NO

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

unjoinable peak
    g(b(x2))
*<- a(x2) ->*
    c(c(x2))
NOTE: input TRS is reduced

original is
   1: a(x1) -> b(x1)
   2: a(x1) -> c(c(x1))
   3: b(x1) -> g(b(x1))
   4: c(x1) -> c(x1)

reduced to
   1: a(x1) -> b(x1)
   2: a(x1) -> c(c(x1))
   3: b(x1) -> g(b(x1))