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 = [msort^#(.(_0,_1)) -> msort^#(del(min(_0,_1),.(_0,_1)))]
  TRS = {msort(nil) -> nil, msort(.(_0,_1)) -> .(min(_0,_1),msort(del(min(_0,_1),.(_0,_1)))), min(_0,nil) -> _0, min(_0,.(_1,_2)) -> if(<=(_0,_1),min(_0,_2),min(_1,_2)), del(_0,nil) -> nil, del(_0,.(_1,_2)) -> if(=(_0,_1),_2,.(_1,del(_0,_2)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (32)! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      msort > [., if, <=, del, nil, min, =], . > [if, <=, del, nil, min, =], del > [if, nil, =], min > [if, <=]
      and the argument filtering:
      {msort:[0], .:[0, 1], if:[0], <=:[0], del:[0], min:[0], =:[0], msort^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [del^#(_0,.(_1,_2)) -> del^#(_0,_2)]
  TRS = {msort(nil) -> nil, msort(.(_0,_1)) -> .(min(_0,_1),msort(del(min(_0,_1),.(_0,_1)))), min(_0,nil) -> _0, min(_0,.(_1,_2)) -> if(<=(_0,_1),min(_0,_2),min(_1,_2)), del(_0,nil) -> nil, del(_0,.(_1,_2)) -> if(=(_0,_1),_2,.(_1,del(_0,_2)))}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [min^#(_0,.(_1,_2)) -> min^#(_0,_2), min^#(_0,.(_1,_2)) -> min^#(_1,_2)]
  TRS = {msort(nil) -> nil, msort(.(_0,_1)) -> .(min(_0,_1),msort(del(min(_0,_1),.(_0,_1)))), min(_0,nil) -> _0, min(_0,.(_1,_2)) -> if(<=(_0,_1),min(_0,_2),min(_1,_2)), del(_0,nil) -> nil, del(_0,.(_1,_2)) -> if(=(_0,_1),_2,.(_1,del(_0,_2)))}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (32)! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      msort > [., if, <=, del, nil, min, min, =], . > [if, <=, del, nil, min, min, =], del > [if, nil, =], min > [if, <=]
      and the argument filtering:
      {msort:[0], .:[0, 1], if:[0], <=:[0], del:[0], min:[0], =:[0], min^#:[0, 1]}
  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 = 128