NO

1 decompositions
 #1 -----------
   1: a(b(a(a(a(a(a(a(a(a(a(x1))))))))))) -> a(a(a(a(a(a(a(a(a(a(a(b(a(b(x1))))))))))))))

unjoinable peak
    a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(a(b(a(b(a(a(b(a(b(a(b(a(b(x1)))))))))))))))))))))))))))))))))
*<- a(b(a(a(a(a(a(a(a(a(a(b(a(a(a(a(a(a(a(a(a(x1))))))))))))))))))))) ->*
    a(a(a(a(a(a(a(a(a(a(a(b(a(b(b(a(a(a(a(a(a(a(a(a(x1))))))))))))))))))))))))