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 = [quot^#(s(_0),s(_1)) -> quot^#(min(_0,_1),s(_1))]
  TRS = {plus(0,_0) -> _0, plus(s(_0),_1) -> s(plus(_0,_1)), min(_0,0) -> _0, min(s(_0),s(_1)) -> min(_0,_1), min(min(_0,_1),Z) -> min(_0,plus(_1,Z)), quot(0,s(_0)) -> 0, quot(s(_0),s(_1)) -> s(quot(min(_0,_1),s(_1)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (17)! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      plus > [min, s], quot > [min, s], s > [min]
      and the argument filtering:
      {plus:[0, 1], min:[0], s:[0], quot:[0], quot^#:[0, 1]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [min^#(s(_0),s(_1)) -> min^#(_0,_1), min^#(min(_0,_1),Z) -> min^#(_0,plus(_1,Z))]
  TRS = {plus(0,_0) -> _0, plus(s(_0),_1) -> s(plus(_0,_1)), min(_0,0) -> _0, min(s(_0),s(_1)) -> min(_0,_1), min(min(_0,_1),Z) -> min(_0,plus(_1,Z)), quot(0,s(_0)) -> 0, quot(s(_0),s(_1)) -> s(quot(min(_0,_1),s(_1)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (17)! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      plus > [min, s], quot > [min, s], s > [min]
      and the argument filtering:
      {plus:[0, 1], min:[0], s:[0], quot:[0], min^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [plus^#(s(_0),_1) -> plus^#(_0,_1)]
  TRS = {plus(0,_0) -> _0, plus(s(_0),_1) -> s(plus(_0,_1)), min(_0,0) -> _0, min(s(_0),s(_1)) -> min(_0,_1), min(min(_0,_1),Z) -> min(_0,plus(_1,Z)), quot(0,s(_0)) -> 0, quot(s(_0),s(_1)) -> s(quot(min(_0,_1),s(_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 = 29