YES

Proof:
This system is quasi-decreasing.
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:
  plus(0, y) -> y
  plus(s(x), y) -> plus(x, s(y))
  f(x, y) -> plus(x, y)
  f(x, y) -> x
  f(x, y) -> y
  s(x) -> x
  plus(x, y) -> x
  plus(x, y) -> y

 DP Processor:
  DPs:
   plus#(s(x),y) -> s#(y)
   plus#(s(x),y) -> plus#(x,s(y))
   f#(x,y) -> plus#(x,y)
  TRS:
   plus(0(),y) -> y
   plus(s(x),y) -> plus(x,s(y))
   f(x,y) -> plus(x,y)
   f(x,y) -> x
   f(x,y) -> y
   s(x) -> x
   plus(x,y) -> x
   plus(x,y) -> y
  TDG Processor:
   DPs:
    plus#(s(x),y) -> s#(y)
    plus#(s(x),y) -> plus#(x,s(y))
    f#(x,y) -> plus#(x,y)
   TRS:
    plus(0(),y) -> y
    plus(s(x),y) -> plus(x,s(y))
    f(x,y) -> plus(x,y)
    f(x,y) -> x
    f(x,y) -> y
    s(x) -> x
    plus(x,y) -> x
    plus(x,y) -> y
   graph:
    f#(x,y) -> plus#(x,y) -> plus#(s(x),y) -> plus#(x,s(y))
    f#(x,y) -> plus#(x,y) -> plus#(s(x),y) -> s#(y)
    plus#(s(x),y) -> plus#(x,s(y)) -> plus#(s(x),y) -> plus#(x,s(y))
    plus#(s(x),y) -> plus#(x,s(y)) -> plus#(s(x),y) -> s#(y)
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 4/9
    DPs:
     plus#(s(x),y) -> plus#(x,s(y))
    TRS:
     plus(0(),y) -> y
     plus(s(x),y) -> plus(x,s(y))
     f(x,y) -> plus(x,y)
     f(x,y) -> x
     f(x,y) -> y
     s(x) -> x
     plus(x,y) -> x
     plus(x,y) -> y
    Subterm Criterion Processor:
     simple projection:
      pi(plus#) = 0
     problem:
      DPs:
       
      TRS:
       plus(0(),y) -> y
       plus(s(x),y) -> plus(x,s(y))
       f(x,y) -> plus(x,y)
       f(x,y) -> x
       f(x,y) -> y
       s(x) -> x
       plus(x,y) -> x
       plus(x,y) -> y
     Qed