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