YES

1 decompositions
 #1 -----------
   1: a(b(x1)) -> c(a(x1))
   2: b(a(x2)) -> a(b(x2))
   3: a(c(x3)) -> b(b(x3))
   4: b(c(x4)) -> c(b(x4))
   5: c(b(x5)) -> b(a(x5))
   7: c(a(x7)) -> b(c(x7))
   8: b(a(x8)) -> c(c(x8))
   9: b(b(x9)) -> c(c(x9))

@Rule Labeling
--- R
   1: a(b(x1)) -> c(a(x1))
   2: b(a(x2)) -> a(b(x2))
   3: a(c(x3)) -> b(b(x3))
   4: b(c(x4)) -> c(b(x4))
   5: c(b(x5)) -> b(a(x5))
   7: c(a(x7)) -> b(c(x7))
   8: b(a(x8)) -> c(c(x8))
   9: b(b(x9)) -> c(c(x9))

--- S
   1: a(b(x1)) -> c(a(x1))
   2: b(a(x2)) -> a(b(x2))
   3: a(c(x3)) -> b(b(x3))
   4: b(c(x4)) -> c(b(x4))
   5: c(b(x5)) -> b(a(x5))
   7: c(a(x7)) -> b(c(x7))
   8: b(a(x8)) -> c(c(x8))
   9: b(b(x9)) -> c(c(x9))


NOTE: input TRS is reduced

original is
   1: a(b(x1)) -> c(a(x1))
   2: b(a(x2)) -> a(b(x2))
   3: a(c(x3)) -> b(b(x3))
   4: b(c(x4)) -> c(b(x4))
   5: c(b(x5)) -> b(a(x5))
   6: b(a(x6)) -> c(c(x6))
   7: c(a(x7)) -> b(c(x7))
   8: b(a(x8)) -> c(c(x8))
   9: b(b(x9)) -> c(c(x9))

reduced to
   1: a(b(x1)) -> c(a(x1))
   2: b(a(x2)) -> a(b(x2))
   3: a(c(x3)) -> b(b(x3))
   4: b(c(x4)) -> c(b(x4))
   5: c(b(x5)) -> b(a(x5))
   7: c(a(x7)) -> b(c(x7))
   8: b(a(x8)) -> c(c(x8))
   9: b(b(x9)) -> c(c(x9))