YES
ignored inputs:
(COMMENT Example 4.7 of [ Suzuki et al. , PPL 2014 ] )

NRS:
   [ (0): a#X |- (f []X) -> [a][]X ]
Check confluence by Knuth-Bendix criterion
uniform

writing to temporary file...
./run_snprover.sh ./SMLNJ-sKzi57.trs
YES

Problem:
 f(X) -> lambda(X)

Proof:
 DP Processor:
  DPs:
   
  TRS:
   f(X) -> lambda(X)
  Qed
terminating
check each BCP has alpha-equivalent normal forms or not
BCPs:
(0 on 0): 
   { a#X_1 |- < [a][]X_1 <= (f []X_1) => [a][]X_1 >,
     a#X_1,b#X_1 |- < [a][]X_1 <= (f []X_1) => [b][]X_1 > }
all BCPs are joinable
result: YES
time: 5 msec.