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 = [i^#(.(_0,_1)) -> i^#(_1), i^#(.(_0,_1)) -> i^#(_0)]
  TRS = {.(1,_0) -> _0, .(_0,1) -> _0, .(i(_0),_0) -> 1, .(_0,i(_0)) -> 1, i(1) -> 1, i(i(_0)) -> _0, .(i(_0),.(_0,_1)) -> _1, .(_0,.(i(_0),_1)) -> _1, .(.(_0,_1),_2) -> .(_0,.(_1,_2)), i(.(_0,_1)) -> .(i(_1),i(_0))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [.^#(.(_0,_1),_2) -> .^#(_0,.(_1,_2)), .^#(.(_0,_1),_2) -> .^#(_1,_2)]
  TRS = {.(1,_0) -> _0, .(_0,1) -> _0, .(i(_0),_0) -> 1, .(_0,i(_0)) -> 1, i(1) -> 1, i(i(_0)) -> _0, .(i(_0),.(_0,_1)) -> _1, .(_0,.(i(_0),_1)) -> _1, .(.(_0,_1),_2) -> .(_0,.(_1,_2)), i(.(_0,_1)) -> .(i(_1),i(_0))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
      The constraints are satisfied by the polynomials:
      {.(_0,_1):[_0 * _1], i(_0):[_0], 1:[2], .^#(_0,_1):[_0]}
      for all instantiations of the variables with values greater than or equal to mu = 2.
  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 = 29