YES

1 decompositions
 #0 -----------
   1: b(a(a(b(b(x))))) -> b(a(a(a(a(b(b(x)))))))
   2: b(a(b(b(x)))) -> b(b(x))
   3: b(a(b(a(a(a(a(b(x)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
   4: b(a(a(b(a(a(a(a(b(x))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))
   5: b(a(a(a(b(a(a(a(a(b(x)))))))))) -> b(x)

@Strongly Commuting
--- R
   1: b(a(a(b(b(x))))) -> b(a(a(a(a(b(b(x)))))))
   2: b(a(b(b(x)))) -> b(b(x))
   3: b(a(b(a(a(a(a(b(x)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
   4: b(a(a(b(a(a(a(a(b(x))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))
   5: b(a(a(a(b(a(a(a(a(b(x)))))))))) -> b(x)

--- S
   1: b(a(a(b(b(x))))) -> b(a(a(a(a(b(b(x)))))))
   2: b(a(b(b(x)))) -> b(b(x))
   3: b(a(b(a(a(a(a(b(x)))))))) -> b(a(a(a(a(b(a(a(a(a(b(a(b(a(a(a(b(a(a(a(a(b(x))))))))))))))))))))))
   4: b(a(a(b(a(a(a(a(b(x))))))))) -> b(a(b(a(a(b(a(a(a(b(a(a(a(a(b(x)))))))))))))))
   5: b(a(a(a(b(a(a(a(a(b(x)))))))))) -> b(x)