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 = [f^#(_0,c(_1)) -> f^#(_1,_1)]
  TRS = {f(_0,c(_1)) -> f(_0,s(f(_1,_1))), f(s(_0),_1) -> f(_0,s(c(_1)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      s > [f], c > [f]
      and the argument filtering:
      {f:[0], s:[0], c:[0], f^#:[0, 1]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [f^#(s(_0),_1) -> f^#(_0,s(c(_1)))]
  TRS = {f(_0,c(_1)) -> f(_0,s(f(_1,_1))), f(s(_0),_1) -> f(_0,s(c(_1)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Failed!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      f > [s, f, c], s > [f]
      and the argument filtering:
      {f:[0], s:[0], c:[0], f^#:[0, 1]}
  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 = 99