YES

1 decompositions
 #0 -----------
   1: g(g(g(c(),d()),g(b(),e())),b()) -> a()
   2: g(a(),y) -> g(b(),b())
   3: g(x,y) -> g(y,x)

@Jouannaud and Kirchner's criterion
--- R
   1: g(g(g(c(),d()),g(b(),e())),b()) -> a()
   2: g(a(),y) -> g(b(),b())
   3: g(x,y) -> g(y,x)

--- S
   1: g(g(g(c(),d()),g(b(),e())),b()) -> a()
   2: g(a(),y) -> g(b(),b())
   3: g(x,y) -> g(y,x)