YES

Problem:
 F(c(x)) -> G(x)
 G(x) -> F(x)
 c(x) -> x

Proof:
 Church Rosser Transformation Processor:
  strict:
   F(c(x)) -> G(x)
   G(x) -> F(x)
   c(x) -> x
  weak:
   
  critical peaks: 1
   F(x) <-2|0[]- F(c(x)) -0|[]-> G(x)
  Closedness Processor (*strongly -- <=7 steps*):
   strict:
    
   weak:
    
   Qed