YES

1 decompositions
 #1 -----------
   1: f(i(x1),g(a())) -> f(j(x1,x1),g(b()))
   2: b() -> a()
   3: i(x2) -> j(x2,x2)

@Knuth and Bendix' criterion
--- R
   1: f(i(x1),g(a())) -> f(j(x1,x1),g(b()))
   2: b() -> a()
   3: i(x2) -> j(x2,x2)

--- S
   1: f(i(x1),g(a())) -> f(j(x1,x1),g(b()))
   2: b() -> a()
   3: i(x2) -> j(x2,x2)