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:
  ?1(y, x, y) -> G(x)
  F(x, y) -> ?1(x, x, y)
  a -> b

 DP Processor:
  DPs:
   F#(x,y) -> ?1#(x,x,y)
  TRS:
   ?1(y,x,y) -> G(x)
   F(x,y) -> ?1(x,x,y)
   a() -> b()
  TDG Processor:
   DPs:
    F#(x,y) -> ?1#(x,x,y)
   TRS:
    ?1(y,x,y) -> G(x)
    F(x,y) -> ?1(x,x,y)
    a() -> b()
   graph:
    
   Qed