyFormula()) {
-                if (formula.isUntilFormula()) {
-                    storm::logic::UntilFormula const& untilFormula = formula.asUntilFormula();
-                    if (untilFormula.getLeftSubformula().isPropositionalFormula() && untilFormula.getRightSubformula().isPropositionalFormula()) {
-                        return true;
-                    }
-                } else if (formula.isEventuallyFormula()) {
-                    storm::logic::EventuallyFormula const& eventuallyFormula = formula.asEventuallyFormula();
-                    if (eventuallyFormula.getSubformula().isPropositionalFormula()) {
-                        return true;
-                    }
-                }
-            }
-            return false;
+            storm::logic::FragmentSpecification fragment = storm::logic::reachability();
+            return formula.isInFragment(fragment) && checkTask.isOnlyInitialStatesRelevantSet();
         }
                 
         template<storm::dd::DdType Type, typename ValueType>
@@ -56,7 +44,7 @@ namespace storm {
         }
         
         template<storm::dd::DdType Type, typename ValueType>
-        std::unique_ptr<CheckResult> GameBasedMdpModelChecker<Type, ValueType>::computeEventuallyProbabilities(CheckTask<storm::logic::EventuallyFormula> const& checkTask) {
+        std::unique_ptr<CheckResult> GameBasedMdpModelChecker<Type, ValueType>::computeReachabilityProbabilities(CheckTask<storm::logic::EventuallyFormula> const& checkTask) {
             storm::logic::EventuallyFormula const& pathFormula = checkTask.getFormula();
             return performGameBasedAbstractionRefinement(CheckTask<storm::logic::Formula>(pathFormula), originalProgram.getManager().boolean(true), getExpression(pathFormula.getSubformula()));
         }
diff --git a/src/modelchecker/abstraction/GameBasedMdpModelChecker.h b/src/modelchecker/abstraction/GameBasedMdpModelChecker.h
index c10510ec0..6f289859b 100644
--- a/src/modelchecker/abstraction/GameBasedMdpModelChecker.h
+++ b/src/modelchecker/abstraction/GameBasedMdpModelChecker.h
@@ -28,7 +28,7 @@ namespace storm {
             virtual bool canHandle(CheckTask<storm::logic::Formula> const& checkTask) const override;
             
             virtual std::unique_ptr<CheckResult> computeUntilProbabilities(CheckTask<storm::logic::UntilFormula> const& checkTask) override;
-            virtual std::unique_ptr<CheckResult> computeEventuallyProbabilities(CheckTask<storm::logic::EventuallyFormula> const& checkTask) override;
+            virtual std::unique_ptr<CheckResult> computeReachabilityProbabilities(CheckTask<storm::logic::EventuallyFormula> const& checkTask) override;
             
         private:
             std::unique_ptr<CheckResult> performGameBasedAbstractionRefinement(CheckTask<storm::logic::Formula> const& checkTask, storm::expressions::Expression const& constraintExpression, storm::expressions::Expression const& targetStateExpression);