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 = [half^#(s(s(_0))) -> half^#(_0)]
  TRS = {terms(_0) -> cons(recip(sqr(_0))), sqr(0) -> 0, sqr(s(_0)) -> s(add(sqr(_0),dbl(_0))), dbl(0) -> 0, dbl(s(_0)) -> s(s(dbl(_0))), add(0,_0) -> _0, add(s(_0),_1) -> s(add(_0,_1)), first(0,_0) -> nil, first(s(_0),cons(_1)) -> cons(_1), half(0) -> 0, half(s(0)) -> 0, half(s(s(_0))) -> s(half(_0)), half(dbl(_0)) -> _0}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [sqr^#(s(_0)) -> sqr^#(_0)]
  TRS = {terms(_0) -> cons(recip(sqr(_0))), sqr(0) -> 0, sqr(s(_0)) -> s(add(sqr(_0),dbl(_0))), dbl(0) -> 0, dbl(s(_0)) -> s(s(dbl(_0))), add(0,_0) -> _0, add(s(_0),_1) -> s(add(_0,_1)), first(0,_0) -> nil, first(s(_0),cons(_1)) -> cons(_1), half(0) -> 0, half(s(0)) -> 0, half(s(s(_0))) -> s(half(_0)), half(dbl(_0)) -> _0}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [dbl^#(s(_0)) -> dbl^#(_0)]
  TRS = {terms(_0) -> cons(recip(sqr(_0))), sqr(0) -> 0, sqr(s(_0)) -> s(add(sqr(_0),dbl(_0))), dbl(0) -> 0, dbl(s(_0)) -> s(s(dbl(_0))), add(0,_0) -> _0, add(s(_0),_1) -> s(add(_0,_1)), first(0,_0) -> nil, first(s(_0),cons(_1)) -> cons(_1), half(0) -> 0, half(s(0)) -> 0, half(s(s(_0))) -> s(half(_0)), half(dbl(_0)) -> _0}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [add^#(s(_0),_1) -> add^#(_0,_1)]
  TRS = {terms(_0) -> cons(recip(sqr(_0))), sqr(0) -> 0, sqr(s(_0)) -> s(add(sqr(_0),dbl(_0))), dbl(0) -> 0, dbl(s(_0)) -> s(s(dbl(_0))), add(0,_0) -> _0, add(s(_0),_1) -> s(add(_0,_1)), first(0,_0) -> nil, first(s(_0),cons(_1)) -> cons(_1), half(0) -> 0, half(s(0)) -> 0, half(s(s(_0))) -> s(half(_0)), half(dbl(_0)) -> _0}
    ## Trying with homeomorphic embeddings... Success!
  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 = 0