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(t, x) -> A
  f(x) -> ?1(s(x), x)
  ?2(t, x) -> B
  f(x) -> ?2(s(x), x)
  s(a) -> t
  s(b) -> t
  a -> c
  b -> c
  g(x, x) -> h(x, x)

 DP Processor:
  DPs:
   f#(x) -> s#(x)
   f#(x) -> ?1#(s(x),x)
   f#(x) -> ?2#(s(x),x)
  TRS:
   ?1(t(),x) -> A()
   f(x) -> ?1(s(x),x)
   ?2(t(),x) -> B()
   f(x) -> ?2(s(x),x)
   s(a()) -> t()
   s(b()) -> t()
   a() -> c()
   b() -> c()
   g(x,x) -> h(x,x)
  TDG Processor:
   DPs:
    f#(x) -> s#(x)
    f#(x) -> ?1#(s(x),x)
    f#(x) -> ?2#(s(x),x)
   TRS:
    ?1(t(),x) -> A()
    f(x) -> ?1(s(x),x)
    ?2(t(),x) -> B()
    f(x) -> ?2(s(x),x)
    s(a()) -> t()
    s(b()) -> t()
    a() -> c()
    b() -> c()
    g(x,x) -> h(x,x)
   graph:
    
   Qed