NO

1 decompositions
 #0 -----------
   1: 0(1(2(1(x)))) -> 1(2(1(1(0(1(2(0(1(2(x))))))))))
   2: 0(1(2(1(x)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(x)))))))))))))
   3: 0(1(2(1(x)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(x))))))))))))))))
   4: 0(1(2(1(x)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x)))))))))))))))))))
   5: 0(1(2(1(x)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x))))))))))))))))))))))
   6: 0(1(2(1(x)))) -> 1(2(1(1(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(0(1(2(x)))))))))))))))))))))))))

unjoinable peak
    1(2(1(1(0(1(2(0(1(2(_y8))))))))))
*<- 0(1(2(1(_y8)))) ->*
    1(2(1(1(0(1(2(0(1(2(0(1(2(_y8)))))))))))))