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:
  not(x) -> false
  not(x) -> x
  not(x) -> true
  not(x) -> x

 DP Processor:
  DPs:
   
  TRS:
   not(x) -> false()
   not(x) -> x
   not(x) -> true()
  Qed