YES

Proof:
This system is quasi-decreasing.
By \cite{O02}, p. 214, Proposition 7.2.50.
This system is of type 3 or smaller.
This system is deterministic.
System R transformed to U(R).
Call external tool:
ttt2 - trs 30
Input:
  plus(0, y) -> y
  plus(s(x), y) -> plus(x, s(y))
  ?1(plus(z, z'), x, y) -> z
  f(x, y) -> ?1(plus(x, y), x, y)

 DP Processor:
  DPs:
   plus#(s(x),y) -> plus#(x,s(y))
   f#(x,y) -> plus#(x,y)
   f#(x,y) -> ?1#(plus(x,y),x,y)
  TRS:
   plus(0(),y) -> y
   plus(s(x),y) -> plus(x,s(y))
   ?1(plus(z,z'),x,y) -> z
   f(x,y) -> ?1(plus(x,y),x,y)
  TDG Processor:
   DPs:
    plus#(s(x),y) -> plus#(x,s(y))
    f#(x,y) -> plus#(x,y)
    f#(x,y) -> ?1#(plus(x,y),x,y)
   TRS:
    plus(0(),y) -> y
    plus(s(x),y) -> plus(x,s(y))
    ?1(plus(z,z'),x,y) -> z
    f(x,y) -> ?1(plus(x,y),x,y)
   graph:
    f#(x,y) -> plus#(x,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))
   SCC Processor:
    #sccs: 1
    #rules: 1
    #arcs: 2/9
    DPs:
     plus#(s(x),y) -> plus#(x,s(y))
    TRS:
     plus(0(),y) -> y
     plus(s(x),y) -> plus(x,s(y))
     ?1(plus(z,z'),x,y) -> z
     f(x,y) -> ?1(plus(x,y),x,y)
    Subterm Criterion Processor:
     simple projection:
      pi(plus#) = 0
     problem:
      DPs:
       
      TRS:
       plus(0(),y) -> y
       plus(s(x),y) -> plus(x,s(y))
       ?1(plus(z,z'),x,y) -> z
       f(x,y) -> ?1(plus(x,y),x,y)
     Qed