NO

1 decompositions
 #1 -----------
   1: a(a(x1)) -> b(c(x1))
   2: b(b(x2)) -> c(d(x2))
   3: c(c(x3)) -> d(d(d(x3)))
   4: d(d(d(x4))) -> a(c(x4))

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