YES

(VAR x0 x)
(RULES
  u(v(v(x0))) -> v(v(u(x0)))
  c(u(u(x0))) -> u(u(c(x0)))
  c(u(v(x0))) -> b(b(u(u(v(c(u(x0)))))))
  u(b(x0)) -> b(b(u(v(x0))))
  c(b(x0)) -> v(c(x0))
  c(u(c(x0))) -> u(x0)
  u(v(u(x0))) -> v(x0)
  a(x0) -> b(u(v(x0)))
  w(x0) -> b(u(v(c(u(x0)))))
  v(b(x)) -> x
  b(v(x)) -> x
  c(v(x)) -> b(c(x))
)

(COMMENT
Termination is shown by LPO with precedence:

  w > a > c > u > b > v
)