It is clear that L is recursive : Because given any input 
, we can verify whether it defines a CSG 
. If not, then 
. If wi defines a CSG , then 
must be recursive as proved already in the previous theorems. The membership algorithm given in the previous theorem can be used to verify whether 
. If not, then .
, we can verify whether it defines a CSG . If not, then . If wi defines a CSG , then must be recursive as proved already in the previous theorems. The membership algorithm given in the previous theorem can be used to verify whether . If not, then .
But L is not context-sensitive : Assume, for contradiction, that L is a CSL. Then there exists some 
such that 
. Consider the question : is 
?
If , then by definition of L , 
. A contradiction.
If 
, then again by definiton of L , . Again a contradiction.
Hence our original assumption that L is a CSL must be wrong.
Hence L is recursive but not a CSL.