YES
ignored inputs:
(COMMENT completed version of Example 5 of [ FR12 , doi:10.1007/978-3-642-31585-5_21 ] )

NRS:
   [ (0): a#X |- (lam [a](app <[]X,a>)) -> []X,
     (1):  |- (app <(bot <>),[]Y>) -> (bot <>),
     (2):  |- (lam [a](bot <>)) -> (bot <>) ]
Check confluence by parallel closed criterion
left-linear
uniform
BCPs:
(0 on 0(out)): 
   { a#X_1 |- < []X_1 <= (lam [a](app <[]X_1,a>)) => []X_1 >,
     b#X_1,a#X_1 |- < [(a b)]X_1 <= (lam [b](app <[]X_1,b>)) => []X_1 > }
(1 on 0(in)): 
   {  |- < (lam [a](bot <>)) <= (lam [a](app <(bot <>),a>)) => (bot <>) >,
      |- < (lam [b](bot <>)) <= (lam [b](app <(bot <>),b>)) => (bot <>) > }
(1 on 1(out)): 
   {  |- < (bot <>) <= (app <(bot <>),[]Y_1>) => (bot <>) > }
(2 on 2(out)): 
   {  |- < (bot <>) <= (lam [a](bot <>)) => (bot <>) >,
      |- < (bot <>) <= (lam [b](bot <>)) => (bot <>) > }
all BCPs are parallel closed
result: YES
time: 4 msec.