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(true, x) -> false
  not(x) -> ?1(x, x)
  ?2(false, x) -> true
  not(x) -> ?2(x, x)

 DP Processor:
  DPs:
   not#(x) -> ?1#(x,x)
   not#(x) -> ?2#(x,x)
  TRS:
   ?1(true(),x) -> false()
   not(x) -> ?1(x,x)
   ?2(false(),x) -> true()
   not(x) -> ?2(x,x)
  TDG Processor:
   DPs:
    not#(x) -> ?1#(x,x)
    not#(x) -> ?2#(x,x)
   TRS:
    ?1(true(),x) -> false()
    not(x) -> ?1(x,x)
    ?2(false(),x) -> true()
    not(x) -> ?2(x,x)
   graph:
    
   Qed