YES

1 decompositions
 #1 -----------
   2: f(x3) -> g(x3,f(x3))
   3: h(x4) -> g(f(x4),x4)
   4: g(x5,x6) -> h(g(f(x5),f(x6)))

@Development Closedness
--- R
   2: f(x3) -> g(x3,f(x3))
   3: h(x4) -> g(f(x4),x4)
   4: g(x5,x6) -> h(g(f(x5),f(x6)))

--- S
   2: f(x3) -> g(x3,f(x3))
   3: h(x4) -> g(f(x4),x4)
   4: g(x5,x6) -> h(g(f(x5),f(x6)))


NOTE: input TRS is reduced

original is
   1: g(f(f(h(x1))),x2) -> g(g(f(h(x1)),f(f(h(x1)))),x2)
   2: f(x3) -> g(x3,f(x3))
   3: h(x4) -> g(f(x4),x4)
   4: g(x5,x6) -> h(g(f(x5),f(x6)))

reduced to
   2: f(x3) -> g(x3,f(x3))
   3: h(x4) -> g(f(x4),x4)
   4: g(x5,x6) -> h(g(f(x5),f(x6)))