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 = [g^#(s(_0)) -> g^#(_0), g^#(s(_0)) -> g^#(_0), g^#(s(_0)) -> g^#(_0), g^#(s(_0)) -> g^#(_0)]
  TRS = {f(0) -> 0, f(s(0)) -> s(0), f(s(s(_0))) -> p(h(g(_0))), g(0) -> pair(s(0),s(0)), g(s(_0)) -> h(g(_0)), h(_0) -> pair(+(p(_0),q(_0)),p(_0)), p(pair(_0,_1)) -> _0, q(pair(_0,_1)) -> _1, +(_0,0) -> _0, +(_0,s(_1)) -> s(+(_0,_1)), f(s(s(_0))) -> +(p(g(_0)),q(g(_0))), g(s(_0)) -> pair(+(p(g(_0)),q(g(_0))),p(g(_0)))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [+^#(_0,s(_1)) -> +^#(_0,_1)]
  TRS = {f(0) -> 0, f(s(0)) -> s(0), f(s(s(_0))) -> p(h(g(_0))), g(0) -> pair(s(0),s(0)), g(s(_0)) -> h(g(_0)), h(_0) -> pair(+(p(_0),q(_0)),p(_0)), p(pair(_0,_1)) -> _0, q(pair(_0,_1)) -> _1, +(_0,0) -> _0, +(_0,s(_1)) -> s(+(_0,_1)), f(s(s(_0))) -> +(p(g(_0)),q(g(_0))), g(s(_0)) -> pair(+(p(g(_0)),q(g(_0))),p(g(_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