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 = [if^#(if(_0,_1,_2),u,v) -> if^#(_0,if(_1,u,v),if(_2,u,v)), if^#(if(_0,_1,_2),u,v) -> if^#(_1,u,v), if^#(if(_0,_1,_2),u,v) -> if^#(_2,u,v)]
  TRS = {if(true,_0,_1) -> _0, if(false,_0,_1) -> _1, if(_0,_1,_1) -> _1, if(if(_0,_1,_2),u,v) -> if(_0,if(_1,u,v),if(_2,u,v))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (13)! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      if > [u, v]
      and the argument filtering:
      {if:[0, 1, 2], if^#:[0, 1, 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 = 20