YES

   4: f(h(x1),h(x2)) -> f(x2,x1)
   5: f(x1,x2) -> f(x2,x1)
   6: g(x1) -> h(x1)
   7: h(x1) -> g(x1)

@Rule Labeling
--- R
   4: f(h(x1),h(x2)) -> f(x2,x1)
   5: f(x1,x2) -> f(x2,x1)
   6: g(x1) -> h(x1)
   7: h(x1) -> g(x1)

--- S
   4: f(h(x1),h(x2)) -> f(x2,x1)
   5: f(x1,x2) -> f(x2,x1)
   6: g(x1) -> h(x1)
   7: h(x1) -> g(x1)


NOTE: input TRS is reduced

original is
   1: f(g(x1),g(x2)) -> f(g(x1),h(x2))
   2: f(h(x1),g(x2)) -> f(g(x1),g(x2))
   3: f(g(x1),h(x2)) -> f(x1,x2)
   4: f(h(x1),h(x2)) -> f(x2,x1)
   5: f(x1,x2) -> f(x2,x1)
   6: g(x1) -> h(x1)
   7: h(x1) -> g(x1)

reduced to
   4: f(h(x1),h(x2)) -> f(x2,x1)
   5: f(x1,x2) -> f(x2,x1)
   6: g(x1) -> h(x1)
   7: h(x1) -> g(x1)