NO

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

unjoinable peak
    g(h(b(x10)))
*<- a(x10) ->*
    g(c(x10))