YES

   2: f(x1) -> g(x1,f(x1))
   3: h(x1) -> g(f(x1),x1)
   4: g(x1,x2) -> h(g(f(x1),f(x2)))

@Development Closedness
--- R
   2: f(x1) -> g(x1,f(x1))
   3: h(x1) -> g(f(x1),x1)
   4: g(x1,x2) -> h(g(f(x1),f(x2)))

--- S
   2: f(x1) -> g(x1,f(x1))
   3: h(x1) -> g(f(x1),x1)
   4: g(x1,x2) -> h(g(f(x1),f(x2)))


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(x1) -> g(x1,f(x1))
   3: h(x1) -> g(f(x1),x1)
   4: g(x1,x2) -> h(g(f(x1),f(x2)))

reduced to
   2: f(x1) -> g(x1,f(x1))
   3: h(x1) -> g(f(x1),x1)
   4: g(x1,x2) -> h(g(f(x1),f(x2)))