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 = [f^#(s(_0),_1,_2,_3,_4) -> f^#(_0,_1,_2,_3,_4), f^#(0,s(_0),_1,_2,_3) -> f^#(_0,_0,_1,_2,_3), f^#(0,0,s(_0),_1,_2) -> f^#(_0,_0,_0,_1,_2), f^#(0,0,0,s(_0),_1) -> f^#(_0,_0,_0,_0,_1), f^#(0,0,0,0,s(_0)) -> f^#(_0,_0,_0,_0,_0)]
  TRS = {f(s(_0),_1,_2,_3,_4) -> f(_0,_1,_2,_3,_4), f(0,s(_0),_1,_2,_3) -> f(_0,_0,_1,_2,_3), f(0,0,s(_0),_1,_2) -> f(_0,_0,_0,_1,_2), f(0,0,0,s(_0),_1) -> f(_0,_0,_0,_0,_1), f(0,0,0,0,s(_0)) -> f(_0,_0,_0,_0,_0), f(0,0,0,0,0) -> 0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (36)! Aborting!
    ## Trying with lexicographic path orders...
    Successfully decomposed the DP problem into smaller problems to solve!
## Round 2:
  ## DP problem: 
  Dependency pairs = [f^#(s(_0),_1,_2,_3,_4) -> f^#(_0,_1,_2,_3,_4), f^#(0,s(_0),_1,_2,_3) -> f^#(_0,_0,_1,_2,_3), f^#(0,0,s(_0),_1,_2) -> f^#(_0,_0,_0,_1,_2), f^#(0,0,0,s(_0),_1) -> f^#(_0,_0,_0,_0,_1)]
  TRS = {f(s(_0),_1,_2,_3,_4) -> f(_0,_1,_2,_3,_4), f(0,s(_0),_1,_2,_3) -> f(_0,_0,_1,_2,_3), f(0,0,s(_0),_1,_2) -> f(_0,_0,_0,_1,_2), f(0,0,0,s(_0),_1) -> f(_0,_0,_0,_0,_1), f(0,0,0,0,s(_0)) -> f(_0,_0,_0,_0,_0), f(0,0,0,0,0) -> 0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (36)! Aborting!
    ## Trying with lexicographic path orders...
    Successfully decomposed the DP problem into smaller problems to solve!
## Round 3:
  ## DP problem: 
  Dependency pairs = [f^#(s(_0),_1,_2,_3,_4) -> f^#(_0,_1,_2,_3,_4), f^#(0,s(_0),_1,_2,_3) -> f^#(_0,_0,_1,_2,_3), f^#(0,0,s(_0),_1,_2) -> f^#(_0,_0,_0,_1,_2)]
  TRS = {f(s(_0),_1,_2,_3,_4) -> f(_0,_1,_2,_3,_4), f(0,s(_0),_1,_2,_3) -> f(_0,_0,_1,_2,_3), f(0,0,s(_0),_1,_2) -> f(_0,_0,_0,_1,_2), f(0,0,0,s(_0),_1) -> f(_0,_0,_0,_0,_1), f(0,0,0,0,s(_0)) -> f(_0,_0,_0,_0,_0), f(0,0,0,0,0) -> 0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (36)! Aborting!
    ## Trying with lexicographic path orders...
    Successfully decomposed the DP problem into smaller problems to solve!
## Round 4:
  ## DP problem: 
  Dependency pairs = [f^#(s(_0),_1,_2,_3,_4) -> f^#(_0,_1,_2,_3,_4), f^#(0,s(_0),_1,_2,_3) -> f^#(_0,_0,_1,_2,_3)]
  TRS = {f(s(_0),_1,_2,_3,_4) -> f(_0,_1,_2,_3,_4), f(0,s(_0),_1,_2,_3) -> f(_0,_0,_1,_2,_3), f(0,0,s(_0),_1,_2) -> f(_0,_0,_0,_1,_2), f(0,0,0,s(_0),_1) -> f(_0,_0,_0,_0,_1), f(0,0,0,0,s(_0)) -> f(_0,_0,_0,_0,_0), f(0,0,0,0,0) -> 0}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (36)! Aborting!
    ## Trying with lexicographic path orders...
    Successfully decomposed the DP problem into smaller problems to solve!
## Round 5:
  ## DP problem: 
  Dependency pairs = [f^#(s(_0),_1,_2,_3,_4) -> f^#(_0,_1,_2,_3,_4)]
  TRS = {f(s(_0),_1,_2,_3,_4) -> f(_0,_1,_2,_3,_4), f(0,s(_0),_1,_2,_3) -> f(_0,_0,_1,_2,_3), f(0,0,s(_0),_1,_2) -> f(_0,_0,_0,_1,_2), f(0,0,0,s(_0),_1) -> f(_0,_0,_0,_0,_1), f(0,0,0,0,s(_0)) -> f(_0,_0,_0,_0,_0), f(0,0,0,0,0) -> 0}
    ## 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 = 127