NO

1 decompositions
 #0 -----------
   1: a(x) -> g(h(b(x)))
   2: a(x) -> g(c(x))
   3: b(x) -> g(b(x))
   4: g(a(x)) -> g(h(a(x)))

unjoinable peak
    g(h(b(_y6)))
*<- a(_y6) ->*
    g(c(_y6))