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 = [g_5^#(s(_0),_1) -> g_5^#(_0,_1)]
  TRS = {f_0(_0) -> a, f_1(_0) -> g_1(_0,_0), g_1(s(_0),_1) -> b(f_0(_1),g_1(_0,_1)), f_2(_0) -> g_2(_0,_0), g_2(s(_0),_1) -> b(f_1(_1),g_2(_0,_1)), f_3(_0) -> g_3(_0,_0), g_3(s(_0),_1) -> b(f_2(_1),g_3(_0,_1)), f_4(_0) -> g_4(_0,_0), g_4(s(_0),_1) -> b(f_3(_1),g_4(_0,_1)), f_5(_0) -> g_5(_0,_0), g_5(s(_0),_1) -> b(f_4(_1),g_5(_0,_1))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [g_4^#(s(_0),_1) -> g_4^#(_0,_1)]
  TRS = {f_0(_0) -> a, f_1(_0) -> g_1(_0,_0), g_1(s(_0),_1) -> b(f_0(_1),g_1(_0,_1)), f_2(_0) -> g_2(_0,_0), g_2(s(_0),_1) -> b(f_1(_1),g_2(_0,_1)), f_3(_0) -> g_3(_0,_0), g_3(s(_0),_1) -> b(f_2(_1),g_3(_0,_1)), f_4(_0) -> g_4(_0,_0), g_4(s(_0),_1) -> b(f_3(_1),g_4(_0,_1)), f_5(_0) -> g_5(_0,_0), g_5(s(_0),_1) -> b(f_4(_1),g_5(_0,_1))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [g_3^#(s(_0),_1) -> g_3^#(_0,_1)]
  TRS = {f_0(_0) -> a, f_1(_0) -> g_1(_0,_0), g_1(s(_0),_1) -> b(f_0(_1),g_1(_0,_1)), f_2(_0) -> g_2(_0,_0), g_2(s(_0),_1) -> b(f_1(_1),g_2(_0,_1)), f_3(_0) -> g_3(_0,_0), g_3(s(_0),_1) -> b(f_2(_1),g_3(_0,_1)), f_4(_0) -> g_4(_0,_0), g_4(s(_0),_1) -> b(f_3(_1),g_4(_0,_1)), f_5(_0) -> g_5(_0,_0), g_5(s(_0),_1) -> b(f_4(_1),g_5(_0,_1))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [g_2^#(s(_0),_1) -> g_2^#(_0,_1)]
  TRS = {f_0(_0) -> a, f_1(_0) -> g_1(_0,_0), g_1(s(_0),_1) -> b(f_0(_1),g_1(_0,_1)), f_2(_0) -> g_2(_0,_0), g_2(s(_0),_1) -> b(f_1(_1),g_2(_0,_1)), f_3(_0) -> g_3(_0,_0), g_3(s(_0),_1) -> b(f_2(_1),g_3(_0,_1)), f_4(_0) -> g_4(_0,_0), g_4(s(_0),_1) -> b(f_3(_1),g_4(_0,_1)), f_5(_0) -> g_5(_0,_0), g_5(s(_0),_1) -> b(f_4(_1),g_5(_0,_1))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [g_1^#(s(_0),_1) -> g_1^#(_0,_1)]
  TRS = {f_0(_0) -> a, f_1(_0) -> g_1(_0,_0), g_1(s(_0),_1) -> b(f_0(_1),g_1(_0,_1)), f_2(_0) -> g_2(_0,_0), g_2(s(_0),_1) -> b(f_1(_1),g_2(_0,_1)), f_3(_0) -> g_3(_0,_0), g_3(s(_0),_1) -> b(f_2(_1),g_3(_0,_1)), f_4(_0) -> g_4(_0,_0), g_4(s(_0),_1) -> b(f_3(_1),g_4(_0,_1)), f_5(_0) -> g_5(_0,_0), g_5(s(_0),_1) -> b(f_4(_1),g_5(_0,_1))}
    ## 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