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 = [max^#(g(g(g(_0,_1),_2),u)) -> max^#(g(g(_0,_1),_2))]
  TRS = {f(_0,nil) -> g(nil,_0), f(_0,g(_1,_2)) -> g(f(_0,_1),_2), ++(_0,nil) -> _0, ++(_0,g(_1,_2)) -> g(++(_0,_1),_2), null(nil) -> true, null(g(_0,_1)) -> false, mem(nil,_0) -> false, mem(g(_0,_1),_2) -> or(=(_1,_2),mem(_0,_2)), mem(_0,max(_0)) -> not(null(_0)), max(g(g(nil,_0),_1)) -> max'(_0,_1), max(g(g(g(_0,_1),_2),u)) -> max'(max(g(g(_0,_1),_2)),u)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [mem^#(g(_0,_1),_2) -> mem^#(_0,_2)]
  TRS = {f(_0,nil) -> g(nil,_0), f(_0,g(_1,_2)) -> g(f(_0,_1),_2), ++(_0,nil) -> _0, ++(_0,g(_1,_2)) -> g(++(_0,_1),_2), null(nil) -> true, null(g(_0,_1)) -> false, mem(nil,_0) -> false, mem(g(_0,_1),_2) -> or(=(_1,_2),mem(_0,_2)), mem(_0,max(_0)) -> not(null(_0)), max(g(g(nil,_0),_1)) -> max'(_0,_1), max(g(g(g(_0,_1),_2),u)) -> max'(max(g(g(_0,_1),_2)),u)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [++^#(_0,g(_1,_2)) -> ++^#(_0,_1)]
  TRS = {f(_0,nil) -> g(nil,_0), f(_0,g(_1,_2)) -> g(f(_0,_1),_2), ++(_0,nil) -> _0, ++(_0,g(_1,_2)) -> g(++(_0,_1),_2), null(nil) -> true, null(g(_0,_1)) -> false, mem(nil,_0) -> false, mem(g(_0,_1),_2) -> or(=(_1,_2),mem(_0,_2)), mem(_0,max(_0)) -> not(null(_0)), max(g(g(nil,_0),_1)) -> max'(_0,_1), max(g(g(g(_0,_1),_2),u)) -> max'(max(g(g(_0,_1),_2)),u)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [f^#(_0,g(_1,_2)) -> f^#(_0,_1)]
  TRS = {f(_0,nil) -> g(nil,_0), f(_0,g(_1,_2)) -> g(f(_0,_1),_2), ++(_0,nil) -> _0, ++(_0,g(_1,_2)) -> g(++(_0,_1),_2), null(nil) -> true, null(g(_0,_1)) -> false, mem(nil,_0) -> false, mem(g(_0,_1),_2) -> or(=(_1,_2),mem(_0,_2)), mem(_0,max(_0)) -> not(null(_0)), max(g(g(nil,_0),_1)) -> max'(_0,_1), max(g(g(g(_0,_1),_2),u)) -> max'(max(g(g(_0,_1),_2)),u)}
    ## 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