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 = [*^#(_0,*(_1,_2)) -> *^#(*(_0,_1),_2), *^#(_0,*(_1,_2)) -> *^#(_0,_1), i^#(*(_0,_1)) -> *^#(i(_1),i(_0)), i^#(*(_0,_1)) -> i^#(_1), i^#(*(_0,_1)) -> i^#(_0), *^#(*(i(_0),k(_1,_2)),_0) -> i^#(_0), *^#(*(i(_0),k(_1,_2)),_0) -> i^#(_0), *^#(*(i(_0),k(_1,_2)),_0) -> *^#(*(i(_0),_1),_0), *^#(*(i(_0),k(_1,_2)),_0) -> *^#(i(_0),_1), *^#(*(i(_0),k(_1,_2)),_0) -> *^#(*(i(_0),_2),_0), *^#(*(i(_0),k(_1,_2)),_0) -> *^#(i(_0),_2)]
  TRS = {*(_0,1) -> _0, *(1,_0) -> _0, *(i(_0),_0) -> 1, *(_0,i(_0)) -> 1, *(_0,*(_1,_2)) -> *(*(_0,_1),_2), i(1) -> 1, *(*(_0,_1),i(_1)) -> _0, *(*(_0,i(_1)),_1) -> _0, i(i(_0)) -> _0, i(*(_0,_1)) -> *(i(_1),i(_0)), k(_0,1) -> 1, k(_0,_0) -> 1, *(k(_0,_1),k(_1,_0)) -> 1, *(*(i(_0),k(_1,_2)),_0) -> k(*(*(i(_0),_1),_0),*(*(i(_0),_2),_0)), k(*(_0,i(_1)),*(_1,i(_0))) -> 1}
    ## 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], k(_0,_1):[_0 + _1], i^#(_0):[2 * _0], *^#(_0,_1):[_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 = 7607