YES

Prover = TRS(tech=PATTERN_RULES, nb_unfoldings=unlimited, max_nb_unfolded_rules=200)

** 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 = [f^#(s(_0),s(_1),_2,_3) -> f^#(_0,_3,_2,_3), f^#(s(_0),0,_1,_2) -> f^#(_0,_2,minus(_1,s(_0)),_2)]
  TRS = {perfectp(0) -> false, perfectp(s(_0)) -> f(_0,s(0),s(_0),s(_0)), f(0,_0,0,_1) -> true, f(0,_0,s(_1),_2) -> false, f(s(_0),0,_1,_2) -> f(_0,_2,minus(_1,s(_0)),_2), f(s(_0),s(_1),_2,_3) -> if(le(_0,_1),f(s(_0),minus(_1,_0),_2,_3),f(_0,_3,_2,_3))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (40)! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      perfectp > [le, f, if, 0, minus, false, true, s], f > [le, if, minus], 0 > [false, true], s > [0, minus, false, true]
      and the argument filtering:
      {le:[0, 1], perfectp:[0], f:[0, 1, 2, 3], if:[0, 1, 2], minus:[0], s:[0], f^#:[0, 1, 2, 3]}
  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 = 250