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:
  u -> a
  w -> a
  v -> b
  w -> b
  ?1(v) -> D
  G -> ?1(u)

 DP Processor:
  DPs:
   G#() -> u#()
   G#() -> ?1#(u())
  TRS:
   u() -> a()
   w() -> a()
   v() -> b()
   w() -> b()
   ?1(v()) -> D()
   G() -> ?1(u())
  TDG Processor:
   DPs:
    G#() -> u#()
    G#() -> ?1#(u())
   TRS:
    u() -> a()
    w() -> a()
    v() -> b()
    w() -> b()
    ?1(v()) -> D()
    G() -> ?1(u())
   graph:
    
   Qed