YES
TRS:
 {f(h(x)) -> f(i(x)),
   i(a()) -> b(),
   h(a()) -> b(),
  g(i(x)) -> g(h(x))}
 RUF:
  Strict:
   {f(h(x)) -> f(i(x)),
    g(i(x)) -> g(h(x))}
  Weak:
   {}
  DP:
   Strict:
    {f#(h(x)) -> f#(i(x)),
     g#(i(x)) -> g#(h(x))}
   Weak:
   {f(h(x)) -> f(i(x)),
    g(i(x)) -> g(h(x))}
   EDG:
    {}
    SCCS:
     
     Qed