YES
ignored inputs:
(COMMENT eta reduction rule of the lambda calculus )

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

writing to temporary file...
./run_snprover.sh ./SMLNJ-lXbl34.trs
YES

Problem:
 lam(lambda(app(pair_2(X,diamond())))) -> X

Proof:
 DP Processor:
  DPs:
   
  TRS:
   lam(lambda(app(pair_2(X,diamond())))) -> X
  Qed
terminating
check each BCP has alpha-equivalent normal forms or not
BCPs:
(0 on 0): 
   { 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 > }
all BCPs are joinable
result: YES
time: 0 msec.