YES

Prover = TRS(tech=PATTERN_RULES, nb_unfoldings=unlimited, max_nb_unfolded_rules=200)

** 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 = [rem^#(g(_0,_1),s(_2)) -> rem^#(_0,_2)]
  TRS = {norm(nil) -> 0, norm(g(_0,_1)) -> s(norm(_0)), f(_0,nil) -> g(nil,_0), f(_0,g(_1,_2)) -> g(f(_0,_1),_2), rem(nil,_0) -> nil, rem(g(_0,_1),0) -> g(_0,_1), rem(g(_0,_1),s(_2)) -> rem(_0,_2)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [f^#(_0,g(_1,_2)) -> f^#(_0,_1)]
  TRS = {norm(nil) -> 0, norm(g(_0,_1)) -> s(norm(_0)), f(_0,nil) -> g(nil,_0), f(_0,g(_1,_2)) -> g(f(_0,_1),_2), rem(nil,_0) -> nil, rem(g(_0,_1),0) -> g(_0,_1), rem(g(_0,_1),s(_2)) -> rem(_0,_2)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [norm^#(g(_0,_1)) -> norm^#(_0)]
  TRS = {norm(nil) -> 0, norm(g(_0,_1)) -> s(norm(_0)), f(_0,nil) -> g(nil,_0), f(_0,g(_1,_2)) -> g(f(_0,_1),_2), rem(nil,_0) -> nil, rem(g(_0,_1),0) -> g(_0,_1), rem(g(_0,_1),s(_2)) -> rem(_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