YES

   1: F(c(x1)) -> G(x1)
   2: G(x1) -> F(x1)
   3: c(x1) -> x1

@Jouannaud and Kirchner's criterion
--- R
   1: F(c(x1)) -> G(x1)
   2: G(x1) -> F(x1)
   3: c(x1) -> x1

--- S
   1: F(c(x1)) -> G(x1)
   2: G(x1) -> F(x1)
   3: c(x1) -> x1