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:
  f(x', x'') -> g(x'')
  f(x', x'') -> x''
  f(x', x'') -> x'
  f(y', h(y'')) -> g(y'')
  f(y', h(y'')) -> y''
  f(y', h(y'')) -> y'
  h(x) -> x
  g(x) -> x
  f(x, y) -> x
  f(x, y) -> y

 DP Processor:
  DPs:
   f#(x',x'') -> g#(x'')
   f#(y',h(y'')) -> g#(y'')
  TRS:
   f(x',x'') -> g(x'')
   f(x',x'') -> x''
   f(x',x'') -> x'
   f(y',h(y'')) -> g(y'')
   f(y',h(y'')) -> y''
   f(y',h(y'')) -> y'
   h(x) -> x
   g(x) -> x
   f(x,y) -> x
   f(x,y) -> y
  TDG Processor:
   DPs:
    f#(x',x'') -> g#(x'')
    f#(y',h(y'')) -> g#(y'')
   TRS:
    f(x',x'') -> g(x'')
    f(x',x'') -> x''
    f(x',x'') -> x'
    f(y',h(y'')) -> g(y'')
    f(y',h(y'')) -> y''
    f(y',h(y'')) -> y'
    h(x) -> x
    g(x) -> x
    f(x,y) -> x
    f(x,y) -> y
   graph:
    
   Qed