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, y) -> y
  F(x, y) -> x
  G(x) -> C
  G(x) -> x
  F(x, y) -> x
  F(x, y) -> y

 DP Processor:
  DPs:
   
  TRS:
   F(x,y) -> y
   F(x,y) -> x
   G(x) -> C()
   G(x) -> x
  Qed