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 = [mem^#(_0,union(_1,_2)) -> mem^#(_0,_1), mem^#(_0,union(_1,_2)) -> mem^#(_0,_2)]
  TRS = {or(true,_0) -> true, or(_0,true) -> true, or(false,false) -> false, mem(_0,nil) -> false, mem(_0,set(_1)) -> =(_0,_1), mem(_0,union(_1,_2)) -> or(mem(_0,_1),mem(_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 = 0