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 = [:^#(:(:(:(C,_0),_1),_2),_3) -> :^#(:(_0,_2),:(:(:(_0,_1),_2),_3)), :^#(:(:(:(C,_0),_1),_2),_3) -> :^#(_0,_2), :^#(:(:(:(C,_0),_1),_2),_3) -> :^#(:(:(_0,_1),_2),_3), :^#(:(:(:(C,_0),_1),_2),_3) -> :^#(:(_0,_1),_2), :^#(:(:(:(C,_0),_1),_2),_3) -> :^#(_0,_1)]
  TRS = {:(:(:(:(C,_0),_1),_2),_3) -> :(:(_0,_2),:(:(:(_0,_1),_2),_3))}
    ## 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:
      {}
      and the argument filtering:
      {':':[0, 1], :^#:[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 = 97