MAYBE
ignored inputs:
(COMMENT rules to obtain PNF of first-order formulas with additional rules )
(COMMENT Example 44 [ FG07 , doi:10.1016/j.ic.2006.12.002 ] )

NRS:
   [ (0): a#P |- (and <[]P,(forall [a][]Q)>) -> (forall [a](and <[]P,[]Q>)),
     (1): a#P |- (and <(forall [a][]Q),[]P>) -> (forall [a](and <[]Q,[]P>)),
     (2): a#P |- (or <[]P,(forall [a][]Q)>) -> (forall [a](or <[]P,[]Q>)),
     (3): a#P |- (or <(forall [a][]Q),[]P>) -> (forall [a](or <[]Q,[]P>)),
     (4): a#P |- (and <[]P,(exists [a][]Q)>) -> (exists [a](and <[]P,[]Q>)),
     (5): a#P |- (and <(exists [a][]Q),[]P>) -> (exists [a](and <[]Q,[]P>)),
     (6): a#P |- (or <[]P,(exists [a][]Q)>) -> (exists [a](or <[]P,[]Q>)),
     (7): a#P |- (or <(exists [a][]Q),[]P>) -> (exists [a](or <[]Q,[]P>)),
     (8):  |- (not <(exists [a][]Q)>) -> (forall [a](not []Q)),
     (9):  |- (not <(forall [a][]Q)>) -> (exists [a](not []Q)),
     (10): a#X |- (forall [a][]X) -> []X,
     (11):  |- (and <(forall [a][]X),(forall [a][]Y)>) -> (forall [a](and <[]X,[]Y>)),
     (12): a#X |- (exists [a][]X) -> []X,
     (13):  |- (or <(exists [a][]X),(exists [a][]Y)>) -> (exists [a](or <[]X,[]Y>)) ]
Check confluence by orthogonality
abstract skeleton preserving
left-linear
check proper overlapping
a proper overlap exists
0-1
 |- < (forall [a](and <(forall [a][]Q_1),[]Q>)) <= (and <(forall [a][]Q_1),(forall [a][]Q)>) => (forall [a](and <[]Q_1,(forall [a][]Q)>)) >
found proper overlaps
result: MAYBE
time: 5 msec.