YES

1 decompositions
 #1 -----------
   1: H(H(x1)) -> K(x1)
   2: H(K(x1)) -> K(H(x1))

@Jouannaud and Kirchner's criterion
--- R
   1: H(H(x1)) -> K(x1)
   2: H(K(x1)) -> K(H(x1))

--- S
   1: H(H(x1)) -> K(x1)
   2: H(K(x1)) -> K(H(x1))