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:
  a -> c
  a -> d
  ?2(x, x) -> x
  ?1(c, x) -> ?2(d, x)
  f(x) -> ?1(x, x)

 DP Processor:
  DPs:
   ?1#(c(),x) -> ?2#(d(),x)
   f#(x) -> ?1#(x,x)
  TRS:
   a() -> c()
   a() -> d()
   ?2(x,x) -> x
   ?1(c(),x) -> ?2(d(),x)
   f(x) -> ?1(x,x)
  TDG Processor:
   DPs:
    ?1#(c(),x) -> ?2#(d(),x)
    f#(x) -> ?1#(x,x)
   TRS:
    a() -> c()
    a() -> d()
    ?2(x,x) -> x
    ?1(c(),x) -> ?2(d(),x)
    f(x) -> ?1(x,x)
   graph:
    f#(x) -> ?1#(x,x) -> ?1#(c(),x) -> ?2#(d(),x)
   SCC Processor:
    #sccs: 0
    #rules: 0
    #arcs: 1/4