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(y, x) -> y
  f(x) -> ?1(x, x)
  a -> b
  b -> c

 DP Processor:
  DPs:
   f#(x) -> ?1#(x,x)
   a#() -> b#()
  TRS:
   ?1(y,x) -> y
   f(x) -> ?1(x,x)
   a() -> b()
   b() -> c()
  TDG Processor:
   DPs:
    f#(x) -> ?1#(x,x)
    a#() -> b#()
   TRS:
    ?1(y,x) -> y
    f(x) -> ?1(x,x)
    a() -> b()
    b() -> c()
   graph:
    
   Qed