YES

Proof:
This system is confluent.
By \cite{ALS94}, Theorem 4.1.
This system is of type 3 or smaller.
This system is strongly deterministic.
There are no critical pairs.
By \cite{A14}, Theorem 11.5.9.
This system is of type 3 or smaller.
This system is deterministic.
System R transformed to V(R) + Emb.
Call external tool:
ttt2 - trs 30
Input:
  sub(z, 0) -> z
  sub(s(z), s(y)) -> sub(z, y)
  s(x) -> x
  sub(x, y) -> x
  sub(x, y) -> y

 DP Processor:
  DPs:
   sub#(s(z),s(y)) -> sub#(z,y)
  TRS:
   sub(z,0()) -> z
   sub(s(z),s(y)) -> sub(z,y)
   s(x) -> x
   sub(x,y) -> x
   sub(x,y) -> y
  Subterm Criterion Processor:
   simple projection:
    pi(sub#) = 0
   problem:
    DPs:
     
    TRS:
     sub(z,0()) -> z
     sub(s(z),s(y)) -> sub(z,y)
     s(x) -> x
     sub(x,y) -> x
     sub(x,y) -> y
   Qed