YES

Problem:
 F(H(x),y) -> F(H(x),I(I(y)))
 F(x,G(y)) -> F(I(x),G(y))
 I(x) -> x

Proof:
 Church Rosser Transformation Processor:
  strict:
   F(H(x),y) -> F(H(x),I(I(y)))
   F(x,G(y)) -> F(I(x),G(y))
   I(x) -> x
  weak:
   
  critical peaks: 2
   F(H(x27),I(I(G(y)))) <-0|[]- F(H(x27),G(y)) -1|[]-> F(I(H(x27)),G(y))
   F(I(H(x)),G(x30)) <-1|[]- F(H(x),G(x30)) -0|[]-> F(H(x),I(I(G(x30))))
  Closedness Processor (*strongly -- <=7 steps*):
   strict:
    
   weak:
    
   Qed