YES

1 decompositions
 #0 -----------
   1: f(g(x,a(),b())) -> x
   2: g(f(h(c(),d())),x,y) -> h(k1(x),k2(y))
   3: k1(a()) -> c()
   4: k2(b()) -> d()
   5: f(h(k1(a()),k2(b()))) -> f(h(c(),d()))
   6: f(h(c(),k2(b()))) -> f(h(c(),d()))
   7: f(h(k1(a()),d())) -> f(h(c(),d()))

@Strongly Commuting
--- R
   1: f(g(x,a(),b())) -> x
   2: g(f(h(c(),d())),x,y) -> h(k1(x),k2(y))
   3: k1(a()) -> c()
   4: k2(b()) -> d()
   5: f(h(k1(a()),k2(b()))) -> f(h(c(),d()))
   6: f(h(c(),k2(b()))) -> f(h(c(),d()))
   7: f(h(k1(a()),d())) -> f(h(c(),d()))

--- S
   1: f(g(x,a(),b())) -> x
   2: g(f(h(c(),d())),x,y) -> h(k1(x),k2(y))
   3: k1(a()) -> c()
   4: k2(b()) -> d()
   5: f(h(k1(a()),k2(b()))) -> f(h(c(),d()))
   6: f(h(c(),k2(b()))) -> f(h(c(),d()))
   7: f(h(k1(a()),d())) -> f(h(c(),d()))