NO

   1: a(x1) -> b(b(b(x1)))
   2: a(x1) -> c(x1)

unjoinable peak
    b(b(b(x6)))
*<- a(x6) ->*
    c(x6)
NOTE: input TRS is reduced

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

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