NO

1 decompositions
 #1 -----------
   1: a(x1) -> b(b(b(x1)))
   2: a(x2) -> c(x2)

unjoinable peak
    b(b(b(x7)))
*<- a(x7) ->*
    c(x7)
NOTE: input TRS is reduced

original is
   1: a(x1) -> b(b(b(x1)))
   2: a(x2) -> c(x2)
   3: b(x3) -> b(x3)

reduced to
   1: a(x1) -> b(b(b(x1)))
   2: a(x2) -> c(x2)