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:
  u -> a
  w -> a
  v -> b
  w -> b
  G -> D
  G -> u

 DP Processor:
  DPs:
   G#() -> u#()
  TRS:
   u() -> a()
   w() -> a()
   v() -> b()
   w() -> b()
   G() -> D()
   G() -> u()
  TDG Processor:
   DPs:
    G#() -> u#()
   TRS:
    u() -> a()
    w() -> a()
    v() -> b()
    w() -> b()
    G() -> D()
    G() -> u()
   graph:
    
   Qed