YES

1 decompositions
 #1 -----------
   1: f(g(x1)) -> f(h(x1,x1))
   2: g(a()) -> g(g(a()))
   3: h(a(),a()) -> g(g(a()))

@Rule Labeling
--- R
   1: f(g(x1)) -> f(h(x1,x1))
   2: g(a()) -> g(g(a()))
   3: h(a(),a()) -> g(g(a()))

--- S
   1: f(g(x1)) -> f(h(x1,x1))
   2: g(a()) -> g(g(a()))
   3: h(a(),a()) -> g(g(a()))