NO

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

unjoinable peak
    g(g(b(x8)))
*<- a(x8) ->*
    g(c(x8))