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 = [mod^#(s(_0),s(_1)) -> if_mod^#(le(_1,_0),s(_0),s(_1)), if_mod^#(true,s(_0),s(_1)) -> mod^#(minus(_0,_1),s(_1))]
  TRS = {le(0,_0) -> true, le(s(_0),0) -> false, le(s(_0),s(_1)) -> le(_0,_1), minus(_0,0) -> _0, minus(s(_0),s(_1)) -> minus(_0,_1), mod(0,_0) -> 0, mod(s(_0),0) -> 0, mod(s(_0),s(_1)) -> if_mod(le(_1,_0),s(_0),s(_1)), if_mod(true,s(_0),s(_1)) -> mod(minus(_0,_1),s(_1)), if_mod(false,s(_0),s(_1)) -> s(_0)}
    ## Trying with homeomorphic embeddings... Failed!
    ## Trying with polynomial interpretations... Too many coefficients (26)! Aborting!
    ## Trying with lexicographic path orders...
      The constraints are satisfied by the lexicographic path order using the precedence:
      mod > [if_mod], mod > [le, if_mod], 0 > [true], s > [mod, if_mod, false, true, 0, minus]
      and the argument filtering:
      {le:[0, 1], mod:[0], if_mod:[1], s:[0], minus:[0], if_mod^#:[1], mod^#:[0]}
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [minus^#(s(_0),s(_1)) -> minus^#(_0,_1)]
  TRS = {le(0,_0) -> true, le(s(_0),0) -> false, le(s(_0),s(_1)) -> le(_0,_1), minus(_0,0) -> _0, minus(s(_0),s(_1)) -> minus(_0,_1), mod(0,_0) -> 0, mod(s(_0),0) -> 0, mod(s(_0),s(_1)) -> if_mod(le(_1,_0),s(_0),s(_1)), if_mod(true,s(_0),s(_1)) -> mod(minus(_0,_1),s(_1)), if_mod(false,s(_0),s(_1)) -> s(_0)}
    ## Trying with homeomorphic embeddings... Success!
  This DP problem is finite.
  ## DP problem: 
  Dependency pairs = [le^#(s(_0),s(_1)) -> le^#(_0,_1)]
  TRS = {le(0,_0) -> true, le(s(_0),0) -> false, le(s(_0),s(_1)) -> le(_0,_1), minus(_0,0) -> _0, minus(s(_0),s(_1)) -> minus(_0,_1), mod(0,_0) -> 0, mod(s(_0),0) -> 0, mod(s(_0),s(_1)) -> if_mod(le(_1,_0),s(_0),s(_1)), if_mod(true,s(_0),s(_1)) -> mod(minus(_0,_1),s(_1)), if_mod(false,s(_0),s(_1)) -> s(_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 = 16