NO

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

unjoinable peak
    g(h(b(x2)))
*<- a(x2) ->*
    g(c(x2))