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 = [purge^#(.(_0,_1)) -> purge^#(remove(_0,_1))]
  TRS = {purge(nil) -> nil, purge(.(_0,_1)) -> .(_0,purge(remove(_0,_1))), remove(_0,nil) -> nil, remove(_0,.(_1,_2)) -> if(=(_0,_1),remove(_0,_2),.(_1,remove(_0,_2)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (24)! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      purge > [., =, nil, if, remove], . > [=, nil, if, remove], remove > [=, nil, if]
      and the argument filtering:
      {purge:[0], .:[0, 1], if:[0], =:[0], remove:[0], purge^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [remove^#(_0,.(_1,_2)) -> remove^#(_0,_2), remove^#(_0,.(_1,_2)) -> remove^#(_0,_2)]
  TRS = {purge(nil) -> nil, purge(.(_0,_1)) -> .(_0,purge(remove(_0,_1))), remove(_0,nil) -> nil, remove(_0,.(_1,_2)) -> if(=(_0,_1),remove(_0,_2),.(_1,remove(_0,_2)))}
    ## Trying with homeomorphic embeddings... Success!
  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 = 27