YES

Prover = TRS(tech=GUIDED_UNF_TRIPLES, nb_unfoldings=unlimited, unfold_variables=false, max_nb_coefficients=12, max_nb_unfolded_rules=-1, strategy=LEFTMOST_NE)

** BEGIN proof argument **
All the DP problems were proved finite.
As all the involved DP processors are sound,
the TRS under analysis terminates.
** END proof argument **

** BEGIN proof description **
## Searching for a generalized rewrite rule
(a rule whose right-hand side contains a variable
that does not occur in the left-hand side)...
No generalized rewrite rule found!

## Applying the DP framework...
## Round 1:
  ## DP problem: 
  Dependency pairs = [admit^#(_0,.(_1,.(_2,.(w,_3)))) -> admit^#(carry(_0,_1,_2),_3)]
  TRS = {admit(_0,nil) -> nil, admit(_0,.(_1,.(_2,.(w,_3)))) -> cond(=(sum(_0,_1,_2),w),.(_1,.(_2,.(w,admit(carry(_0,_1,_2),_3))))), cond(true,_0) -> _0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (36)! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      admit > [cond, .]
      and the argument filtering:
      {carry:[0, 1, 2], admit:[1], cond:[1], =:[0], sum:[0], .:[1], admit^#:[1]}
  This DP problem is finite.

** END proof description **

Proof stopped at iteration 0
Number of unfolded rules generated by this proof = 0
Number of unfolded rules generated by all the parallel proofs = 167