YES
TRS:
 {f(g(i(a(), b(), b'()), c()), d()) -> if(e(), f(.(b(), c()), d'()), f(.(b'(), c()), d'())),
        f(g(h(a(), b()), c()), d()) -> if(e(), f(.(b(), g(h(a(), b()), c())), d()), f(c(), d'()))}
 RUF:
  Strict:
   {f(g(h(a(), b()), c()), d()) -> if(e(), f(.(b(), g(h(a(), b()), c())), d()), f(c(), d'()))}
  Weak:
   {}
  DP:
   Strict:
    {f#(g(h(a(), b()), c()), d()) -> f#(.(b(), g(h(a(), b()), c())), d()),
     f#(g(h(a(), b()), c()), d()) -> f#(c(), d'())}
   Weak:
   {f(g(h(a(), b()), c()), d()) -> if(e(), f(.(b(), g(h(a(), b()), c())), d()), f(c(), d'()))}
   EDG:
    {}
    SCCS:
     
     Qed