NO

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

unjoinable peak
    b(a(b(a(b(x)))))
*<- b(a(a(a(x)))) ->*
    a(a(x))