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 = [i^#(:(_0,_1)) -> :^#(_1,_0), :^#(i(_0),:(_1,:(_0,_2))) -> i^#(_2), :^#(i(_0),:(_1,_0)) -> i^#(_1), :^#(_0,:(_1,:(i(_0),_2))) -> i^#(_2), :^#(_0,:(_1,i(_0))) -> i^#(_1), :^#(e,_0) -> i^#(_0), :^#(:(_0,_1),_2) -> i^#(_1), :^#(:(_0,_1),_2) -> :^#(_0,:(_2,i(_1))), :^#(:(_0,_1),_2) -> :^#(_2,i(_1)), :^#(_0,:(_1,:(i(_0),_2))) -> :^#(i(_2),_1), :^#(i(_0),:(_1,:(_0,_2))) -> :^#(i(_2),_1)]
  TRS = {:(_0,_0) -> e, :(_0,e) -> _0, i(:(_0,_1)) -> :(_1,_0), :(:(_0,_1),_2) -> :(_0,:(_2,i(_1))), :(e,_0) -> i(_0), i(i(_0)) -> _0, i(e) -> e, :(_0,:(_1,i(_0))) -> i(_1), :(_0,:(_1,:(i(_0),_2))) -> :(i(_2),_1), :(i(_0),:(_1,_0)) -> i(_1), :(i(_0),:(_1,:(_0,_2))) -> :(i(_2),_1)}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations...
      The constraints are satisfied by the polynomials:
      {:(_0,_1):[_0 * _1], i(_0):[_0], e:[2], i^#(_0):[2 * _0], :^#(_0,_1):[_0 + _0 * _1]}
      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 = 239