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 = [app^#(app(lt,app(s,_0)),app(s,_1)) -> app^#(app(lt,_0),_1), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(app(if,app(app(lt,_0),_2)),app(app(member,_0),_1)),app(app(app(if,app(app(eq,_0),_2)),true),app(app(member,_0),_3))), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(if,app(app(lt,_0),_2)),app(app(member,_0),_1)), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(lt,_0),_2), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(member,_0),_1), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(app(if,app(app(eq,_0),_2)),true),app(app(member,_0),_3)), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(eq,_0),_2), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(member,_0),_3)]
  TRS = {app(app(lt,app(s,_0)),app(s,_1)) -> app(app(lt,_0),_1), app(app(lt,0),app(s,_0)) -> true, app(app(lt,_0),0) -> false, app(app(eq,_0),_0) -> true, app(app(eq,app(s,_0)),0) -> false, app(app(eq,0),app(s,_0)) -> false, app(app(member,_0),null) -> false, app(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app(app(app(if,app(app(lt,_0),_2)),app(app(member,_0),_1)),app(app(app(if,app(app(eq,_0),_2)),true),app(app(member,_0),_3)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (15)! Aborting!
    ## Trying with lexicographic path orders...
    Successfully decomposed the DP problem into smaller problems to solve!
## Round 2:
  ## DP problem: 
  Dependency pairs = [app^#(app(lt,app(s,_0)),app(s,_1)) -> app^#(app(lt,_0),_1), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(member,_0),_1), app^#(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app^#(app(member,_0),_3)]
  TRS = {app(app(lt,app(s,_0)),app(s,_1)) -> app(app(lt,_0),_1), app(app(lt,0),app(s,_0)) -> true, app(app(lt,_0),0) -> false, app(app(eq,_0),_0) -> true, app(app(eq,app(s,_0)),0) -> false, app(app(eq,0),app(s,_0)) -> false, app(app(member,_0),null) -> false, app(app(member,_0),app(app(app(fork,_1),_2),_3)) -> app(app(app(if,app(app(lt,_0),_2)),app(app(member,_0),_1)),app(app(app(if,app(app(eq,_0),_2)),true),app(app(member,_0),_3)))}
    ## 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 = 110